Institute of Mathematics AS CR, v. v. i.
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On special Rees matrix semigroups over semigroups
No full textsummary:We study the right regular representation of special Rees matrix semigroups over semigroups, and discuss their embedding in idempotent-free left simple semigroups
Complex interpolation of function spaces with general weights
No full textsummary:We present the complex interpolation of Besov and Triebel--Lizorkin spaces with generalized smoothness. In some particular cases these function spaces are just weighted Besov and Triebel--Lizorkin spaces. As a corollary of our results, we obtain the complex interpolation between the weighted Triebel--Lizorkin spaces and with suitable assumptions on the parameters and , and the pair of weights
Some results on quasi-t-dual Baer modules
No full textsummary:Let be a ring and let be an -module with . Consider the preradical for the category of right -modules Mod- introduced by Y. Talebi and N. Vanaja in 2002 and defined by is small in its injective hull. The module is called quasi-t-dual Baer if is a direct summand of for every two-sided ideal of , where . In this paper, we show that is quasi-t-dual Baer if and only if is a direct summand of and is a quasi-dual Baer module. It is also shown that any direct summand of a quasi-t-dual Baer module inherits the property. The last part of the paper is devoted to the comparison of the notions of quasi-dual Baer modules and quasi-t-dual Baer modules. Also, right quasi-t-dual Baer rings are investigated
Energy dissipation and hysteresis cycles in pre-sliding transients of kinetic friction
No full textsummary:The problem of transient hysteresis cycles induced by the pre-sliding kinetic friction is relevant for analyzing the system dynamics, e.g., of micro- and nano-positioning instruments and devices and their controlled operation. The associated energy dissipation and consequent convergence of the state trajectories occur due to the structural hysteresis damping of contact surface asperities during reversals, and it is neither exponential (i.e., viscous type) nor finite-time (i.e., Coulomb type). In this paper, we discuss the energy dissipation and convergence during the pre-sliding cycles and show how a piecewise smooth force-displacement hysteresis map enters into the energy balance of an unforced system of the second order. An existing friction modeling approach with a low number of the free parameters, the Dahl model, is then exemplified alongside the developed analysis
1-planar graphs with girth at least 6 are (1,1,1,1)-colorable
No full textsummary:A graph is 1-planar if it can be drawn in the Euclidean plane so that each edge is crossed by at most one other edge. A 1-planar graph on vertices is optimal if it has edges. We prove that 1-planar graphs with girth at least 6 are (1,1,1,1)-colorable (in the sense that each of the four color classes induces a subgraph of maximum degree one). Inspired by the decomposition of 1-planar graphs, we conjecture that every 1-planar graph is (2,2,2,0,0)-colorable
Does the endomorphism poset determine whether a finite poset is connected? An issue Duffus raised in 1978
Get PDFsummary:Duffus wrote in his 1978 Ph.D. thesis, ``It is not obvious that is connected and imply that is connected'', where and are finite nonempty posets. We show that, indeed, under these hypotheses is connected and
Nonoscillatory solutions of discrete fractional order equations with positive and negative terms
Get PDFsummary:This paper aims at discussing asymptotic behaviour of nonoscillatory solutions of the forced fractional difference equations of the form \begin{align} \Delta ^{\gamma }u(\kappa )&+\Theta [\kappa +\gamma ,w(\kappa +\gamma )]\\=&\Phi (\kappa +\gamma )+\Upsilon (\kappa +\gamma )w^{\nu }(\kappa +\gamma ) +\Psi [\kappa +\gamma ,w(\kappa +\gamma )],\quad \kappa \in \mathbb {N}_{1-\gamma },\\ u_{0} =&c_{0}, \end{align} where , , is a Caputo-like fractional difference operator. Three cases are investigated by using some salient features of discrete fractional calculus and mathematical inequalities. Examples are presented to illustrate the validity of the theoretical results
Isomorphic properties in spaces of compact operators
Get PDFsummary:We introduce the definition of -limited completely continuous operators, . The question of whether a space of operators has the property that every -limited subset is relative compact when the dual of the domain and the codomain have this property is studied using -limited completely continuous evaluation operators
Practical -stability behavior of time-varying nonlinear systems
Get PDFsummary:We deal with the problem of practical uniform -stability for nonlinear time-varying perturbed differential equations. The main aim is to give sufficient conditions on the linear and perturbed terms to guarantee the global existence and the practical uniform -stability of the solutions based on Gronwall's type integral inequalities. Several numerical examples and an application to control systems with simulations are presented to illustrate the applicability of the obtained results
