Wyniki wyszukiwania - BazTech

1

On multiplicative (generalized) - derivations and central valued conditions in prime rings

Sandhu Gurninder S., Ayran Ayşe, Aydin Neşet

Journal of Mathematics and Applications

|

2021

|

Vol. 44

93--105

EN

Let R be a prime ring with multiplicative (generalized)- derivations (F, f) and (G, g) on R. This paper gives a number of central valued algebraic identities involving F and G that are equivalent to the commutativity of R under some suitable assumptions. Moreover, in order to optimize our results, we show that the assumptions taken cannot be relaxed.

2

On Commuting Parikh q-Matrices

Bera Somnath, Mahalingam Kalpana

Fundamenta Informaticae

|

2020

|

Vol. 172, nr 4

327--341

EN

This paper investigates properties of words such that their Parikh q-matrices commute. For any two words u , v ∈ ∑ k *, the concept of q-weak ratio property between u and v is introduced. Based on this property a necessary and sufficient condition for the Parikh q-matrices of any two words over binary alphabet to commute is given. This paper also provides a special class of words over an arbitrary alphabet ∑k such that their Parikh q-matrices commute.

3

Explicit commutativity conditions for second-order linear time-varying systems with non-zero initial conditions

Koksal Mehmet Emir

Archives of Control Sciences

|

2019

|

Vol. 29, No. 3

529--548

EN

Although the explicit commutativitiy conditions for second-order linear time-varying systems have been appeared in some literature, these are all for initially relaxed systems. This paper presents explicit necessary and sufficient commutativity conditions for commutativity of second-order linear time-varying systems with non-zero initial conditions. It has appeared interesting that the second requirement for the commutativity of non-relaxed systems plays an important role on the commutativity conditions when non-zero initial conditions exist. Another highlight is that the commutativity of switched systems is considered and spoiling of commutativity at the switching instants is illustrated for the first time. The simulation results support the theory developed in the paper.

4

An Efficient Equivalence-checking Algorithm for a Model of Programs with Commutative and Absorptive Statements

Podymov V.

Fundamenta Informaticae

|

2016

|

Vol. 147, nr 2/3

315--336

EN

For many program analysis problems it is useful to have means to efficiently prove that given programs have similar (equivalent) behaviors. Unfortunately, in most cases to prove the behavioral equivalence is an undecidable problem. A common way to overcome such undecidability is to consider a model of programs with an abstract semantics based on the real one, in which only some simple properties are captured, and to provide an efficient equivalence-checking algorithm for the model. We focus on two kinds of properties of data-modifying statements of imperative programs. Statements a and b are commutative, if the execution of sequences ab and ba lead to the same result. A statement b is (left-)absorptive for a statement a, if the execution of sequences ab and b lead to the same result. We consider propositional program models in which commutativity and absorption properties are caprtured (CA-models). Formally, data states for a CA-model are elements of a monoid over the set of statement symbols, defined by an arbitrary set of relations of the form ab = ba (for commutativity) and ab = b (for absorption). We propose an equivalence-checking algorithm for CA-models based on (what we call) progressive monoids. The algorithm terminates in time polynomial in size of programs. As a consequence, we prove a polynomial-time decidability for the equivalence problem in such CA-models.

5

Comparison of descriptions of continuous-time and teletraffic systems

Borys A., Aleksiewicz M.

Zeszyty Naukowe. Telekomunikacja i Elektronika / Uniwersytet Technologiczno-Przyrodniczy w Bydgoszczy

|

2012

|

z. 16

5--15

EN

In a fundamental book [5] on the so-called network calculus and research papers using this technique, as for example those cited in this paper, the notion of causal linear time-invariant teletraffic systems (networks) is used. It has been mentioned in [5] that these systems are analogous to the causal linear time-invariant systems (circuits) described by integral convolution (or convolution sum in the case of discrete ones) in classical systems theory. Note that networks considered in the network calculus are described by other type of convolution that uses the infimum operation. Moreover, the algebra used in the above technique is also different. This is the so-called min-plus (or max-plus) algebra. Therefore, it is not obvious that the teletraffic systems (networks) described by the infimum convolution fulfill the following basic properties: linearity, causality, time-invariance, associativity and commutativity of their convolution operator, known from the classical theory of systems. The objective of this paper is to prove or show in detail that the above properties hold.

PL

W znanej monografii nt. rachunku sieciowego (network calculus), napisanej przez J.-Y. Le Boudeca i P. Thirana, zostało wprowadzone pojęcie liniowych systemów teleinformatycznych niezależnych od czasu. Wskazano w niej na podobieństwa istniejące pomiędzy powyższą klasą systemów a liniowymi systemami analogowymi niezależnymi od czasu, jednakże zrobiono to w sposób dosyć pobieżny. W tym artykule podobieństwa te są przeanalizowane w sposób systematyczny, a także bez uciekania się do bardzo abstrakcyjnej teorii systemów opisywanych za pomocą algebry min-plus – jedynie przy wykorzystaniu elementarnych pojęć matematyki wyższej. Wiele przedstawionych tutaj wyprowadzeń nie było dotychczas nigdzie publikowanych, jak na przykład twierdzenie 1.

6

On the closedness, the self-adjointness and the normality of the product of two unbounded operators

Mortad M. H.

Demonstratio Mathematica

|

2012

|

Vol. 45, nr 1

161-167

EN

Let A and B be two unbounded densely defined operators on a Hilbert space H . The purpose of this work is to give simple conditions that make the product AB closed, self-adjoint and normal provided the two operators are so.

7

Perspective case of the Pappus theorem in the n-dimensional projective space

Witczyński K.

Demonstratio Mathematica

|

2007

|

Vol. 40, nr 4

925-928

EN

A generalisation to the n-dimensional projective space Pn(F) of the perspective case of the Pappus theorem is given. It is shown, additionally, that in such a case the ground field F might be non-commutative.

8

The existence and uniqueness of solution of one coupled plate thermomechanics problem

Krysko V. A., Awrejcewicz J., Bruk V. M.

Journal of Applied Analysis

|

2002

|

Vol. 8, nr 1

129-139

EN

The thermo-elastic plate system of equations is analysed. The sufficient conditions of existence, uniqueness and continuity dependence on initial data of the Cauchy problem solutions for differential-operational equation of mixed type (a part of the equation of hyperbolic type, and a part of parabolic type) are given in this paper. If the operational coefficients are suitably chosen, the investigated equation can be used to obtain a differential equation describing vibrations of a plate — the modified Germain-Lagrange equation of hyperbolic type. Moreover, in order to define the temperature field, one can use a three-dimensional equation of thermal conductivity (a parabolic equation).