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The results of studies conducted in this paper form a complete picture of strains acquired during film growth and further processing. With comprehensive thermodynamic and crystal chemistry analysis evaluated the presence of impurities in the technological structures LaGa-YIG/GGG, and studied their effects on structural perfection of films and shows the results of data recovery X-ray analysis of full tensor strain and non-diagonal elements of the tensor distortion arising in the epitaxial heterostructure in the process of growing and with further technological processing. The presence of a large planar anisotropy of mechanical characteristics of epitaxial films that arise after cutting. Keywords: yttrium-iron garnet, epitaxial ferrite-garnet film, liquid phase epitaxy, tensor strain, misfit dislocations.

In this paper, we prove the estimates for the Jacobi transform in $L^{p}(\mathbb{R}^{+}, J^{\alpha,\beta}(x)dx)$ as applied to some classes of functions characterized by a generalized modulus of continuity.

In this paper we study the controllability of a finite dimensional system obtained by discretizing in space and time the linear 1-D Schrodinger equation with a boundary control. As for other problems, we can expect that the uniform controllability does not hold in general due to high frequency spurious modes. Based on a uniform boundary observability estimate for filtered solutions of the corresponding conservative discrete system, we show the uniform controllability of the projection of the solutions over the space generated by the remaining eigenmodes.

Let $\mathbb{N}_0$ denote the set of all non-negative integers and $\mathcal{P}(\mathbb{N}_0)$ be its power set. An integer additive set-labeling (IASL) of a graph $G$ is an injective set-valued function $f:V(G)\to\mathcal{P}(\mathbb{N}_0)\setminus\{\emptyset\}$ such that the induced function $f^+:E(G) \to \mathcal{P}(\mathbb{N}_0)\setminus \{\emptyset\}$ is defined by $f^+(uv) = f(u)+ f(v)$, where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$. A graph which has an IASL is usually called an IASL-graph. An IASL $f$ of a graph $G$ is said to be an integer additive set-indexer (IASI) of $G$ if the associated function $f^+$ is also injective. In this paper, we define the notion of integer additive set-labeling of signed graphs and discuss certain properties of signed graphs which admits certain types of integer additive set-labelings.

The purpose of the paper is to study the notion of CR-submanifold and the existence of some structures on a hypersurface of a quarter symmetric non metric connection in a quasi-Sasakian manifold. We study the existence of a Kahler structure on $M$ and the existence of a globally metric frame $f$-structure in sence of Goldberg S.I., Yano K. We discuss the integrability of distributions on $M$ and geometry of their leaves. We have tries to relate this result with those before obtained by Goldberg V., Rosca R. devoted to Sasakian manifold and conformal connections.

We consider recursive binary finite field extensions $E_{i+1} =E_{i} (x_{i+1} )$, $i\ge -1$, defined by D. Wiedemann. The main object of the paper is to give some proper divisors of the Fermat numbers $N_{i} $ that are not equal to the multiplicative order $O(x_{i} )$.

In this paper we investigate the boundedness of holomorphic functionals on a Banach space with a normalized basis $\{e_n\}$ which have a very special form $f(x)=f(0)+\sum_{n=1}^\infty c_nx_n^n$ and which we call strictly diagonal. We consider under which conditions strictly diagonal functions are entire and uniformly continuous on every ball of a fixed radius.

In this paper, we consider a generalization of almost Kenmotsu f-manifolds. We get basic Riemannian curvature, sectional curvatures and scalar curvature properties such type manifolds. Finally, we give two examples to clarify some our results.

In the paper the homomorphisms of algebras of entire functions on Banach spaces to a commutative Banach algebra are studied. In particular, it is proposed a method of constructing of homomorphisms vanishing on homogeneous polynomials of degree less or equal than a fixed number $n$.

In this paper we prove that the condition $\sum_{k=\left[\frac{n}{2}\right] }^{2n}\frac{\lambda _{k}(p)}{(|n-k|+1)^{2-p}}=o(1)\, \left(=O(1) \right),$ is a necessary condition for the $L^{p} (0

In this paper, we consider a continuous in mean square homogeneous and isotropic Gaussian random field. A criterion for testing hypotheses about the covariance function of such field using estimates for its norm in the space $L_p(\mathbb{T}), p\geq 1$ is constructed.

This paper presents the results of computer simulation of optimal dynamic modes of thermoelectric device for cryodestruction. The optimal time function for controlling the supply current to thermoelectric micromodule in a device for cryodestruction is determined, which ensures given cyclic temperature effect on the local area of human body.Keywords: computer simulation, optimal dynamic mode, cryodestruction, thermoelectric cooling.

This paper presents results of an investigation of the features of phase and structure formation of a ternary compound during thermal sintering use of compacted TiH2-Al-C powder blends. The thermal sintering was carried out in vacuum furnace at temperature 1150, 1300 and 1400 0С. The x-ray diffraction pattern and structural analysis show that the main phase after synthesis at 1150 0С is titanium carbide. The ternary Ti2AlC and intermetallic Ti3Al compound were also identified in the phase composition of the alloy. Increasing the sintering temperature to 1300 °C leads to significant increases the content of Ti2AlC ternary compounds and accordingly decrease the content of titanium carbide TiC. After synthesis at 1400 ° C, the base phase of the alloy becomes the Ti3AlC2.ternary compound. Is propose a modified model thermal synthesis of ternary compounds of the Ti-Al-C system, which includes the melting of aluminum and its interaction with titanium at low-temperature stages of the process, formation of the Ti3Al intermetallic compound, formation titanium carbide grains as a result of interaction of the Al4C3 intermediate metastable phase with titanium or Ti3Al intermetallic compound and the synthesis of ternary Ti2AlC and Ti3AlC2 compounds as a result of interaction of the Ti3Al intermetallic compound with carbon and Ti2AlC with titanium carbide TiC. Key words: MAX-phase, titanium, aluminum, powder, thermal synthesis, structure, intermetallic compound, carbide, X-ray phase analysis.

The operators of stochastic differentiation, which are closely related with the extended Skorohod stochastic integral and with the Hida stochastic derivative, play an important role in the classical (Gaussian) white noise analysis. In particular, these operators can be used in order to study properties of the extended stochastic integral and of solutions of stochastic equations with Wick-type nonlinearities. In this paper we introduce and study bounded and unbounded operators of stochastic differentiation in the Levy white noise analysis. More exactly, we consider these operators on spaces from parametrized regular rigging of the space of square integrable with respect to the measure of a Levy white noise functions, using the Lytvynov's generalization of the chaotic representation property. This gives a possibility to extend to the Levy white noise analysis and to deepen the corresponding results of the classical white noise analysis.

The algebra $\mathcal{H}_{bs}(\ell_1)$ of symmetric analytic functions of bounded type is investigated. In particular, we study continuity of some homomorphisms of the algebra of symmetric polynomials on $\ell_p$ and composition operators of the algebra of symmetric analytic functions. The paper contains several open questions.

In this paper we obtained new automorphic analogue of Baer's theorem for the case when an arbitrary subgroup $A\leq Aut(G)$ includes a group of inner automorphisms $Inn(G)$ of agroup $G$ and the factor-group $A/Inn(G)$ is co-layer-finite.

The paper found the explicit form of the fundamental solution of Cauchy problem for the equation of Kolmogorov type that has a finite number groups of spatial variables which are degenerate parabolic.

Recently, Berinde and Borcut [Berinde, V. and Borcut, M., Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011), 4889-4897] introduced the concept of tripled fixed point and by now, there are several researches on this subject, in partially metric spaces and in cone metric spaces. In this paper, we introduce the notion of stability definition of tripled fixed point iteration procedures and establish stability results for mixed monotone mappings which satisfy various contractive conditions. Our results extend and complete some existing results in the literature. An illustrative example is also given.

In this paper we study $\tau$-curvature tensor in $N(k)$-contact metric manifold. We study $\tau$-$\phi$-recurrent,$\tau$-$\phi$-symmetric and globally $\tau$-$\phi$-symmetric $N(k)$-contact metric manifold.

In this paper the heat equation with random right part is examined. In particular, we give conditions for existence with probability one of the solutions in the case when the right part is a random field, sample continuous with probability one from the Orlicz space. Estimation for the distribution of the supremum of solutions of such equations is found.

Using a generalized Dunkl translation, we obtain an analog of Theorem 5.2 in Younis' paper [2] for the Dunkl transform for functions satisfying the $(\delta, \gamma)$-Dunkl Lipschitz condition in the space $\mathrm{L}^{2}(\mathbb{R}, |x|^{2\alpha+1}dx)$.}

Let $L$ be a Levy process on $[0,+\infty)$. In particular cases, when $L$ is a Wiener or Poisson process, any square integrable random variable can be decomposed in a series of repeated stochastic integrals from nonrandom functions with respect to $L$. This property of $L$, known as the chaotic representation property (CRP), plays a very important role in the stochastic analysis. Unfortunately, for a general Levy process the CRP does not hold. There are different generalizations of the CRP for Levy processes. In particular, under the Ito's approach one decomposes a Levy process $L$ in the sum of a Gaussian process and a stochastic integral with respect to a Poisson random measure, and then uses the CRP for both terms in order to obtain a generalized CRP for $L$. The Nualart-Schoutens's approach consists in decomposition of a square integrable random variable in a series of repeated stochastic integrals from nonrandom functions with respect to so-called orthogonalized centered power jump processes, these processes are constructed with using of a cadlag version of $L$. The Lytvynov's approach is based on orthogonalization of continuous monomials in the space of square integrable random variables. In this paper we construct the extended stochastic integral with respect to a Levy process and the Hida stochastic derivative in terms of the Lytvynov's generalization of the CRP; establish some properties of these operators; and, what is most important, show that the extended stochastic integrals, constructed with use of the above-mentioned generalizations of the CRP, coincide.

In this paper, we give the strong and $\Delta$-convergence theorems of the modified $S$-iteration and the modified two-step iteration processes for total asymptotically nonexpansive mappings on a CAT(0) space. Our results extend and improve the corresponding recent results announced by many authors in the literature.

The paper contains proof of the hypercyclicity of ``symmetrictranslation'' on the algebras of block-symmetric analyticfunctions of bounded type on an isomorphic copy of $ell_1$

The paper contains proof of the hypercyclicity of “symmetric translation” on the algebras of block-symmetric analytic functions of bounded type on an isomorphic copy of $l_1$.

In the paper we study the semigroup $\mathcal{C}_{\mathbb{Z}}$ which is a generalization of the bicyclic semigroup. We describe main algebraic properties of the semigroup $\mathcal{C}_{\mathbb{Z}}$ and prove that every non-trivial congruence $\mathbb{C}$ on the semigroup $\mathcal{C}_{\mathbb{Z}}$ is a group congruence, and moreover the quotient semigroup $\mathcal{C}_{\mathbb{Z}}/\mathbb{C}$ is isomorphic to a cyclic group. Also we show that the semigroup $\mathcal{C}_{\mathbb{Z}}$ as a Hausdorff semitopological semigroup admits only the discrete topology. Next we study the closure ${cl}_T\left(\mathcal{C}_{\mathbb{Z}}\right)$ of these migroup $\mathcal{C}_{\mathbb{Z}}$ in a topological semigroup $T$. We show that the non-empty remainder of $\mathcal{C}_{\mathbb{Z}}$ in a topological inverse semigroup $T$ consists of a group of units $H(1_T)$ of $T$ and a two-sided ideal $I$ of $T$ in the case when $H(1_T)\neq\emptyset$ and $I\neq\emptyset$. In the case when $T$ is a locally compact topological inverse semigroup and $I\neq\emptyset$ we prove that an ideal $I$ is topologically isomorphic to the discrete additive group of integers and describe the topology on the subsemigroup $\mathcal{C}_{\mathbb{Z}}\cup I$. Also we show that if the group of units $H(1_T)$ of the semigroup $T$ is non-empty, then $H(1_T)$ is either singleton or $H(1_T)$ is topologically isomorphic to the discrete additive group ofintegers.

In the classical Gaussian analysis the Clark-Ocone formula allows to reconstruct an integrand if we know the Ito stochastic integral. This formula can be written in the form$$F=\mathbf EF+\int\mathbf E\big\{\partial_t F|_{\mathcal F_t}\big\}dW_t,$$where a function (a random variable) $F$ is square integrable with respect to the Gaussian measure and differentiable by Hida; $\mathbf E$ --- the expectation; $\mathbf E\big\{\circ|_{\mathcal F_t}\big\}$ --- the conditional expectation with respect to a full $\sigma$-algebra $\mathcal F_t$ that is generated by the Wiener process $W$ up to the point of time $t$; $\partial_\cdot F$ --- the Hida derivative of $F$; $\int\circ (t)dW_t$ --- the Ito stochastic integral with respect to the Wiener process.In this paper we explain how to reconstruct an integrand in the case when instead of the Gaussian measure one considers the so-called generalized Meixner measure $\mu$ (depending on parameters, $\mu$ can be the Gaussian, Poissonian, Gamma measure etc.) and obtain corresponding Clark-Ocone type formulas.

We consider the multiplicative polynomial mappings on commutative algebras in this work. We call a multiplicative polynomial trivial, if it can be represented as a product of characters. In the paper we investigate the following question: does there exists a nontrivial multiplicative polynomial functional on a commutative algebra?

The paper contains a description of sets of generators of algebra of vector-symmetric polynomials on products of Banach spaces. Some applications to complex homomorphisms of these algebras are obtained.

In this paper we consider the multidimensional $g$-fraction with nonequivalent variables which is the generalization of the continued $g$-fraction. The correspondence between the formal multiple power series and the above mentioned fraction is studied.

A map $f:X\rightarrow Y$ between topological spaces is called scatteredly continuous (pointwise discontinuous) if for each non-empty (closed) subspace $A\subset X$ the restriction $f|_{A}$ has a point of continuity. We define a map $f:X\to Y$ to be weakly discontinuous if for every non-empty subspace $A\subset X$ the set $D(f|_A)$ of discontinuity points of the restriction $f|_A$ is nowhere dense in $A$.In this paper we consider the composition, Cartesian and diagonal product of weakly discontinuous, scatteredly continuous and pointwise discontinuous maps.

In this paper we study the semigroup $\mathcal{I}_{\,\infty}^{?\nearrow}(\mathbb{N})$ of partial co-finite almost monotone bijective transformations of the set of positive integers $\mathbb{N}$. We show that the semigroup $\mathcal{I}_{\,\infty}^{?\nearrow}(\mathbb{N})$ has algebraic properties similar to the bicyclic semigroup: it is bisimple and all of its non-trivial group homomorphisms are either isomorphisms or group homomorphisms. Also we prove that every Baire topology $\tau$ on $\mathcal{I}_{\,\infty}^{?\nearrow}(\mathbb{N})$ such that $(\mathcal{I}_{\infty}^{\,?\nearrow}(\mathbb{N}),\tau)$ is a semitopological semigroup is discrete, describe the closure of $(\mathcal{I}_{\infty}^{\,?\nearrow}(\mathbb{N}),\tau)$ in a topological semigroup and construct non-discrete Hausdorff semigroup topologies on $\mathcal{I}_{\infty}^{\,?\nearrow}(\mathbb{N})$.

We consider the multiplicative polynomial mappings on commutativealgebras in this work. We call a multiplicative polynomialtrivial, if it can be represented as a product of characters. Inthe paper we investigate the following question: does there existsa nontrivial multiplicative polynomial functional on a commutativealgebra?

The paper contains a survey of the most important results about structures of spectra of algebras of analytic functions of bounded type on Banach spaces and some new results in this area. Also, we have some applications to interpolations in algebras of analytic functions on unit balls of Banach spaces.

We consider the multiplicative polynomial mappings on commutative algebras in this work. We call a multiplicative polynomial trivial, if it can be represented as a product of characters. In the paper we investigate the following question: does there exists a nontrivial multiplicative polynomial functional on a commutative algebra?

In the paper we study the semigroup $mathscr{C}_{mathbb{Z}}$which is a generalization of the bicyclic semigroup. We describemain algebraic properties of the semigroup$mathscr{C}_{mathbb{Z}}$ and prove that every non-trivialcongruence $mathfrak{C}$ on the semigroup$mathscr{C}_{mathbb{Z}}$ is a group congruence, and moreover thequotient semigroup $mathscr{C}_{mathbb{Z}}/mathfrak{C}$ isisomorphic to a cyclic group. Also we show that the semigroup$mathscr{C}_{mathbb{Z}}$ as a Hausdorff semitopological semigroupadmits only the discrete topology. Next we study the closure$operatorname{cl}_Tleft(mathscr{C}_{mathbb{Z}}ight)$ of thesemigroup $mathscr{C}_{mathbb{Z}}$ in a topological semigroup $T$.We show that the non-empty remainder of $mathscr{C}_{mathbb{Z}}$in a topological inverse semigroup $T$ consists of a group of units$H(1_T)$ of $T$ and a two-sided ideal $I$ of $T$ in the case when$H(1_T)eqvarnothing$ and $Ieqvarnothing$. In the case when $T$is a locally compact topological inverse semigroup and$Ieqvarnothing$ we prove that an ideal $I$ is topologicallyisomorphic to the discrete additive group of integers and describethe topology on the subsemigroup $mathscr{C}_{mathbb{Z}}cup I$.Also we show that if the group of units $H(1_T)$ of the semigroup$T$ is non-empty, then $H(1_T)$ is either singleton or $H(1_T)$ istopologically isomorphic to the discrete additive group ofintegers.

A map $f:Xightarrow Y$ between topological spaces is calledscatteredly continuous (pointwise discontinuous) if for eachnon-empty (closed) subspace $Asubset X$ the restriction $f|_{A}$has a point of continuity. We define a map $f:Xo Y$ to be weaklydiscontinuous if for every non-empty subspace $Asubset X$ the set$D(f|_A)$ of discontinuity points of the restriction $f|_A$ isnowhere dense in $A$.In this paper we consider the composition, Cartesian and diagonalproduct of weakly discontinuous, scatteredly continuous andpointwise discontinuous maps.

Clark-Ocone type formulas in the Meixner white noiseanalysis}%{In the classical Gaussian analysis the Clark-Ocone formula allowsto reconstruct an integrand if we know the It^ostochastic integral. This formula can be written in the form$$F=mathbf EF+intmathbf Eig{partial_t F|_{mathcal F_t}ig}dW_t,$$where a function (a random variable) $F$ is square integrable withrespect to the Gaussian measure and differentiable by Hida;$mathbf E$ --- the expectation; $mathbf Eig{circ|_{mathcalF_t}ig}$ --- the conditional expectation with respect to a full$sigma$-algebra $mathcal F_t$ that is generated by the Wienerprocess $W$ up to the point of time $t$; $partial_cdot F$ ---the Hida derivative of $F$; $intcirc (t)dW_t$ --- the It^ostochastic integral with respect to the Wiener process.In this paper we explain how to reconstruct an integrand in thecase when instead of the Gaussian measure one considers theso-called generalized Meixner measure $mu$ (depending onparameters, $mu$ can be the Gaussian, Poissonian, Gamma measureetc.) and obtain corresponding Clark-Ocone type formulas.

In this paper we study the semigroup$mathscr{I}_{infty}^{,Rsh!!!earrow}(mathbb{N})$ of partialco-finite almost monotone bijective transformations of the set ofpositive integers $mathbb{N}$. We show that the semigroup$mathscr{I}_{infty}^{,Rsh!!!earrow}(mathbb{N})$ hasalgebraic properties similar to the bicyclic semigroup: it isbisimple and all of its non-trivial group homomorphisms are eitherisomorphisms or group homomorphisms. Also we prove that every Bairetopology $au$ on$mathscr{I}_{infty}^{,Rsh!!!earrow}(mathbb{N})$ such that$(mathscr{I}_{infty}^{,Rsh!!!earrow}(mathbb{N}),au)$ isa semitopological semigroup is discrete, describe the closure of$(mathscr{I}_{infty}^{,Rsh!!!earrow}(mathbb{N}),au)$ ina topological semigroup and construct non-discrete Hausdorffsemigroup topologies on$mathscr{I}_{infty}^{,Rsh!!!earrow}(mathbb{N})$.

The paper contains a description of sets of generators of algebra of vector-symmetric polynomials on products of Banach spaces. Some applications to complex homomorphisms of these algebras are obtained.

In this paper we consider the multidimensional $g$-fraction withnonequivalent variables which is the generalization of thecontinued $g$-fraction. The correspondence between the formalmultiple power series and the above mentioned fraction isstudied.

The paper contains a survey of the most important results about structures of spectra of algebras of analytic functions of bounded type on Banach spaces and some new results in this area. Also, we have some applications to interpolations in algebras of analytic functions on unit balls of Banach spaces.