Using matrix model,Mironov and Morozov recently gave a formula which represents Kontsevich-Witten tau function as a linear expansion of Schur Q-polynomials.In this paper,we will show directly that the Q-polynomial exp...Using matrix model,Mironov and Morozov recently gave a formula which represents Kontsevich-Witten tau function as a linear expansion of Schur Q-polynomials.In this paper,we will show directly that the Q-polynomial expansion in this formula satisfies the Virasoro constraints,and consequently obtains a proof of this formula without using matrix model.We also give a proof for Alexandrov’s conjecture that Kontsevich-Witten tau function is a hypergeometric tau function of theBKPhierarchy after re-scaling.展开更多
Functions with difference uniformity have important applications in cryptography. Some planar functions and almost perfect nonlinear（APN） functions are presented in the note. In addition, an upper bound of the unifo...Functions with difference uniformity have important applications in cryptography. Some planar functions and almost perfect nonlinear（APN） functions are presented in the note. In addition, an upper bound of the uniformity of some power mappings is provided by using an interesting identity on Dickson polynomials. When the character of the finite field is less than 11, the upper bound is proved to be the best possibility.展开更多
The main purpose of this paper is to show that the Poincaré q-polynomials admit a representation in terms of the symmetric functions and the Patterson-Selberg (or Ruelle-type) spectral functions. We have shown th...The main purpose of this paper is to show that the Poincaré q-polynomials admit a representation in terms of the symmetric functions and the Patterson-Selberg (or Ruelle-type) spectral functions. We have shown that the q-series elliptic genera can be expressed in terms of q-analogs of the classical special functions, specially the equivalence between the spectral Patterson-Selberg and the Ruelle functions. The main result of this manuscript is to show that this representation can be used in theoretical physics and we analyze them in terms of the Patterson-Selberg spectral function R (s).展开更多
It is known that a distance-regular graph with valency k at least three admits at most two Qpolynomial structures. We show that all distance-regular graphs with diameter four and valency at least three admitting two Q...It is known that a distance-regular graph with valency k at least three admits at most two Qpolynomial structures. We show that all distance-regular graphs with diameter four and valency at least three admitting two Q-polynomial structures are either dual bipartite or almost dual bipartite. By the work of Dickie(1995) this implies that any distance-regular graph with diameter d at least four and valency at least three admitting two Q-polynomial structures is, provided it is not a Hadamard graph, either the cube H(d, 2)with d even, the half cube 1/2H(2d + 1, 2), the folded cube?H(2d + 1, 2), or the dual polar graph on [2A2d-1(q)]with q 2 a prime power.展开更多
基金partially supported by NSFC grants 11890662 and 11890660.
文摘Using matrix model,Mironov and Morozov recently gave a formula which represents Kontsevich-Witten tau function as a linear expansion of Schur Q-polynomials.In this paper,we will show directly that the Q-polynomial expansion in this formula satisfies the Virasoro constraints,and consequently obtains a proof of this formula without using matrix model.We also give a proof for Alexandrov’s conjecture that Kontsevich-Witten tau function is a hypergeometric tau function of theBKPhierarchy after re-scaling.
文摘Functions with difference uniformity have important applications in cryptography. Some planar functions and almost perfect nonlinear（APN） functions are presented in the note. In addition, an upper bound of the uniformity of some power mappings is provided by using an interesting identity on Dickson polynomials. When the character of the finite field is less than 11, the upper bound is proved to be the best possibility.
文摘The main purpose of this paper is to show that the Poincaré q-polynomials admit a representation in terms of the symmetric functions and the Patterson-Selberg (or Ruelle-type) spectral functions. We have shown that the q-series elliptic genera can be expressed in terms of q-analogs of the classical special functions, specially the equivalence between the spectral Patterson-Selberg and the Ruelle functions. The main result of this manuscript is to show that this representation can be used in theoretical physics and we analyze them in terms of the Patterson-Selberg spectral function R (s).
基金supported by Natural Science Foundation of Hebei Province(Grant No.A2012205079)Science Foundation of Hebei Normal University(Grant No.L2011B02)the 100 Talents Program of the Chinese Academy of Sciences for support
文摘It is known that a distance-regular graph with valency k at least three admits at most two Qpolynomial structures. We show that all distance-regular graphs with diameter four and valency at least three admitting two Q-polynomial structures are either dual bipartite or almost dual bipartite. By the work of Dickie(1995) this implies that any distance-regular graph with diameter d at least four and valency at least three admitting two Q-polynomial structures is, provided it is not a Hadamard graph, either the cube H(d, 2)with d even, the half cube 1/2H(2d + 1, 2), the folded cube?H(2d + 1, 2), or the dual polar graph on [2A2d-1(q)]with q 2 a prime power.
