Editorial backlog
- Babajanov B.A., Yakhshimuratov A.B. Integration of equation of Kaup system kind with a self-consistent
source in the class of periodic functions
Status: reviewing
Abstract. In this paper, the inverse spectral problem is applied to the equation of Kaup system kind with a self-consistent
source in the class of periodic functions.
Date of submission: 25 February 2019 г.
- Shcherbina V.V. On the algebraicity of the lattice of $\tau$-closed totally $\omega$-saturated formations of finite groups
Status: reviewing
Abstract. All groups considered in the paper are assumed to be finite. The paper studies
properties of the lattice of all partially closed functorially totally saturated formations which are related to the concept of
being algebraic for a lattice of formations. We prove that for any subgroup functor $\tau$, the lattice
$l_{\omega_{\infty}}^{\tau}$ of all $\tau$-closed totally $\omega$-saturated formations is algebraic. This
generalizes results of V.G.~Safonov. In particular, we show that the lattice $l_{p_{\infty}}^{\tau}$ of all
$\tau$-closed totally $p$-saturated formations is algebraic as well as the lattice $l_{\infty}^{\tau}$ of all
$\tau$-closed totally saturated formations.
Date of submission: 12 Aprel 2019 г.
- Rakhmelevich I.V. О многомерных детерминантных дифференциально-операторных уравнениях
Status: reviewing
Abstract. We consider a class of multi-dimensional determinant differential-operator equations, the left side of which represents a determinant with the elements containing a production of linear one-dimensional differential operators of arbitrary order. The right side of the equation depends on the unknown function and its first derivatives. There are separately investigated both homogeneous and inhomogeneous determinant differential-operator equations. The theorems on decreasing of dimension of equation are prooved. The theorem on interconnection between the solutions of initial equation and the solutions of some auxiliary linear equation is prooved for the homogeneous equation. Also there is obtained the solution of the homogeneous equation for the case when the linear differential operators containing in it, have proportional eigenvalues. There are received the solutions of travelling wave type, the solutions in the form of generalized monomials, and also the solutions expressed through the eigenfunctions of linear operators containing in the equation and the solutions expressed through the functions belong to the kernels of these operators.
Date of submission: 22 Aprel 2019 г.
- Allahverdiev B.P., Tuna H. Existence of the solutions for a nonlinear singular $q$-Sturm-Liouville problems
Status: reviewing
Abstract. In this paper, we investigate a nonlinear $q$-Sturm-Liouville prob-
lem on the semi in…nite interval in which the limit-circle case holds at
in…nity for $q$-Sturm-Liouville expression. We show the existence and
uniqueness of the solutions for this problem.
Date of submission: 24 Aprel 2019 г.
- Bichegkuev M.S. Почти периодические на бесконечности решения интегро-дифференциальных уравнений с необратимым оператором при производной
Status: reviewing
Abstract. The spectral conditions of almost periodicity at infinity for bounded solutions of integro-differential equations with an irreversible operator at the derivative are obtained. The main results of the article are obtained on the basis of the use of the spectral theory of operator beams and methods of harmonic analysis. Applications to nonlinear differential equations are given.
Date of submission: 30 Aprel 2019 г.
- AZARI Y., MESGARANI H., NIKAZAD T. SELF-REGULARIZATION PROPERTY OF LANDWEBER-TYPE
ITERATIVE METHODS AND ITS APPLICATION FOR SOLVING
ILL-POSED INTEGRAL EQUATIONS
Status: reviewing
Abstract. We consider Fredholm integral equation of the first kind that is intrinsically ill-
posed inverse problem. Due to the ill-posedness of the problem, numerical solutions are very
sensitive to perturbations and noises. These kinds of perturbations come from observation,
measuring and rounding errors. Therefore, in practical applications our problem is always
accompanied by noise. Hence the classical numerical methods, such as LU, QR and Cholesky
factorizations, are failed to compute an appropriate solution. The regularization methods are
well-known for solving these problems. We use Landweber-type iterative method and present its
self-regularization property. Furthermore, we present a necessary and sufficient condition for the
convergence analysis of the iterative method. The performance of the method is confirmed by
four examples taken from Fredholm integral equation of the first kind. The efficiency, accuracy,
and usefulness of the suggested method are illustrated by using numerical examples.
Date of submission: 29 May 2019 г.
- AZARI Y., MESGARANI H., NIKAZAD T. A NEW ITERATIVE APPROACH FOR SOLVING ILL-POSED PROBLEMS
Status: reviewing
Abstract. Landweber-type methods are commonly applied to large-scale systems as an iter-
ative method. However, there is no idea for initial iterate of the method and typically, it sets
zero vector in the literature. In this paper, we use an inexpensive approach to compute initial
iterate by combining the Golub-Kahan bidiagonalization and Tikhonov regularization method
that improves the results of the component averaging (CAV) method and gives faster results.
Furthermore, we present a necessary and sufficient condition for the convergence analysis of the
iterative method. The new method easily applied to a variety of ill-posed problems affected by
noise. Numerical experiments illustrate the performance of our iterative algorithms compared to
the standard CAV method with fixed relaxation parameter and different strategy of relaxation
parameter as well as modulus-based iterative methods for constrained Tikhonov regularization
(MBI method).
Date of submission: 29 May 2019 г.
- Rathod A. Uniqueness and Value Sharing of Meromomorphic
Functions on Annuli
Status: reviewing
Abstract. In this paper, we study meromorphic functions that share only one
value on annuli and prove the following results. Let f(z) and g(z) two non
constant meromorphic functions on annli and For n ≥ 11, if f n f 0 and g n g 0
share the same nonzero and finite value a with the same multiplicities on an-
nuli, then f ≡ dg or g = c 1 e cz and f = c 2 e −cz , where d is an (n + 1) th root of
unity, c, c 1 and c 2 being constants.
Date of submission: 04 June 2019 г.
- Rathod A. Uniqueness Theorems for Meromorphic Functions on Annuli
Status: reviewing
Abstract. In this paper, we discuss the uniqueness problems of meromorphic func-
tions on annuli, we prove a general theorem on the uniqueness of meromorphic
functions on annuli and from which an analog of Nevanlinna’s famous five-value
theorem is proposed.
Date of submission: 04 June 2019 г.
- Ishkin Kh.K., Marvanov R.I. Критерий эквивалентности двух асимптотических формул
Status: reviewing
Abstract. Исследуются условия эквивалентности двух асимптотических формул для произвольной неубывающей неограниченной последовательности $\{\lambda_n\}$. Получены две теоремы, доставляющие необходимое и достаточное условие на функцию $g$ или последовательность $\{f_n\}$, при котором одна из асимптотических формул $\lambda_n\sim f(n),\ n\to+\infty,$ или $N(\lambda)\sim g(\lambda), $ $ \lambda\to+\infty$, влечет другую.
Date of submission: 20 June 2019 г.
- Fedotov A.I. On the asymptotic convergence of the polynomial collocation
method for one class of singular integro-differential equations.
Status: accepted в т.0 №0
Abstract. For one class of singular integro-differential equations on the interval the polynomial collocation method is justified. For the justification the technic of reducing the polynomial collocation method to Galerkin method is used. This technic was first used by the author to justify the polynomial collocation method for the wide class of periodic singular integro-differential and pseudo-differential equations. Now for the first time this technic is used for the non-periodic case. It became possible due to the lemma, proved in this article by the author, that the interpolative Lagrange operator is bounded in the Sobolev spaces with the Chebyshev weight-function of the second kind. Just this result gives an opportunity to show that in non-periodic Sobolev spaces the poly-nomial collocation method converges to the exact solution with the same speed as Galerkin method.
Date of submission: 24 June 2019 г.
- Shaikhullina P.A. Sectorial normalization of simplest germs of semihyperbolic maps in half-neighborhood
Status: reviewing
Abstract. There are considered the problem of analytical classification of the semi-hyperbolic maps by example of the simplest class of such germs on the plane (namely, the class of germs that are formally equivalent of 1-time shift of vector field $x^2\frac{\partial}{\partial x}+e^{\lambda}y\frac{\partial}{\partial y},~\lambda\in\mathbb{R}_+$). The theorem of sectorial normalization of such germs in semi-neighborhood in which is not exist a central manifold is proved. Also it's proved that the semi-formal normalizing map is asymptotic for the sectorial analytic normalizing map.
Date of submission: 25 June 2019 г.
- Baishya K.K., BISWAS A., Das S. $\eta$-RICCI SOLITONS ON KENMOTSU MANIFOLDS ADMITTING GENERALIZED TANAKA WEBSTER-CONNECTION
Status: reviewing
Abstract. The object of the present paper is to study Ricci soli-
tons with respect to generalized Tanaka-Webster connection [briefly
(GT-W)] in Kenmotsu manifolds under some conditions and deter-
mine the behaviour of Ricci soliton when the potential vector field
V is pointwise collinear with the characteristic vector field ξ. Hav-
ing found some incorrect results in ([1], [2], [3]), we attempt to
rectify them.
Date of submission: 16 July 2019 г.
- МАСТАЛИЕВ R.O. ОСОБЫЕ УПРАВЛЕНИЯ В СТОХАСТИЧЕСКИХ СИСТЕМАХ С ЗАПАЗДЫВАНИЕМ
Status: reviewing
Abstract. Рассматривается задача оптимального управления, в который состояние процессы определяется систем стохастических дифференциальных уравнений Ито с запаздывающим аргументом. На основе вариаций управления установлены новые необходимые условия оптимальности особых управлений в процессах, описываемых системой стохастических дифференциальных уравнений с запаздывающим аргументом.
Date of submission: 17 July 2019 г.
- MANJULAMMA U., Nagaraja H.G. Almost Kenmotsu manifolds
Status: reviewing
Abstract. The object of this paper is to study almost Kenmotsu manifolds
with characteristic vector field ξ belonging to (k,µ)
0 -nullity distribution.
We prove that these manifolds reduce to Kenmotsu manifolds with scalar
curvature -1. Further we establish the relations among the associated 1-
forms and proved the conditons under which gradient Ricci almost soliton
reduces to gradient Ricci soliton.
Date of submission: 21 July 2019 г.
- Chernov A.V. О СОХРАНЕНИИ ГЛОБАЛЬНОЙ РАЗРЕШИМОСТИ
УПРАВЛЯЕМОГО ОПЕРАТОРНОГО УРАВНЕНИЯ ВТОРОГО РОДА.
Status: reviewing
Abstract. For a controlled evolutionary operator equation of the second kind
in a Banach space we obtain sufficient conditions for
the preservation of global solvability under small
(with respect to the right-hand side increment with a fixed state)
control variations.
As examples we investigate the preservation of global solvability for
the nonlinear Navier--Stokes system,
the Benjamin--Bona--Mahony--Burgers
equation, and also for certain strongly nonlinear
pseudoparabolic equations.
Date of submission: 27 Avgust 2019 г.
- Iskhokov S.A., Rakhmonov B.A. On solvability and smoothness of a solution of the variational Dirichlet problem in the whole space
associated with a noncoercive form
Status: reviewing
Abstract. We study the Variational Dirichlet problem for a class of higher order degenerate elliptic operators in the whole $n$-dimensional Euclidean space. A theorem on unique solvability of the problem is proved and under some additional condition on smoothness of coefficients and the right-hand side of the equation, differential properties of the solution are studied. A case when a solution of the variational Dirichlet problem stabilizes to a given polynomial at infinity. Formulation of the problem under consideration is connected with integro-differential sesquilinear form that may not satisfy the coercitivity condition.
Date of submission: 02 September 2019 г.
- Falaleev M.V. Fundamental Operator-functions of Integro-Differential Operators Under Spectral or Polynomial Constraints
Status: reviewing
Abstract. This paper investigates the Cauchy problem for a degenerate high order integro-differential equation in Banach spaces. For the equations under study, the corresponding fundamental operator functions are constructed, with the help of which the only generalized solution of the original Cauchy problem in the class of distributions with a left-bounded carrier is restored. The analysis of the resulting generalized solution allows us to investigate the solvability problem in the classical sense. The fundamental operator-function is constructed in terms of the theory of semigroups of operators with kernels. Abstract results are illustrated by examples of initial-boundary value problems of viscoelasticity theory.
Date of submission: 25 September 2019 г.
- Nazarov M., Mukhamadiev E.M. Regularity of almost periodic solutions of Poisson's equation
Status: reviewing
Abstract. The paper discusses almost periodic solutions of the Poisson's
equation $-\Delta u = f$ in $\mR^n$, where $f$ is an almost periodic
function. It is proven that if $u$ is {\em a bounded generalized
solution} of the Poisson's equation, then $u$ and its
partial derivatives $\p u/ \p x_i$ are continuous, bounded and
almost periodic functions.
Date of submission: 28 September 2019 г.
- Halim B., Senouci A., Sofrani M. Some Chebyshev type Inequalities for a certain integral operator
Status: reviewing
Abstract. In this work,
some weighted Chebyshev type inequalities are obtained by using a more general fractional integral operator, than the Riemann-Liouvile one.
Date of submission: 30 September 2019 г.
- Garif'yanov F.N., Strezhneva E.V. On the moment problem for entire functions generated by a doubly periodic group
Status: reviewing
Abstract. The lacunar problem of Stieltjes moments with exponential weight is considered. The solution is sought in the class of entire functions of exponential type, the indicator diagram of which is a certain square. Nontrivial solutions of the corresponding homogeneous problem are constructed. This problem boils down to the study of a linear total equation in the class of functions holomorphic outside four squares. At infinity, they have zero multiplicities of at least three. Their boundary values ??satisfy the Holder condition on any compactum that does not contain square vertices. At the vertices, at most, logarithmic features are allowed. The solution is sought in the form of an integral of Cauchy type with an unknown density along the boundary of these squares. A method for regularizing the total equation is proposed. The condition of equivalence of this regularization is clarified. Particular cases are highlighted when the obtained Fredholm equation of the second kind is solvable. For this, the principle of compressive mappings in a Banach space is used.
Date of submission: 09 October 2019 г.
- HEIDARI TAVANI M.R., NAZARI A. TRIPLE WEAK SOLUTIONS FOR THREE-POINT BOUNDARY VALUE
PROBLEMS OF KIRCHHOFF-TYPE
Status: reviewing
Abstract. In this paper , we establish the existence of at least three positive weak
solutions for a perturbed three-point boundary value problem of Kirchhoff-type. The
approach is based on variational methods and critical point theory. As applications of these
methods, we get several multiplicity results for the problems under consideration. Are
presented the results were extention of some existing results.
Date of submission: 18 October 2019 г.
- Mirsaburov M., KHurramov N. KH. Problem for the Gellerstedtequation with singular coefficient with the Bicadze-Samarskiy condition on the characteristics of one family and the common joint conditions on the degeneration line
Status: reviewing
Abstract. For the Gellerstedt equation with singular coefficient, we prove the theoremsof uniqueness and existence of the solution of the problem with local and nonlocal conditions on parts of the boundary characteristics and with disconnecting conditions of gluing on the degeneration line
Date of submission: 19 October 2019 г.
- Dyavanal R.S., Muttagi J.B. Growth of a solution of a difference-differential equation generated by derivatives of shifts and q-shifts of a meromorphic function
Status: reviewing
Abstract. In this paper, we prove Clunie lemmas for a polynomial generated by shifts, q-shifts of a meromorphic function and their derivatives which in turn allow us to study the growth of a solution of larger class of difference-differential equations. The results obtained in this paper generalize earlier results on clunie lemmas.
Date of submission: 22 October 2019 г.
- ZUBELEVICH O. ON EXISTENCE OF COINCIDENCE POINTS FOR
MAPPINGS IN BANACH SPACES
Status: reviewing
Abstract. In this article we prove an existence theorem for co-
incidence points of mappings in Banach spaces. This theorem gen-
eralizes the Kantorovich fixed point theorem.
Date of submission: 23 October 2019 г.
- Mirzaev O.E., Khasanov A.B. О семейства изоспектральных краевых задачи Штурма-Лиувилля
Status: reviewing
Abstract. In this paper is presented an algorithm for constructing a family of different Sturm-Liouville boundary-value problems whith a same spectrum.
Date of submission: 24 October 2019 г.
- Khasanov A.B., Khasanov T.G. Интегрирование нагруженного уравнения Кортевега-де Фриза с источником в классе периодических функций
Status: reviewing
Abstract. In this paper, the method of the inverse spectral problem is applied to the integration of the loaded Korteweg-de Vries equation with source in the class of periodic functions.
Date of submission: 24 October 2019 г.
- Volchkov V.V., Volchkov V.V. An overdetermined boundary Neumann problem on unbounded domains
Status: reviewing
Abstract. The study of overdetermined boundary value problems for elliptic partial differential equations was
initiated by D.~Serrin in 1971. In his work, he established the property of radial symmetry for
solutions of some overdetermined Poisson problem. In addition to significant independent interest,
problems of this type have important applications in potential theory, integral geometry,
hydrodynamics, electrostatics, and the theory of capillarity. Usually their the solution is based
on the maximum principle, the Hopf lemma on an angular boundary point and the method of moving
hyperplanes introduced by A.D.~Alexandrov to study some geometric problems associated with the
characterization of spheres. Among other, more modern methods that do not use the maximum
principle in the problems under consideration, we note the duality method, the volume derivative
method, and also the integral method.
This article discusses the overdetermined Neumann problem for the Laplace equation $\Delta f = 0$ on flat
unbounded domains. It is shown that under certain conditions (see Theorem~\ref{th 1} in Section~1) such a
problem is solvable only for the exterior of the circle. A distinctive feature of Theorem~\ref{th 1} is
that for the first time in such problems an exact condition is obtained for the growth of
$f$
at infinity. In addition, as can be seen from Theorem~\ref{th 2} in Section~2, other conditions in
Theorem~\ref{th 1} are also necessary. In contrast to the works of predecessors, the proof of Theorem~\ref{th 1}
uses some boundary properties of conformal mappings, the V.I.~Smirnov theorem on functions of
the class $H_p$, and the Fejer-Riesz theorem on non-negative trigonometric polynomials.
Date of submission: 31 October 2019 г.
- Dagli M.C. Some relations on certain Hardy sums and two-term exponential sums
Status: reviewing
Abstract. In this paper, we deal with a computational problem of one kind mean value
involving certain Hardy sums and the two-term exponential sum with the help of
the properties of Gauss sums, and derive some interesting precise
computational formulae.
Date of submission: 04 November 2019 г.
- Sacvhin V.M., Trinh P.T. Nonpotentiality of the Sobolev system and the construction of a semibounded functional
Status: reviewing
Abstract. The nonpotentiality of the operator of a boundary value problem for the Sobolev system of partial differential equations with respect to the classical bilinear form is proved. It is shown that this system does not admit a matrix variational multiplier of the given form. A semibounded functional for the given problem is constructed.
Date of submission: 10 November 2019 г.
- Zarifzoda S.Q. A Construction of exact solutions for some classes of singular partial integro-differential equations
Status: reviewing
Abstract. In this work for one class of second order model and nonmodel partial integro-differential equation with singularity in the kernel, obtained integral representation manifold solution by arbitrary functions. First of all in the given paper it is entered a new class of such functions that at point (a,b) is converted to zero with some asymptotic behavior and the solution of given equation is found in this class. Also, singular integro-differential operators are entered and main property of entered operators are learned. For these operators the inverse operators are found. It is shown that the solution of studied equation is equivalent to the solution of system of two ordinary integro-differential equations by variable x and y.
In the cases when the solution of given integro-differential equation depends of any arbitrary constant a Cauchy type problems are investigated. For the investigation of Cauchy type problems first of all the property of obtained solution studied. It is shown that, when some conditions are fulfilled the Cauchy type problems have only unique solution.
Date of submission: 20 November 2019 г.
- ALLABERGANOV O.R. Inverse Problem for Sturm-Liouville Operator with Infinite Zone Potential in the Half Line
Status: reviewing
Abstract. In the present paper it is studied inverse problem in the half line for Sturm-Liouville operator with infinite zone potential, more exactly it is derived trace formula, the formula expressing boundary conditions via spectral data and the system of Dubrowin-Trubowits differential equations.
Date of submission: 22 November 2019 г.
- Абдушукуров Ф.А. Пуассоновские предельные теоремы в схемах размещения различимых частиц
Status: reviewing
Abstract. Рассматривается случайная величина $\mu_r(n, K, N)$ - число ячеек, содержащих $r$ частиц, среди первых $K$ ячеек
в равновероятной схеме размещения не более $n$ различимых частиц по $N$ различным ячейкам. Найдены условия, обеспечивающие сходимость этих случайных величин
к пуассоновской случайной величине. Получено описание предельного распределения. Эти условия имеют наиболее простой вид, когда количество частиц $r$ принадлежит ограниченному множеству (\ref{th2}) или
$K$ эквивалентно $\sqrt{N}$ (теорема 3). Тогда случайные величины $\mu_r(n, K, N)$ ведут себя как суммы независимых одинаково распределенных индикаторов
(биномиальные случайные величины) и наши условия совпадают с условиями классической пуассоновской предельной теоремы. Получены аналоги этих теорем для равновероятной схемы размещения $n$ различимых частиц по $N$ различным ячейкам. Доказательства теорем основаны на пуассоновской предельной теореме для сумм перестановочных индикаторов и аналоге локальной предельной теореме Гнеденко.
Date of submission: 24 November 2019 г.
- Singh G., Singh G., Singh G. Certain Subclasses of Analytic Functions Defined with Generalized Sãlãgean Operator Subordinate to Bilinear Transformation
Status: reviewing
Abstract. The present investigation deals with certain subclasses of analytic-univalent functions
in the open unit disc
: 1 E z z . The coefficient estimates, distortion theorem, argument
theorem and relation of these classes with some other class have been studied and the results so
obtained generalize the results of several earlier works.
Date of submission: 26 November 2019 г.
- Egorova A.E., Khabibullin B.N. Growth of subharmonic functions along the line and distribution of their Riesz measures
Status: reviewing
Abstract. Let $u\not\equiv -\infty$ and $M\not\equiv -\infty$
are two subharmonic functions in the complex plane $\mathbb C$ with the Riesz measures $\nu_u$ and $\mu_M$ such that $u(z)\leq O(|z|)$ and $M(z)\leq O(|z|)$ as $z\to \infty$.
If the growth of this function $M$ in some sense exceeds the growth of the function $u$ on some straight line, then we can expect the measure $\mu_M$ to dominate the measure $\nu_u$ in some sense. We give quantitative forms of such dominance.
The main results are illustrated by a new uniqueness theorem for entire functions of exponential type.
Date of submission: 26 November 2019 г.
- Saba N. Al-khafaji , Ahmed Hadi Hussain , Ali A. Shukur , Ali Al-Fayadh Third Hankel and Toeplitz Determinant for Certain
Class of non-Bazilevic Functions and Pseudospectrum of Associated Toeplitz Matrix
Status: reviewing
Abstract. The main object in this paper is give an upper bound for the third determinant
of the Hankel and the Toeplitz matrices for which the entries are belong to a new introduced
certain class of non-Bazilevi? c functions N µ , analytic in the open unit disk D and associated
with exponential function.
Also, we studied so-called pseudospectrum of the Toeplitz matrix with entries belong to
the introduced class of function N µ to give a particular view about the behavior of such
matrix.
Date of submission: 04 December 2019 г.
- Lakaev S.N., Hamidov Sh.I. Пороговые эффекты в спектре одно-частичного оператора Шредингера на целочисленной решетке
Status: reviewing
Abstract. We consider a wide class of the Schrӧdinger operators describing a particle in an external field , on a - dimensional integer cubic lattice . We study the threshold effects in the spectrum of the one-particle Schrӧdinger operator , as well as the existence or absence of its bound states depending on the potential and dimension of the lattice . We found that the appearance of bound states of the operator depends on whether the threshold of its essential spectrum is a regular or singular point: namely, if the lower threshold of the essential spectrum of the operator is a regular point of its essential spectrum, then for small perturbations, the number of eigenvalues below the essential spectrum does not change, but if the lower threshold of the essential spectrum of the operator is a singular point, then for certain small perturbations the operator has eigenvalues below the essential spectrum. In addition, we obtained easily verifiable conditions for the existence of the eigenvalues of the operator lying below the essential spectrum.
Date of submission: 04 December 2019 г.
- Ashoke Das , Baishya K.K., Manoj ray bakshi $\eta$-RICCI SOLITONS ON HYPER GENERALISED PSEUDO
$\hat W$-SYMMETRIC $(LCS)_n$-MANIFOLD
Status: reviewing
Abstract. The object of the present paper aims to study the prop-
erties of ?-Ricci solitons on hyper generalized pseudo
^
W-symmetric
(LCS) n -manifold.
Date of submission: 05 December 2019 г.
- Abdollah Borhanifar , Alaeddin Malek , Sohrab Valizadeh Compact ADI method for two-dimensional
Riesz space fractional diffusion equation
Status: reviewing
Abstract. In this paper, a compact alternating direction implicit (ADI)
method has been developed for solving two-dimensional Riesz space frac-
tional diffusion equation. The precision of the discretization method
used in spatial directions is twice the order of the corresponding frac-
tional derivatives. It is proved that the proposed method is uncondi-
tionally stable via the matrix analysis method and the maximum error
in achieving convergence is discussed. Numerical example is considered
aiming to demonstrate the validity and applicability of the proposed
technique.
Date of submission: 06 December 2019 г.
- Myrzakul T.R., Tayshieva A.G., Nugmanova G.N. On the equivalence of one spin system and the two-component Kamass-Holm equation
Status: reviewing
Abstract. The work is devoted to the study of the equivalence of the two-component Camassa-Holm equation (CHE) and the spin system, which is a generalization of the Heisenberg ferromagnet equation. It is known that equivalence between nonlinear integrable equations enables an advanced search for their various exact solutions. For the CHE we apply the method of the inverse scattering problem through the system of linear partial differential equations with scalar coefficients. Compared to the CHE, the coefficients of linear systems corresponding to spin equations are related to the symmetric matrix Lax representations. There-fore when establishing equivalence between the above equations, additional difficulties arise. Based on this, the matrix Lax representation for the CHE in symmetric space is proposed. Using the result, a gauge equivalence between the two-component CHE and the spin system is established. The relationship between their solutions is shown.
Date of submission: 10 December 2019 г.
- Mukhamadiev E.M., Nazimov A.B., Naimov A.N. On the solvability a class of nonlinear equations
Status: reviewing
Abstract. В статье исследована разрешимость
одного класса нелинейных уравнений с малым параметром в
банаховом пространстве. Исследование данного класса
уравнений затруднено тем, что главная линейная часть уравнения не
обратима. Для исследования разрешимости рассматриваемого класса
уравнений применен новый метод, в котором сочетаются метод
Понтрягина из теории автономных систем на плоскости и методы
вычисления вращения векторных полей. Сформулирована и доказана
теорема об условиях разрешимости исследуемого класса нелинейных
уравнений. В качестве приложения доказаны новые теоремы о
разрешимости периодических задач для нелинейных дифференциальных
уравнений.
Date of submission: 11 December 2019 г.
- K. R. PRASAD, M. RASHMITA, N. SOLVABILITY OF HIGHER ORDER THREE-POINT
ITERATIVE SYSTEMS
Status: reviewing
Abstract. This paper is concerned to determine intervals of the eigenvalues λ 1 ,λ 2 ,· ·
·,λ m for which the iterative system of n th order three-point non-homogeneous boundary
value problem possesses a positive solution by an application of Guo–Krasnosel’skii
fixed point theorem on a cone in a Banach space.
Date of submission: 12 December 2019 г.
- Abenov M.M. The exact solutions of the Euler equations in hydrodynamics
Status: reviewing
Abstract. В статье описывается один класс массовых сил в гидродинамике, когда система дифференциальных уравнений Эйлера допускает точные решения.
Date of submission: 13 December 2019 г.