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<Text-field style="Title" layout="Title"><Font size="26">The Simulation and Optimization of NMR Experiments using a Liouville Space Method</Font></Text-field>
<Text-field style="Author" layout="Author" spaceabove="0" spacebelow="0">Christopher Kumar Anand, Alex D. Bain, <Font underline="true">Zhenghua Nie</Font></Text-field>
<Text-field style="Author" layout="Author" spaceabove="0" spacebelow="0">Department of Computing and Software, Department of Chemistry</Text-field>
<Text-field style="Author" layout="Author" spaceabove="0" spacebelow="0">McMaster University</Text-field>
<Text-field style="Author" layout="Author" spaceabove="0" spacebelow="0">1280 Main St. West </Text-field>
<Text-field style="Author" layout="Author" spaceabove="0" spacebelow="0">Hamilton, ON L8S 4M1, Canada</Text-field>
<Text-field style="Author" layout="Author" spaceabove="0" spacebelow="0"><Font bold="true">anandc@mcmaster.ca</Font></Text-field>
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<Text-field style="Heading 1" layout="Heading 1">Abstract</Text-field>
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<Text-field style="Normal" layout="Normal">We simulate, using symbolic computation in Maple, the dynamics of coupled two-spin systems without relaxation, including the basic elements of NMR (Nuclear Magnetic Resonance) pulse sequences, as used in experimental Chemistry.  This extends previous work by other authors on single-spin and weakly-coupled systems.  This technique extends directly to n-spin systems, including relaxation, but our aim in this paper is to demonstrate the feasibility of doing these calculations symbolically, and validate our implementation against existing analytic solutions, which are for special cases of two-spin systems.  For the purposes of illustration, we simulate a two-parameter family of spin-echo experiments, for a representative spin system, and show graphically that this simulation can be visually optimized.  This lays the groundwork for the optimization of more complicated pulse sequences, with many parameters.</Text-field>
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<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Introduction</Text-field></Title>
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<Text-field style="Text" layout="Normal">Magnetic resonance is widely used in experimental, clinical and industrial applications, including medical diagnosis, experimental and industrial chemistry, and petroleum exploration.  Magnetic Resonance Imaging (MRI) and chemical Nuclear Magnetic Resonance (NMR) are based on the same physical models and this work applies equally to both, although multi-spin systems are not yet part of standard clinical practice.  Magnetic resonance arises from the interaction of spins (hydrogen nuclei in the present case) with magnetic fields and radio frequency radiation.  Water, by far the most common molecule in the body, is a single signal, with a rel</Text-field>
<Text-field style="Text" layout="Normal">MRI which gives diagnostic information of various organs detects signal from protons in water of body tissues so as to obtain medical images of slices or volumes from inside a body. atively easy to analyze response to imaging pulse sequence.  Quantum mechanics is not needed to understand the water signal.  In contrast, in NMR and MR Spectroscopy, most chemical compounds have many different protons with detectable signals, some of whose spins are coupled.  Coupling of the protons complicates the response, but it can be calculated analytically, using tools such as Maple.  In the body, although the effects on the image from other hydrogen nuclei which have coupled spins are small, information about their concentration and distribution is valuable diagnostically [5, 6, 9, 10]. These spins include hydrogen in creatine or n-acetyl aspartate (NAA). This is our original motivation for doing this research:  to use Maple software and optimization methods to design sequences which enhance signals from biologically-significant molecules in the brain or body.</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">Maple and other computer algebra methods have been applied to NMR before [11-29]. An important part of this calculation is the use of  angular momentum methods, which are facilitated with Maple [18-25]. This previous work mostly involves simulation of weakly-coupled spins, but little work has yet been done to use them for optimizing NMR experiments, or simulate strong-coupling.  We will show how to construct the linear systems which govern the evolution of coupled spin systems in different stages of the experiment.  Uncoupled systems correspond to simultaneously block-diagonal systems.  Weakly-coupled systems have numerically-small off-diagonal blocks, and strongly-coupled systems require numerically-large off-diagonal elements to reproduce empirically-observed behaviour.  We will show how to use Maple to simulate the more complicated strongly-coupled systems.</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">In quantum mechanics, the density matrix gives all possible information about a system. Operator formalisms are methods to deal with the density matrix so as to give reasonable solutions to show what a pulse does and what a delay does in NMR [6].  We use the Liouville space method for pulse NMR as the theory to directly work on the density matrix [1, 2, 3, 4], implementing the linear algebra symbolically in Maple. </Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">In NMR, each spin has four observables |1<Font subscript="true">0</Font>), |1<Font subscript="true">+1</Font>) ,  |1<Font subscript="true">-1</Font>)  and |0). The behaviour of a single spin is straightforward, but two coupled spins offer significant challenges. Two coupled spins have 16 elements, written here in direct product form:</Text-field>
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<Text-field style="Text" layout="Normal">A spin system is represented by a 16-element vector. Our manipulation of the spin system is represented by matrices acting on this vector.  A pulse sequence of  NMR is a series of short radio-frequency pulses interleaved with delays.  Behaviour in a delay is defined by a matrix called a Liouvillian which encodes information about chemical structure, frequencies, and couplings.  A pulse is equivalent to a rotation of the reference frame. A rotation is defined by a special matrix called a Wigner rotation matrix and is easy to set up for one spin. The direct product provides the rotation for multiple spins. </Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">In the Maple implementation, the Liouvillian is expressed in a different basis in which it is block diagonal. Then we do a permutation which brings it into the basis we use. The actual evolution is defined by the exponential of the Liouvillian matrix,  exp<Font superscript="true">iLt.</Font>  There are many ways of calculating the exponential of matrices; Maple provides a function to calculate the exponential of a matrix, but it does not give the answer when it works on our Liouvillian matrix.  Specifically, the Maple command </Text-field>
<Text-field style="Text" layout="Normal">&lt;MatrixExponential(L,I*t)&gt;  or  &lt; MatrixExponential(I*L*t)&gt;, was left to run half of a day on a PowerMac G5, and didn't complete the computation before we interrupted it. Whereas, explicitly calculating the eigenvalues, eigenvectors and forming the diagonalization executes almost instantaneously. We use the method based on diagonalization and a priori knowledge of  eigenvalues and eigenvectors of the Liouvillian matrix [8].  </Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">In Liouville space, we detect observables by taking the dot (scalar) product with the density matrix.  A scalar product between two Liouville space vectors is defined as the trace of their product as operators in spin space. This product gives the projection of one vector on the other vector [3].</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="centred" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">(P|Q) = </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">trace</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">(PQ)</Font></Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">The main steps of the Liouville space method are the following: (1) to define the basis of Liouville space; (2) to construct the Liouvillian matrix; (3) to calculate the equation of the motion; (4) to design NMR experiments such as series of pulses (Wigner rotation matrices) and delays (the equation of the motion); (5) to detect the NMR signal by means of the scalar product.</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" encoding="UTF-8" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">The main tasks of the present Maple application, which is a specific application of the Liouville space method to spin echo, are:  (1) to calculate the exact formula of NMR signal for spin echo (the first pulse is \317\200</Font><Equation executable="false" style="2D Math"></Equation><Equation executable="false" style="2D Math"></Equation><Equation executable="false" style="2D Math"></Equation><Equation executable="false" style="2D Math"></Equation><Equation executable="false" style="2D Math"></Equation><Equation executable="false" style="2D Math"></Equation><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" encoding="UTF-8" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">/2 , the second pulse is \317\200)  on a two-spin system;  (2) to calculate the general formula of NMR signal for spin echo (the first pulse is \317\200/2, the second pulse is \316\261), so \316\261 will be a variable in the spin-evolution; and then (3) to give an objective function for an optimization problem.</Font></Text-field>
<Group labelreference="L6" drawlabel="true">
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"></Text-field>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Initialization</Text-field></Title>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">In this stage, we set up a Liouvillian matrix for an <Font bold="true">AB </Font>(two-spin) system.  J is the coupling constant and <Font encoding="UTF-8">\317\211</Font><Font subscript="true">A</Font> and <Font encoding="UTF-8">\317\211</Font><Font subscript="true">B</Font> are their two Larmor frequencies.  A Liouvillian matrix, <Font bold="true">L</Font>, is divided into several blocks in the coherence order basis.  Usually, the Liouvillian matrix is built in the coherence order basis and then immediately permuted into the direct product order basis so to keep consistent with other vectors and matrices. </Text-field>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:
with (LinearAlgebra):
assume(omega[A]&gt;0,omega[B]&gt;0, theta&gt;0,theta&lt;Pi/4,omega[A]&gt;omega[B],delta&gt;0,J&gt;0,omega[av]&gt;0,omega[av]&gt;delta);</Text-field>
</Input>
<Input>
<Text-field style="Text" layout="Normal">One block is for the single quantum [2]:</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sqPos := Matrix(4,4,[[omega[A],J/2,0,-J/2],[J/2,omega[A],-J/2,0],[0,-J/2,omega[B],J/2],[-J/2,0,J/2,omega[B]]]):</Text-field>
</Input>
<Input>
<Text-field style="Text" layout="Normal">Another block is for the other single quantum:</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sqNeg := Matrix(4,4,[[-omega[A],-J/2,0,J/2],[-J/2,-omega[A],J/2,0],[0,J/2,-omega[B],-J/2],[J/2,0,-J/2,-omega[B]]]):</Text-field>
</Input>
<Input>
<Text-field style="Text" layout="Normal">The following code is to construct the Liouvillian matrix from its blocks.</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">L := &lt; &lt;Matrix(1,1,[[omega[A]+omega[B]]])|ZeroMatrix(1,15)&gt;, &lt;ZeroMatrix(4,1)|sqPos|ZeroMatrix(4,11)&gt; ,
&lt;ZeroMatrix(1,5)|Matrix(1,6,[[-omega[A]+omega[B],0,J/2,-J/2,0,0]])|ZeroMatrix(1,5)&gt;,&lt;ZeroMatrix(1,16)&gt;,
&lt;ZeroMatrix(1,5)|Matrix(1,6,[[J/2,0,0,0,0,-J/2]])|ZeroMatrix(1,5)&gt;,
&lt;ZeroMatrix(1,5)|Matrix(1,6,[[-J/2,0,0,0,0,J/2]])|ZeroMatrix(1,5)&gt;,
&lt;ZeroMatrix(1,16)&gt;, 
&lt;ZeroMatrix(1,5)|Matrix(1,6,[[0,0,-J/2,J/2,0,omega[A]-omega[B]]])|ZeroMatrix(1,5)&gt;,&lt;ZeroMatrix(4,11)|sqNeg|ZeroMatrix(4,1)&gt;,
&lt;ZeroMatrix(1,15)|Matrix(1,1,[[-omega[A]-omega[B]]])&gt;&gt;:</Text-field>
</Input>
<Input>
<Text-field style="Text" layout="Normal"><Font bold="true">PermutationDirect</Font><Font encoding="UTF-8"> is a 16\303\22716 matrix which is for the permutation between coherence order basis and direct product order basis.</Font></Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">PermutationDirect := &lt; &lt;ZeroMatrix(1,5)|Matrix(1,1,[1])|ZeroMatrix(1,10)&gt;,
&lt;Matrix(1,2,[[0,1]])|ZeroMatrix(1,14)&gt;,
&lt;ZeroMatrix(1,9)|Matrix(1,1,[1])|ZeroMatrix(1,6)&gt;,
&lt;ZeroMatrix(1,4)|Matrix(1,1,[1])|ZeroMatrix(1,11)&gt;,
&lt;ZeroMatrix(1,6)|Matrix(1,1,[1])|ZeroMatrix(1,9)&gt;,
&lt;ZeroMatrix(1,7)|Matrix(1,1,[1])|ZeroMatrix(1,8)&gt;,
&lt;Matrix(1,1,[1])|ZeroMatrix(1,15)&gt;,
&lt;ZeroMatrix(1,8)|Matrix(1,1,[1])|ZeroMatrix(1,7)&gt;,
&lt;ZeroMatrix(1,2)|Matrix(1,1,[1])|ZeroMatrix(1,13)&gt;,
&lt;ZeroMatrix(1,10)|Matrix(1,1,[1])|ZeroMatrix(1,5)&gt;,
&lt;ZeroMatrix(1,13)|Matrix(1,1,[1])|ZeroMatrix(1,2)&gt;,
&lt;ZeroMatrix(1,3)|Matrix(1,1,[1])|ZeroMatrix(1,12)&gt;,
&lt;ZeroMatrix(1,11)|Matrix(1,1,[1])|ZeroMatrix(1,4)&gt;,
&lt;ZeroMatrix(1,12)|Matrix(1,1,[1])|ZeroMatrix(1,3)&gt;,
&lt;ZeroMatrix(1,14)|Matrix(1,1,[1])|ZeroMatrix(1,1)&gt;,
&lt;ZeroMatrix(1,15)|Matrix(1,1,[1])&gt;&gt;:</Text-field>
</Input>
<Input>
<Text-field style="Text" layout="Normal">The Liouvillian matrix (<Font bold="true">NL</Font>) is in the direct product order basis. To simplify the formulae, <Font encoding="UTF-8">\317\211</Font><Font subscript="true">A</Font> and <Font encoding="UTF-8">\317\211</Font><Font subscript="true">B</Font> are substituted by <Font encoding="UTF-8">\317\211</Font><Font subscript="true">av</Font><Font encoding="UTF-8"> and \316\264. </Font></Text-field>
</Input>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="centred" initial="0" spacebelow="0"></Text-field>
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">NL := simplify(subs({omega[A]=omega[av]+delta,omega[B]=omega[av]-delta},L)):
NL := Multiply(MatrixInverse(PermutationDirect),Multiply(NL,PermutationDirect)):</Text-field>
</Input>
<Input>
<Text-field style="Text" layout="Normal"><Font bold="true">d1</Font> is the Wigner rotation matrix in the spherical tensor basis for one spin. <Font bold="true">WignerAlpha</Font><Font encoding="UTF-8"> is a 16\303\22716 matrix for two-spin rotation in the direct product order basis. We will use it to calculate the effect of a pulse on a two-spin system. For a multiple spin system, the rotation also can be represented by multiple direct product.</Font></Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">d1 := Matrix(3,3,[[(cos(alpha/2))^2,-sin(alpha)/sqrt(2),(sin(alpha/2))^2],[sin(alpha)/sqrt(2),cos(alpha),-sin(alpha)/sqrt(2)],[(sin(alpha/2))^2,sin(alpha)/sqrt(2),(cos(alpha/2))^2]]):</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">WignerA := &lt;&lt;matrix(1,1,[1])|ZeroMatrix(1,3)&gt;,&lt;ZeroMatrix(3,1)|d1&gt;&gt;;</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">DirectProduct := (A,B) -&gt; Matrix([seq([seq(ScalarMultiply(B,A[i,j]),j=1..ColumnDimension(A))],i=1..RowDimension(A))]):</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">WignerAlpha := DirectProduct(WignerA,WignerA):</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">We have now set up the Liouvillian for delays and the rotation matrix for pulses. We need to define detection of signal. The vector (<Font bold="true">TotalXYVector</Font>) which represents the total magnetization in the xy plane is used to detect the signal.</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">TotalXYVector := &lt;0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0&gt;: </Text-field>
</Input>
<Input>
<Text-field style="Text" layout="Normal">A Maple function gives the eigenvalues and eigenvectors of the Liouvillian matrix symbolically. The eigenvectors of <Font bold="true">NL</Font> correspond to density matrix elements and the eigenvalue represents a &quot;resonant frequency&quot; of that density matrix element if the spin space basis consists of eigenfunctions of the Hamiltonian. If the observable is one of the basis elements, its expectation value is just the corresponding density matrix element [3]. Currently, Maple 10 could not give the symbolic eigenvectors of a matrix which includes trigonometric elements. <Font encoding="UTF-8">After the eigenvectors are calculated, J is substituted by  \316\270 and \316\264. </Font></Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="Text" input-equation="Typesetting:-mrow(Typesetting:-mi(&quot;&quot;), Typesetting:-mo(&quot;tan&quot;, form = &quot;&quot;, fence = &quot;false&quot;, separator = &quot;false&quot;, lspace = &quot;0em&quot;, rspace = &quot;0em&quot;, stretchy = &quot;false&quot;, symmetric = &quot;false&quot;, maxsize = &quot;infinity&quot;, minsize = &quot;1&quot;, largeop = &quot;false&quot;, movablelimits = &quot;false&quot;, accent = &quot;false&quot;, font_style_name = &quot;Text&quot;, size = &quot;12&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[255,255,255]&quot;), Typesetting:-mo(&quot;&quot;, form = &quot;infix&quot;, fence = &quot;false&quot;, separator = &quot;false&quot;, lspace = &quot;0em&quot;, rspace = &quot;0em&quot;, stretchy = &quot;false&quot;, symmetric = &quot;false&quot;, maxsize = &quot;infinity&quot;, minsize = &quot;1&quot;, largeop = &quot;false&quot;, movablelimits = &quot;false&quot;, accent = &quot;false&quot;, font_style_name = &quot;Text&quot;, size = &quot;12&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[255,255,255]&quot;), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mn(&quot;2&quot;), Typesetting:-mi(&quot;\316\270&quot;))), Typesetting:-mo(&quot;=&quot;, form = &quot;infix&quot;, fence = &quot;false&quot;, separator = &quot;false&quot;, lspace = &quot;thickmathspace&quot;, rspace = &quot;thickmathspace&quot;, stretchy = &quot;false&quot;, symmetric = &quot;false&quot;, maxsize = &quot;infinity&quot;, minsize = &quot;1&quot;, largeop = &quot;false&quot;, movablelimits = &quot;false&quot;, accent = &quot;false&quot;, font_style_name = &quot;Text&quot;, size = &quot;12&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[0,0,0]&quot;), Typesetting:-mrow(Typesetting:-mi(&quot;&quot;), Typesetting:-mfrac(Typesetting:-mn(&quot;1&quot;), Typesetting:-mrow(Typesetting:-mi(&quot;&quot;), Typesetting:-mn(&quot;2&quot;), Typesetting:-mi(&quot;&quot;)), linethickness = &quot;1&quot;, denomalign = &quot;center&quot;, numalign = &quot;center&quot;, bevelled = &quot;false&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[255,255,255]&quot;), Typesetting:-mo(&quot;&quot;, form = &quot;infix&quot;, fence = &quot;false&quot;, separator = &quot;false&quot;, lspace = &quot;0em&quot;, rspace = &quot;0em&quot;, stretchy = &quot;false&quot;, symmetric = &quot;false&quot;, maxsize = &quot;infinity&quot;, minsize = &quot;1&quot;, largeop = &quot;false&quot;, movablelimits = &quot;false&quot;, accent = &quot;false&quot;, font_style_name = &quot;Text&quot;, size = &quot;12&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[255,255,255]&quot;), Typesetting:-mspace(height = &quot;0.0 ex&quot;, width = &quot;0.4 em&quot;, depth = &quot;0.0 ex&quot;, linebreak = &quot;auto&quot;), Typesetting:-mi(&quot;&quot;)), Typesetting:-mi(&quot;&quot;), Typesetting:-mrow(Typesetting:-mi(&quot;&quot;), Typesetting:-mfrac(Typesetting:-mi(&quot;J&quot;), Typesetting:-mrow(Typesetting:-mi(&quot;&quot;), Typesetting:-mi(&quot;\316\264&quot;)), linethickness = &quot;1&quot;, denomalign = &quot;center&quot;, numalign = &quot;center&quot;, bevelled = &quot;false&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[255,255,255]&quot;), Typesetting:-mo(&quot;=&quot;, form = &quot;infix&quot;, fence = &quot;false&quot;, separator = &quot;false&quot;, lspace = &quot;thickmathspace&quot;, rspace = &quot;thickmathspace&quot;, stretchy = &quot;false&quot;, symmetric = &quot;false&quot;, maxsize = &quot;infinity&quot;, minsize = &quot;1&quot;, largeop = &quot;false&quot;, movablelimits = &quot;false&quot;, accent = &quot;false&quot;, font_style_name = &quot;Text&quot;, size = &quot;12&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[0,0,0]&quot;), Typesetting:-mrow(Typesetting:-mi(&quot;&quot;), Typesetting:-mfrac(Typesetting:-mi(&quot;J&quot;), Typesetting:-mrow(Typesetting:-mi(&quot;&quot;), Typesetting:-mi(&quot;\317\211&quot;), Typesetting:-mi(&quot;A&quot;), Typesetting:-mo(&quot;\342\210\222&quot;, form = &quot;&quot;, fence = &quot;false&quot;, separator = &quot;false&quot;, lspace = &quot;0em&quot;, rspace = &quot;0em&quot;, stretchy = &quot;false&quot;, symmetric = &quot;false&quot;, maxsize = &quot;infinity&quot;, minsize = &quot;1&quot;, largeop = &quot;false&quot;, movablelimits = &quot;false&quot;, accent = &quot;false&quot;, font_style_name = &quot;Text&quot;, size = &quot;12&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[0,0,0]&quot;), Typesetting:-mi(&quot;\317\211&quot;), Typesetting:-mi(&quot;B&quot;), Typesetting:-mi(&quot;&quot;)), linethickness = &quot;1&quot;, denomalign = &quot;center&quot;, numalign = &quot;center&quot;, bevelled = &quot;false&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[255,255,255]&quot;), Typesetting:-mo(&quot;&quot;, form = &quot;infix&quot;, fence = &quot;false&quot;, separator = &quot;false&quot;, lspace = &quot;0em&quot;, rspace = &quot;0em&quot;, stretchy = &quot;false&quot;, symmetric = &quot;false&quot;, maxsize = &quot;infinity&quot;, minsize = &quot;1&quot;, largeop = &quot;false&quot;, movablelimits = &quot;false&quot;, accent = &quot;false&quot;, font_style_name = &quot;2D Math&quot;, size = &quot;12&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[255,255,255]&quot;)), Typesetting:-mi(&quot;&quot;)), Typesetting:-mi(&quot;&quot;))">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</Equation></Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">(V,E) := Eigenvectors(NL):
E := simplify(subs({J=(sin(2*theta)/cos(2*theta))*2*delta},E)):</Text-field>
</Input>
<Input>
<Text-field style="Text" layout="Normal">In order to get the exponential of a matrix, we use the eigen decomposition method.  The eigenvectors which are returned by Maple are not normalized, so the required inverse is given by a Maple function. If the eigenvectors are normalized, the inverse can be directly calculated by a transpose.</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ExpV := &lt;seq(exp(I*V[i]*t),i=1..Dimension(V))&gt;:</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ExpVdiagonal := Matrix(1..16,1..16,ExpV,shape=diagonal):</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ExpL := MatrixMatrixMultiply(E,MatrixMatrixMultiply(ExpVdiagonal,simplify(MatrixInverse(E)))):</Text-field>
</Input>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The spectrum of the two-spin system consists of four lines, so only four quantities are observed where they are in the density matrix. <Font bold="true">IndexofSQ</Font> stores the index of the eigenvalues vector <Font bold="true">V</Font> in which the value is the frequency of the signals. Every time the eigenvectors are calculated, the index needs to be set up again.</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">GetSQIndex := proc(V)
local i,j,SQIndex;
j := 1;
i := 1;
while j &lt; 5 do 
   if V[i] = omega[av]+1/2*J+1/2*sqrt(J^2+4*delta^2) then SQIndex[j] := i;  j := j + 1;   end if;
   if V[i] = omega[av]+1/2*J-1/2*sqrt(J^2+4*delta^2) then SQIndex[j] := i;  j := j + 1;   end if;
   if V[i] = omega[av]-1/2*J+1/2*sqrt(J^2+4*delta^2) then SQIndex[j] := i;  j := j + 1;   end if;
   if V[i] = omega[av]-1/2*J-1/2*sqrt(J^2+4*delta^2) then SQIndex[j] := i;  j := j + 1;   end if;
i := i + 1;
end do;
[SQIndex[1],SQIndex[2],SQIndex[3],SQIndex[4]]
end proc:</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">IndexofSQ := GetSQIndex(V):</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Frequency := V[IndexofSQ];</Text-field>
</Input>
<Input>
<Text-field style="Text" layout="Normal"><Font bold="true">SQEigenvectorsNorm</Font> stores the normalized eigenvectors which are associated with the eigenvalues.  These eigenvectors represent the transitions.</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">SQEigenvectors := E[1..16,IndexofSQ]:</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">SQEigenvectorsNorm := [seq(SQEigenvectors[1..16,i]/VectorNorm(SQEigenvectors[1..16,i],2,conjugate=false),i=1..ColumnDimension(SQEigenvectors))]:</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Spin Echo of a Coupled System</Text-field></Title>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"></Text-field>
<Text-field style="Normal" layout="Normal"><Font style="Text">We will implement the calculation of the NMR signal of spin echo.  This is a series of pulse, delay, and detection. Since each of these manipulations is a matrix operation, we only need the multiply function between matrices and vectors.</Font></Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"><Image height="128" width="297" zoomable="false">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</Image></Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal"> The main steps are: </Text-field>
<Text-field style="Text" layout="Normal">(1) setting up the equilibrium state of the system;</Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">(2) applying the first pulse. In general, Wigner matrix is for any \316\261; \316\261 can be a variable. In this case, the first pulse is \317\200/2;</Font></Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">(3) evolving during a delay \317\204;</Font></Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">(4) applying the second pulse. (Normally, \316\261 = \317\200). For optimization problems, we allow the flip angle of the second pulse, \316\261, to vary. In this present case, \316\261 is equal to \317\200;</Font></Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">(5) evolving during a delay \317\204;   </Font></Text-field>
<Text-field style="Text" layout="Normal">(6) detecting.</Text-field>
</Input>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Font bold="true">EquVector</Font> represents the equilibrium state, in which most experiments begin:</Text-field>
</Input>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">EquVector := &lt;0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0&gt;:</Text-field>
</Input>
<Input>
<Text-field style="Text" layout="Normal">The first pulse, which is a <Font encoding="UTF-8">\317\200/2 pulse,</Font> acts on the system:</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">RotateEqu1 := MatrixVectorMultiply(eval(WignerAlpha,[alpha=Pi/2]),EquVector): </Text-field>
</Input>
<Input>
<Text-field style="Text" layout="Normal">The first delay:</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Evaluation1 := simplify(simplify(simplify(MatrixVectorMultiply(ExpL,RotateEqu1)))): </Text-field>
</Input>
<Input>
<Text-field style="Text" layout="Normal">The second pulse (<Font encoding="UTF-8">\317\200</Font>) acts on the system:</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">WignerAlpha2 := eval(WignerAlpha,[alpha=Pi]):
RotateEqu2 := MatrixVectorMultiply(WignerAlpha2,Evaluation1): </Text-field>
</Input>
<Input>
<Text-field style="Text" layout="Normal">The second delay:</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Evaluation2 := MatrixVectorMultiply(ExpL,RotateEqu2): </Text-field>
</Input>
<Input>
<Text-field style="Text" layout="Normal">Detection:</Text-field>
<Text-field style="Text" layout="Normal">The vector <Font bold="true">Intensity</Font> and <Font bold="true">IntensityOriginal</Font> will return the intensity of the NMR signal with respect to the frequency vector <Font bold="true">Frequency</Font>. </Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Evaluation := simplify(eval(Evaluation2,[t=tau])):</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">scalar1 := [seq(Multiply(Transpose(Evaluation),SQEigenvectorsNorm[i]),i=1..ColumnDimension(SQEigenvectors))]:
scalar2 := [seq(Multiply(Transpose(SQEigenvectorsNorm[i]),TotalXYVector),i=1..ColumnDimension(SQEigenvectors))]:</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">IntensityOriginal := &lt;seq(simplify(scalar1[i]*scalar2[i]),i=1..ColumnDimension(SQEigenvectors))&gt;:</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Intensity := factor(subs({cos(2*theta)^2=1-sin(2*theta)^2},IntensityOriginal)):</Text-field>
</Input>
<Input>
<Text-field style="Text" layout="Normal">Display one of the intensities.</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Intensity[1];
</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiQtSSNtb0dGJTYzUSomdW1pbnVzMDtGKC8lJWZvcm1HUSdwcmVmaXhGKC8lJmZlbmNlR1EmZmFsc2VGKC8lKnNlcGFyYXRvckdGNS8lJ2xzcGFjZUdRJDBlbUYoLyUncnNwYWNlR0Y6LyUpc3RyZXRjaHlHRjUvJSpzeW1tZXRyaWNHRjUvJShtYXhzaXplR1EpaW5maW5pdHlGKC8lKG1pbnNpemVHUSIxRigvJShsYXJnZW9wR0Y1LyUubW92YWJsZWxpbWl0c0dGNS8lJ2FjY2VudEdGNS8lMGZvbnRfc3R5bGVfbmFtZUdRKjJEfk91dHB1dEYoLyUlc2l6ZUdRIzEyRigvJStmb3JlZ3JvdW5kR1EqWzAsMCwyNTVdRigvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYoLUYkNiUtSSZtZnJhY0dGJTYqLUkjbW5HRiU2OUZGLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRigvJSVzaXplR0ZSLyUlYm9sZEdGNS8lJ2l0YWxpY0dGNS8lKnVuZGVybGluZUdGNS8lKnN1YnNjcmlwdEdGNS8lLHN1cGVyc2NyaXB0R0Y1LyUrZm9yZWdyb3VuZEdGVS8lK2JhY2tncm91bmRHRlgvJSdvcGFxdWVHRjUvJStleGVjdXRhYmxlR0Y1LyUpcmVhZG9ubHlHUSV0cnVlRigvJSljb21wb3NlZEdGNS8lKmNvbnZlcnRlZEdGNS8lK2ltc2VsZWN0ZWRHRjUvJSxwbGFjZWhvbGRlckdGNS8lMGZvbnRfc3R5bGVfbmFtZUdGTy8lKm1hdGhjb2xvckdGVS8lL21hdGhiYWNrZ3JvdW5kR0ZYLyUrZm9udGZhbWlseUdGXW8vJSxtYXRodmFyaWFudEdRJ25vcm1hbEYoLyUpbWF0aHNpemVHRlItRmluNjlRIjRGKEZbb0Zeb0Zgb0Zib0Zkb0Zmb0Zob0Zqb0ZccEZecEZgcEZicEZlcEZncEZpcEZbcUZdcUZfcUZhcUZjcUZlcUZocS8lLmxpbmV0aGlja25lc3NHUSIxRigvJStkZW5vbWFsaWduR1EnY2VudGVyRigvJSludW1hbGlnbkdGYnIvJSliZXZlbGxlZEdGNUZTRlYtRi02M1ExJkludmlzaWJsZVRpbWVzO0YoL0YxUSZpbmZpeEYoRjNGNkY4RjtGPUY/RkFGREZHRklGS0ZNRlBGU0ZWLUYkNiUtRiQ2JS1GLTYzUSIoRihGMC9GNEZkcEY2L0Y5US50aGlubWF0aHNwYWNlRigvRjxGZXMvRj5GZHBGP0ZBRkRGR0ZJRktGTUZQRlNGVi1GJDYqRiwtRiQ2JS1JJW1zdXBHRiU2JS1GLTYzUSJlRigvRjFRIUYoRjNGNkY4RjtGPUY/RkFGREZHRklGS0ZNRlBGU0ZWLUYkNiVGYHMtRiQ2Jy1GaW42OVEiSUYoRltvRl5vRmBvRmJvRmRvRmZvRmhvRmpvRlxwRl5wRmBwRmJwRmVwRmdwRmlwRltxRl1xRl9xRmFxRmNxRmVxRmhxRmdyLUkjbWlHRiU2OVEkdGF1RihGW29GXm9GYG9GYm9GZG9GZm9GaG9Gam9GXHBGXnBGYHBGYnBGZXBGZ3BGaXBGW3FGXXFGX3FGYXFGY3FGZXFGaHFGZ3ItRlx1NjlRI0p8aXJGKEZbb0Zeb0Zgby9GY29GZHBGZG9GZm9GaG9Gam9GXHBGXnBGYHBGYnBGZXBGZ3BGaXBGW3FGXXFGX3FGYXFGY3EvRmZxUSdpdGFsaWNGKEZocS1GLTYzUSIpRigvRjFRKHBvc3RmaXhGKEZjc0Y2RmRzL0Y8UTJ2ZXJ5dGhpbm1hdGhzcGFjZUYoRmdzRj9GQUZERkdGSUZLRk1GUEZTRlYvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYoRmdyLUYkNiVGYHMtRiQ2JUZobi1GLTYzUSgmbWludXM7RihGanJGM0Y2L0Y5UTBtZWRpdW1tYXRoc3BhY2VGKC9GPEZndkY9Rj9GQUZERkdGSUZLRk1GUEZTRlYtRiQ2Iy1GXXQ2JS1GJDYlLUZcdTY5USRzaW5GKEZbb0Zeb0Zgb0Zib0Zkb0Zmb0Zob0Zqb0ZccEZecEZgcEZicEZlcEZncEZpcEZbcUZdcUZfcUZhcUZjcUZlcUZocS1GLTYzUTAmQXBwbHlGdW5jdGlvbjtGKEZqckYzRjZGOEY7Rj1GP0ZBRkRGR0ZJRktGTUZQRlNGVi1GJDYlRmBzLUYkNiMtRiQ2JS1GaW42OVEiMkYoRltvRl5vRmBvRmJvRmRvRmZvRmhvRmpvRlxwRl5wRmBwRmJwRmVwRmdwRmlwRltxRl1xRl9xRmFxRmNxRmVxRmhxRmdyLUZcdTY5USd0aGV0YXxpckYoRltvRl5vRmBvRmJ1RmRvRmZvRmhvRmpvRlxwRl5wRmBwRmJwRmVwRmdwRmlwRltxRl1xRl9xRmFxRmNxRmN1RmhxRmV1Rlt4Rlx2RmV1LUYtNjNRIitGKEZqckYzRjZGZnZGaHZGPUY/RkFGREZHRklGS0ZNRlBGU0ZWLUYkNiUtRl10NiVGX3QtRiQ2JUZgcy1GJDYnRmh0RmdyRlt1RmdyLUYkNiVGYHMtRiQ2JUZfdUZheC1GJDYjLUkmbXNxcnRHRiU2JS1GJDYlLUYkNiVGanFGZ3ItRl10NiUtRlx1NjlRJ2RlbHRhfGlyRihGW29GXm9GYG9GYnVGZG9GZm9GaG9Gam9GXHBGXnBGYHBGYnBGZXBGZ3BGaXBGW3FGXXFGX3FGYXFGY3FGY3VGaHFGW3hGXHZGYXgtRiQ2Iy1GXXQ2JUZfdUZbeEZcdkZTRlZGZXVGZXVGXHZGZ3JGX3ZGY3ZGZnhGYXgtRiQ2JUZmeEZnckZdd0ZldUZnci1GY3k2JUZbeEZTRlY3IywkKigjIiIiIiIlRmp6LCoqJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0YqNiMqKF4jRmp6Rmp6SSR0YXVHRihGanpJI0p8aXJHRihGanpGanosJkZqekZqeiokKS1JJHNpbkdGYFtsNiMsJComIiIjRmp6SSd0aGV0YXxpckdGKEZqekZqekZfXGxGanohIiJGanpGYVxsKiYtRl9bbDYjKihGZFtsRmp6RmVbbEZqeiwmRmZbbEZqeiokKSwmKiZGW1tsRmp6KUknZGVsdGF8aXJHRihGX1xsRmp6Rmp6KiQpRmZbbEZfXGxGanpGanojRmp6Rl9cbEZqekZqekZqekZqekZnW2xGanpGanpGY1xsRmFcbComRmNcbEZqekZqW2xGanpGanpGanopRl9cbEZfXWxGanpGYVxs</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The above result is the same as [4]. </Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">For the weak coupling limit \316\270\342\206\2220, we observe a simple phase modulation at frequency J [4]. This result is also the same as [4].</Font></Text-field>
</Input>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">WeakIntensity := simplify(eval(IntensityOriginal,[theta=0])):</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">'WeakIntensity[1]' = WeakIntensity[1]; 
plot(Re(eval(WeakIntensity[1],[J=8])),tau=0..3);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field>
</Output>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="400" type="two-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" 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<Input>
<Text-field style="Text" layout="Normal">For a strong AB system, i.e. tan<Font encoding="UTF-8">(2\316\270)\342\211\2101,</Font> the behaviour is more complex, but still matches [4].</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">StrongIntensity := simplify(eval(IntensityOriginal,[theta=Pi/8])):</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">'StrongIntensity[1]' = StrongIntensity[1]; 
plot(Re(eval(StrongIntensity[1],[J=8,delta=4])),tau=0..3);</Text-field>
</Input>
<Output>
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<Text-field style="Text" layout="Normal">At this stage, the difference between these plots illustrates the complications that strong coupling introduces. Maple provides a reliable way of dealing with these complications.</Text-field>
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<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Optimization Spin Echo Detection </Text-field></Title>
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<Text-field style="Text" layout="Normal">We choose the sum of the squares of the real parts of the spectrum as our objective function. This will give us the strongest spectrum. This is a simple function and we optimize it visually.  The capabilities of Maple will support much more complicated objective functions corresponding to longer pulse trains and multiple chemical species in the future, but visualization of two-dimensional subspaces will still be important in understanding the design spaces.</Text-field>
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<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">In order to optimize the pulse sequence, we need to control the second pulse and the delay time, which gives two variables:  \316\261 and \317\204.  Maple gives the general formulae with \316\261 and \317\204.  Maple can differentiate the objective functions we give, which is important for rapid convergence, but for the moment we simply plot the objective function.  In order to simulate the variation in magnetic field present in real experiments, we average \317\211</Font><Font subscript="true">av</Font> over a Gaussian spread of values. The steps to calculate the formulae are the same as before.</Text-field>
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<Text-field style="Text" layout="Normal"><Font bold="true">EquVector</Font> represents the equilibrium state:</Text-field>
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<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">EquVector := &lt;0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0&gt;:</Text-field>
</Input>
<Input>
<Text-field style="Text" layout="Normal">The first pulse (<Font encoding="UTF-8">\317\200</Font>/2) acts on the system:</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">RotateEqu1 := MatrixVectorMultiply(eval(WignerAlpha,[alpha=Pi/2]),EquVector): </Text-field>
</Input>
<Input>
<Text-field style="Text" layout="Normal">The first delay:</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"> Evaluation1 := simplify(simplify(simplify(MatrixVectorMultiply(ExpL,RotateEqu1)))): </Text-field>
</Input>
<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">The second pulse (\316\261) acts on the system, we leave \316\261</Font> as a variable:</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">WignerAlpha2 := eval(WignerAlpha,[alpha=alpha]):
RotateEqu2 := MatrixVectorMultiply(WignerAlpha2,Evaluation1): </Text-field>
</Input>
<Input>
<Text-field style="Text" layout="Normal">The second delay:</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Evaluation2 := MatrixVectorMultiply(ExpL,RotateEqu2): </Text-field>
</Input>
<Input>
<Text-field style="Text" layout="Normal">Detecting:</Text-field>
<Text-field style="Text" layout="Normal">The vector <Font bold="true">IntensityOriginal</Font> will return the intensity of the NMR signal with respect to the frequency vector <Font bold="true">Frequency</Font>. </Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Evaluation := simplify(eval(Evaluation2,[t=tau])):</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">scalar1 := [seq(Multiply(Transpose(Evaluation),SQEigenvectorsNorm[i]),i=1..ColumnDimension(SQEigenvectors))]:
scalar2 := [seq(Multiply(Transpose(SQEigenvectorsNorm[i]),TotalXYVector),i=1..ColumnDimension(SQEigenvectors))]:</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">IntensityOriginal := &lt;seq(simplify(scalar1[i]*scalar2[i]),i=1..ColumnDimension(SQEigenvectors))&gt;:</Text-field>
</Input>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">We now have an expression for a spin echo using a general value of alpha. This would have been prohibitive with hand calculation, but Maple handles it easily.  In order to optimize the system, we need an objective function. </Text-field>
<Text-field style="Text" layout="Normal">The objective function we choose is <Font bold="true">ObjFunc </Font><Font encoding="UTF-8">which has two variables \317\204 and \316\261 (without a Gaussian distribution).</Font></Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">SumofRealIntensity := (Re(IntensityOriginal[1]))^2+(Re(IntensityOriginal[2]))^2+(Re(IntensityOriginal[3]))^2+(Re(IntensityOriginal[4]))^2:</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ObjFunc := evalf(eval(SumofRealIntensity,[J=8,delta=4,omega[av]=0,theta= arctan(1/1)/2])):</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot3d(ObjFunc,tau=0..1,alpha=0..2*Pi,axes=normal);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="400" type="three-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0">6%-I%GRIDG6$%*protectedGI(_syslibG6"6%;$""!F,$"""F,;F+$"0ezrI&=$G'!#9X,F(F(F([gl'!%"!!#\bm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tauGF(I&alphaGF(Q!F(-I*AXESSTYLEGF%6#I'NORMALGF%</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The following code simulates field variation by integrating <Font encoding="UTF-8">\317\211</Font>av taken from a Gaussian distribution. </Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Case 1: \317\211</Font><Font subscript="true">av</Font><Font encoding="UTF-8">=0, J=8hz, 2\316\264=20J;</Font></Text-field>
</Input>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">GaussianSignal := &lt;seq(int(eval(IntensityOriginal[i]*exp(-omega[av]^2/(2*(2)^2))/(2*(sqrt(2*Pi))),[J=8,delta=10*8,theta=arctan(1/(20))/2]),omega[av]=-infinity..infinity),i=1..Dimension(IntensityOriginal))&gt;:</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ObjFunc := (Re(GaussianSignal[1]))^2+(Re(GaussianSignal[2]))^2+(Re(GaussianSignal[3]))^2+(Re(GaussianSignal[4]))^2:</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot3d(ObjFunc,tau=0..1,alpha=0..2*Pi,axes=normal);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="400" type="three-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0">6%-I%GRIDG6$%*protectedGI(_syslibG6"6%;$""!F,$"""F,;F+$"0ezrI&=$G'!#9X,F(F(F([gl'!%"!!#\bm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</Output>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Case 2: \317\211</Font><Font subscript="true">av</Font><Font encoding="UTF-8">=0, J=8hz, 2\316\264=J;</Font></Text-field>
</Input>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">GaussianSignal := &lt;seq(int(eval(IntensityOriginal[i]*exp(-omega[av]^2/(2*(2)^2))/(2*(sqrt(2*Pi))),[J=8,delta=4,theta=arctan(8/(2*4))/2]),omega[av]=-infinity..infinity),i=1..Dimension(IntensityOriginal))&gt;:</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ObjFunc := (Re(GaussianSignal[1]))^2+(Re(GaussianSignal[2]))^2+(Re(GaussianSignal[3]))^2+(Re(GaussianSignal[4]))^2:</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot3d(ObjFunc,tau=0..1,alpha=0..2*Pi,axes=normal);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="400" type="three-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" 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</Output>
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<Input>
<Text-field style="Text" layout="Normal">With several thousand basic operations, an expression for the derivatives of this objective are clearly beyond our ability to compute by hand, but simple enough for Maple or Maple CodeGeneration.</Text-field>
</Input>
</Group>
<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">codegen[cost](diff(ObjFunc,alpha));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field>
</Output>
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</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">Conclusion</Text-field></Title>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">Maple provides a good way to simulate NMR of strongly coupled nuclear spins, both symbolically and numerically.  Using Maple plots, we can quickly understand the design space for two-dimensional families of pulse sequences and, by projection, for more complicated families.  Using symbolic computation, we have access to derivatives, which enables future efficient numerical optimization of pulse sequences.  In this application, we have defined tools for pulse, delay, and detection.  With these tools, we can easily construct any pulse sequence and then observe the signals.  The same method can be applied to code the relaxation and phase cycling, and generalize to n-spins.  Finally, it is relatively easy to scale up for more than two spins. The computational complexity grows quickly in Liouville space, since we need to calculate eigenvalues for a system of size <Equation executable="false" style="Text" input-equation="Typesetting:-mrow(Typesetting:-mi(&quot;&quot;), Typesetting:-msup(Typesetting:-mn(&quot;4&quot;), Typesetting:-mi(&quot;n&quot;), superscriptshift = &quot;0&quot;), Typesetting:-mi(&quot;&quot;))">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</Equation>.  Most applications are for small numbers of spins, which we can treat in the same way.  For the last few percent which involve more than 5 spins, we may calculate it in the single quantum subspace which complexity is reduced to <Equation executable="false" style="Text" input-equation="Typesetting:-mrow(Typesetting:-mi(&quot;&quot;), Typesetting:-mfenced(Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-mn(&quot;2&quot;), Typesetting:-mo(&quot; &quot;, form = &quot;infix&quot;, fence = &quot;false&quot;, separator = &quot;false&quot;, lspace = &quot;0em&quot;, rspace = &quot;0em&quot;, stretchy = &quot;false&quot;, symmetric = &quot;false&quot;, maxsize = &quot;infinity&quot;, minsize = &quot;1&quot;, largeop = &quot;false&quot;, movablelimits = &quot;false&quot;, accent = &quot;false&quot;, font_style_name = &quot;Text&quot;, size = &quot;12&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[0,0,0]&quot;), Typesetting:-mi(&quot;n&quot;)), Typesetting:-mrow(Typesetting:-mi(&quot;n&quot;), Typesetting:-mo(&quot;\342\210\222&quot;, form = &quot;infix&quot;, fence = &quot;false&quot;, separator = &quot;false&quot;, lspace = &quot;thickmathspace&quot;, rspace = &quot;thickmathspace&quot;, stretchy = &quot;false&quot;, symmetric = &quot;false&quot;, maxsize = &quot;infinity&quot;, minsize = &quot;1&quot;, largeop = &quot;false&quot;, movablelimits = &quot;false&quot;, accent = &quot;false&quot;, font_style_name = &quot;Text&quot;, size = &quot;12&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[0,0,0]&quot;), Typesetting:-mn(&quot;1&quot;)), linethickness = &quot;0&quot;, denomalign = &quot;center&quot;, numalign = &quot;center&quot;, bevelled = &quot;false&quot;, foreground = &quot;[0,0,0]&quot;, background = &quot;[255,255,255]&quot;), Typesetting:-msemantics = &quot;binomial&quot;), Typesetting:-mi(&quot;&quot;))">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</Equation>.</Text-field>
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<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">References</Text-field></Title>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">[1]. Alex D. Bain,  </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">Coherence levels and coherence pathways in NMR. A simple way to design phase cycling procedures</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, Journal of Magnetic Resonance (1969), vol. 56, no. 3, pp. 418-427, 1984.</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">[2]. Alex D. Bain, D. A.  Fletcher, and Paul Hazendonk,   </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">What is a transition?</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12"> , Concepts in Magnetic Resonance, vol. 10, no. 2, pp.85-98, 1998.</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">[3]. Alex D. Bain, and John S. Martin, </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">FT NMR of nonequilibrium states of complex spin systems. I. A Liouville space description</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, Journal of Magnetic Resonance (1969), vol. 29, no. 1, pp. 125-135, 1978.</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">[4]. Alex D. Bain,  </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">Modulation of NMR spin echoes in coupled systems</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, Chemical Physics Letters, vol. 57, no. 2, pp. 281-284, 1978.</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">[5]. Hyeonjin Kim, James M. Wild, and Peter S. Allen. </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">Strategy for the spectral filtering of Myo-Inositol and other strongly coupled spins</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, Magnetic Resonance in Medicine, vol. 51, no. 2, pp.263- 272,2004</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">[6]. Tim Allman, Alex D. Bain, and Joel R. Garbow, </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">SIMPLTN, a Program for the Simulation of Pulse NMR Spectra, </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">Journal of Magnetic Resonance, Series A, vol. 123, no. 1, pp. 26-31, 1996.</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">[7]. Alan Carrington, Andrew D. McLachlan, </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">Introduction to Magnetic Resonance</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, Harper &amp; Row, 1967</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">[8]. Eric W. Weisstein. </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">Eigen Decomposition</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">. From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/EigenDecomposition.html</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">[9].  E. Mark Haacke, Robert W. Brown, Michael R. Thompson, Ramesh Venkatesan, </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">Magnetic Resonance Imaging- Physical Principles and Sequence Design</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, John Wiley &amp; Sons, 1999  </Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">[10]. Magnetic Resonance - Technology Information Portal,  http://www.mr-tip.com/serv1.php?type=db1&amp;dbs=Magnetic%20Resonance%20Imaging%20MRI</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">[11]. Christophe Odin, </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">Calculations of Multipulse Sequence in NQR of Spins</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, Journal of Magnetic Resonance, vol. 141, no. 2, pp. 239-255, 1999</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">[12]. S.Z.Ageev, P.P.Man and B.C.Sanctuary, </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">Detection of Double and Four Quantum Coherences for SpinExcited by Spin Lock Pulse Sequences</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, Journal of Magnetic Resonance, vol. 128, no. 1, pp. 12-20, 1997</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">[13]. S.Z.Ageev, P.P.Man, J.Fraissard and B.C.Sanctuary, </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">Determination of quadrupolar spin coupling for spin 7/2 using two pulse sequences</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, Molecular Physics vol. 91, no.1, pp. 75-80, 1997.</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">[14]. D.J.Isbister, M.S.Krishnan and B.C.Sanctuary, </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">Use of computer algebra for the study of quadrupole spin systems</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, Molecular Physics vol. 86, pp. 1517-1535, 1995.</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">[15]. S.Bahceli and A.Tokatli, </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">The product operator description of INEPT experiments for IS (I=1/2; S=5/2) spin systems and its applications to microcline and TMP-AlCl3 complex in NaX zeolite</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, Appl.Magn.Reson. vol. 29, pp. 617-626, 2005.</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">[16]. A.Tokatli, A.Gencten, M.Sahin, O.Tezel and S.Bahceli, </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">Product operator descriptions of INEPT and RINEPT NMR spectroscopies for ISn (I=1/2, S=3/2) spin systems</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, J.Magn.Reson. vol. 169, no.1, pp. 68-72, 2004.</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">[17]. Yuval Zur,  </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">An algorithm to calculate the NMR signal of a multi spin-echo sequence with relaxation and spin-diffusion</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, Journal of Magnetic Resonance, vol. 171, no. 1, pp. 97-106, 2004</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">[18]. S. Fritzsche,  </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">Maple procedures for the coupling of angular momenta I. Data structures and numerical computations</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, Computer Physics Communications, vol. 103, no. 1, pp. 51-73, 1997</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12"> [19]. S. Fritzsche, S. Varga,  D. Geschke &amp; B. Fricke,  </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">Maple procedures for the coupling of angular momenta II. Sum rule evaluation</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, Computer Physics Communications, vol. 111, no. 1-3, pp. 167-184, 1998</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12"> [20]. G. Gaigalas,  S. Fritzsche &amp; B. Fricke,  </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">Maple procedures for the coupling of angular momenta. III. Standard quantities for evaluating many-particle matrix elements</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, Computer Physics Communications, vol. 135, no. 2, pp. 219-237, 2001</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12"> [21]. T. Inghoff, S. Fritzsche &amp; B. Fricke,  </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">Maple procedures for the coupling of angular momenta. IV. Spherical harmonics</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, Computer Physics Communications, vol. 139, no. 3, pp. 297-313, 2001</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">[22]. S. Fritzsche,  T. Inghoff, T.  Bastug &amp; M. Tomaselli,  </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">Maple procedures for the coupling of angular momenta. V. Recoupling coefficients</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, Computer Physics Communications, vol. 139, no. 3, pp. 314-326, 2001</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">[23]. G. Gaigalas &amp; S.  Fritzsche, </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">Maple procedures for the coupling of angular momenta. VI. LS-jj transformations</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, Computer Physics Communications, vol. 149, no. 1, pp. 39-60, 2002</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">[24]. S. Fritzsche, T.  Inghoff &amp; M. Tomaselli,  </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">Maple procedures for the coupling of angular momenta. VII. Extended and accelerated computations</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, Computer Physics Communications, vol. 153, no. 3, pp. 424-444, 2003</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">[25]. G. Gaigalas, O. Scharf &amp; S.  Fritzsche, </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">Maple procedures for the coupling of angular momenta. VIII. Spin-angular coefficients for single-shell configurations</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, Computer Physics Communications, vol. 166, no. 2, pp. 141-169, 2005</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">[26]. A. Jerschow, </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">MathNMR: Spin and spatial tensor manipulations in Mathematica</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, Journal of Magnetic Resonance, vol. 176, no. 1, pp. 7-14, 2005</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12"> [27]. M. P. Barnett, J. F. Capitani, J.  von zur Gathen &amp; J. Gerhard, </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">Symbolic calculation in chemistry: Selected examples</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, International Journal of Quantum Chemistry, vol. 100, no. 2, pp. 80-104, 2004</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">[28]. N.A.  Nguyen &amp; T. T.  Nguyen-Dang, </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">Symbolic calculations of unitary transformations in quantum dynamics</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, Computer Physics Communications, vol. 115, no. 2-3, pp. 183-199, 1998</Font></Text-field>
<Text-field executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="8" rightmargin="0" bullet="none" firstindent="0" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">[29]. R.P.F.  Kanters, B.W. Char &amp;  A.W. Addison, </Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">A Computer-Algebra Application for the Description of NMR Experiments Using the Product-Operator Formalism</Font><Font executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">,  Journal of Magnetic Resonance, Series A, vol. 101, no. 1, pp. 23-29, 1993</Font></Text-field>
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