Mediterranean Journal of Mathematics最新文献

In this article, we focus on the formulation of dissipative mechanical systems through contact Hamiltonian systems. Different forms of symmetry of a contact dynamical system (geometric, dynamic, and gage) are defined to, in the realm of Noether, find their corresponding dissipated quantities. We also address the existence of dissipated quantities associated with a general vector field X on (TQtimes mathbb {R},) focusing on the case where its contact Hamiltonian function is dissipative.

As a consequence of a general result, we prove that in the case of singular integrals the set of convergence consists only of the two functions (textbf{1}) and (cos ). We prove also a multivariate version of this result and apply it to find the necessary and sufficient conditions for the convergence of the sequences of positive linear operators associated to the rectangular and triangular summation.

As part of their construction of the Khovanov spectrum, Lawson, Lipshitz and Sarkar assigned to each cube in the Burnside category of finite sets and finite correspondences, a finite cellular spectrum. In this paper, we extend this assignment to cubes in Burnside categories of infinite sets. This is later applied to the work of Akhmechet, Krushkal and Willis on the quantum annular Khovanov spectrum with an action of a finite cyclic group: we obtain a quantum annular Khovanov spectrum with an action of the infinite cyclic group.

By means of fixed point index theory for multivalued maps, we provide an analogue of the classical Birkhoff–Kellogg Theorem in the context of discontinuous operators acting on affine wedges in Banach spaces. Our theory is fairly general and can be applied, for example, to eigenvalues and parameter problems for ordinary differential equations with discontinuities. We illustrate in detail this fact for a class of second-order boundary value problem with deviated arguments and discontinuous terms. In a specific example, we explicitly compute the terms that occur in our theory.

Given a set ({mathcal {F}}) of graphs, we call a copy of a graph in ({mathcal {F}}) an ({mathcal {F}})-graph. The ({mathcal {F}})-isolation number of a graph G, denoted by (iota (G,{mathcal {F}})), is the size of a smallest set D of vertices of G such that the closed neighborhood of D intersects the vertex sets of the ({mathcal {F}})-graphs contained by G (equivalently, (G - N[D]) contains no ({mathcal {F}})-graph). Thus, (iota (G,{K_1})) is the domination number of G. For any integer (k ge 1), let ({mathcal {F}}_{1,k}) be the set of regular graphs of degree at least (k-1), let ({mathcal {F}}_{2,k}) be the set of graphs whose chromatic number is at least k, and let ({mathcal {F}}_{3,k}) be the union of ({mathcal {F}}_{1,k}) and ({mathcal {F}}_{2,k}). Thus, k-cliques are members of both ({mathcal {F}}_{1,k}) and ({mathcal {F}}_{2,k}). We prove that for each (i in {1, 2, 3}), (frac{m+1}{{k atopwithdelims ()2} + 2}) is a best possible upper bound on (iota (G, {mathcal {F}}_{i,k})) for connected m-edge graphs G that are not k-cliques. The bound is attained by infinitely many (non-isomorphic) graphs. The proof of the bound depends on determining the graphs attaining the bound. This appears to be a new feature in the literature on isolation. Among the result’s consequences are a sharp bound of Fenech, Kaemawichanurat, and the present author on the k-clique isolation number and a sharp bound on the cycle isolation number.

This research focuses on analyzing the depth of generalized binomial edge ideals. We extend the notion of d-compatible map and use it to give a combinatorial lower bound for the depth of generalized binomial edge ideals. Subsequently, we determine an upper bound for the depth of generalized binomial edge ideals in terms of the vertex-connectivity of graphs. We demonstrate that the difference between the upper and lower bounds can be arbitrarily large, even in cases when one of the bounds is sharp. In addition, we calculate the depth of generalized binomial edge ideals of certain classes of graphs, including cycles and graphs with Cohen-Macaulay binomial edge ideals.

An adaptive finite difference scheme for variable-order fractional-time subdiffusion equations in the Caputo form is studied. The fractional-time derivative is discretized by the L1 procedure but using nonhomogeneous timesteps. The size of these timesteps is chosen by an adaptive algorithm to keep the local error bounded around a preset value, a value that can be chosen at will. For some types of problems, this adaptive method is much faster than the corresponding usual method with fixed timesteps while keeping the local error of the numerical solution around the preset values. These findings turn out to be similar to those found for constant-order fractional diffusion equations.

We represent Klein surfaces as the orbit spaces of Riemann surfaces under actions of multiplicative subgroups of real Clifford algebras. We define a partial order on the set of all Klein surfaces and we prove that the defining action of any Klein surface Y can be obtained by induction from the defining action of a minimal element of the chain to which Y belongs.

In this paper, we study composition and weighted composition operators that are close to isometries on ({mathcal {H}}^2) but not necessarily isometric. We also obtain a Wold type decomposition for such operators.

In this article, we establish a transference between the n-dimensional Euclidean space ( mathbb {R} ^{n}) and the n-torus (mathbb {T}^{n}) about the (H^{p}-L^{p,infty }) boundedness of maximal multipliers. As an application, we obtain that the maximal oscillatory integral (S_{alpha ,beta }^{*}) is bounded from ( H^{p}left( mathbb {R} ^{n}right) ) to (L^{p,infty }left( mathbb {R} ^{n}right) ) under the sharp relation among (alpha ,beta ) and p.