monodromies at infinity of confluent a hypergeometric functions abstract we study the monodromies at infinity of confluent a hypergeometric functions introduced by adolphson 2 in particular we extend the result of 38 for non confluent a hypergeometric functions to the confluent case the integral representation by rapid decay homology cycles proved in 9 will play a central role in the proof

voter model on sierpinski fractals abstract we investigate the ordering of voter model on fractal lattices sierpinski carpets and sierpinski gasket we obtain a power law ordering in all cases but the dynamics is found to differ significantly for finite and infinite ramification order of investigated fractals

asymptotic improvement of the gilbert varshamov bound on the size of binary codes given positive integers n and d let a sub 2 n d denote the maximum size of a binary code of length n and minimum distance d the well known gilbert varshamov bound asserts that a sub 2 n d spl ges 2 sup n v n d l where v n d spl sigma sub i 0 sup d sub i sup n is the volume of a hamming sphere of radius d we show that in fact there exists a positive constant c such that a sub 2 n d spl ges c2 sup n v n d 1 log sub 2 v n d 1 whenever d n spl les 0 499 the result follows by recasting the gilbert varshamov bound into a graph theoretic framework and using the fact that the corresponding graph is locally sparse generalizations and extensions of this result are briefly discussed

monodromy at infinity of a hypergeometric functions and toric compactifications we study non confluent a hypergeometric systems introduced by gelfand et al funct anal appl 23 94 106 1989 and prove a formula for the eigenvalues of their monodromy automorphisms defined by the analytic continuations along large loops contained in complex lines parallel to the coordinate axes the method of toric compactifications introduced in libgober and sperber compositio math 95 287 307 1995 and matsui and takeuchi mathematische zeitschrift will be used to prove our main theorem

periods for irregular singular connections on surfaces given an integrable connection on a smooth quasi projective algebraic surface u over a subfield k of the complex numbers we define rapid decay homology groups with respect to the associated analytic connection which pair with the algebraic de rham cohomology in terms of period integrals these homology groups generalize the analogous groups in the same situation over curves defined by bloch and esnault in dimension two however new features appear in this context which we explain in detail assuming a conjecture of sabbah on the formal classification of meromorphic connections on surfaces known to be true if the rank is lower than or equal to 5 we prove perfectness of the period pairing in dimension two

free energy of magnetic model systems at the fractal to euclidian crossover abstract we prove that the free energy per spin of the nearest neighbour classical n vector spin model situated on the sierpinski gasket sg family of fractals tends to the free energy per spin of the same model situated on the standard triangular lattice when the linear size b of the sg fractal generator tends to infinity this finding can be regarded as the first step in the analytical investigation of the spin system thermodynamics at the fractal to euclidean crossover

mellin barnes integrals as fourier mukai transforms we study the generalized hypergeometric system introduced by gelfand kapranov and zelevinsky and its relationship with the toric deligne mumford dm stacks recently studied by borisov chen and smith we construct series solutions with values in a combinatorial version of the chen ruan orbifold cohomology and in the k theory of the associated dm stacks in the spirit of the homological mirror symmetry conjecture of kontsevich we show that the k theory action of the fourier mukai functors associated to basic toric birational maps of dm stacks are mirrored by analytic continuation transformations of mellin barnes type

the average value for the probability of an undetected error a new identity for the weight enumerator of a code is derived the new identity is shown to be related to the average value of the probability of an undetected error when is a continuous random variable

ising model on the sierpinski gasket thermodynamic limit versus infinitesimal field abstract owing to extremely slow decay of correlations the limit h 0 presents a poor approximation for the ising model on the sierpinski gasket we present evidence of the competitive interplay between finite size scaling and thermodynamic scaling for this model where both finite size and finite field induce an apparent phase transition these observations may be relevant for the behavior of porous magnetic materials in real laboratory conditions

confluent a hypergeometric functions and rapid decay homology cycles we study confluent a hypergeometric functions introduced by adolphson in particular we give their integral representations by using rapid decay homology cycles of hien the method of toric compactifications introduced in our previous works will be used to prove our main theorem moreover we apply it to obtain a formula for the asymptotic expansions at infinity of confluent a hypergeometric functions

bounds for the weight distribution of weakly self dual codes upper bounds are given for the weight distribution of binary weakly self dual codes to get these new bounds we introduce a novel method of utilizing unitary operations on hilbert spaces this method is motivated by recent progress on quantum computing this new approach leads to much simpler proofs for such genre of bounds on the weight distributions of certain classes of codes moreover in some cases our bounds are improvements on the earlier bounds these improvements are achieved either by extending the range of the weights over which the bounds apply or by extending the class of codes subjected to these bounds

periods for flat algebraic connections in previous work hien math ann 337 631 669 2007 we established a duality between the algebraic de rham cohomology of a flat algebraic connection on a smooth quasi projective surface over the complex numbers and the rapid decay homology of the dual connection relying on a conjecture by c sabbah in the present article we generalize this result to arbitrary dimensions unconditionally using recent results of t mochizuki

on spectra of bch codes derives an estimate for the error term in the binomial approximation of spectra of bch codes this estimate asymptotically improves on the bounds by sidelnikov 1971 kasami et al 1985 and sole 1990

phase transitions on fractals ii sierpinski gaskets for pt i see ibid vol 16 p 1267 1983 the authors construct and investigate a family of fractals which are generalisations of the sierpinski gaskets sgs to all euclidean dimensionalities these fractal lattices have a finite order of ramification and can be considered marginal between one dimensional and higher dimensional geometries physical models defined on them are exactly solvable the authors argue that short range spin models on the sg show no finite temperature phase transitions as examples they solve a few spin models and study the resistor network and percolation problems on these lattices

criticality of two and three spin ising model in an external field on a fractal family abstract we study the ising model with pair and alternate triplet interactions subjected to an external magnetic field on a family of infinitely ramified fractal lattices with a triangular topology the three dimensional phase diagram and correlation length critical exponents are calculated within an exact real space renormalization group framework the zero field results for the ferromagnetic model show that although the pure triplet case and the pure nearest neighbor pair interaction model are in different universality classes there is no crossover phenomenon since the system becomes paramagnetic in the mixed case in the pure nearest neighbor antiferromagnetic model the appearance of an unusual berker and kadanoff s phase type with a power law decay of correlations when the fractal dimension is sufficiently high is destroyed by the application of a magnetic field or a triplet interaction field

an approximation to the weight distribution of binary linear codes binary primitive bch codes form a large class of powerful error correcting codes the weight distributions of primitive bch codes are unknown except for some special classes such as the single double triple error correcting codes and some very low rate primitive bch codes however asymptotic results for the weight distribution of a large subclass of primitive bch codes have been derived by sidel nikov these results provide some insight into the weight structure of primitive bch codes sidel nikov s approach is improved and applied to the weight distribution of any binary linear block code then sidel nikov s results on the weight distributions of binary primitive bch codes are improved and it is shown that the weights of a binary primitive code have approximate binomial distribution

irregular modified a hypergeometric systems a modified a hypergeometric system is a system of differential equations for the function f tw x where f y is a solution of an a hypergeometric system in n variables and w is an n dimensional integer vector which is called the weight vector we study the irregularity of modified systems by adapting to this case the notion of umbrella introduced by m schulze and u walther especially we study slopes and gevrey series solutions we develop some applications of this study under some conditions we give laplace integral representations of divergent series solutions of the modified system and we show that certain gevrey series solutions of the original a hypergeometric system along coordinate varieties are gevrey asymptotic expansions of holomorphic solutions of the a hypergeometric system

pfaffian systems of a hypergeometric equations i bases of twisted cohomology groups abstract we consider bases of pfaffian systems for a hypergeometric systems these are given by grobner deformations they also provide bases for twisted cohomology groups for a hypergeometric system associated with a class of order polytopes these bases have a combinatorial description the size of the bases associated with a subclass of the order polytopes has a growth rate of polynomial order

weight distribution of cosets of small codes with good dual properties the bilateral minimum distance of a binary linear code is the maximum d such that all nonzero codewords have weights between d and n d let q subset 0 1 n be a binary linear code whose dual has bilateral minimum distance at least d where d is odd roughly speaking we show that the average l infty distance and consequently the l 1 distance between the weight distribution of a random cosets of q and the binomial distribution decays quickly as the bilateral minimum distance d of the dual of q increases for d theta 1 it decays like n theta d on the other d theta n extreme it decays like and e theta d it follows that almost all cosets of q have weight distributions very close to the to the binomial distribution in particular we establish the following bounds if the dual of q has bilateral minimum distance at least d 2t 1 where t geq 1 is an integer then the average vphantom sum r r l infty distance is at most min e ln n 2t t 2t n t 2 sqrt 2 e t 10 for the average l 1 distance we conclude the bound min 2t 1 e ln n 2t t 2t n t 2 1 sqrt 2 n 1 e t 10 which gives nontrivial results for t geq 3 we give applications to the weight distribution of cosets of extended hadamard codes and extended dual bch codes our argument is based on fourier analysis linear programming and polynomial approximation techniques

irregularity of hypergeometric systems via slopes along coordinate subspaces we study the irregularity sheaves attached to the a hypergeometric d module ma introduced by gel fand et al where a z d n is pointed of full rank and c more precisely we investigate the slopes of this module along coordinate subspaces in the process we describe the associated graded ring to a positive semigroup ring for a filtration defined by an arbitrary weight vector l on torus equivariant generators to this end we introduce the a l umbrella a simplicial complex determined by a and l and identify its facets with the components of the associated graded ring we then establish a correspondence between the full a l umbrella and the components of the l characteristic variety of ma we compute in combinatorial terms the multiplicities of these components in the l characteristic cycle of the associated euler koszul complex identifying them with certain intersection multiplicities we deduce from this that slopes of ma are combinatorial independent of and in one to one correspondence with jumps of the a l umbrella this confirms a conjecture of sturmfels and gives a converse of a theorem of hotta ma is regular if and only if a defines a projective variety 1991 mathematics subject classification 13n10 14m25 16w70

monodromy zeta functions at infinity newton polyhedra and constructible sheaves by using sheaf theoretical methods such as constructible sheaves we generalize the formula of libgober sperber concerning the zeta functions of monodromy at infinity of polynomial maps into various directions in particular some formulas for the zeta functions of global monodromy along the fibers of bifurcation points of polynomial maps will be obtained

a geometric degree formula for a discriminants and euler obstructions of toric varieties abstract we give explicit formulas for the dimensions and the degrees of a discriminant varieties introduced by gelfand kapranov and zelevinsky our formulas can be applied also to the case where the a discriminant varieties are higher codimensional and their degrees are described by the geometry of the configurations a moreover combinatorial formulas for the euler obstructions of general not necessarily normal toric varieties will be also given

phase transitions in regularly diluted 2d ising models with a complicated inherent structure of a lattice cell abstract we analyze the critical point and study the nonuniversal peculiarities occuring in the temperature dependence of the specific heat for a sequence of the exactly solvable highly decorated two dimensional triangular type ferromagnetic ising models with a complicated fractal type inherent structure of elementary cell the lattices are indexed by the decoration parameter n 0 1 2 3 the elementary cell for the n lattice is the n th order lattice approximation of the sierpinski gasket fractal at any finite n there is the second order phase transition indicated by the logarithmic singularity in the specific heat the critical temperature decreases as 4 ln 4 n 1 with increasing decoration the specific heat critical amplitude vanishes as 3 n n ln n 2 as n the basic nonuniversal features observable in the specific heat at strong decoration are the anomalous narrowing of the critical interval and the appearance of a rounded peak above the true t c point these effects are closely related and can both be explained by the above t c local ordering in the local lattice inhomogeneities the mechanism of the above t c local ordering is analyzed the models under discussion can as well be interpreted as the regular bond diluted 2d ising ferromagnets with a hierarchy of the nonmagnetic holes at different scales and varying dilution a comparative discussion on the properties of the regularly and randomly diluted 2d ising ferromagnets is given

on the accuracy of the binomial approximation to the distance distribution of codes the binomial distribution is a well known approximation to the distance spectra of many classes of codes we derive a lower estimate for the deviation from the binomial approximation

estimates for the range of binomiality in codes spectra we derive new estimates for the range of binomiality in a code s spectra where the distance distribution of a code is upperbounded by the corresponding normalized binomial distribution the estimates depend on the code s dual distance

hypergeometric d modules and twisted gaus manin systems abstract the euler koszul complex is the fundamental tool in the homological study of a hypergeometric differential systems and functions we compare euler koszul homology with d module direct images from the torus to the base space through orbits in the corresponding toric variety our approach generalizes a result by gel fand et al i m gel fand m m kapranov a v zelevinsky generalized euler integrals and a hypergeometric functions adv math 84 2 1990 255 271 mr mr1080980 92e 33015 thm 4 6 and yields a simpler more algebraic proof in the process we extend the euler koszul functor to a category of infinite toric modules and describe multigraded localizations of euler koszul homology

a limit law on the distance distribution of binary codes an approximation is given of the distance distribution of a binary code by the binomial distribution with an exponentially decreasing error term specifically the upper bound of the relative error term between the normalized distance distribution of a binary code and the binomial distribution has been asymptotically improved in particular the bound becomes exponentially small for large distances in families of codes with small sigma and rate 0 5 the approach used was based on an integral representation of krawtchouk polynomials examples of interest are bch codes of primitive length duals of irreducible cyclic codes and preparata codes

phase transitions on fractals i quasi linear lattices magnetic spin models and resistor networks are studied on certain self similar fractal lattices which are described as quasi linear because they share a significant property of the line finite portions can be isolated from the rest by removal of two points sites in all cases there is no long range order at finite temperature the transition at zero temperature has a discontinuity in the magnetisation and the associated magnetic exponent is equal to the fractal dimensionality d when the lattice reduces to a non branching curve the thermal exponent v 1 y is equal to d when the lattice is a branching curve y is related respectively to the dimensionality of the single channel segments of the curve for the ising model or to the exponent describing the resistivity for models with continuous spin symmetry

on irregularities of fourier transforms of regular holonomic d modules abstract we study fourier transforms of regular holonomic d modules by using the theory of fourier sato transforms of enhanced ind sheaves developed by kashiwara schapira and d agnolo kashiwara a formula for their enhanced solution complexes will be obtained moreover we show that some parts of their characteristic cycles and irregularities are expressed by the geometries of the original d modules