Degenerate Maximal Hyponormal Differential Operators For The First Order,
2019
TÜBİTAK
Degenerate Maximal Hyponormal Differential Operators For The First Order, Meltem Sertbaş, Fati̇h Yilmaz
Turkish Journal of Mathematics
In this study, all maximal hyponormal extensions are given for the degenerate first order in the Hilbert space of vector-functions on a finite interval. The extensions are defined in terms of the boundary values. The structure of the spectrum of the maximal hyponormal extensions is also investigated.
The $X$-Coordinates Of Pell Equations And Padovan Numbers,
2019
TÜBİTAK
The $X$-Coordinates Of Pell Equations And Padovan Numbers, Salah Eddine Rihane, Mohand Ouamar Hernane, Alain Togbe
Turkish Journal of Mathematics
In this paper, we show that there is at most one value of the positive integer $X$ participating in the Pell equation $X^2-dY^2=k$, where $k\in\{\pm1,\pm4\}$, which is a Padovan number, with a few exceptions that we completely characterize.
A Neutral Relation Between Metallic Structure And Almost Quadratic $\Phi $-Structure,
2019
TÜBİTAK
A Neutral Relation Between Metallic Structure And Almost Quadratic $\Phi $-Structure, Si̇nem Gönül, İrem Küpeli̇ Erken, Azi̇z Yazla, Cengi̇zhan Murathan
Turkish Journal of Mathematics
In this paper, we give a neutral relation between metallic structure and almost quadratic metric $\phi $-structure. Considering $N$ as a metallic Riemannian manifold, we show that the warped product manifold $\mathbb{R} \times _{f}N$ has an almost quadratic metric $\phi $-structure. We define Kenmotsu quadratic metric manifolds, which include cosymplectic quadratic manifolds when $\beta =0$. Then we give nice almost quadratic metric $\phi $-structure examples. In the last section, we construct a quadratic $\phi $-structure on the hypersurface $M^{n}$ of a locally metallic Riemannian manifold $\tilde{M}^{n+1}.$
Enveloping Algebras Of Color Hom-Lie Algebras,
2019
TÜBİTAK
Enveloping Algebras Of Color Hom-Lie Algebras, Abdoreza Armakan, Sergei Silvestrov, Mohammad Reza Farhangdoost
Turkish Journal of Mathematics
In this paper, the universal enveloping algebra of color hom-Lie algebras is studied. A construction of the free involutive hom-associative color algebra on a hom-module is described and applied to obtain the universal enveloping algebra of an involutive hom-Lie color algebra. Finally, the construction is applied to obtain the well-known Poincaré-Birkhoff-Witt theorem for Lie algebras to the enveloping algebra of an involutive color hom-Lie algebra.
Properties In $L_P$ Of Root Functions For A Nonlocal Problem With Involution,
2019
TÜBİTAK
Properties In $L_P$ Of Root Functions For A Nonlocal Problem With Involution, Leonid Kritskov, Makhmud Sadybekov, Abdizhahan Sarsenbi
Turkish Journal of Mathematics
The spectral problem $-u''(x)+\alpha u''(-x)=\lambda u(x)$, $-1$%lt; $x$ < $1$, with nonlocal boundary conditions $u(-1)=\beta u(1)$, $u'(-1)=u'(1)$, is studied in the spaces $L_p(-1,1)$ for any $\alpha\in (-1,1)$ and $\beta\ne\pm 1$. It is proved that if $r=\sqrt{(1-\alpha)/(1+\alpha)}$ is irrational then the system of its eigenfunctions is complete and minimal in $L_p(-1,1)$ for any $p>1$, but does not form a basis. In the case of a rational value of $r$, the way of supplying this system with associated functions is specified to make all the root functions a basis in $L_p(-1,1)$.
On Linear Dynamics Of Sets Of Operators,
2019
TÜBİTAK
On Linear Dynamics Of Sets Of Operators, Mohamed Amouch, Otmane Benchiheb
Turkish Journal of Mathematics
Let $X$ be a complex topological vector space with $dim(X)>1$ and $\mathcal{B}(X)$ the set of all continuous linear operators on $X$. The concept of hypercyclicity for a subset of $\mathcal{B}(X)$ was introduced in [1]. In this work, we introduce the notion of hypercyclic criterion for a subset of $\mathcal{B}(X)$. We extend some results known for a single operator and $C_0$-semigroup to a subset of $\mathcal{B}(X)$ and we give applications for $C$-regularized groups of operators.
On Product Complex Finsler Manifolds,
2019
TÜBİTAK
On Product Complex Finsler Manifolds, Hongchuan Xia, Qian Wei
Turkish Journal of Mathematics
Let $(M, F)$ be the product complex Finsler manifold of two strongly pseudoconvex complex Finsler manifolds $(M_1, F_1)$ and $(M_2, F_2)$ with $F=\sqrt{f(K, H)}$ and $K=F_1^2$, $H=F_2^2$. In this paper, we prove that $(M, F)$ is a weakly Käahler-Finsler (resp. weakly complex Berwald) manifold if and only if $(M_1, F_1)$ and $(M_2, F_2)$ are both weakly Kähler-Finsler (resp. weakly complex Berwald) manifolds, which is independent of the choice of function $f$. Meanwhile, we prove that $(M, F)$ is a complex Landsberg manifold if and only if either $(M_1, F_1)$ and $(M_2, F_2)$ are both complex Landsberg manifolds and $f=c_1K+c_2H$ with …
Properties Of A Generalized Class Of Analytic Functions With Coefficient Inequality,
2019
TÜBİTAK
Properties Of A Generalized Class Of Analytic Functions With Coefficient Inequality, Ben Wongsaijai, Nattakorn Sukantamala
Turkish Journal of Mathematics
Let $(\beta_n)_{n\ge 2}$ be a sequence of nonnegative real numbers and $\delta$ be a positive real number. We introduce the subclass $\mathcal{A}(\beta_n,\delta)$ of analytic functions, with the property that the Taylor coefficients of the function $f$ satisfies $\sum_{n\ge2}^{\infty}\beta_n a_n \le \delta$, where $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$. The class $\mathcal{A}(\beta_n,\delta)$ contains nonunivalent functions for some choices of $(\beta_n)_{n\ge 2}$. In this paper, we provide some general properties of functions belonging to the class $\mathcal{A}(\beta_n,\delta)$, such as the radii of univalence, distortion theorem, and invariant property. Furthermore, we derive the best approximation of an analytic function in such class by using the semiinfinite quadratic programming. …
Some General Results On Fractional Banach Sets,
2019
TÜBİTAK
Some General Results On Fractional Banach Sets, Faruk Özger
Turkish Journal of Mathematics
The gamma function which is expressed by an improper integral is used to establish the fractional difference operators and fractional Banach sets. In this study, we achieve some comprehensive and complementary results related to characterizations of the matrix classes of fractional Banach sets. We also obtain some identities or inequalities for the Hausdorff measure of noncompactness of the corresponding matrix operators, and finally find the necessary and sufficient conditions for those matrix operators to be compact.
A Bernstein-Type Theorem For $\Xi$-Submanifolds Withflat Normal Bundle In The Euclidean Spaces,
2019
TÜBİTAK
A Bernstein-Type Theorem For $\Xi$-Submanifolds Withflat Normal Bundle In The Euclidean Spaces, Xu-Yong Jiang, He-Jun Sun, Peibiao Zhao
Turkish Journal of Mathematics
$\xi$-Submanifolds in the Euclidean spaces are a natural extension of self-shrinkers and a generalization of $\lambda$-hypersurfaces. Moreover, $\xi$-submanifolds are expected to take the place of submanifolds with parallel mean curvature vector. In this paper, we establish a Bernstein-type theorem for $\xi$-submanifolds in the Euclidean spaces. More precisely, we prove that an $n$-dimensional smooth graphic $\xi$-submanifold with flat normal bundle in $\mathbb{R}^{n+p}$ is an affine $n$-plane.
Converse Theorems In Lyapunov's Second Method And Applications For Fractional Order Systems,
2019
TÜBİTAK
Converse Theorems In Lyapunov's Second Method And Applications For Fractional Order Systems, Javier Gallegos, Manuel Duarte-Mermoud
Turkish Journal of Mathematics
We establish a characterization of the Lyapunov and Mittag-Leffler stability through (fractional) Lyapunov functions, by proving converse theorems for Caputo fractional order systems. A hierarchy for the Mittag-Leffler order convergence is also proved which shows, in particular, that fractional differential equation with derivation order lesser than one cannot be exponentially stable. The converse results are then applied to show that if an integer order system is (exponentially) stable, then its corresponding fractional system, obtained from changing its differentiation order, is (Mittag-Leffler) stable. Hence, available integer order control techniques can be disposed to control nonlinear fractional systems. Finally, we provide examples …
On The Cover Ideals Of Chordal Graphs,
2019
TÜBİTAK
On The Cover Ideals Of Chordal Graphs, Nursel Erey
Turkish Journal of Mathematics
The independence complex of a chordal graph is known to be shellable which is equivalent to the fact that cover ideal of a chordal graph has linear quotients. We use this result to obtain recursive formulas for the Betti numbers of cover ideals of chordal graphs. Moreover, we give a new proof of such result which yields different shellings of the independence complex.
A Circulant Functional Equation For The Additive Function And Its Stability,
2019
TÜBİTAK
A Circulant Functional Equation For The Additive Function And Its Stability, Vichian Laohakosol, Watcharapon Pimsert, Kanet Ponpetch
Turkish Journal of Mathematics
A general solution of a matrix functional equation involving circulant matrices of the additive function is determined, and its stability is established.
A (Co)Algebraic Approach To Hennessy-Milner Theorems For Weakly Expressive Logics,
2019
Université de Lorraine
A (Co)Algebraic Approach To Hennessy-Milner Theorems For Weakly Expressive Logics, Zeinab Bakhtiari, Helle Hvid Hansen, Alexander Kurz
Engineering Faculty Articles and Research
"Coalgebraic modal logic, as in [9, 6], is a framework in which modal logics for specifying coalgebras can be developed parametric in the signature of the modal language and the coalgebra type functor T. Given a base logic (usually classical propositional logic), modalities are interpreted via so-called predicate liftings for the functor T. These are natural transformations that turn a predicate over the state space X into a predicate over TX. Given that T-coalgebras come with general notions of T-bisimilarity [11] and behavioral equivalence [7], coalgebraic modal logics are designed to respect those. In particular, if two states are behaviourally …
The Exponentiated Generalized Topp Leone-G Family Of Distributions: Properties And Applications,
2019
Qassim University
The Exponentiated Generalized Topp Leone-G Family Of Distributions: Properties And Applications, Hesham Mohammed Reyad, Morad Alizadeh, Farrukh Jamal, Soha Othman, Gholamhossein G. Hamedani
Mathematical and Statistical Science Faculty Research and Publications
In this paper, we propose a new class of continuous distributions called the exponentiated generalized Topp Leone-G family that extends the Topp Leone-G family introduced by Al-Shomrani et al. (2016). We derive explicit expressions for certain mathematical properties of the new family such as; ordinary and incomplete moments, generating functions, reliability analysis, Lorenz and Bonferroni curves, Rényi entropy, stress strength model, moment of residual and reversed residual life, order statistics, extreme values and characterizations. We discuss the maximum likelihood estimates and the observed information matrix for the model parameters. Two real data sets are used to illustrate the flexibility of …
Group Presentations As A Site For Collective Modeling Activity,
2019
Vanderbilt University
Group Presentations As A Site For Collective Modeling Activity, Corey Brady, Hyunyi Jung
Mathematical and Statistical Science Faculty Research and Publications
We approach student presentations of solutions to modeling tasks as occasions for whole-class reflection on the rich conceptual work that small-group teams have done in parallel. Analyzing and interpreting these interactions can offer insights into how a classroom group negotiates a shared sense of what they have learned and what they collectively view as “newsworthy” across groups from their recent (and ongoing) model-building. We describe analytical tools to interpret a classroom’s work during presentations, and we illustrate their use in a single case. This work offers a foothold for design-based research to harness presentations to improve learning, drive instructional decisions, …
Mathematical Modeling Experiences: Narratives From A Preservice Teacher And An Instructor,
2019
Marquette University
Mathematical Modeling Experiences: Narratives From A Preservice Teacher And An Instructor, Sarah Brand, Hyunyi Jung
Mathematical and Statistical Science Faculty Research and Publications
Regardless of the benefits of engaging in mathematical modeling, few preservice teachers (PTs) have experienced mathematical modeling firsthand. This study offers an example of how to make sense of the interaction between the teaching and learning of mathematical modeling by examining a teacher educator’s decision making, her analysis of 36 PTs’ learning, and an in-depth narrative from a PT. Findings show the value of engaging with structurally relevant mathematical modeling tasks and considering social issues via mathematical modeling, resulting in task designs which aim to deepen students’ understanding of society and mathematics.
A Design Of A Material Assembly In Space-Time Generating And Storing Energy,
2019
Embry-Riddle Aeronautical University
A Design Of A Material Assembly In Space-Time Generating And Storing Energy, Mihhail Berezovski, Stan Elektrov, Konstantin Lurie
Publications
The paper introduces a theoretical background of the mechanism of electromagnetic energy and power accumulation and its focusing in narrow pulses travelling along a transmission line with material parameters variable in 1D-space and time. This mechanism may be implemented due to a special material geometry- a distribution of two different dielectrics in a spatio-temporal checkerboard. We concentrate on the practically reasonable means to bring this mechanism into action in a device that may work both as energy generator and energy storage. The basic ideas discussed below appear to be fairly general; we have chosen their electromagnetic implementation as an excellent …
Teaching With Technology: Using A Virtual Learning Community And Peer Mentoring To Create An Interdisciplinary Intervention,
2019
CUNY New York City College of Technology
Teaching With Technology: Using A Virtual Learning Community And Peer Mentoring To Create An Interdisciplinary Intervention, Rebecca Mazumdar, Nadia Benakli, Pamela Brown
Publications and Research
This paper describes the development and implementation of engaging and supportive experiences to promote student engagement, persistence and success at a commuter, open enrollment, public, minority serving institution. Project components included faculty development at the SENCER Summer Institute (SSI) 2016, attended by a team comprised of an academic administrator, full-time faculty from English and math, and part-time faculty in chemistry; creation of a virtual learning community of freshmen enrolled in chemistry, English, and math linked by the specific theme of the environmental impacts of deicing roads with salt and the overarching theme of the impacts of human activities on the …
A New Extension Of Lindley Distribution: Modified Validation Test, Characterizations And Different Methods Of Estimation,
2019
Damietta University
A New Extension Of Lindley Distribution: Modified Validation Test, Characterizations And Different Methods Of Estimation, Mohamed Ibrahim, Abhimanyu Singh Yadav, Haitham M. Yousof, Hafida Goual, Gholamhossein Hamedani
Mathematical and Statistical Science Faculty Research and Publications
In this paper, a new extension of Lindley distribution has been introduced. Certain characterizations based on truncated moments, hazard and reverse hazard function, conditional expectation of the proposed distribution are presented. Besides, these characterizations, other statistical/mathematical properties of the proposed model are also discussed. The estimation of the parameters is performed through different classical methods of estimation. Bayes estimation is computed under gamma informative prior under the squared error loss function. The performances of all estimation methods are studied via Monte Carlo simulations in mean square error sense. The potential of the proposed model is analyzed through two data sets. …
