相关论文: Spectral types of linear $q$-difference equations …
The nonlinear generalization of the von Neumann equation preserving convexity of the state space is studied in the nontrivial case of the qutrit. This equation can be cast into the integrable classical Riccati system of nonlinear ordinary…
In this manuscript we define the right fractional derivative and its corresponding right fractional integral with exponential kernel. Then, we provide the integration by parts formula and we use $Q-$operator to confirm our results. The…
The $p$-adic $q$-integral (= $I_q$-integral) was defined by author in the previous paper [1, 3]. In this paper, we consider $I_q$-Fourier transform and investigate some properties which are related to this transform.
Different analogs of quasiclassical limit for a q-oscillator which result in different (commutative and non-commutative) algebras of ``classical'' observables are derived. In particular, this gives the q-deformed Poisson brackets in terms…
A new $q$-analogue of Appell polynomial sequences and their generalizations are introduced and their main characterizations are proved. As consequences new $q$-analogue of Bernoulli and Euler polynomials and numbers is introduced, their…
We study certain classes of equations for $F_q$-linear functions, which are the natural function field counterparts of linear ordinary differential equations. It is shown that, in contrast to both classical and $p$-adic cases, formal power…
We wish to show that the root lattice of B\"acklund transformations of the $q$-analogue of the third and fourth Painlev\'e equations, which is of type $(A_2+ A_1)^{(1)}$, may be expressed as a quotient of the lattice of connection…
A family of $q$-difference-differential equations in two complex variables is studied, under the action of a so-called Mahler transform on time variable. The appearance of a leading formal $q$-difference operator of irregular type in the…
A model of a q-harmonic oscillator based on q-Charlier polynomials of Al-Salam and Carlitz is discussed. Simple explicit realization of q-creation and q-annihilation operators, q-coherent states and an analog of the Fourier transformation…
S.Block and H.Esnault constructed the local Fourier transform for D-modules. We present a different approach to the local Fourier transform, which makes its properties almost tautological. We apply the local Fourier transform to compute the…
The differential nature of solutions of linear difference equations over the projective line was recently elucidated. In contrast, little is known about the differential nature of solutions of linear difference equations over elliptic…
We study evaluation modules for quantum symmetric pair coideal subalgebras of affine type $\mathsf{AI}$. By computing the action of the generators in Lu and Wang's Drinfeld-type presentation on Gelfand-Tsetlin bases, we determine the…
We consider Kemp's q-analogue of the binomial distribution. Several convergence results involving the classical binomial, the Heine, the discrete normal, and the Poisson distribution are established. Some of them are q-analogues of…
In the present contribution, we study the Landau-Lifshitz-Gilbert equation with two versions of structural derivatives recently proposed: the scale $q-$derivative in the non-extensive statistical mechanics and the axiomatic metric…
We discuss the proof of Kazhdan and Lusztig of the equivalence of the Drinfeld category D(g,h) of g-modules and the category of finite dimensional Uq(g)-modules, q=exp(\pi ih), for h\in C\Q*. Aiming at operator algebraists the result is…
In this paper we present a general scheme to generate constructive solutions to the Riemann--Hilbert problem via middle convolution and illustrate this approach for a Fuchsian system with four singular points.
Assuming that there exist operators which form an irreducible representation of the q-superoscillator algebra, it is proved that any two such representations are equivalent, related by a uniquely determined superunitary transformation. This…
Motivated by the Hankel determinant evaluation of moment sequences, we study a kind of Pfaffian analogue evaluation. We prove an LU-decomposition analogue for skew-symmetric matrices, called Pfaffian decomposition. We then apply this…
The L-fractional derivative is defined as a certain normalization of the well-known Caputo derivative, so alternative properties hold: smoothness and finite slope at the origin for the solution, velocity units for the vector field, and a…
We develop a quasilinear theory of the 2D Euler equation and derive an integro-differential equation for the evolution of the coarse-grained vorticity. This equation respects all the invariance properties of the Euler equation and conserves…