We consider a large class of impulsive retarded functional differential equations (IRFDEs) and prove a result concerning uniqueness of solutions of impulsive FDEs. Also, we present a new result on continuous dependence of solutions on parameters for this class of equations. More precisely, we consider a sequence of initial value problems for impulsive RFDEs in the above setting, with convergent right-hand sides, convergent impulse operators and uniformly convergent initial data. We assume that the limiting equation is an impulsive RFDE whose initial condition is the uniform limit of the sequence of the initial data and whose solution exists and is unique. Then, for sufficient large indexes, the elements of the sequence of impulsive retarded initial value problem admit a unique solution and such a sequence of solutions converges to the solution of the limiting Cauchy problem., Márcia Federson, Jaqueline Godoy Mesquita., and Obsahuje seznam literatury
An n × n ray pattern A is called a spectrally arbitrary ray pattern if the complex matrices in Q(A) give rise to all possible complex polynomials of degree n. In a paper of Mei, Gao, Shao, and Wang (2014) was proved that the minimum number of nonzeros in an n×n irreducible spectrally arbitrary ray pattern is 3n-1. In this paper, we introduce a new family of spectrally arbitrary ray patterns of order n with exactly 3n - 1 nonzeros., Yinzhen Mei, Yubin Gao, Yanling Shao, Peng Wang., and Obsahuje seznam literatury
A quantitatively new analog-to-digital converter (ADC) module has been developed during 2010, in co-operation with Tedia Ltd. The module has a 28-bit final resolution and uses 32-bit arithmetic. There are two versions, with four and twelve analog inputs. The 4-input module replaces the original 21-bit version, produced until 2009. The 12-input module is intended to be deployed in small-aperture seismic arrays. The whole set consists of four 3-channel detached modules that can be interconnected with the main module using a cable of up to 100 m in length. This design increases signal-to-noise ratio (SNR) by placing the A/D part as close to the seismograph as possible in order to transmit digital data for storage. All channels are sampled coherently so that all four sensors are automatically synchronised. It allows the detection of local events even though the sync-signal is absent. In other words, the 12-input module is suitable for ad-hoc field measurements even in places where there is no GPS signal. All arrays operated by the Institute of Rock Structure and Mechanics (IRSM) are going to be upgraded to use these modules and some new sites will also be set-up with this innovative equipment (e.g. Lazy in Western Bohemia and Dobrá Voda in Slovakia)., Milan Brož and Jaroslav Štrunc., and Obsahuje bibliografii
A close relationship between the class of totally positive matrices and anti-Monge matrices is used for suggesting a new direction for investigating totally positive matrices. Some questions are posed and a partial answer in the case of Vandermonde-like matrices is given., Miroslav Fiedler., and Obsahuje seznam literatury
The presented technological procedure makes it possible to assemble large magnetic blocks from permanent magnets with a high value of maximum energy product in such a way that the individual magnets or magnetic plates are moved toward each other at a controlled speed in the direction perpendicular to the future common contact surface of these magnets, i.e. parallel to the induction lines crossing this contact surface. Unlike in the previously used way of assembling the blocks, it is thus possible to eliminate the influence of partial demagnetization as the blocks are being assembled and consequently to reach higher values of magnetic induction in the air gap of the magnetic circuit. When applying the new method of assembling the blocks for instance in circuits of magnetic filters for the purification of ceramic suspensions, a prerequisite for the further improvement of the technological parameters of filtration is thus created., Václav Žežulka and Pavel Straka., and Obsahuje bibliografické odkazy
Let G be a group. If every nontrivial subgroup of G has a proper supplement, then G is called an aS-group. We study some properties of aS-groups. For instance, it is shown that a nilpotent group G is an aS-group if and only if G is a subdirect product of cyclic groups of prime orders. We prove that if G is an aS-group which satisfies the descending chain condition on subgroups, then G is finite. Among other results, we characterize all abelian groups for which every nontrivial quotient group is an aS-group. Finally, it is shown that if G is an aS-group and |G| ≠ pq, p, where p and q are primes, then G has a triple factorization., Reza Nikandish, Babak Miraftab., and Obsahuje seznam literatury
We show that there is a model structure in the sense of Quillen on an arbitrary Frobenius category F such that the homotopy category of this model structure is equivalent to the stable category F as triangulated categories. This seems to be well-accepted by experts but we were unable to find a complete proof for it in the literature. When F is a weakly idempotent complete (i.e., every split monomorphism is an inflation) Frobenius category, the model structure we constructed is an exact (closed) model structure in the sense of Gillespie (2011)., Zhi-Wei Li., and Seznam literatury
We prove that a rank ≥3 Dowling geometry of a group H is partition representable if and only if H is a Frobenius complement. This implies that Dowling group geometries are secret-sharing if and only if they are multilinearly representable., František Matúš and Aner Ben-Efraim., and Obsahuje bibliografické odkazy
A graph X, with a group G of automorphisms of X, is said to be (G, s)-transitive, for some s\geq 1, if G is transitive on s-arcs but not on (s + 1)-arcs. Let X be a connected (G, s)-transitive graph of prime valency s\geq 5, and Gv the vertex stabilizer of a vertex v \in V (X). Suppose that Gv is solvable. Weiss (1974) proved that |Gv | p(p−1)^{2}. In this paper, we prove that Gv\cong (\mathbb{Z}_{p}\rtimes \mathbb{Z}_{m})× \mathbb{Z}_{n} for some positive integers m and n such that n | m and m | p − 1., Song-Tao Guo, Hailong Hou, Yong Xu., and Obsahuje seznam literatury
Let (G) and i(G) be the domination number and the independent domination number of G, respectively. Rad and Volkmann posted a conjecture that i(G)/ (G) 6 (G)/2 for any graph G, where (G) is its maximum degree (see N. J.Rad, L.Volkmann (2013)). In this work, we verify the conjecture for bipartite graphs. Several graph classes attaining the extremal bound and graphs containing odd cycles with the ratio larger than (G)/2 are provided as well., Shaohui Wang, Bing Wei., and Seznam literatury