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arXivA new series of dense graphs of high girth Felix Lazebnik, Vasiliy A. Ustimenko, Andrew J. Woldar... more(3) 19941231 Let $k\ge 1$ be an odd integer, $t=\lfloor {{k+2}\over 4}\rfloor$, and $q$ be a prime power. We construct a bipartite, $q$regular, edgetransitive graph $C\!D(k,q)$ of order $v \le 2q^{kt+1}$ and girth $g \ge k+5$. If $e$ is the the number of edges of $C\!D(k,q)$, then $e =\Omega(v^{1+ {1\over {kt+1}}})$. These graphs provide the best known asymptotic lower bound for the greatest number of edges in graphs of order $v$ and girth at least $g$, $ g\ge 5$, $g \not= 11,12$. For $g\ge 24$, this represents a slight improvement on bounds established by Margulis and Lubotzky, Phillips, Sarnak; for $5\le g\le 23$, $g\not= 11,12$, it improves on or ties existing bounds.
Subject 수학 Source arXiv URL https://arxiv.org/abs/math/9501231view Article Title A new series of dense graphs of high girthAuthors Felix Lazebnik; Vasiliy A. Ustimenko; Andrew J. WoldarAbstract Let $k\ge 1$ be an odd integer, $t=\lfloor {{k+2}\over 4}\rfloor$, and $q$ be a prime power. We construct a bipartite, $q$regular, edgetransitive graph $C\!D(k,q)$ of order $v \le 2q^{kt+1}$ and girth $g \ge k+5$. If $e$ is the the number of edges of $C\!D(k,q)$, then $e =\Omega(v^{1+ {1\over {kt+1}}})$. These graphs provide the best known asymptotic lower bound for the greatest number of edges in graphs of order $v$ and girth at least $g$, $ g\ge 5$, $g \not= 11,12$. For $g\ge 24$, this represents a slight improvement on bounds established by Margulis and Lubotzky, Phillips, Sarnak; for $5\le g\le 23$, $g\not= 11,12$, it improves on or ties existing bounds.Is Part Of Bull. Amer. Math. Soc. (N.S.) 32 (1995) 7379 19941231 Identifier ISSN: Category math.COLicense 
arXivSecondary invariants and the singularity of the Ruelle zetafunction in the central critical point Andreas Juhl 19941231 The Ruelle zetafunction of the geodesic flow on the sphere bundle $S(X)$ of an evendimensional compact locally symmetric space $X$ of rank $1$ is a meromorphic function in the complex plane that satisfies a functional equation relating its values in $s$ and $s$. The multiplicity of its singularity in the central critical point $s = 0$ only depends on the hyperbolic structure of the flow and can be calculated by integrating a secondary characteristic class canonically associated to the flow invariant foliations of $S(X)$ for which a representing differential form is given.
Subject 수학 Source arXiv URL https://arxiv.org/abs/math/9501232view Article Title Secondary invariants and the singularity of the Ruelle zetafunction in the central critical pointAuthors Andreas JuhlAbstract The Ruelle zetafunction of the geodesic flow on the sphere bundle $S(X)$ of an evendimensional compact locally symmetric space $X$ of rank $1$ is a meromorphic function in the complex plane that satisfies a functional equation relating its values in $s$ and $s$. The multiplicity of its singularity in the central critical point $s = 0$ only depends on the hyperbolic structure of the flow and can be calculated by integrating a secondary characteristic class canonically associated to the flow invariant foliations of $S(X)$ for which a representing differential form is given.Is Part Of Bull. Amer. Math. Soc. (N.S.) 32 (1995) 8087 19941231 Identifier ISSN: Category math.DS math.NTLicense 
arXivField Theoretic Description of High Energy Neutrino Interactions G. Domokos, S. KovesiDomokos 19941231 In this paper we begin the development of a formalism for the description of high energy neutrino interactions. It is based upon field theory quantized on a null plane. We set up the general formalism as well as some techniques needed to perform phenomenological calculations. We show that the formalism developed by Wolfenstein is recovered at the cost of making two approximations: one has to treat the charged lepton fields in the HartreeFock approximation and one has to take the short distance limit of the HartreeFock correlation function. As an example, we discuss the resonant interaction of electron neutrinos in an electron gas.
Subject Source arXiv URL https://arxiv.org/abs/hepph/9412396view Article Title Field Theoretic Description of High Energy Neutrino InteractionsAuthors G. Domokos; S. KovesiDomokosAbstract In this paper we begin the development of a formalism for the description of high energy neutrino interactions. It is based upon field theory quantized on a null plane. We set up the general formalism as well as some techniques needed to perform phenomenological calculations. We show that the formalism developed by Wolfenstein is recovered at the cost of making two approximations: one has to treat the charged lepton fields in the HartreeFock approximation and one has to take the short distance limit of the HartreeFock correlation function. As an example, we discuss the resonant interaction of electron neutrinos in an electron gas.Is Part Of 19941231 Identifier ISSN: Category hepphLicense 
arXivNonCommutative (Quantum) Probability, Master Fields and Stochastic Bosonization L. Accardi, Y. G. Lu, I. Volovich... more(3) 19941231 In this report we discuss some results of noncommutative (quantum) probability theory relating the various notions of statistical independence and the associated quantum central limit theorems to different aspects of mathematics and physics including: $q$deformed and free central limit theorems; the description of the master (i.e. central limit) field in matrix models along the recent Singer suggestion to relate it to Voiculescu's results on the freeness of the large $N$ limit of random matrices; quantum stochastic differential equations for the gauge master field in QCD; the theory of stochastic limits of quantum fields and its applications to stochastic bosonization of Fermi fields in any dimensions; new structures in QED such as a nonlinear modification of the Wigner semicircle law and the interacting Fock space: a natural explicit example of a selfinteracting quantum field which exhibits the non crossing diagrams of the Wigner semicircle law.
Subject 수학 Source arXiv URL https://arxiv.org/abs/hepth/9412241view Article Title NonCommutative (Quantum) Probability, Master Fields and Stochastic BosonizationAuthors L. Accardi; Y. G. Lu; I. VolovichAbstract In this report we discuss some results of noncommutative (quantum) probability theory relating the various notions of statistical independence and the associated quantum central limit theorems to different aspects of mathematics and physics including: $q$deformed and free central limit theorems; the description of the master (i.e. central limit) field in matrix models along the recent Singer suggestion to relate it to Voiculescu's results on the freeness of the large $N$ limit of random matrices; quantum stochastic differential equations for the gauge master field in QCD; the theory of stochastic limits of quantum fields and its applications to stochastic bosonization of Fermi fields in any dimensions; new structures in QED such as a nonlinear modification of the Wigner semicircle law and the interacting Fock space: a natural explicit example of a selfinteracting quantum field which exhibits the non crossing diagrams of the Wigner semicircle law.Is Part Of 19941231 Identifier ISSN: Category hepth math.QA qalgLicense 
arXivLocalization of $\frak{u}$modules. II. Configuration spaces and quantum groups M. Finkelberg, V. Schechtman 19941231 This paper is a sequel to "Localization of $\frak{u}$modules. I", hepth/9411050. We are starting here the geometric study of the tensor category $\cal{C}$ associated with a quantum group (corresponding to a Cartan matrix of finite type) at a root of unity. The main results establish isomorphisms between homogeneous components of irreducible objects in $\cal{C}$ and spaces of vanishing cycles at the origin of certain GoreskyMacPherson sheaves on configuration spaces; establish isomorphisms of the stalks at the origin of the above GM sheaves with certain Hochschild complexes (which compute the Hochschild homology of a certain "triangular" subalgebra of our quantum group with coefficients in the coresponding irreducible representation); establish the analogous results for tensor products of irreducibles. In geometry, the tensor product of representations corresponds to a "fusion" of sheaves on configuration spaces  operation defined using the functor of nearby cycles.
Subject 수학 Source arXiv URL https://arxiv.org/abs/qalg/9412017view Article Title Localization of $\frak{u}$modules. II. Configuration spaces and quantum groupsAuthors M. Finkelberg; V. SchechtmanAbstract This paper is a sequel to "Localization of $\frak{u}$modules. I", hepth/9411050. We are starting here the geometric study of the tensor category $\cal{C}$ associated with a quantum group (corresponding to a Cartan matrix of finite type) at a root of unity. The main results establish isomorphisms between homogeneous components of irreducible objects in $\cal{C}$ and spaces of vanishing cycles at the origin of certain GoreskyMacPherson sheaves on configuration spaces; establish isomorphisms of the stalks at the origin of the above GM sheaves with certain Hochschild complexes (which compute the Hochschild homology of a certain "triangular" subalgebra of our quantum group with coefficients in the coresponding irreducible representation); establish the analogous results for tensor products of irreducibles. In geometry, the tensor product of representations corresponds to a "fusion" of sheaves on configuration spaces  operation defined using the functor of nearby cycles.Is Part Of 19941231 Identifier ISSN: Category qalg alggeom math.AG math.QALicense 
arXivMeromorphic Potentials and Smooth CMC Surfaces J. Dorfmeister, G. Haak 19941231 This work is based on the approach developed by J.~Dorfmeister, F.~Pedit and H.~Wu [GANG and KITCS preprint, Report KITCS9441] to construct maps $\Phi:D\rightarrow R^3$, $D$ being the unit disk in $C$, whose images are surfaces of constant mean curvature. They start from certain meromorphic one forms, so called meromorphic potentials, which take values in a twisted loop algebra over $su(2)$. The authors give necessary and sufficient conditions on the meromorphic potential for the constructed map $\Phi$ to be an immersion. This revision corrects several misprints and minor TeX problems.
Subject 수학 Source arXiv URL https://arxiv.org/abs/dgga/9412007view Article Title Meromorphic Potentials and Smooth CMC SurfacesAuthors J. Dorfmeister; G. HaakAbstract This work is based on the approach developed by J.~Dorfmeister, F.~Pedit and H.~Wu [GANG and KITCS preprint, Report KITCS9441] to construct maps $\Phi:D\rightarrow R^3$, $D$ being the unit disk in $C$, whose images are surfaces of constant mean curvature. They start from certain meromorphic one forms, so called meromorphic potentials, which take values in a twisted loop algebra over $su(2)$. The authors give necessary and sufficient conditions on the meromorphic potential for the constructed map $\Phi$ to be an immersion. This revision corrects several misprints and minor TeX problems.Is Part Of 19941231 Identifier ISSN: Category dgga math.DGLicense 
arXivTwo Mode Quantum Systems: Invariant Classification of Squeezing Transformations and Squeezed States Arvind, B. Dutta, N. Mukunda, ... more(4) 19941231 A general analysis of squeezing transformations for two mode systems is given based on the four dimensional real symplectic group $Sp(4,\Re)\/$. Within the framework of the unitary metaplectic representation of this group, a distinction between compact photon number conserving and noncompact photon number nonconserving squeezing transformations is made. We exploit the $Sp(4,\Re)SO(3,2)\/$ local isomorphism and the $U(2)\/$ invariant squeezing criterion to divide the set of all squeezing transformations into a two parameter family of distinct equivalence classes with representative elements chosen for each class. Familiar two mode squeezing transformations in the literature are recognized in our framework and seen to form a set of measure zero. Examples of squeezed coherent and thermal states are worked out. The need to extend the heterodyne detection scheme to encompass all of $U(2)\/$ is emphasized, and known experimental situations where all $U(2)\/$ elements can be reproduced are briefly described.
Subject Source arXiv URL https://arxiv.org/abs/quantph/9412011view Article Title Two Mode Quantum Systems: Invariant Classification of Squeezing Transformations and Squeezed StatesAuthors Arvind; B. Dutta; N. Mukunda; R. SimonAbstract A general analysis of squeezing transformations for two mode systems is given based on the four dimensional real symplectic group $Sp(4,\Re)\/$. Within the framework of the unitary metaplectic representation of this group, a distinction between compact photon number conserving and noncompact photon number nonconserving squeezing transformations is made. We exploit the $Sp(4,\Re)SO(3,2)\/$ local isomorphism and the $U(2)\/$ invariant squeezing criterion to divide the set of all squeezing transformations into a two parameter family of distinct equivalence classes with representative elements chosen for each class. Familiar two mode squeezing transformations in the literature are recognized in our framework and seen to form a set of measure zero. Examples of squeezed coherent and thermal states are worked out. The need to extend the heterodyne detection scheme to encompass all of $U(2)\/$ is emphasized, and known experimental situations where all $U(2)\/$ elements can be reproduced are briefly described.Is Part Of Phys. Rev. A 52, 1609 (1995) 19941231 Identifier ISSN: DOI 10.1103/PhysRevA.52.1609Category quantphLicense 
arXivWiener's Tauberian theorem in L^1(G//K) and harmonic functions in the unit disk Yaakov Ben Natan, Yoav Benyamini, Håkan Hedenmalm, ... more(4) 19941231 Our main result is to give necessary and sufficient conditions, in terms of Fourier transforms, on a closed ideal $I$ in $\loneg$, the space of radial integrable functions on $G=SU(1,1)$, so that $I=\loneg$ or $I=\lonez$the ideal of $\loneg$ functions whose integral is zero. This is then used to prove a generalization of Furstenberg's theorem which characterizes harmonic functions on the unit disk by a mean value property and a ``two circles" Morera type theorem (earlier announced by Agranovski\u{\i}).
Subject 수학 Source arXiv URL https://arxiv.org/abs/math/9501226view Article Title Wiener's Tauberian theorem in L^1(G//K) and harmonic functions in the unit diskAuthors Yaakov Ben Natan; Yoav Benyamini; Håkan Hedenmalm; Yitzhak WeitAbstract Our main result is to give necessary and sufficient conditions, in terms of Fourier transforms, on a closed ideal $I$ in $\loneg$, the space of radial integrable functions on $G=SU(1,1)$, so that $I=\loneg$ or $I=\lonez$the ideal of $\loneg$ functions whose integral is zero. This is then used to prove a generalization of Furstenberg's theorem which characterizes harmonic functions on the unit disk by a mean value property and a ``two circles" Morera type theorem (earlier announced by Agranovski\u{\i}).Is Part Of Bull. Amer. Math. Soc. (N.S.) 32 (1995) 4349 19941231 Identifier ISSN: Category math.CALicense 
arXivThe Fundamental Lemma for the Shalika Subgroup of GL$(4)$ Solomon Friedberg, Hervé Jacquet 19941231 The authors establish the fundamental lemma for a relative trace formula. This trace formula compares generic automorphic representations of GSp$(4)$ with automorphic representations of GL$(4)$ which are distinguished with respect to a character of the Shalika subgroup, the subgroup of matrices of $2\times 2$ block form $$ \pmatrix g&0\\0&g\endpmatrix \pmatrix I&0\\X&O\endpmatrix. $$ The fundamental lemma, giving the equality of two orbital integrals, amounts to a comparison of certain exponential sums arising from these two different groups. On the GSp$(4)$ side one has the Kloosterman sums for this group, and on the GL$(4)$ side certain, new, relative Kloosterman sums. To show that these are equal for each relevant Weyl group element, the authors compute the Mellin transforms of the sums and match them in all cases. The file available from the MSRI preprint server gives the first chapter of the manuscript. The entire manuscript, 147 pages long, is available as an MSRI preprint.
Subject 수학 Source arXiv URL https://arxiv.org/abs/math/9501216view Article Title The Fundamental Lemma for the Shalika Subgroup of GL$(4)$Authors Solomon Friedberg; Hervé JacquetAbstract The authors establish the fundamental lemma for a relative trace formula. This trace formula compares generic automorphic representations of GSp$(4)$ with automorphic representations of GL$(4)$ which are distinguished with respect to a character of the Shalika subgroup, the subgroup of matrices of $2\times 2$ block form $$ \pmatrix g&0\\0&g\endpmatrix \pmatrix I&0\\X&O\endpmatrix. $$ The fundamental lemma, giving the equality of two orbital integrals, amounts to a comparison of certain exponential sums arising from these two different groups. On the GSp$(4)$ side one has the Kloosterman sums for this group, and on the GL$(4)$ side certain, new, relative Kloosterman sums. To show that these are equal for each relevant Weyl group element, the authors compute the Mellin transforms of the sums and match them in all cases. The file available from the MSRI preprint server gives the first chapter of the manuscript. The entire manuscript, 147 pages long, is available as an MSRI preprint.Is Part Of 19941231 Identifier ISSN: Category math.RT math.NTLicense 
arXivLargeangle Polarization of the Cosmic Microwave Background Radiation and Reionization Ka Lok Ng, KinWang Ng, 19 pages, ... more(6) 19941231 We discuss the effect of matter reionization on the largeangularscale anisotropy and polarization of the cosmic microwave background radiation (CMBR) in the standard CDM model. We separate three cases in which the anisotropy is induced by pure scalar, pure tensor, and mixed metric perturbations respectively. It is found that, if reionization occurs early enough, the polarization can reach a detectable level of sequentially $6\%$, $9\%$, and $6.5\%$ of the anisotropy. In general, a higher degree of polarization implies a dominant contribution from the tensor mode or reionization at high redshift. Since early reionization will suppress smallscale CMBR anisotropies and polarizations significantly, measuring the polarization on few degree scales can be a direct probe of the reionization history of the early universe.
Subject Source arXiv URL https://arxiv.org/abs/astroph/9412097view Article Title Largeangle Polarization of the Cosmic Microwave Background Radiation and ReionizationAuthors Ka Lok Ng; KinWang Ng; 19 pages; latex; 10 figures; available upon requestAbstract We discuss the effect of matter reionization on the largeangularscale anisotropy and polarization of the cosmic microwave background radiation (CMBR) in the standard CDM model. We separate three cases in which the anisotropy is induced by pure scalar, pure tensor, and mixed metric perturbations respectively. It is found that, if reionization occurs early enough, the polarization can reach a detectable level of sequentially $6\%$, $9\%$, and $6.5\%$ of the anisotropy. In general, a higher degree of polarization implies a dominant contribution from the tensor mode or reionization at high redshift. Since early reionization will suppress smallscale CMBR anisotropies and polarizations significantly, measuring the polarization on few degree scales can be a direct probe of the reionization history of the early universe.Is Part Of Astrophys.J. 456 (1996) 413421 19941231 Identifier ISSN: DOI 10.1086/176665Category astrophLicense