ԵՊՀ Գիտական տեղեկագիր - Ֆիզիկա և մաթեմատիկա

On a connection between a class of systems of ordinary differential equations and integral operators with semi-separable kernel (Սովորական դիֆերենցիալ հավասարումների մի համակարգի կիսասեպարաբել կորիզով ինտեգրալ օպերատորների կապի մասին)

Ա. Հովհաննիսյան, Ա. Քամալյան, Հ. Քամալյան — Sat, 20 Jan 2018 00:00:00 +0000

In the present paper the connection between a class of systems of differential equations and integral operators with semi-separable kernel is established. Using a matrix of the system the inverse to a given integral operator is constructed. Moreover by putting some additional conditions on the kernel of integral operator and by the help of inverse of integral operator a fundamental matrix of the system is constructed.

On a version of fixed point theorem (Անշարժ կետի թեորեմի մի տարբերակի մասին)

Լ. Միքայելյան — Sat, 20 Jan 2018 00:00:00 +0000

In the present short note we prove a version of the classical fixed-point theorem, as well as present its application.

On a question of A. Sozutov (Ա․Սոզուտովի մի հարցի մասին)

Ն. Միրզախանյան, Հ. Փիլիպոսյան — Sat, 20 Jan 2018 00:00:00 +0000

In the paper an answer to a problem posed by A.I. Sozutov in the Kourovka Notebook is given. The solution is based on some modification of the method that was proposed for constructing a non-abelian analogue of the additive group of rational numbers, i.e. a group whose center is an infinite cyclic group and any two non-trivial subgroups of which have a non-trivial intersection.

On a uniqueness theorem for the Franklin system (Ֆրանկլինի համակարգի միակության մի թեորեմի մասին)

Կ. Նավասարդյան — Sat, 20 Jan 2018 00:00:00 +0000

In this paper we prove that there exist a nontrivial Franklin series and a sequence Mn such that the partial sums SMn (x) of that series converge to 0 almost everywhere and λ · mes{x : sup n |SMn (x)| > λ} → 0 as λ → +∞.

The non-classical problem of an elastically clamped orthotropic beam of variable thickness under the combined action of compressive forces and transverse load (Առաձգական ամրակցված փոփոխական հաստության օրթոտրոպ հեծանի ոչ դասական խնդիրը սեղմող ուժերի և լայն

Ռ. Կիրակոսյան, Ս. Ստեփանյան — Sat, 20 Jan 2018 00:00:00 +0000

On the basis of the refined theory of orthotropic plates of variable thickness, the equations of the beam bending problem are obtained with the simultaneous action of compressive forces and transverse load. It is accepted that the edges of the beam have an elastically clamped support and the reduction of the compressive force by the support due to friction is taking into account. Passing to dimensionless quantities, a certain problem is solved. The stability of a beam is discussed. Based on the results obtained, conclusions are drawn.

On incomparability of interpretation algorithms of typed functional programs with respect to undefined value (Տիպիզացված ֆունկցիոնալ ծրագրերի ինտերպրետացիայի ալգորիթմների անհամեմատելիությունն անորոշ արժեքի նկատմամբ)

Դ. Գրիգորյան — Sat, 20 Jan 2018 00:00:00 +0000

In the paper the interpretation algorithms of typed functional programs are considered. The interpretation algorithm is based on substitution, β-reduction and canonical δ-reduction. It is shown that seven known interpretation algorithms (FS (of full substitution), PES (of parallel external substitution), LES (of left external substitution), PIS (of parallel inner substitution), LIS (of left inner substitution), ACT (active algorithm), PAS (passive algorithm)) are pairwise incomparable with respect to undefined value (⊥-incomparable).

On interpretation of typed and untyped functional programs (Տիպիզացված և ոչ տիպիզացված ֆունկցիոնալ ծրագրերի ինտերպրետացիայի մասին)

Ս. Նիգիյան — Sat, 20 Jan 2018 00:00:00 +0000

In this paper the interpretation algorithms for typed and untyped functional programs are considered. Typed functional programs use variables of any order and constants of order ≤ 1, where constants of order 1 are strongly computable, monotonic functions with indeterminate values of arguments. The basic semantics of the typed functional program is a function with indeterminate values of arguments, which is the main component of its least solution. The interpretation algorithms of typed functional programs are based on substitutions, β-reduction and canonical δ-reduction. The basic semantics of the untyped functional program is the untyped λ-term, which is defined by means of the fixed point combinator. The interpretation algorithms of untyped functional programs are based on substitutions and β-reduction. Interpretation algorithms are examined for completeness and comparability. It is investigated how the “behavior” of the interpretation algorithm changes after translation of typed functional program into untyped functional program.

Measurement of discharges temperature in low-temperature acoustoplasma (Պարպման ջերմաստիճանի չափումը ցածր ջերմաստիճանային ակուստոպլազմայում)

Տ. Բեժանյան — Sat, 20 Jan 2018 00:00:00 +0000

The results of temperature measurements in the Argon discharge in plasma with acoustic perturbation are presented. Possibility of, as decreasing, so increasing of discharge temperature in several times is shown.

A method for multi-criteria decision making under uncertainty (Անորոշությունների առկայության պայմաններում որոշումների ընդունման բազմաչափանիշային եղանակ)

Ա. Գևորգյան, Հ. Ավագյան — Sat, 20 Jan 2018 00:00:00 +0000

This work presents development of a method for multi-criteria decision making under uncertainty conditions based on single-attribute value functions and probabilistic distributions. The values of different criteria are modeled using normal distributions, i.e. the value of the i-th criteria of the j-th option is given by x j i ∼ N(µ j i ,σ j i ) distribution. The method is evaluated and the results are analyzed on a simple example.

Determination of glucose concentration in aqueous solution by using modified Hilbert shaped microwave metamaterial sensor (Ջրային լուծույթում գլյուկոզի խտության որոշումը մետանյութով սենսորի օգտագործմամբ` հիմնված ձևափոխված հիլբերտյան կորի վրա)

Հ. Պարսամյան, Ա. Բաբաջանյան, Շ. Առաքելյան, Կ. ԼԻ — Sat, 20 Jan 2018 00:00:00 +0000

Glucose concentration in the aqueous solution was measured using a microwave metamaterial sensor based on the modified Hilbert curve of the first fractal order. In order to increase the system sensitivity at fixed meta-element sizes, the design of the sensor was optimized by using finite element method. It was observed that S parameters of the metamaterial microstrip line sensor at resonant frequencies strongly depend on the glucose concentration. Consequently, by measuring the microwave responses for the different concentrations one can detect the glucose concentration in the solution. Such structure can be useful in the biological and medical applications.

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