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.
It is well known that the fuzzy sets theory can be successfully used in quantum models ([5, 26]). In this paper we give first a review of recent development in the probability theory on tribes and their generalizations - multivalued (MV)-algebras. Secondly we show some applications of the described method to develop probability theory on IF-events.
In this paper we establish some new nonlinear difference inequalities. We also present an application of one inequality to certain nonlinear sum-difference equation.
Let $$ A=\left [ \begin {matrix} 1 & 2 \\ 0 & 1 \end {matrix} \right ],\quad B_{\lambda }=\left [ \begin {matrix} 1 & 0 \\ \lambda & 1 \end {matrix} \right ]. $$ We call a complex number $\lambda $ “semigroup free“ if the semigroup generated by $A$ and $B_{\lambda }$ is free and “free” if the group generated by $A$ and $B_{\lambda }$ is free. First families of semigroup free $\lambda $'s were described by J. L. Brenner, A. Charnow (1978). In this paper we enlarge the set of known semigroup free $\lambda $'s. To do it, we use a new version of “Ping-Pong Lemma” for semigroups embeddable in groups. At the end we present most of the known results related to semigroup free and free numbers in a common picture.
Certain generalizations of Sister Celine’s polynomials are given which include most of the known polynomials as their special cases. Besides, generating functions and integral representations of these generalized polynomials are derived and a relation between generalized Laguerre polynomials and generalized Bateman’s polynomials is established.