Tbilisi Mathematical Journal Articles (Project Euclid)
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The latest articles from Tbilisi Mathematical Journal on Project Euclid, a site for mathematics and statistics resources.en-usCopyright 2018 Cornell University LibraryEuclid-L@cornell.edu (Project Euclid Team)Fri, 20 Apr 2018 09:47 EDTFri, 20 Apr 2018 09:47 EDThttps://projecteuclid.org/collection/euclid/images/logo_linking_100.gifProject Euclid
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Wreaths, mixed wreaths and twisted coactions
https://projecteuclid.org/euclid.tbilisi/1524232072
<strong>Ross Street</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 10, Number 3, 1--22.</p><p><strong>Abstract:</strong><br/>
Distributive laws between two monads in a 2-category $\mathscr K$, as defined by Jon Beck in the case $\mathscr{K} = \mathrm{Cat}$, were pointed out by the author to be monads in a 2-category $\mathrm{Mnd}\mathscr{K}$ of monads. Steve Lack and the author defined wreaths to be monads in a 2-category $\mathrm{EM}\mathscr{K}$ of monads with different 2-cells from $\mathrm{Mnd}\mathscr{K}$.
Mixed distributive laws were also considered by Jon Beck, Mike Barr and, later, various others; they are comonads in $\mathrm{Mnd}\mathscr{K}$. Actually, as pointed out by John Power and Hiroshi Watanabe, there are a number of dual possibilities for mixed distributive laws.
It is natural then to consider mixed wreaths as we do in this article; they are comonads in $\mathrm{EM}\mathscr{K}$. There are also mixed opwreaths: comonads in the Kleisli construction completion $\mathrm{Kl}\mathscr{K}$ of $\mathscr{K}$. The main example studied here arises from a twisted coaction of a bimonoid on a monoid. A wreath determines a monad structure on the composite of the two endomorphisms involved; this monad is called the wreath product. For mixed wreaths, corresponding to this wreath product, is a convolution operation analogous to the convolution monoid structure on the set of morphisms from a comonoid to a monoid. In fact, wreath convolution is composition in a Kleisli-like construction. Walter Moreira’s Heisenberg product of linear endomorphisms on a Hopf algebra, is an example of such convolution, actually involving merely a mixed distributive law. Monoidality of the Kleisli-like construction is also discussed.
</p>projecteuclid.org/euclid.tbilisi/1524232072_20180420094755Fri, 20 Apr 2018 09:47 EDTProduct of Sheffer sequences: properties and exampleshttps://projecteuclid.org/euclid.tbilisi/1561082571<strong>Mumtaz Riyasat</strong>, <strong>Subuhi Khan</strong>, <strong>Shakir Shah</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 2, 101--118.</p><p><strong>Abstract:</strong><br/>
This article is written with an objective to explore the product of two Sheffer sequences. This article is an attempt to explore such type of product which extends the possibility to consider hybrid type Sheffer polynomials. It is important to remark that although this product can be viewed as the umbral composition of two Sheffer sequences but the results related to this product cannot be deduced from the results of the Sheffer sequences. The set of this product of Sheffer sequences is also a non-abelian group and thus convoluting different members of Sheffer class allows us to consider a number of hybrid type special polynomials as its members. Certain results for this class including the quasi-monomiality and determinant form are established. The article concludes with the possibility of considering the product of $n$-Sheffer sequences.
</p>projecteuclid.org/euclid.tbilisi/1561082571_20190620220255Thu, 20 Jun 2019 22:02 EDTDegree of approximation of genuine Lupaş-Durrmeyer operatorshttps://projecteuclid.org/euclid.tbilisi/1561082572<strong>Nesibe Manav</strong>, <strong>Nurhayat Ispir</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 2, 119--135.</p><p><strong>Abstract:</strong><br/>
The present paper deals with the rate of convergence of genuine type Durrmeyer operators having Lupaş-Szász type basis functions. We study some direct estimates to give the degree of approximation to continuous functions. Further, we investigate pointwise convergence for functions with derivative of bounded variations.
</p>projecteuclid.org/euclid.tbilisi/1561082572_20190620220255Thu, 20 Jun 2019 22:02 EDTSome Qi-type integral inequalities involving several weight functionshttps://projecteuclid.org/euclid.tbilisi/1561082573<strong>Jan-David Hardtke</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 2, 137--152.</p><p><strong>Abstract:</strong><br/>
We prove some integral inequalities related to Feng Qi's inequality from [ Several integral inequalities , J. Inequal. Pure Appl. Math. 1 (2000), No. 2, 7p., Article No. 19] and obtain a few corollaries.
</p>projecteuclid.org/euclid.tbilisi/1561082573_20190620220255Thu, 20 Jun 2019 22:02 EDTHigher chromatic analogues of twisted $K$-theoryhttps://projecteuclid.org/euclid.tbilisi/1561082574<strong>Mehdi Khorami</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 2, 153--162.</p><p><strong>Abstract:</strong><br/>
In this paper we introduce a new family of twisted $K(n)$-local homology theories. These theories are given by the spectra $R_n= E_n^{hS\mathbb G_n}$, twisted by a class $H\in H^{n+2}(X, \mathbb Z_p)$. Here $E_n^{hS\mathbb G_n}$ are the homotopy fixed point spectra under the action of the subgroup $S\mathbb G_n$ of the Morava stabilizer group where $S\mathbb G_n$ is the kernel of the determinant homomorphism $\text{det}:\mathbb G_n\to \mathbb Z_p^\times$. These spectra were utilized in [8] by C. Westerland to study higher chromatic analogues of the J-homomorphism. We investigate some of the properties of these new twisted theories and discuss why we consider them as a generalization of twisted $K$-theory to higher chromatic levels.
</p>projecteuclid.org/euclid.tbilisi/1561082574_20190620220255Thu, 20 Jun 2019 22:02 EDTCoefficient estimates for a general subclass of $m$-fold symmetric bi-univalent functionshttps://projecteuclid.org/euclid.tbilisi/1561082575<strong>Ahmad Motamednezhad</strong>, <strong>Safa Salehian</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 2, 163--176.</p><p><strong>Abstract:</strong><br/>
In the present paper, we introduce and investigate an interesting subclass ${\mathcal B}_{{\Sigma}_m}^{h,p}(\lambda,\gamma)$ of $m$-fold symmetric bi-univalent functions in the open unit disk $\mathbb{U}$. Furthermore, we obtain estimates on the coefficients $|a_{m+1}|$ and $|a_{2m+1}|$ for functions belonging to this subclass. The results presented in this paper would generalize and improve some recent works of several earlier authors.
</p>projecteuclid.org/euclid.tbilisi/1561082575_20190620220255Thu, 20 Jun 2019 22:02 EDTInequalities for complex rational functionshttps://projecteuclid.org/euclid.tbilisi/1561082576<strong>T. Shahmansouri</strong>, <strong>M. Bidkham</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 2, 177--185.</p><p><strong>Abstract:</strong><br/>
In this paper, we consider a class of rational functions $r(s(z))$ of degree at most $mn$, where $s(z)$ is a polynomial of degree $m$ and obtain a certain sharp compact generalization of well-known inequalities for rational functions.
</p>projecteuclid.org/euclid.tbilisi/1561082576_20190620220255Thu, 20 Jun 2019 22:02 EDTSome new $k$-fractional trapezium-like integral inequalities via generalized relative semi-$(r;m,h_{1},h_{2})$-preinvex mappings and applicationshttps://projecteuclid.org/euclid.tbilisi/1569463229<strong>Artion Kashuri</strong>, <strong>Muhammad Adil Khan</strong>, <strong>Rozana Liko</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 3, 1--19.</p><p><strong>Abstract:</strong><br/>
In this article, we first presented a new general identity concerning differentiable mappings defined on $m$-invex set via $k$-fractional integrals. By using the concept of generalized relative semi-$(r;m,h_{1},h_{2})$-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to trapezium-like integral inequalities via $k$-fractional integrals are established. It is pointed out that some new special cases can be deduced from main results of the article. Applications to special means for trapezium-like integral inequalities via $k$-fractional integrals are provided as well.
</p>projecteuclid.org/euclid.tbilisi/1569463229_20190925220040Wed, 25 Sep 2019 22:00 EDTA discrete orthogonal polynomials approach for coupled systems of nonlinear fractional order integro-differential equationshttps://projecteuclid.org/euclid.tbilisi/1569463232<strong>L. Moradi</strong>, <strong>F. Mohammadi</strong>, <strong>D. Conte</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 3, 21--38.</p><p><strong>Abstract:</strong><br/>
This paper develops a numerical approach for solving coupled systems of nonlinear fractional order integro-differential equations(NFIDE). Shifted discrete Chebyshev polynomials (SDCPs) have been introduced and their attributes have been checked. Fractional operational matrices for the orthogonal polynomials are also acquired. A numerical algorithm supported by the discrete orthogonal polynomials and operational matrices are used to approximate solution of coupled systems of NFIDE. The operational matrices of fractional integration and product are applied for approximate the unknown functions directly. These approximations were put in the coupled systems of NFIDE. A comparison has been made between the absolute error of approximate solutions of SDCPs method with previous published. The gained numerical conclusions disclose that utilizing discrete Chebyshev polynomials are more efficient in comparison to the other methods.
</p>projecteuclid.org/euclid.tbilisi/1569463232_20190925220040Wed, 25 Sep 2019 22:00 EDT$(\epsilon-\delta)$ conditions and fixed point theoremshttps://projecteuclid.org/euclid.tbilisi/1569463233<strong>Ravindra K. Bisht</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 3, 39--49.</p><p><strong>Abstract:</strong><br/>
In this paper, we prove some fixed point theorems under generalized $(\epsilon-\delta)$ type rational contractions in which the fixed point may be a point of discontinuity. Our results generalize and improve a host of well-known fixed point theorems existing in the literature. In addition to it we give a fixed point theorem for $(\epsilon-\delta)$ non-expansive mappings in metric spaces. Several examples are given to illustrate our results.
</p>projecteuclid.org/euclid.tbilisi/1569463233_20190925220040Wed, 25 Sep 2019 22:00 EDTOperator splitting method for numerical solution of modified equal width equationhttps://projecteuclid.org/euclid.tbilisi/1569463234<strong>İhsan Çelikkaya</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 3, 51--67.</p><p><strong>Abstract:</strong><br/>
In this manuscript, numerical solutions of the equations in the form of $u_{t}=Au+B(u)$ have been sought for, where $A$ and $B$ are linear and nonlinear operators, respectively. The modified equal width (MEW) equation has been converted into two sub problems. Then, the sub problems were solved according to the Strang splitting scheme by applying the cubic B-spline collocation finite element method. Thus, more accurate results of the equation MEW have been obtained than those non-splitting users. In order to test the accuracy and efficiency of the present method; single soliton, interaction of two solitons and Maxwellian initial condition pulse problems have been considered. Moreover, the stability analysis of each sub problem has been investigated by von-Neumann analysis method.
</p>projecteuclid.org/euclid.tbilisi/1569463234_20190925220040Wed, 25 Sep 2019 22:00 EDTTopological Quillen localization of structured ring spectrahttps://projecteuclid.org/euclid.tbilisi/1569463235<strong>John E. Harper</strong>, <strong>Yu Zhang</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 3, 69--91.</p><p><strong>Abstract:</strong><br/>
The aim of this short paper is two-fold: (i) to construct a $\mathsf{TQ}$-localization functor on algebras over a spectral operad $\mathcal{O}$, in the case where no connectivity assumptions are made on the $\mathcal{O}$-algebras, and (ii) more generally, to establish the associated $\mathsf{TQ}$-local homotopy theory as a left Bousfield localization of the usual model structure on $\mathcal{O}$-algebras, which itself is almost never left proper, in general. In the resulting $\mathsf{TQ}$-local homotopy theory, the ''weak equivalences'' are the $\mathsf{TQ}$-homology equivalences, where ''$\mathsf{TQ}$-homology'' is short for topological Quillen homology, which is also weakly equivalent to stabilization of $\mathcal{O}$-algebras. More generally, we establish these results for $\mathsf{TQ}$-homology with coefficients in a spectral algebra $\mathcal{A} $. A key observation, that goes back to the work of Goerss-Hopkins on moduli problems, is that the usual left properness assumption may be replaced with a strong c ofibration condition in the desired subcell lifting arguments: Our main result is that the $\mathsf{TQ}$-local homotopy theory can be established (e.g., a semi-model structure in the sense of Goerss-Hopkins and Spitzweck, that is both cofibrantly generated and simplicial) by localizing with respect to a set of strong cofibrations that are $\mathsf{TQ}$-equivalences.
</p>projecteuclid.org/euclid.tbilisi/1569463235_20190925220040Wed, 25 Sep 2019 22:00 EDTSolutions to some systems of adjointable operator equations over Hilbert $C^*$-moduleshttps://projecteuclid.org/euclid.tbilisi/1569463236<strong>Zahra Niazi Moghani</strong>, <strong>Mahnaz Khanehgir</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 3, 93--107.</p><p><strong>Abstract:</strong><br/>
In this paper, by using operator matrix techniques, we present necessary and sufficient conditions for the existence of a solution to the system of equations $AXD+FX^{*}B=C,$ $GXF^{*}+FX^{*}G^{*}=H$ for adjointable operators between Hilbert $C^*$-modules, and derive an expression for the general solution to the system. We establish necessary and sufficient conditions for the existence of a solution to the system of adjointable operator equations $AXF=H_{1},$ $CXD=H_{2},$ $BXD=H_{3}$ over Hilbert $C^*$-modules. Some of the findings of this paper extend some known results in the literature.
</p>projecteuclid.org/euclid.tbilisi/1569463236_20190925220040Wed, 25 Sep 2019 22:00 EDTExact solutions of nonlinear evolution equations using the extended modified Exp(-$\Omega (\xi )$) function methodhttps://projecteuclid.org/euclid.tbilisi/1569463237<strong>Berat Karaagac</strong>, <strong>Selcuk Kutluay</strong>, <strong>Nuri Murat Yagmurlu</strong>, <strong>Alaattin Esen</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 3, 109--119.</p><p><strong>Abstract:</strong><br/>
Obtaining exact solutions of the evolution equation is one of the very important subjects in mathematics, science and technology. For this purpose, many different methods have been constructed and developed. In this article, a new technique which is called extended modified Exp(-$\Omega (\xi )$) function method is going to be studied for seeking new exact solutions of Burger-Fisher equation and Phi Four equation. The method is capable of deriving many number of solutions. With the aid of the method, various exact solutions including trigonometric, hyperbolic and rational solutions have been obtained and using a software the graphical representation of the solutions have been presented. In conclusion, we can say that the present method can also be used for the solutions of a wide range of problems.
</p>projecteuclid.org/euclid.tbilisi/1569463237_20190925220040Wed, 25 Sep 2019 22:00 EDTOn moduli of smoothness of functions in Orlicz spaceshttps://projecteuclid.org/euclid.tbilisi/1569463238<strong>Sadulla Z. Jafarov</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 3, 121--129.</p><p><strong>Abstract:</strong><br/>
In this work the estimate about modulus of smoothness of the derivatives of the functions is obtained in Orlicz spaces. The relations between the modulus of smoothness of the functions with $n$th partial and Vallée-Poussin sums of the Fourier series in Orlicz spaces are studied.
</p>projecteuclid.org/euclid.tbilisi/1569463238_20190925220040Wed, 25 Sep 2019 22:00 EDTConnection and duplication formulas for the Boas-Buck-Appell polynomialshttps://projecteuclid.org/euclid.tbilisi/1569463239<strong>Tabinda Nahid</strong>, <strong>Subuhi Khan</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 3, 131--139.</p><p><strong>Abstract:</strong><br/>
The present paper conduct to introduce the connection and duplication formulas associated with the Boas-Buck-Appell polynomials. Examples providing the analogues results for certain members related to the Boas-Buck-Appell polynomials are considered.
</p>projecteuclid.org/euclid.tbilisi/1569463239_20190925220040Wed, 25 Sep 2019 22:00 EDTFinding hybrid relatives of the Bessel polynomialshttps://projecteuclid.org/euclid.tbilisi/1569463240<strong>Mahvish Ali</strong>, <strong>Subuhi Khan</strong>, <strong>Shakeel Ahmad Naikoo</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 3, 141--158.</p><p><strong>Abstract:</strong><br/>
In this work, the 2D-Appell and the Bessel polynomials are combined to introduce the family of the 2D-Appell-Bessel polynomials. The generating function, quasi-monomial properties, series definition and determinant form of these polynomials are established. Examples of some members belonging to this family are considered. The graphs of some hybrid special polynomials are also drawn for suitable values of the indices.
</p>projecteuclid.org/euclid.tbilisi/1569463240_20190925220040Wed, 25 Sep 2019 22:00 EDTA Lumped Galerkin finite element method for the generalized Hirota-Satsuma coupled KdV and coupled MKdV equationshttps://projecteuclid.org/euclid.tbilisi/1569463241<strong>Nuri Murat Yagmurlu</strong>, <strong>Berat Karaagac</strong>, <strong>Alaattin Esen</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 3, 159--173.</p><p><strong>Abstract:</strong><br/>
In the present study, a Lumped Galerkin finite element method using quadratic B-splines has been applied to the generalized Hirota-Satsuma coupled Korteweg de Vries (KdV) and coupled modified Korteweg-de Vries (mKdV) equations. The numerical solutions of discretized equations using Lumped Galerkin finite element method have been obtained using the fourth order Runge-Kutta method which is widely used for the solution of ordinary differential equation system. The numerical solutions obtained for various space and time values have been compared with exact ones using the error norms $L_{2}$ and $L_{\infty}$. Lumped Galerkin finite element method is an effective one which can be applied to a wide range of nonlinear evolution equations.
</p>projecteuclid.org/euclid.tbilisi/1569463241_20190925220040Wed, 25 Sep 2019 22:00 EDTStability and non-stability of generalized radical cubic functional equation in quasi-$\beta$-Banach spaceshttps://projecteuclid.org/euclid.tbilisi/1569463242<strong>Iz-iddine EL-Fassi</strong>, <strong>John Michael Rassias</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 3, 175--190.</p><p><strong>Abstract:</strong><br/>
The object of this paper is to solve the generalized radical cubic functional equation, and discuss the stability problem in quasi-$\beta$-Banach spaces and then the stability by using subadditive and subquadratic functions in ($\beta, p$)-Banach spaces for the generalized radical cubic functional equation. Also certain non-stability results are investigated via specific counterexamples. Our results are generalization of the main results which are established by Z. Alizadeh and A. G. Ghazanfari in 2016.
</p>projecteuclid.org/euclid.tbilisi/1569463242_20190925220040Wed, 25 Sep 2019 22:00 EDTOn $(4, 5)$-regular bipartitions with odd parts distincthttps://projecteuclid.org/euclid.tbilisi/1569463243<strong>M. S. Mahadeva Naika</strong>, <strong>T. Harishkumar</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 3, 191--208.</p><p><strong>Abstract:</strong><br/>
In his work, K. Alladi considered the partition function $pod(n)$, the number of partitions of an integer $n$ with odd parts distinct (the even parts are unrestricted). He obtained a series expansion for the product generating function of these partitions. Later Hirschhorn and Sellers obtained some internal congruences involving the infinite families and Ramanujan's type congruences for $pod(n)$. Let $B_{4, 5}(n)$ denote the number of $(4, 5)$-regular bipartitions of a positive integer $n$ with odd parts distinct. In this paper, we establish many infinite families of congruences modulo powers of $2$ for $B_{4, 5}(n)$.
</p>projecteuclid.org/euclid.tbilisi/1569463243_20190925220040Wed, 25 Sep 2019 22:00 EDTCompact and matrix operators on the space $\left\vert A_{f}^{\theta }\right\vert _{k}$https://projecteuclid.org/euclid.tbilisi/1578020563<strong>Fadime Gökçe</strong>, <strong>G. Canan Hazar Güleç</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 4, 1--13.</p><p><strong>Abstract:</strong><br/>
In this study, we introduce a new space $\left\vert A_{f}^{\theta}\right\vert_{k}$ by using factorable matrix and investigate its certain topological and algebraic structures where $\theta$ is a positive sequence. Also, we characterize some matrix operators on this space and determine their norms and the Hausdorff measure of noncompactness. In the particular case, we get some well known results.
</p>projecteuclid.org/euclid.tbilisi/1578020563_20200102220301Thu, 02 Jan 2020 22:03 ESTStabilities of various multiplicative inverse functional equationshttps://projecteuclid.org/euclid.tbilisi/1578020564<strong>B. V. Senthil Kumar</strong>, <strong>J. M. Rassias</strong>, <strong>S. Sabarinathan</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 4, 15--28.</p><p><strong>Abstract:</strong><br/>
This study deals with the validation of classical stabilities of various multiplicative inverse functional equations pertinent to Ulam stability theory of functional equations in the setting of non-Archimedean fields. Suitable counter-examples are demonstrated to disprove the invalidity of stability results of these equations for singular cases.
</p>projecteuclid.org/euclid.tbilisi/1578020564_20200102220301Thu, 02 Jan 2020 22:03 ESTSufficient conditions for infinite series by absolute $\varphi$-product summable factorhttps://projecteuclid.org/euclid.tbilisi/1578020565<strong>Smita Sonker</strong>, <strong>Alka Munjal</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 4, 29--41.</p><p><strong>Abstract:</strong><br/>
Absolute Cesàro-Riesz summability method has been introduced and later on used to established a theorem containing least set of sufficient conditions for absolute $\varphi$-Cesàro-Riesz summable factor of an infinite series. The result has also been validated with the published literature on $ \varphi-|\bar{N}, p_n|_k$ summable factor by reducing certain conditions in the presented result.
</p>projecteuclid.org/euclid.tbilisi/1578020565_20200102220301Thu, 02 Jan 2020 22:03 ESTFinding hybrid families of special matrix polynomials associated with Sheffer sequenceshttps://projecteuclid.org/euclid.tbilisi/1578020566<strong>Ghazala Yasmin</strong>, <strong>Shahid Ahmad Wani</strong>, <strong>Hibah Islahi</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 4, 43--59.</p><p><strong>Abstract:</strong><br/>
In this paper, three index three variable Hermite matrix based Sheffer polynomials (3I3VHMSP) are introduced by algebraic decomposition of exponential operators. The operational methods combined with the monomiality principle can be used to introduce 3I3VHMSP and also to establish rules of operational nature, framing the special polynomials within the context of particular solutions of generalized forms of partial differential equations of evolution type. The Appell and Sheffer sequences along with the operational formalism offer a powerful tool for investigation of the properties of a wide class of polynomials. Further, operational representation providing connections between 3I3VHMSP families and the known special polynomials are established, which are used to derive new identities and the results for the members of these new families. The approach presented is general.
</p>projecteuclid.org/euclid.tbilisi/1578020566_20200102220301Thu, 02 Jan 2020 22:03 ESTBlow up, exponential growth of solution for a reaction-diffusion equation with multiple nonlinearitieshttps://projecteuclid.org/euclid.tbilisi/1578020567<strong>Erhan Pişkin</strong>, <strong>Fatma Ekinci</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 4, 61--70.</p><p><strong>Abstract:</strong><br/>
In this paper, we consider a reaction diffusion equation with multiple nonlinearities. We prove a blow up and exponential growth of solution with negative initial energy. Our new results generalizes and improves earlier results.
</p>projecteuclid.org/euclid.tbilisi/1578020567_20200102220301Thu, 02 Jan 2020 22:03 ESTOn a fourth order rational difference equationhttps://projecteuclid.org/euclid.tbilisi/1578020568<strong>R. Abo-Zeid</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 4, 71--79.</p><p><strong>Abstract:</strong><br/>
In this paper, we determine and study the behavior of all admissible solutions of the difference equation $$x_{n+1}=\frac{x_{n}x_{n-2}}{ax_{n-2}+ bx_{n-3}},\quad n=0,1,\ldots,$$ where $a,b$ are positive real numbers and the initial conditions $ x_{-3},x_{-2},x_{-1},x_0$ are real numbers. We show when $a=b=1$ that, every admissible solution converges to $0$.
</p>projecteuclid.org/euclid.tbilisi/1578020568_20200102220301Thu, 02 Jan 2020 22:03 ESTUniqueness of a differential polynomial and a differential monomial sharing a small functionhttps://projecteuclid.org/euclid.tbilisi/1578020569<strong>Harina P. Waghamore</strong>, <strong>Ramya Maligi</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 4, 81--96.</p><p><strong>Abstract:</strong><br/>
In this paper, we study the uniqueness of a differential polynomial and monomial sharing a small function with finite weight and obtain two theorems which extend and improves the results of Harina P. Waghamore and Husna V [6].
</p>projecteuclid.org/euclid.tbilisi/1578020569_20200102220301Thu, 02 Jan 2020 22:03 ESTRevisiting Meir-Keeler type fixed operators on Branciari distance spacehttps://projecteuclid.org/euclid.tbilisi/1578020570<strong>Andreea Fulga</strong>, <strong>Erdal Karapinar</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 4, 97--110.</p><p><strong>Abstract:</strong><br/>
In this paper, we are revisiting Meir-Keeler type fixed operators in the setting of Branciari distance space. The presented results improve and generalize several existing results in the literature. We consider an example to illustrate our result.
</p>projecteuclid.org/euclid.tbilisi/1578020570_20200102220301Thu, 02 Jan 2020 22:03 ESTSome properties of the pseudo-Chebyshev polynomials of half-integer degreehttps://projecteuclid.org/euclid.tbilisi/1578020571<strong>Primo Brandi</strong>, <strong>Paolo Emilio Ricci</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 4, 111--121.</p><p><strong>Abstract:</strong><br/>
New sets of orthogonal functions, derived from the first and second kind Chebyshev polynomials, considering half-integer indexes, have been recently introduced. In this article several properties of these new sets are considered and the links with the classical Chebyshev polynomials are underlined.
</p>projecteuclid.org/euclid.tbilisi/1578020571_20200102220301Thu, 02 Jan 2020 22:03 ESTThe Hilali conjecture on product of spaceshttps://projecteuclid.org/euclid.tbilisi/1578020572<strong>Shoji Yokura</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 4, 123--129.</p><p><strong>Abstract:</strong><br/>
The Hilali conjecture claims that a simply connected rationally elliptic space $X$ satisfies the inequality $\dim (\pi_*(X)\otimes \mathbb{Q} ) \leqq \dim H_*(X;\mathbb{Q} )$. In this paper we show that for any such space $X$ there exists a positive integer $n_0$ such that for any $n \geqq n_0$ the strict inequality $\dim (\pi_*(X^n)\otimes \mathbb{Q} ) \lt \dim H_*(X^n; \mathbb{Q} )$ holds, where $X^{n}$ is the product of $n$ copies of $X$.
</p>projecteuclid.org/euclid.tbilisi/1578020572_20200102220301Thu, 02 Jan 2020 22:03 ESTAn efficient method for solving nonlinear time-fractional wave-like equations with variable coefficientshttps://projecteuclid.org/euclid.tbilisi/1578020573<strong>Ali Khalouta</strong>, <strong>Abdelouahab Kadem</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 4, 131--147.</p><p><strong>Abstract:</strong><br/>
In this paper, fractional residual power series method (FRPSM) is effectively applied for finding the approximate analytical solutions of general nonlinear time-fractional wave-like equations with variable coefficients. This method based on constructing series solutions in a form of rapidly convergent series with easily computable components and without need of linearization, discretization, perturbation or unrealistic assumptions. Numerical results are given and then they are compared with the exact solutions both numerically and graphically. By numerical examples, it is shown that the FRPSM is very simple, efficient and convenient for solving different forms of nonlinear fractional partial differential equations.
</p>projecteuclid.org/euclid.tbilisi/1578020573_20200102220301Thu, 02 Jan 2020 22:03 ESTBlow-up solutions of a time-fractional diffusion equation with variable exponentshttps://projecteuclid.org/euclid.tbilisi/1578020574<strong>J. Manimaran</strong>, <strong>L. Shangerganesh</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 4, 149--157.</p><p><strong>Abstract:</strong><br/>
In this paper, we investigate the blow-up of solutions of a time-fractional nonlocal reaction-diffusion equation with variable exponents under the Dirichlet boundary condition. We prove the existence of a solution using the Banach fixed point theorem. Finally, we estimate the blow-up of solutions of the considered model using the Kaplan method.
</p>projecteuclid.org/euclid.tbilisi/1578020574_20200102220301Thu, 02 Jan 2020 22:03 ESTSome new refinement of Hermite-Hadamard type inequalities and their applicationshttps://projecteuclid.org/euclid.tbilisi/1578020575<strong>Artion Kashuri</strong>, <strong>Rozana Liko</strong>, <strong>Silvestru Sever Dragomir</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 4, 159--188.</p><p><strong>Abstract:</strong><br/>
In this paper first, we prove some new refinement of Hermite-Hadamard type inequalities for the convex function $f$. Second, by using five new integral identities, we present some new Riemann-Liouville fractional trapezoid and midpoint type inequalities. Third, using these results, we present applications to $f$-divergence measures. At the end, some new bounds for special means of different positive real numbers and new error estimates for the trapezoidal and midpoint formula are provided as well. These results give us the generalizations and improvements of the earlier results.
</p>projecteuclid.org/euclid.tbilisi/1578020575_20200102220301Thu, 02 Jan 2020 22:03 ESTSome properties of q-Bernstein-Durrmeyer operatorshttps://projecteuclid.org/euclid.tbilisi/1578020576<strong>Harun Karsli</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 4, 189--204.</p><p><strong>Abstract:</strong><br/>
In the present paper we shall investigate the pointwise approximation properties of the q analogue of the Bernstein-Durrmeyer operators and estimate the rate of pointwise convergence of these operators to the functions $f$ whose q-derivatives are bounded variation on the interval $[0,1]$. We give an estimate for the rate of convergence of the operator $\left( L_{n,q}f \right)$ at those points $x$ at which the one sided q-derivatives $ D_{q}^{+}f(x),D_{q}^{-} f(x)$ exist. We shall also prove that the operators $L_{n,q}f$ converges to the limit $f(x).$ To the best of my knowledge, the present study will be the first study on the approximation of q- operators in the space of $D_{q}BV$.
</p>projecteuclid.org/euclid.tbilisi/1578020576_20200102220301Thu, 02 Jan 2020 22:03 ESTSolution to time fractional non homogeneous first order PDE with non constant coefficientshttps://projecteuclid.org/euclid.tbilisi/1578020577<strong>Arman Aghili</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 4, 205--211.</p><p><strong>Abstract:</strong><br/>
In this study, the author used the joint Fourier- Laplace transform to solve non-homogeneous time fractional first order partial differential equation with non-constant coefficients. Constructive examples are also provided throughout the paper. It is a remarkable feature of the first order fractional differential equations that a procedure can be developed for solving this equation, regardless of its complexity.
</p>projecteuclid.org/euclid.tbilisi/1578020577_20200102220301Thu, 02 Jan 2020 22:03 ESTA note on the spherical images of W-partially null curves in Minkowski space-time $\mathbb{E}_{1}^{4}$https://projecteuclid.org/euclid.tbilisi/1578020578<strong>Yasin Ünlütürk</strong>, <strong>Zeynelabidin Karakaş</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 4, 213--225.</p><p><strong>Abstract:</strong><br/>
In this study, we investigate the tangent, principal normal and trinormal spherical images of a W-partially null curve in pseudohyperbolic space $\mathbb{H}_{0}^{3}$ of Minkowski space time $\mathbb{E}_{1}^{4}$. The tangent, principal normal spherical images of a W-partially null curve occur as spacelike curves lying in pseudosphere $\mathbb{S}_{0}^{3}$, then the Frenet-Serret invariants of the mentioned image curves are obtained in terms of the invariants of W-partially null curve. The trinormal spherical images of a W-partially null curve occur as spacelike curves lying in pseudohyperbolic space $\mathbb{H}_{0}^{3}$, then the Frenet-Serret invariants of the mentioned image curves are obtained in terms of the invariants of W-partially null curve. Finally, we give some characterizations of the spherical images being helices.
</p>projecteuclid.org/euclid.tbilisi/1578020578_20200102220301Thu, 02 Jan 2020 22:03 ESTResults on entire and meromorphic functions that share small function with their homogeneous and linear differential polynomialshttps://projecteuclid.org/euclid.tbilisi/1578020579<strong>Subhas S. Bhoosnurmath</strong>, <strong>N. Shilpa</strong>, <strong>Mahesh Barki</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 4, 227--236.</p><p><strong>Abstract:</strong><br/>
Using the results of S. S. Bhoosnurmath, we mainly study the uniqueness of entire and meromorphic functions that share small functions with their homogeneous and linear differential polynomials. In this paper, we obtain significant improvements and generalizations of the results of H. X. Yi.
</p>projecteuclid.org/euclid.tbilisi/1578020579_20200102220301Thu, 02 Jan 2020 22:03 ESTOn embeddings of grand grand Sobolev-Morrey spaces with dominant mixed derivativeshttps://projecteuclid.org/euclid.tbilisi/1585015215<strong>Alik M. Najafov</strong>, <strong>Rovshan F. Babayev</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 13, Number 1, 1--10.</p><p><strong>Abstract:</strong><br/>
In this paper it is constructed a new grand grand Sobolev-Morrey $S_{p),\varkappa ),a,\alpha }^{l}W(G)$ spaces with dominant mixed derivatives. With help integral representation of generalized mixed derivatives of functions, defined on $n$-dimensional domains satisfying flexible horn condition, an embedding theorem is proved. In other works, the embedding theorem is proved in these spaces and belonging of the generalized mixed derivatives of functions from these spaces to the Holder class, was studied.
</p>projecteuclid.org/euclid.tbilisi/1585015215_20200323220019Mon, 23 Mar 2020 22:00 EDTAttainable set of a $SIR$ epidemiological model with constraints on vaccination and treatment stockshttps://projecteuclid.org/euclid.tbilisi/1585015216<strong>A. S. Nazlipinar</strong>, <strong>B. Basturk</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 13, Number 1, 11--22.</p><p><strong>Abstract:</strong><br/>
In this paper the controllable spread of some infectious disease is considered. The evolution model of the disease is described by the 3-dimensional nonlinear ordinary differential equations system. Vaccination and treatment are accepted as control parameters of the system. It is assumed that the stocks of vaccination and treatment is limited. Attainable sets of the system are approximately calculated for different control stocks. Graphical results are presented and possible biological applications are discussed.
</p>projecteuclid.org/euclid.tbilisi/1585015216_20200323220019Mon, 23 Mar 2020 22:00 EDTCharacterizations for the fractional maximal operators on Carleson curves in local generalized Morrey spaceshttps://projecteuclid.org/euclid.tbilisi/1585015217<strong>Hatice Armutcu</strong>, <strong>Ahmet Eroglu</strong>, <strong>Fatai Isayev</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 13, Number 1, 23--38.</p><p><strong>Abstract:</strong><br/>
In this paper we study the fractional maximal operator $\mathcal{M}^{\alpha}$ in the local generalized Morrey space $LM_{p,\varphi}^{\{t_0\}}(\Gamma)$ and the generalized Morrey space $M_{p,\varphi}(\Gamma)$ defined on Carleson curves $\Gamma$, respectively. For the operator $\mathcal{M}^{\alpha}$ we shall give a characterization the strong and weak Spanne-Guliyev type boundedness on $LM_{p,\varphi}^{\{t_0\}}(\Gamma)$ and the strong and weak Adams-Guliyev type boundedness on $M_{p,\varphi}(\Gamma)$.
</p>projecteuclid.org/euclid.tbilisi/1585015217_20200323220019Mon, 23 Mar 2020 22:00 EDTOn boundedness of multidimensional Hausdorff operator in weighted Lebesgue spaceshttps://projecteuclid.org/euclid.tbilisi/1585015218<strong>Rovshan A. Bandaliyev</strong>, <strong>Kamala H. Safarova</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 13, Number 1, 39--45.</p><p><strong>Abstract:</strong><br/>
In this paper the boundedness of multidimensional Hausdorff operator in weighted Lebesgue spaces is proved. In particular, necessary and sufficient condition for the boundedness of multidimensional Hausdorff operator are established in weighted Lebesgue spaces.
</p>projecteuclid.org/euclid.tbilisi/1585015218_20200323220019Mon, 23 Mar 2020 22:00 EDTLipschitz estimates for rough fractional multilinear integral operators on local generalized Morrey spaceshttps://projecteuclid.org/euclid.tbilisi/1585015219<strong>I. Ekincioglu</strong>, <strong>C. Keskin</strong>, <strong>R. V. Guliyev</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 13, Number 1, 47--60.</p><p><strong>Abstract:</strong><br/>
We obtain the Lipschitz boundedness for a class of fractional multilinear operators $I_{\Omega,\alpha}^{A,m}$ with rough kernels $\Omega\in L_{s}(\mathbb S^{n-1})$, $s>n/(n-\alpha)$ on the local generalized Morrey spaces $LM_{p,\varphi}^{\{x_0\}}$, generalized Morrey spaces $M_{p,\varphi}$ and vanishing generalized Morrey spaces $VM_{p,\varphi}$, where the functions $A$ belong to homogeneous Lipschitz space $\dot{\Lambda}_{\beta}$, $0<\beta<1$. We find the sufficient conditions on the pair $(\varphi_1,\varphi_2)$ which ensures the boundedness of the operators $I_{\Omega,\alpha}^{A,m}$ from $LM_{p,\varphi_1}^{\{x_0\}}$ to $LM_{q,\varphi_2}^{\{x_0\}}$, from $M_{p,\varphi_1}$ to $M_{q,\varphi_2}$ and from $VM_{p,\varphi_1}$ to $VM_{q,\varphi_2}$ for $1<p<q <\infty$ and $1/p-1/q=(\alpha+\beta)/n$. In all cases the conditions for the boundedness of the operator $I_{\Omega,\alpha}^{A,m}$ is given in terms of Zygmund-type integral inequalities on $(\varphi_1,\varphi_2)$, which do not assume any assumption on monotonicity of $\varphi_1(x,r), \varphi_2(x,r)$ in $r$.
</p>projecteuclid.org/euclid.tbilisi/1585015219_20200323220019Mon, 23 Mar 2020 22:00 EDTSpaces of strongly lacunary invariant summable sequenceshttps://projecteuclid.org/euclid.tbilisi/1585015220<strong>E. Savaş</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 13, Number 1, 61--68.</p><p><strong>Abstract:</strong><br/>
In this paper, we introduce and examine some properties of three sequence spaces defined using lacunary sequence and invariant mean which generalize several known sequence spaces.
</p>projecteuclid.org/euclid.tbilisi/1585015220_20200323220019Mon, 23 Mar 2020 22:00 EDTOscillatory integrals with variable Calderón-Zygmund kernel on vanishing generalized Morrey spaceshttps://projecteuclid.org/euclid.tbilisi/1585015221<strong>V. S. Guliyev</strong>, <strong>A. Ahmadli</strong>, <strong>S. E. Ekincioglu</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 13, Number 1, 69--82.</p><p><strong>Abstract:</strong><br/>
In this paper, the authors investigate the boundedness of the oscillatory singular integrals with variable Calderón-Zygmund kernel on generalized Morrey spaces $M^{p,\varphi}(\mathbb R^n)$ and the vanishing generalized Morrey spaces $VM^{p,\varphi}(\mathbb R^n)$. When $1<p<\infty$ and $(\varphi_1,\varphi_2)$ satisfies some conditions, we show that the oscillatory singular integral operators $T_{\lambda}$ and $T_{\lambda}^{*}$ are bounded from $M^{p,\varphi_1}(\mathbb R^n)$ to $M^{p,\varphi_2}(\mathbb R^n)$ and from $VM^{p,\varphi_1}(\mathbb R^n)$ to $VM^{p,\varphi_2}(\mathbb R^n)$. Meanwhile, the corresponding result for the oscillatory singular integrals with standard Calderón-Zygmund kernel are established.
</p>projecteuclid.org/euclid.tbilisi/1585015221_20200323220019Mon, 23 Mar 2020 22:00 EDTA quadrature approach to the generalized frictionless shearing contact problemhttps://projecteuclid.org/euclid.tbilisi/1585015222<strong>Elçin Yusufoğlu</strong>, <strong>İlkem Turhan Çetinkaya</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 13, Number 1, 83--96.</p><p><strong>Abstract:</strong><br/>
In this study, the generalization of a frictionless contact problem in case of shearing deformation for an elastic inhomogeneous half space is presented. The basic equations of the elasticity theory and Fourier transform technique are applied to the problem to derive the system of singular integral equations. The obtained system of singular integral equations is solved by a quadrature approach. The numerical results are presented for the case of $N=1$, $N=2$, $N=3$, where $N$ denotes the number of the punches whose base are flat.
</p>projecteuclid.org/euclid.tbilisi/1585015222_20200323220019Mon, 23 Mar 2020 22:00 EDTCharacterizations for the commutator of parabolic nonsingular integral operator on parabolic generalized Orlicz-Morrey spaceshttps://projecteuclid.org/euclid.tbilisi/1585015223<strong>M. N. Omarova</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 13, Number 1, 97--111.</p><p><strong>Abstract:</strong><br/>
We show continuity in parabolic generalized Orlicz-Morrey spaces $M^{\Phi,\varphi}$ of commutator of parabolic nonsingular integral operators. We shall give necessary and sufficient conditions for the boundedness of the commutator of parabolic nonsingular integral operator on $M^{\Phi,\varphi}$ spaces with $BMO$ functions.
</p>projecteuclid.org/euclid.tbilisi/1585015223_20200323220019Mon, 23 Mar 2020 22:00 EDTSimplicial algebroids and internal categories within $R$-algebroidshttps://projecteuclid.org/euclid.tbilisi/1585015224<strong>Özgün Gürmen Alansal</strong>, <strong>Erdal Ulualan</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 13, Number 1, 113--121.</p><p><strong>Abstract:</strong><br/>
In this work, by defining Peiffer pairings in the Moore complex of a simplicial algebgroid, we give the close relationship between the category of simplicial algebroids with Moore complex of length 1 and that of internal categories in the category of R-algebroids.
</p>projecteuclid.org/euclid.tbilisi/1585015224_20200323220019Mon, 23 Mar 2020 22:00 EDTApproximation by trigonometric polynomials in weighted Morrey spaceshttps://projecteuclid.org/euclid.tbilisi/1585015225<strong>Z. Cakir</strong>, <strong>C. Aykol</strong>, <strong>D. Soylemez</strong>, <strong>A. Serbetci</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 13, Number 1, 123--138.</p><p><strong>Abstract:</strong><br/>
In this paper we investigate the best approximation by trigonometric polynomials in weighted Morrey spaces $\mathcal{M}_{p,\lambda}(I_{0},w)$, where the weight function $w$ is in the Muckenhoupt class $A_{p}(I_{0})$ with $1 < p < \infty$ and $I_{0}=[0, 2\pi]$. We prove the direct and inverse theorems of approximation by trigonometric polynomials in the spaces $\mathcal{\widetilde{M}}_{p,\lambda}(I_{0},w)$ the closure of $C^{\infty}(I_{0})$ in $\mathcal{M}_{p,\lambda}(I_{0},w)$. We give the characterization of $K-$functionals in terms of the modulus of smoothness and obtain the Bernstein type inequality for trigonometric polynomials in the spaces $\mathcal{M}_{p,\lambda}(I_{0},w)$.
</p>projecteuclid.org/euclid.tbilisi/1585015225_20200323220019Mon, 23 Mar 2020 22:00 EDTAbstract versions of Korovkin theorems on modular spaces via statistical relative summation process for double sequenceshttps://projecteuclid.org/euclid.tbilisi/1585015226<strong>Sevda Yildiz</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 13, Number 1, 139--156.</p><p><strong>Abstract:</strong><br/>
In this paper, we studied the abstract versions of Korovkin type approximation theorems via statistical relative $\mathcal{A-}$Summation process in modular spaces for double sequences. Then, we discuss the results which are obtained by special choice of the scale function and the matrix sequences and we give an application that shows our results are stronger than studied before. Finally, we study an extension to non-positive linear operators.
</p>projecteuclid.org/euclid.tbilisi/1585015226_20200323220019Mon, 23 Mar 2020 22:00 EDTOn Hermite-Hadamard type inequalities for co-ordinated trigonometrically $\rho$-convex functionshttps://projecteuclid.org/euclid.tbilisi/1593223217<strong>Hüseyin Budak</strong>, <strong>Hasan Kara</strong>, <strong>Mehmet Eyüp Kiriş</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 13, Number 2, 1--26.</p><p><strong>Abstract:</strong><br/>
In this study, we first introduce the co-ordinated trigonometrically $\rho$-convex functions. Then we establish some Hermite-Hadamard type inequalities for this kind of functions. We also give refinement of the obtained inequalities by using the result given by Budak. The inequalities obtained in this study provide generalizations of some result given in earlier works.
</p>projecteuclid.org/euclid.tbilisi/1593223217_20200626220022Fri, 26 Jun 2020 22:00 EDTGrowth estimates of derivatives of a polynomialhttps://projecteuclid.org/euclid.tbilisi/1593223218<strong>Abdullah Mir</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 13, Number 2, 27--37.</p><p><strong>Abstract:</strong><br/>
This paper deals with the problem of finding an upper bound for the maximal modulus of the derivative and higher order derivatives of a complex polynomial on a disk under the assumption that the polynomial has no zeros in another disk. The estimates involve the maximal modulus of the polynomial in some disk, the degree, the coefficients and the radii of the disks.
</p>projecteuclid.org/euclid.tbilisi/1593223218_20200626220022Fri, 26 Jun 2020 22:00 EDTFamilies of exact solutions of Biswas-Milovic equation by an exponential rational function methodhttps://projecteuclid.org/euclid.tbilisi/1593223219<strong>Behzad Ghanbari</strong>, <strong>Mustafa Inc</strong>, <strong>Abdullahi Yusuf</strong>, <strong>Dumitru Baleanu</strong>, <strong>Mustafa Bayram</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 13, Number 2, 39--65.</p><p><strong>Abstract:</strong><br/>
In this paper, we introduce generalized exponential rational function method (GERFM) to obtain an exact satisfies satisfies solutions for the Biswas-Milovic (BM) equation with quadratic-cubic and parabolic nonlinearities. A wide range of closed solutions are acquired. The most important feature of the new method is that it is very effective and simple. The main merits of the proposed is that it gives more general solutions with some free parameters and can be applied to other types of nonlinear partial differential equations.Some interesting Figures for the physical features of some of the obtained solutions are also presented.
</p>projecteuclid.org/euclid.tbilisi/1593223219_20200626220022Fri, 26 Jun 2020 22:00 EDTArithmetic properties of $2$-color overpartition pairshttps://projecteuclid.org/euclid.tbilisi/1593223220<strong>M. S. Mahadeva Naika</strong>, <strong>S. Shivaprasada Nayaka</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 13, Number 2, 67--85.</p><p><strong>Abstract:</strong><br/>
Let $\overline{p}_{k, -2}(n)$ counts the number of overpartition pairs of $n$ with 2-color in which one of the colors appears only in parts that are multiples of $k$. We establish several infinite families of congruences modulo powers of $2$ and $3$ for $\overline{p}_{k, -2}(n)$ where $k= 2$ and $3$. For example, for all $n \geq 0$ and $\alpha\geq0$, we have $$\overline{p}_{2, -2}(16\cdot 3^{4\alpha+2}n+34\cdot 3^{4\alpha+1})\equiv 0 \pmod{128},$$ $$\overline{p}_{3, -2}(6\cdot 25^{\alpha+2}n+20\cdot 25^{\alpha+2})\equiv 0 \pmod{27}.$$
</p>projecteuclid.org/euclid.tbilisi/1593223220_20200626220022Fri, 26 Jun 2020 22:00 EDTOn uniqueness of meromorphic functions and their derivativeshttps://projecteuclid.org/euclid.tbilisi/1593223221<strong>Chao Meng</strong>, <strong>Xu Li</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 13, Number 2, 87--99.</p><p><strong>Abstract:</strong><br/>
In this paper, we deal with the uniqueness problem for the $k$-th derivative of power of meromorphic function and obtain some results which improve and supplement the previous theorem given by V.H. An and H.H. Khoai.
</p>projecteuclid.org/euclid.tbilisi/1593223221_20200626220022Fri, 26 Jun 2020 22:00 EDTDecomposition spaces and poset-stratified spaceshttps://projecteuclid.org/euclid.tbilisi/1593223222<strong>Shoji Yokura</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 13, Number 2, 101--127.</p><p><strong>Abstract:</strong><br/>
In 1920s R. L. Moore introduced upper semicontinuous and lower semicontinuous decompositions in studying decomposition spaces. Upper semicontinuous decompositions were studied very well by himself and later by R.H. Bing in 1950s. In this paper we consider lower semicontinuous decompositions $\mathcal D$ of a topological space $X$ such that the decomposition spaces $X/\mathcal D$ are Alexandroff spaces. If the associated proset (preordered set) of the decomposition space $X/\mathcal D$ is a poset, then the decomposition map $\pi:X \to X/\mathcal D$ is a continuous map from the topological space $X$ to the poset $X/\mathcal D$ with the associated Alexandroff topology , which is nowadays called a poset-stratified space . As an application, we capture the face poset of a real hyperplane arrangement $\mathcal A$ of $\mathbb R^n$ as the associated poset of the decomposition space $\mathbb R^n/\mathcal D(\mathcal A)$ of the decomposition $\mathcal D(\mathcal A)$ determined by the arrangement $\mathcal A$. We also show that for any locally small category $\mathcal C$ the set $hom_{\mathcal C}(X,Y)$ of morphisms from $X$ to $Y$ can be considered as a poset-stratified space, and that for any objects $S, T$ (where $S$ plays as a source object and $T$ as a target object) there are a covariant functor $\mathfrak{st}^S_*: \mathcal C \to \mathcal Strat$ and a contravariant functor $\mathfrak{st}^*_T$ $\mathfrak{st}^*_T: \mathcal C \to \mathcal Strat$ from $\mathcal C$ to the category $\mathcal Strat$ of poset-stratified spaces. We also make a remark about Yoneda's Lemmas as to poset-stratified space structures of $hom_{\mathcal C}(X,Y)$.
</p>projecteuclid.org/euclid.tbilisi/1593223222_20200626220022Fri, 26 Jun 2020 22:00 EDTJacobi spectral discretization for nonlinear fractional generalized seventh-order KdV equations with convergence analysishttps://projecteuclid.org/euclid.tbilisi/1593223223<strong>R. M. Hafez</strong>, <strong>Y. H. Youssri</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 13, Number 2, 129--148.</p><p><strong>Abstract:</strong><br/>
We developed a numerical scheme to solve the nonlinear fractional (NF) generalized seventh order KdV (sKdV) equation with time-space-fractional using the shifted Jacobi collocation method. Basically, a time-space collocation approximation for temporal and spatial discretizations is employed efficiently to tackle these equations. The convergence and stability analyses of the suggested basis functions are presented in-depth. The validity and efficiency of the proposed method are investigated and verified through numerical examples.
</p>projecteuclid.org/euclid.tbilisi/1593223223_20200626220022Fri, 26 Jun 2020 22:00 EDTUniqueness of some differential-difference polynomials of entire functions sharing small functionhttps://projecteuclid.org/euclid.tbilisi/1593223224<strong>S. H. Naveenkumar</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 13, Number 2, 149--159.</p><p><strong>Abstract:</strong><br/>
In this article, we discuss the uniqueness problems of differential-difference polynomials of hyper order $(\geq 1)$ meromorphic functions sharing a small function and prove some results, which generalise and improve the results due to Y. Liu, J. P. Wang and F. H. Liu.
</p>projecteuclid.org/euclid.tbilisi/1593223224_20200626220022Fri, 26 Jun 2020 22:00 EDTOn the nonexistence of global solutions for wave equations with double damping terms and nonlinear memoryhttps://projecteuclid.org/euclid.tbilisi/1593223225<strong>Mohamed Berbiche</strong>, <strong>Messaouda Terchi</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 13, Number 2, 161--178.</p><p><strong>Abstract:</strong><br/>
In this work, we consider the Cauchy problem for a wave equations with frictional and displacement dependent damping terms with nonlinear memory in multi-dimensional space $\mathbb{R}^{n}$, $n\geq 1$, we will prove the existence and uniqueness of the local solution and the nonexistence of global weak solutions theorems for any dimension space.
</p>projecteuclid.org/euclid.tbilisi/1593223225_20200626220022Fri, 26 Jun 2020 22:00 EDT$Z$-transform for integrable Boehmianshttps://projecteuclid.org/euclid.tbilisi/1593223226<strong>Deshna Loonker</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 13, Number 2, 179--185.</p><p><strong>Abstract:</strong><br/>
Boehmians, being the specific class of the generalized functions (the theory of distributions), are exposed to applications within mathematics and beyond. This paper is involved into the investigation of the $Z$ - transform for integrable Boehmians.
</p>projecteuclid.org/euclid.tbilisi/1593223226_20200626220022Fri, 26 Jun 2020 22:00 EDTMonodromy matrices as universal set of quantum gates and dynamics of cold trapped ionshttps://projecteuclid.org/euclid.tbilisi/1593223227<strong>G. Giorgadze</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 13, Number 2, 187--206.</p><p><strong>Abstract:</strong><br/>
In this paper we describe a feasible construction of universal set of quantum gates using monodromy matrices of Fuchsian system. Fuchsian systems are considered as Schrödinger type equations and it is shown that such quantum systems are exactly solvable. We also show that dynamics of trapped cold ions may be described by a Fuchsian system which also describes the critical points of logarithmic potential associated with equilibrium positions of trapped ions in line geometry. Two different approaches to the inverse problem are also discussed.
</p>projecteuclid.org/euclid.tbilisi/1593223227_20200626220022Fri, 26 Jun 2020 22:00 EDTAlmost tri-cubic functions with Lipschitz conditionhttps://projecteuclid.org/euclid.tbilisi/1593223228<strong>Ismail Nikoufar</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 13, Number 2, 207--216.</p><p><strong>Abstract:</strong><br/>
In this paper, we approximate a family of functions with a tri-symmetric left invariant mean property by tri-cubic functions in Lipschitz spaces.
</p>projecteuclid.org/euclid.tbilisi/1593223228_20200626220022Fri, 26 Jun 2020 22:00 EDTOn cohomologies and algebraic $K$-theory of Lie $p$-superalgebrashttps://projecteuclid.org/euclid.tbilisi/1593223229<strong>Giorgi Rakviashvili</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 13, Number 2, 217--224.</p><p><strong>Abstract:</strong><br/>
An enveloping associative superalgebra $\Lambda [L,\alpha ,\beta ]$ and its groups of cohomologies are defined and it is proved that there exists Frobenius multiplication of the Quillen algebraic $K$-functors of $\Lambda [L,\alpha ,\beta ]$. These results generalize corresponding results for Lie $p$-algebras which were proved by the author earlier.
</p>projecteuclid.org/euclid.tbilisi/1593223229_20200626220022Fri, 26 Jun 2020 22:00 EDTSymmretric functions for second-order recurrence sequenceshttps://projecteuclid.org/euclid.tbilisi/1593223230<strong>Khadidja Boubellouta</strong>, <strong>Ali Boussayoud</strong>, <strong>Mohamed Kerada</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 13, Number 2, 225--237.</p><p><strong>Abstract:</strong><br/>
In this paper, we introduce new symmetric endomorphism operators on appropriate infinite product series. The main results show that after direct calculations, the proposed operators are qualified to obtain new generating functions for second-order recurrence sequences.
</p>projecteuclid.org/euclid.tbilisi/1593223230_20200626220022Fri, 26 Jun 2020 22:00 EDT