Institute of Mathematics AS CR, v. v. i.
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Counting paths between points on a circle
No full textsummary:The paper deals with counting sets of given magnitude whose elements are self-avoiding paths with nodes from a fixed set of points on a circle. Some of the obtained formulae provide new properties of entries in ``The On-line Encyclopaedia of Integer Sequences", while others generate new entries therein
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No full textsummary:Docent Oldřich Lepil - 90 let. Pavel Drábek slaví sedmdesátin
Commutative rings whose certain modules decompose into direct sums of cyclic submodules
No full textsummary:We provide some characterizations of rings for which every (finitely generated) module belonging to a class of -modules is a direct sum of cyclic submodules. We focus on the cases, where the class is one of the following classes of modules: semiartinian modules, semi-V-modules, V-modules, coperfect modules and locally supplemented modules
Covering energy of posets and its bounds
Get PDFsummary:The concept of covering energy of a poset is known and its McClelland type bounds are available in the literature. In this paper, we establish formulas for the covering energy of a crown with elements and a fence with elements. A lower bound for the largest eigenvalue of a poset is established. Using this lower bound, we improve the McClelland type bounds for the covering energy for some special classes of posets
Investigations on unique range sets of meromorphic functions in an angular domain
Get PDFsummary:We study unique range sets of meromorphic functions over an angular domain in the light of weighted sharing. One of our main results generalizes and improves a result of Xu et al. (2014). Most importantly, we have pointed out a gap in the proofs of some main results of Rathod (2021) and subsequently rectifying the gap we have conveniently improved the results
The maximum regularity property of the steady Stokes problem associated with a flow through a profile cascade in -framework
No full textsummary:We deal with the steady Stokes problem, associated with a flow of a viscous incompressible fluid through a spatially periodic profile cascade. Using the reduction to domain , which represents one spatial period, the problem is formulated by means of boundary conditions of three types: the conditions of periodicity on curves and (lower and upper parts of ), the Dirichlet boundary conditions on (the inflow) and (boundary of the profile) and an artificial ``do nothing''-type boundary condition on (the outflow). We show that the considered problem has a strong solution with the -maximum regularity property for appropriately integrable given data. From this we deduce a series of properties of the corresponding strong Stokes operator
Another version of cosupport in
No full textsummary:The goal of the article is to develop a theory dual to that of support in the derived category . This is done by introducing `big' and `small' cosupport for complexes that are different from the cosupport in D. J. Benson, S. B. Iyengar, H. Krause (2012). We give some properties for cosupport that are similar, or rather dual, to those of support for complexes, study some relations between `big' and `small' cosupport and give some comparisons of support and cosupport. Finally, we investigate the dual notion of associated primes
Weighted -core inverses in rings
No full textsummary:Let be a unital -ring. For any we define the weighted -core inverse and the weighted dual -core inverse, extending the -core inverse and the dual -core inverse, respectively. An element has a weighted -core inverse with the weight if there exists some such that , and . Dually, an element has a weighted dual -core inverse with the weight if there exists some such that , and . Several characterizations of weighted -core invertible and weighted dual -core invertible elements are given when weights and are invertible Hermitian elements. Also, the relations among the weighted -core inverse, the weighted dual -core inverse, the -core inverse, the dual -core inverse, the weighted Moore-Penrose inverse and the --inverse are considered
Solution of 3D contact shape optimization problems with Coulomb friction based on TFETI
No full textsummary:The present paper deals with the numerical solution of 3D shape optimization problems in frictional contact mechanics. Mathematical modelling of the Coulomb friction problem leads to an implicit variational inequality which can be written as a fixed point problem. Furthermore, it is known that the discretized problem is uniquely solvable for small coefficients of friction. Since the considered problem is nonsmooth, we exploit the generalized Mordukhovich's differential calculus to compute the needed subgradient information.\looseness -1 \endgraf The state problem is solved using successive approximations combined with the Total FETI (TFETI) method. The latter is based on tearing the bodies into ``floating'' subdomains, discretization by finite elements, and solving the resulting quadratic programming problem by augmented Lagrangians. \endgraf The presented numerical experiments demonstrate our method's power and the importance of the proper modelling of 3D frictional contact problems. The state problem solution and the sensitivity analysis process were implemented in parallel