相关论文: Jacobi polynomials for the first-order generalized…
Using the adjoint representations of Lie algebras, we classify all Jacobi structures on real two- and three-dimensional Lie groups. Also, we study Jacobi-Lie systems on these real low-dimensional Lie groups. Our results are illustrated…
Recently the problem of constructing a perfect Euler cuboid was related with three conjectures asserting the irreducibility of some certain three polynomials depending on integer parameters. In this paper a partial result toward proving the…
We look for spectral type differential equations satisfied by the generalized Jacobi polynomials which are orthogonal on the interval [-1,1] with respect to a weight function consisting of the classical Jacobi weight function together with…
We introduce, characterise and provide a combinatorial interpretation for the so-called $q$-Jacobi-Stirling numbers. This study is motivated by their key role in the (reciprocal) expansion of any power of a second order $q$-differential…
In the paper, we first classify all polynomial maps of the form $H=(u(x,y,z),v(x,y,z), h(x,y))$ in the case that $JH$ is nilpotent and $\deg_zv\leq 1$. After that, we generalize the structure of $H$ to…
In this paper, we study the Jacobi sums over Galois rings of arbitrary characteristics and completely determine their absolute values, which extends the work in \cite{feng1}, where the Jacobi sums over Galois rings with characteristics a…
In this paper, we give an algorithm for finding general rational solutions of a given first-order ODE with parametric coefficients that occur rationally. We present an analysis, complete modulo Hilbert's irreducibility problem, of the…
A new class of vector fields enabling the integration of first-order ordinary differential equations (ODEs) is introduced. These vector fields are not, in general, Lie point symmetries. The results are based on a relation between…
Determining deep holes is an important topic in decoding Reed-Solomon codes. In a previous paper [8], we showed that the received word $u$ is a deep hole of the standard Reed-Solomon codes $[q-1, k]_q$ if its Lagrange interpolation…
We compute the subgroup of the monodromy group of a generalized Kummer variety associated to equivalences of derived categories of abelian surfaces. The result was previously announced in arXiv:1201.0031. Mongardi showed that the subgroup…
The purpose of this note is to show how calculi on unital associative algebra with universal right bimodule generalize previously studied constructions by Pusz and Woronowicz [1989] and by Wess and Zumino [1990] and that in this language…
Jacobi groupoids are introduced as a generalization of Poisson and contact groupoids and it is proved that generalized Lie bialgebroids are the infinitesimal invariants of Jacobi groupoids. Several examples are discussed.
Classical Jacobi polynomials $P_{n}^{(\alpha,\beta)}$, with $\alpha, \beta>-1$, have a number of well-known properties, in particular the location of their zeros in the open interval $(-1,1)$. This property is no longer valid for other…
In this paper, we consider an extension of Jacobi's symbol, the so called rational $2^k$-th power residue symbol. In Section 3, we prove a novel generalization of Zolotarev's lemma. In Sections 4, 5 and 6, we show that several hard…
We give a formula for the coefficients of the Yablonskii-Vorob'ev polynomial. Also the reduction modulo a prime number of the polynomial is studied.
We propose higher-order generalizations of Jacobsthal's $p$-adic approximation for binomial coefficients. Our results imply explicit formulae for linear combinations of binomial coefficients $\binom{ip}{p}$ ($i=1,2,\dots$) that are…
Jacobi-Nijenhuis algebroids are defined as a natural generalization of Poisson-Nijenhuis algebroids, in the case where there exists a Nijenhuis operator on a Jacobi algebroid which is compatible with it. We study modular classes of Jacobi…
In this work we show how to get advantage from the Riemann--Hilbert analysis in order to obtain first and second order differential equations for the orthogonal polynomials and associated functions with a weight on the unit circle. We…
We discuss the notion of Jacobi forms of degree one with matrix index, we state dimension formulas, give explicit examples, and indicate how closely their theory is connected to the theory of invariants of Weil representations associated to…
In this paper we use the combinatorics of alcove walks to give a uniform combinatorial formula for Macdonald polynomials for all Lie types. These formulas are generalizations of the formulas of Haglund-Haiman-Loehr for Macdonald polynoimals…