相关论文: A Generalization of Gajda's Equation on Commutativ…

We indicate a natural generalization of the concept of subgroup commutativity degree of a finite group and a list of open problems on these new concepts.

The present paper solves the problem of the group classification of the general Burgers' equation $u_t=f(x,u)u_x^2+g(x,u)u_{xx}$, where $f$ and $g$ are arbitrary smooth functions of the variable $x$ and $u$, by using Lie method. The paper…

We extend the twisted gauge theory model of topological orders in three spatial dimensions to the case where the three spaces have two dimensional boundaries. We achieve this by systematically constructing the boundary Hamiltonians that are…

Let $T$ be a bilinear Calder\'{o}n-Zygmund singular integral operator and $T_*$ be its corresponding truncated maximal operator. The commutators in the $i$-$th$ entry and the iterated commutators of $T_*$ are defined by $$…

A two-dimensional topological sigma-model on a generalized Calabi-Yau target space $X$ is defined. The model is constructed in Batalin-Vilkovisky formalism using only a generalized complex structure $J$ and a pure spinor $\rho$ on $X$. In…

A group element is called a generalized torsion if a finite product of its conjugates is equal to the identity. We prove that in a nilpotent or FC-group, the generalized torsion elements are all torsion elements. Moreover, we compute the…

Let F be a local non-archimedean field and let G be the group of F-valued points of a reductive algebraic group over F. In this paper we compute the Ext-groups of generalized Steinberg representations in the category of smooth…

We derive an asymptotic formula for the sum $$ H = \sum_{0<\gamma_k\leqslant T,\, 1\leqslant k\leqslant m}h(a_1\gamma_1+a_2\gamma_2+\cdots + a_m\gamma_m), $$ where $a_1, a_2, \ldots, a_m$ are integers whose sum equals zero, $\gamma_1,…

In this paper we introduce a new family of the KP tau-functions. This family can be described by a deformation of the generalized Kontsevich matrix model. We prove that the simplest representative of this family describes a generating…

The classical Gindikin-Karpelevich formula appears in Langlands' calculation of the constant terms of Eisenstein series on reductive groups and in Macdonald's work on p-adic groups and affine Hecke algebras. The formula has been generalized…

A complete classification of generalized symmetries of the Yang-Mills equations on Minkowski space with a semi-simple structure group is carried out. It is shown that any generalized symmetry, up to a generalized gauge symmetry, agrees with…

We investigate an arithmetic function representing a generalization of the gcd-sum function, considered by Kurokawa and Ochiai in 2009 in connection with the multivariable global Igusa zeta function for a finite cyclic group. We show that…

We present a general algebraic framework for gauging a 0-form compact, connected Lie group symmetry in (2+1)d topological phases. Starting from a symmetry fractionalization pattern of the Lie group $G$, we first extend $G$ to a larger…

In $D$-dimensional gauge theory with a kinetic term based on the p-form tensor gauge field, we introduce a gauge invariant operator associated with the composite formed from a electric $(p-1)$-brane and a magnetic $(q-1)$-brane in $D=p+q+1$…

The generalized H\'enon-Heiles Hamiltonian $H=1/2(P_X^2+P_Y^2+c_1X^2+c_2Y^2)+aXY^2-bX^3/3$ with an additional nonpolynomial term $\mu Y^{-2}$ is known to be Liouville integrable for three sets of values of $(b/a,c_1,c_2)$. It has been…

We recall the emergence of a generalized gauge theory from a noncommutative Riemannian spin manifold, viz. a real spectral triple $(A,H,D;J)$. This includes a gauge group determined by the unitaries in the $*$-algebra $A$ and gauge fields…

Bigraded Toda hierarchy $L_1^M(n)=L_2^N(n)$ is generalized to $L_1^M(n)=L_2^{N}(n)+\sum_{j\in \mathbb Z}\sum_{i=1}^{m}q^{(i)}_n\Lambda^jr^{(i)}_{n+1}$, which is the analogue of the famous constrained KP hierarchy $L^{k}=…

An integrable system is introduced, which is a generalization of the $\mathfrak{sl}(2)$ quantum affine Gaudin model. Among other things, the Hamiltonians are constructed and their spectrum is calculated within the ODE/IQFT approach. The…

We introduce a fairly general concept of functional equation for $k$-tuples of functions $f_1,\dots,f_k\colon X \to Y$ between arbitrary sets. The homomorphy equations for mappings between groups and other algebraic systems, as well as…

The $_{3}F_{2}$ hypergeometric function plays a very significant role in the theory of hypergeometric and generalized hypergeometric series. Despite that $_{3}F_{2}$ hypergeometric function has several applications in mathematics, also it…