In the Hilbert space ?2 ?(Z; E) (Z := {0,? 1, ? 2, ...}, dim E = N < ?), maximal dissipative singular second-order matrix difference operators that extensions of a minimal symmetric operator with deficiency indices (2N, 2N) (in limit-circle cases at ?) are considered. The general boundary conditions investigated. For operator, self-adjoint dilation and is its incoming outgoing spectral repre...

Abstract. The Stieltjes–Wigert polynomials, which correspond to an indeterminate moment problem on the positive half-line, are eigenfunctions of a second order q-difference operator. We consider the orthogonality measures for which the difference operator is symmetric in the corresponding weighted L-spaces. Under some additional assumptions these measures are exactly the solutions to the q-Pear...

For the creation operator a† and the annihilation operator a of a harmonic oscillator, we consider Weyl ordering expression of (a†a)n and obtain a new symmetric expression of Weyl ordering w.r.t. a†a ≡ N and aa† = N + 1 where N is the number operator. Moreover, we interpret intertwining formulas of various orderings in view of the difference theory. Then we find that the noncommutative paramete...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}, $h$-...

where ∆u(k) = u(k+1)−u(k) is the forward difference operator, Z∗ := {k ∈ Z : k 6= 0} and a, α, δ, f, g are functions to be defined later. Difference equations can be seen as a discrete counterpart of PDEs and are usually studied in connection with numerical analysis. In this way, the main operator in Problem (1.1) −∆(a(k − 1,∆u(k − 1))) can be seen as a discrete counterpart of the anisotropic o...

We study a product rule and a difference operator equipped with Leibniz rule in a general framework of lattice field theory. It is shown that the difference operator can be determined by the product rule and some initial data through the Leibniz rule. This observation leads to a no-go theorem that it is impossible to construct any difference operator and product rule on a lattice with the prope...

In this paper we develop the new semi-analytical model of a tidally perturbed or tidally disrupted star proposed recently by two of us. This model is effectively a one dimensional Lagrangian model and it can be evolved numerically much faster than the conventional 3D models. A self-consistent derivation of dynamical equations of the model is performed and several important theorems about the dy...

For one space dimension, the phenomenological theory of sedimentation of flocculated suspensions yields a model that consists of an initial-boundary value problem for a second order partial differential equation of mixed hyperbolic–parabolic type. Due to the mixed hyperbolic-parabolic nature of the model, its solutions may be discontinuous and difficulties arise if one tries to construct these ...

In some recent works [11, 12] we developed a general framework for the construction of hybrid algorithms which are able to face efficiently the multiscale nature of some hyperbolic and kinetic problems. Here, at variance with respect to the previous methods, we construct a method form-fitting to any type of finite volume or finite difference scheme for the reduced equilibrium system. Thanks to ...

There exists a considerably body of literature on the development, analysis and implementation of multiplicative and additive operator splitting methods for solving large and sparse systems of finite difference equations arising from the discretization of partial differential equations. In this note, we will review the Newton–Arithmetic Mean and the Modified Newton–Arithmetic Mean methods for s...