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Lattices
, 2008
"... It occurs frequently in algorithmic number theory that a problem has both a discrete and a continuous component. A typical example is the search for a system of integers that satisfies certain inequalities. A problem of this nature can often be successfully approached by means of the algorithmic t ..."
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theory of lattices, a lattice being a discrete subgroup of a Euclidean vector space. This article provides an introduction to this theory, including a generous
the lattice.
, 1659
"... 16. Although the TEMPO EPR line is dominated by inhomogeneous broadening, the thermal mixing effect is not necessarily precluded. Our preliminary studies indicate that electronelectron crossrelaxation across the 200 G EPR line is substantially faster than T1e at low temperature, allowing the inho ..."
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16. Although the TEMPO EPR line is dominated by inhomogeneous broadening, the thermal mixing effect is not necessarily precluded. Our preliminary studies indicate that electronelectron crossrelaxation across the 200 G EPR line is substantially faster than T1e at low temperature, allowing the inhomogeneous EPR line to be treated as a quasihomogeneous line. Thus, offcenter irradiation of the EPR line can significantly perturb the electronic dipolar reservoir. Because the TEMPO EPR line is substantially broader than the proton resonance frequency, a flipflop transition of two electron spins can drive a nuclear spin flip in an energyconserving process, and thus polarize the nuclear spins. Both themicrowave power and magnetic field dependences of the DNP enhancement indicate that thermal mixing is the predominant mechanism, with the solid effect making a relatively small contribution.
Lattice Path Proofs For Determinantal Formulas For Symplectic And Orthogonal Characters
 J. Combin. Theory, Ser. A
"... . We give bijective proofs for JacobiTruditype and Giambellitype identities for symplectic and orthogonal characters. These proofs base on interpreting King and ElSharkaway's symplectic tableaux, Proctor's odd and intermediate symplectic tableaux, Proctor's and King and Welsh& ..."
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's orthogonal tableaux, and Sundaram's odd orthogonal tableaux in terms of certain families of nonintersecting lattice paths. This work is intended to be the counterpart of the GesselViennot proof of the JacobiTrudi identities for Schur functions for the case of symplectic and orthogonal characters
THE LATTICE OF INTEGRAL FLOWS AND THE LATTICE OF INTEGRAL CUTS ON A FINITE GRAPH
, 1997
"... The set of integral flows on a finite graph Î is naturally an integral lattice ÎÂ¹(Î) in the Euclidean space Ker(â1) of harmonic realvalued functions on the edge set of Î. Various properties of Î (bipartite character, girth, complexity, separability) are shown to correspond to properties of ..."
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The set of integral flows on a finite graph Î is naturally an integral lattice ÎÂ¹(Î) in the Euclidean space Ker(â1) of harmonic realvalued functions on the edge set of Î. Various properties of Î (bipartite character, girth, complexity, separability) are shown to correspond to properties
TENSORING GENERALIZED CHARACTERS WITH THE STEINBERG CHARACTER
"... Abstract. Let G be a reductive connected algebraic group over an algebraic closure of a finite field of characteristic p. Let F be a Frobenius endomorphism on G and write G: = G F for the corresponding finite group of Lie type. We consider projective characters of G in characteristic p of the form S ..."
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Abstract. Let G be a reductive connected algebraic group over an algebraic closure of a finite field of characteristic p. Let F be a Frobenius endomorphism on G and write G: = G F for the corresponding finite group of Lie type. We consider projective characters of G in characteristic p of the form
Quantum characters:
"... The conventional metaphors for quantum characters serve poorly. In the place of particle and wave, this paper proposes use of the same metaphor as used in the context of spacetime. In an extended thoughtexperiment, we research potential usefulness by attempting to conceive how particular quantum ac ..."
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The conventional metaphors for quantum characters serve poorly. In the place of particle and wave, this paper proposes use of the same metaphor as used in the context of spacetime. In an extended thoughtexperiment, we research potential usefulness by attempting to conceive how particular quantum
Character Animation
"... Graphical display of deformable objects has been extensively studied in computer graphics. With the addition of haptic feedback, deformable objects gain a new characteristic. Now, our models should not only estimate the direction and the amount of deformation of each node but also the magnitude and ..."
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Graphical display of deformable objects has been extensively studied in computer graphics. With the addition of haptic feedback, deformable objects gain a new characteristic. Now, our models should not only estimate the direction and the amount of deformation of each node but also the magnitude and direction of interaction forces that will be reflected to the user via a haptic device. This tutorial note discusses the modeling and programming principles of forcereflecting deformable objects.
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