We study the solutions and attractivity of the difference equation xn+1 = xn−3/(−1 + xnxn−1xn−2xn−3) for n = 0, 1, 2, . . . where x−3, x−2, x−1 and x0 are real numbers such that x0x−1x−2x−3 ≠ 1.
We analyse multivalued stochastic differential equations driven by semimartingales. Such equations are understood as the corresponding multivalued stochastic integral equations. Under suitable conditions, it is shown that the considered multivalued stochastic differential equation admits at least one solution. Then we prove that the set of all solutions is closed and bounded., Marek T. Malinowski, Ravi P. Agarwal., and Obsahuje bibliografii
A subgroup H of a finite group G is said to be ss-supplemented in G if there exists a subgroup K of G such that G = HK and H ∩ K is s-permutable in K. In this paper, we first give an example to show that the conjecture in A.A. Heliel’s paper (2014) has negative solutions. Next, we prove that a finite group G is solvable if every subgroup of odd prime order of G is ss-supplemented in G, and that G is solvable if and only if every Sylow subgroup of odd order of G is ss-supplemented in G. These results improve and extend recent and classical results in the literature., Jiakuan Lu, Yanyan Qiu., and Obsahuje seznam literatury
Consider boundary value problems for a functional differential equation ( x (n) (t) = (T +x)(t) − (T −x)(t) + f(t), t ∈ [a, b], lx = c, where T +, T − : C[a, b] → L[a, b] are positive linear operators; l: ACn−1 [a, b] → R n is a linear bounded vector-functional, f ∈ L[a, b], c ∈ ℝ n , n ≥ 2. Let the solvability set be the set of all points (T +, T −) ∈ ℝ + 2 such that for all operators T +, T − with kT ±kC→L = T ± the problems have a unique solution for every f and c. A method of finding the solvability sets are proposed. Some new properties of these sets are obtained in various cases. We continue the investigations of the solvability sets started in R. Hakl, A. Lomtatidze, J. Šremr: Some boundary value problems for first order scalar functional differential equations. Folia Mathematica 10, Brno, 2002.
In this paper we consider several Neural Network architectures for
solving nonlinear programming problems with inequality constrains. This is an extension of previous authors’ work and here we present a new architecture for convex programming problems. The architecture is based on alternativě pseudocost function, which do not require large penalty pararneter values. Simulation results based on SIMULINK® models are given and compared.
We investigate two boundary value problems for the second order differential equation with p-Laplacian (a(t)Φp(x ′ ))′ = b(t)F(x), t ∈ I = [0, ∞), where a, b are continuous positive functions on I. We give necessary and sufficient conditions which guarantee the existence of a unique (or at least one) positive solution, satisfying one of the following two boundary conditions: i) x(0) = c > 0, lim t→∞ x(t) = 0; ii) x ′ (0) = d < 0, lim t→∞ x(t) = 0.
The aim of this paper is to investigate quasi-corational, comonoform, copolyform and $\alpha $-(co)atomic modules. It is proved that for an ordinal $\alpha $ a right $R$-module $M$ is $\alpha $-atomic if and only if it is $\alpha $-coatomic. And it is also shown that an $\alpha $-atomic module $M$ is quasi-projective if and only if $M$ is quasi-corationally complete. Some other results are developed.
The external derivative d on differential manifolds inspires graded operators on complexes of spaces Λr g ∗ , Λr g ∗ ⊗ g, Λr g ∗ ⊗ g ∗ stated by g ∗ dual to a Lie algebra g. Cohomological properties of these operators are studied in the case of the Lie algebra g = se(3) of the Lie group of Euclidean motions.