A Heyting algebra is a distributive lattice with implication and a dual $BCK$-algebra is an algebraic system having as models logical systems equipped with implication. The aim of this paper is to investigate the relation of Heyting algebras between dual $BCK$-algebras. We define notions of $i$-invariant and $m$-invariant on dual $BCK$-semilattices and prove that a Heyting semilattice is equiva...

Lifting modules and their various generalizations as some main concepts in module theory have been studied and investigated extensively in recent decades. Some authors tried to present some homological aspects of lifting modules and -supplemented modules. In this work, we shall present a homological approach to -supplemented modules via fully invariant submodules. Lifting modules and H-suppleme...

We consider quasiperiodic nonconservative perturbations of two-dimensional nonlinear Hamiltonian systems. introduce the notion a degenerate resonance and study topology zone with odd even orders degeneracy. A special attention is paid oscillation synchronization while an invariant torus passing through zone. establish existence intervals respect to control parameter. The based on analysis pendu...

a common method to determine the order of minimal realization of a continuous linear time invariant descriptor system is to decompose it into slow and fast subsystems using the weierstrass canonical form. the weierstrass decomposition should be avoided because it is generally an ill-conditioned problem that requires many complex calculations especially for high-dimensional systems. the present ...

environment assigning intervals to program variables. Writing X = {x1 ← �1� � � � � x� ← ��} for the function X mapping x� to �� such that X (x�) = ��, � = 1� � � � � �, the interval invariance equations would be 4 One of the 64 bits is used for garbage collection. 12 P. C�����   X1 = {x ← [min_int� max_int]} X2 = {x ← [1� 1] � L X3(x) = ∅ ? ∅ : let [�� �] = X3(x) in [min(� + 1� ma...

This paper investigates controllability for linear time-invariant systems under irregular and random sampling, and develops adaptive control algorithms with respect to sampling intervals. Using block erasure channels as themainmotivating communicationplatform, it first establishes a sufficient condition on sampling density that ensures controllability of sampled systems, which is necessary for ...

The state of the art in the spectral theory of linear time-varying differential-algebraic equations (DAEs) is surveyed. To characterize the asymptotic behavior and the growth rate of solutions, basic spectral notions such as Lyapunovand Bohl exponents, and Sacker-Sell spectra are discussed. For DAEs in strangeness-free form, the results extend those for ordinary differential equations, but only...

A number of studies have resulted in the finding of a 3-D perceptual anisotropy, whereby spatial intervals oriented in depth are perceived to be smaller than physically equal intervals in the frontoparallel plane. In this experiment, we examined whether this anisotropy is scale invariant. The stimuli were L shapes created by two rods placed flat on a level grassy field, with one rod defining a ...