Related papers: On a conjecture about Dirac's delta representation…
In this paper, we derive new matrix representation for Daehee numbers and polynomials, the lambda-Daehee numbers and polynomials and the twisted Daehee numbers and polynomials. This helps us to obtain simple and short proofs of many…
Conjectured links between the distribution of values taken by the characteristic polynomials of random orthogonal matrices and that for certain families of L-functions at the centre of the critical strip are used to motivate a series of…
The electric or magnetic field of an ideal dipole is known to have a Dirac delta function at the origin. The usual textbook derivation of this delta function is rather ad hoc and cannot be used to calculate the delta-function structure for…
We consider vertices, a notion originating in local representation theory of finite groups, for the category $\mathcal{O}$ of a rational Cherednik algebra and prove the analogue of the Dipper-Du Conjecture for Hecke algebras of symmetric…
We construct a Dirac morphism and prove that if this Dirac morphism is invertible, then the isomorphism conjecture for non-connective algebraic K-theory holds true.
Given a random real quadratic field from $\{ \mathbb{Q}(\sqrt{p}\,) ~|~ p \text{ primes} \}$, the conjectural probability $\mathbb{P}(h=q)$ that it has class number $q$ is given for all positive odd integers $q$. Some related conjectures of…
We provide a probabilistic representation for the derivative of the semigroup corresponding to a diffusion process killed at the boundary of a half interval. In particular, we show that the derivative of the semi-group can be expressed as…
The Dirac exchange interaction is derived from recent quantum kinetic theory for collisionless plasmas. For this purpose, the kinetic equation is written in the semiclassical and long wavelength approximations. The validity of the model for…
The family of q-Gaussian and q-exponential probability densities fit the statistical behavior of diverse complex self-similar non-equilibrium systems. These distributions, independently of the underlying dynamics, can rigorously be obtained…
We study a class of q-analogues of multiple zeta values given by certain formal q-series with rational coefficients. After introducing a notion of weight and depth for these q-analogues of multiple zeta values we present dimension…
This comment on the recently published article "Why Einstein, Podolsky and Rosen did not prove that quantum mechanics is 'incomplete'" (arXiv:0805.0217) by J.H.Field shows that some conclusions, made in the referred-to article, result from…
We give an explicit formula proving Xu's Conjecture on alternating double zeta values. We also discuss the limitations of Glanois' motivic Galois descent criterion in this case, as it cannot specify the depth of the descent.
Motivated by derivation of the Dirac type delta-function for quantum states in Fock-Bargmann representation, we find q-binomial expansion in terms of q-Hermite polynomials, analytic in two complex arguments. Based on this representation, we…
We conjecture two combinatorial interpretations for the symmetric function $\Delta_{e_k} e_n$, where $\Delta_f$ is an eigenoperator for the modified Macdonald polynomials defined by Bergeron, Garsia, Haiman, and Tesler. Both interpretations…
Some weighted inequalities for the maximal operator with respect to the discrete diffusion semigroups associated with exceptional Jacobi and Dunkl-Jacobi polynomials are given. This setup allows to extend the corresponding results obtained…
We provide combinatorial as well as probabilistic interpretations for the q-analogue of the Pochhammer k-symbol introduced by Diaz and Teruel. We introduce q-analogues of the Mellin transform in order to study the q-analogue of the k-gamma…
We postulate a new nonlinear generalization of the Dirac equation for an electron. Basic properties of the new equation are considered.
In this paper, we revisit the diffusive representations of fractional integrals established in \cite{diethelm2023diffusive} to explore novel variants of such representations which provide highly efficient numerical algorithms for the…
In this paper we extend the umbral calculus, developed to deal with difference equations on uniform lattices, to q-difference equations. We show that many of the properties considered for shift invariant difference operators satisfying the…
In this paper, we introduce a new type of $ pq $-calculus. The $ pq $-derivative and $ pq $-integration are investigated and various properties of these concepts are given. The fundamental theorem of $ pq $-calculus and formulas of $ pq…