In the current work, a new notion of n-weak amenability of Banach algebras using homomorphisms, namely (ϕ, ψ)-n-weak amenability is introduced. Among many other things, some relations between (ϕ, ψ)-n-weak amenability of a Banach algebra A and Mm(A), the Banach algebra of m × m matrices with entries from A, are studied. Also, the relation of this new concept of amenability of a Banach algebra and its unitization is investigated. As an example, it is shown that the group algebra L 1 (G) is (ϕ, ψ)-n-weakly amenable for any bounded homomorphisms ϕ and ψ on L 1 (G).
The paper presents analysis of the stress changes due to creep in statically determinate reinforced wood beams. Each beam consists of glue-laminated timber []-section, acting compositely with steel rods, or steel-plate; U-profile, symmetrical or unsymmetrical attached to the upper or lower surface of the beams. The mathematical formulation of this problem involves the equation of equilibrium, compatibility and constitutive relationship, i.e. an elastic law for the steel part and an integral-type creep law for the wooden part. For determining the redistribution of stresses in beam section between wood beam and steel part with respect no time ‘t‘, Volterra integral equations of the second kind have been derived, on the basis of the theory of the viscoelastic body of Boltzmann - Volterra. Analytical method, which makes use of Laplace transformation and numerical method, which makes quadrature formulae for solving these equations, are proposed. The computer programs are realized in environment of a high-performance language for technical computing MATLAB®, Some relevant examples with the model proposed are investigated and discussed. In this mathematical model, different creep function are assumed and compared by describing of the time depended behavior of the wood. Finally, this analysis shows the way how to be integrated the advantages of the highly perfect model of visco-elastic body, describing the creep of wood, and availability of powerful software productts. The proposed methods give us the possibilities for realistic estimates of the behaviour of the reinforced glue-laminated wood beams, subjected to sustained service. and Obsahuje seznam literatury
In this paper, sufficient conditions are obtained for oscillation of all solutions of third order difference equations of the form yn+3 + rnyn+2 + qnyn+1 + pnyn = 0, n ≥ 0. These results are generalization of the results concerning difference equations with constant coefficients yn+3 + ryn+2 + qyn+1 + pyn = 0, n ≥ 0. Oscillation, nonoscillation and disconjugacy of a certain class of linear third order difference equations are discussed with help of a class of linear second order difference equations.
Biological systems are able to switch their neural systems into inhibitory states and it is therefore important to build mathematical models that can explain such phenomena. If we interpret such inhibitory modes as `positive' or `negative' steady states of neural networks, then we will need to find the corresponding fixed points. This paper shows positive fixed point theorems for a particular class of cellular neural networks whose neuron units are placed at the vertices of a regular polygon. The derivation is based on elementary analysis. However, it is hoped that our easy fixed point theorems have potential applications in exploring stationary states of similar biological network models.
The motion of GPS permanent stations during three earthquakes has been investigated with the use of Precise Point Positioning (PPP) technique and the seismological data. The study examines the ability of high-rate GPS observations to reflect the ground motion retrieved by the strong motion instruments (SM), considered to be more reliable and precise. The goal of this article is to show the sensitivity of GPS PPP kinematic high-rate positioning with position domain filtering using the band-pass Butterworth filter on small samples of position time series. The kinematic PPP approach in RTKLib software was used, supported by the CODE precise orbit and clock products to estimate positions from 5-hour long GPS phase datasets. Obtained position time series were reduced to 5-minute samples covering the time of co-seismic motion. The application of Butterworth band-pass filtering of GPS and seismological time series increased the agreement between them up to 72 % in terms of correlation, resulting in correlations within the range 0.34 to 0.99. The comparison of peak ground displacements (PGD) revealed that for Italian events, GPS–SM absolute value of the average difference is 6 mm with GPS–SM distances within the range of 0.05 to 2.14 km. In all analysed earthquakes, the agreement between GPSgrams and seismograms in terms of the first P-arrival polarity was checked and it was found that it is consistent in all cases. This confirms the GNSS technique capability for determining fault plane solution for earthquakes with magnitudes over 6.