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Articles 37831 - 37860 of 302515

Full-Text Articles in Physical Sciences and Mathematics

Classical Solutions For 1-Dimensional And 2-Dimensional Boussinesq Equations, Svetlin Georgiev, Aissa Boukarou, Khaled Zennir Jan 2022

Classical Solutions For 1-Dimensional And 2-Dimensional Boussinesq Equations, Svetlin Georgiev, Aissa Boukarou, Khaled Zennir

Turkish Journal of Mathematics

In this article we investigate the IVPs for 1-dimensional and 2-dimensional Boussinesq equations. A new topological approach is applied to prove the existence of at least one classical solution and at least two nonnegative classical solutions for the considered IVPs. The arguments are based upon recent theoretical results.

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New Form Of Laguerre Fractional Differential Equation And Applications, Zahra Kavooci, Kazem Ghanbari, Hanif Mirzaei Jan 2022

New Form Of Laguerre Fractional Differential Equation And Applications, Zahra Kavooci, Kazem Ghanbari, Hanif Mirzaei

Turkish Journal of Mathematics

Laguerre differential equation is a well known equation that appears in the quantum mechanical description of the hydrogen atom. In this paper, we aim to develop a new form of Laguerre Fractional Differential Equation (LFDE) of order $2\alpha$ and we investigate the solutions and their properties. For a positive real number $\alpha$, we prove that the equation has solutions of the form $L_{n,\alpha}(x)=\sum_{k=0}^na_kx^k$, where the coefficients of the polynomials are computed explicitly. For integer case $\alpha=1$ we show that these polynomials are identical to classical Laguerre polynomials. Finally, we solve some fractional differential equations by defining a suitable integral transform.

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On A Subclass Of The Analytic And Bi-Univalent Functions Satisfying Subordinate Condition Defined By $Q$-Derivativ, Ni̇zami̇ Mustafa, Semra Korkmaz Jan 2022

On A Subclass Of The Analytic And Bi-Univalent Functions Satisfying Subordinate Condition Defined By $Q$-Derivativ, Ni̇zami̇ Mustafa, Semra Korkmaz

Turkish Journal of Mathematics

In this paper, we introduce and examine certain subclass $\ M_{q,\Sigma }\left( \varphi ,\beta \right) $ of analytic and bi-univalent functions on the open unit disk in the complex plane. Here, we give coefficient bound estimates, upper bound estimate for the second Hankel determinant and Fekete-Szegö inequality for the function belonging to this class. Some interesting special cases of the results obtained here are also discussed.

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A Galerkin-Type Approach To Solve Systems Of Linear Volterra-Fredholm Integro-Differential Equations, Murat Karaçayir, Şuayi̇p Yüzbaşi Jan 2022

A Galerkin-Type Approach To Solve Systems Of Linear Volterra-Fredholm Integro-Differential Equations, Murat Karaçayir, Şuayi̇p Yüzbaşi

Turkish Journal of Mathematics

The main interest of this paper is to propose a numerical scheme in order to solve linear systems of Volterra-Fredholm integro-differential equations given with mixed conditions. The proposed method is a weighted residual scheme which uses monomials up to a prescribed degree $N$ as the basis functions. By taking inner product of the equation system with the elements of this basis set in a Galerkin-like fashion, the original problem is transformed into a linear algebraic equation system. After a suitable incorporation of the mixed conditions, a final algebraic system is obtained, from which the approximate solutions of the problem are …

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Maximising The Number Of Connected Induced Subgraphs Of Unicyclic Graphs, Audace A V Dossou Olory Jan 2022

Maximising The Number Of Connected Induced Subgraphs Of Unicyclic Graphs, Audace A V Dossou Olory

Turkish Journal of Mathematics

Denote by $\mathcal{G}(n,c,g,k)$ the set of all connected graphs of order $n$, having $c$ cycles, girth $g$, and $k$ pendant vertices. In this paper, we give a partial characterisation of the structure of those graphs in $\mathcal{G}(n,c,g,k)$ maximising the number of connected induced subgraphs. For the special case where $c=1$, we find a complete characterisation of all maximal unicyclic graphs. We also derive a precise formula for the corresponding maximum number given the following parameters: (1) order, girth, and number of pendant vertices; (2) order and girth; (3) order.

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On Unbounded Order Continuous Operators, Bahri̇ Turan, Bi̇rol Altin, Hüma Gürkök Jan 2022

On Unbounded Order Continuous Operators, Bahri̇ Turan, Bi̇rol Altin, Hüma Gürkök

Turkish Journal of Mathematics

Let $U$ and $V$ be two Archimedean Riesz spaces. An operator $S:U\rightarrow V$ is said to be unbounded order continuous ($uo$-continuous), if $r_{\alpha }\overset{uo}{\rightarrow }0$ in $U$ implies $Sr_{\alpha }\overset{uo}{% \rightarrow }0$ in $V$. In this paper, we give some properties of the $uo$% -continuous dual $U_{uo}^{\sim }$ of $U$. We show that a nonzero linear functional $f$ on $U$ is $uo$-continuous if and only if $f$ is a linear combination of finitely many order continuous lattice homomorphisms. The result allows us to characterize the $uo$-continuous dual $U_{uo}^{\sim }.$ In general, by giving an example that the $uo$-continuous dual $U_{uo}^{\sim …

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Subsequence Characterization Of Statistical Boundedness, Leila Miller Van Wieren Jan 2022

Subsequence Characterization Of Statistical Boundedness, Leila Miller Van Wieren

Turkish Journal of Mathematics

In this paper, we present some relationships between statistical boundedness and statistical monotonicity of a given sequence and its subsequences. The results concerning statistical boundedness and monotonicity presented here are also closely related to earlier results regarding statistical convergence and are dealing with the Lebesgue measure and with the Baire category.

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Remote Sensing And Luminescence Dating Of Archaeological Sites In Buriram Province, Northeastern Thailand, Sutthikan Khamsiri Jan 2022

Remote Sensing And Luminescence Dating Of Archaeological Sites In Buriram Province, Northeastern Thailand, Sutthikan Khamsiri

Chulalongkorn University Theses and Dissertations (Chula ETD)

This research aims to apply remote sensing and luminescence dating to study archaeological sites in Buriram Province, Northeastern Thailand. There are three main objectives including 1) to model the ancient path from the mountain passes along the Dângrêk mountain to ancient community on Angkor Highland or Northeast Thailand, 2) to directly date slag from the ancient iron smelting site at Ban Sai To 7, and 3) determine the terminal age of Ban Sai To 7 site using technical ceramics. Firstly, the results of the GIS-based least cost path (LCP) route, using topographic factors, show that Ta Muen, Sai Ta Ku, …

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Medical Applications Of Ultrasound: T-Cell Drug Delivery, Osteoporosis Diagnosis, And Biofilm Mitigation, Alina Karki Jan 2022

Medical Applications Of Ultrasound: T-Cell Drug Delivery, Osteoporosis Diagnosis, And Biofilm Mitigation, Alina Karki

Graduate College Dissertations and Theses

The ability of ultrasound to localize acoustic energy deposition and induce a biological effect within a target is examined in three novel biomedical applications: sonoporation, osteoporosis diagnosis, and biofilm mitigation.Ultrasound can excite encapsulated microbubbles, causing an acoustic cavitation effect in the vicinity of cells, temporarily increasing membrane permeability, and allowing cells to uptake foreign molecules. This non-viral transfection technique is called sonoporation. Our experimental study demonstrated that it could be effective for small interfering RNA (siRNA) delivery into an isolated mouse and human T-cells, which is a complex process despite its importance in treating numerous diseases. T-cells are non-proliferating, while …

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A Novel Energy Consumption Model For Autonomous Mobile Robot, Gürkan Gürgöze, İbrahi̇m Türkoğlu Jan 2022

A Novel Energy Consumption Model For Autonomous Mobile Robot, Gürkan Gürgöze, İbrahi̇m Türkoğlu

Turkish Journal of Electrical Engineering and Computer Sciences

In this study, a novel predictive energy consumption model has been developed to facilitate the development of tasks based on efficient energy consumption strategies in mobile robot systems. For the proposed energy consumption model, an advanced mathematical system model that takes into account all parameters during the motion of the mobile robot is created. The parameters of inclination, load, dynamic friction, wheel slip and speed-torque saturation limit, which are often neglected in existing models, are especially used in our model. Thus, the effects of unexpected disruptors on energy consumption in the real world environment are also taken into account. As …

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Peripherally Restricted Opioid Conjugates And Its Use As Pharmacological Probes And Potential Therapeutics, Md Tariqul Haque Tuhin Jan 2022

Peripherally Restricted Opioid Conjugates And Its Use As Pharmacological Probes And Potential Therapeutics, Md Tariqul Haque Tuhin

University of the Pacific Theses and Dissertations

Opioid-induced constipation (OIC) is one of the major adverse effects of opioid analgesics used by millions of patients each year. While progress has been made, there remains a significant unmet medical need in the treatment of OIC. Major gaps remain in our understanding of the role of the gastrointestinal tract and central nervous system (CNS) in precipitating OIC. For the last four decades, numerous investigations to study the sites of action of opioid analgesics have utilized peripherally acting mu-opioid receptor antagonists (PAMORAs), which have been incorrectly believed to have limited penetration across the blood-brain barrier (BBB). Several preclinical and clinical …

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On Some Fractional Operators Generated From Abel's Formula, Eki̇n Uğurlu Jan 2022

On Some Fractional Operators Generated From Abel's Formula, Eki̇n Uğurlu

Turkish Journal of Mathematics

This work aims to share some fractional integrals and derivatives containing three real parameters. The main tool to introduce such operators is the corresponding Abel's equation. Solvability conditions for the Abel's equations are shared. Semigroup properties for fractional integrals are introduced. Integration by parts rule is given. Moreover, mean value theorems and related results are shared. At the end of the paper, some directions for some fractional operators are given.

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Hyperelastic Curves In $3-$Dimensional Lightlike Cone, Sümeyra Tuğçe Kağizman, Ahmet Yücesan Jan 2022

Hyperelastic Curves In $3-$Dimensional Lightlike Cone, Sümeyra Tuğçe Kağizman, Ahmet Yücesan

Turkish Journal of Mathematics

We study hyperelastic curves known as a generalization of elastic curves in $3-$dimensional lightlike cone which is a degenerate hypersurface in Minkowski $4-$space as critical points of the cone curvature energy functional constructed with the $r-$th power of the cone curvature depending on the given boundary conditions for the natural number $r \geq 2$. We derive the Euler-Lagrange equations for the critical points of this functional that is namely the hyperelastic curves and solve completely the Euler-Lagrange equations by quadratures. Then, we construct Killing vector fields along the hyperelastic curves. Lastly, we give explicitly the hyperelastic curves by integral according …

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On Isolated Gaps In Numerical Semigroups, Harold J. Smith Jan 2022

On Isolated Gaps In Numerical Semigroups, Harold J. Smith

Turkish Journal of Mathematics

A numerical semigroup is said to be perfect if it does not contain any isolated gaps. In this paper, we will look at some basic properties of isolated gaps in numerical semigroups. In particular, we will see how they are related to elements of the Apery set. We will use these properties to find all of the isolated gaps in a numerical semigroup of embedding dimension two and demonstrate a simple method of generating some examples of perfect numerical semigroups of embedding dimension three.

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On Bounded Solutions Of A Second-Order Iterative Boundary Value Problem, Safa Chouaf, Ahleme Bouakkaz, Rabah Khemis Jan 2022

On Bounded Solutions Of A Second-Order Iterative Boundary Value Problem, Safa Chouaf, Ahleme Bouakkaz, Rabah Khemis

Turkish Journal of Mathematics

In this article, we investigate a second-order iterative differential equation with boundary conditions. The use of the principle of contraction mappings and the Schauder's fixed point theorem allows us to prove some existence and uniqueness results. Finally, an example is given to check the validity of our findings, which are new, and complete some published manuscripts to some degree.

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Solvability Of Gripenberg's Equations Of Fractional Order With Perturbation Term In Weighted $L_P$-Spaces On ${\Mathbb{R}}^+$, Mohamed M. A. Metwali Jan 2022

Solvability Of Gripenberg's Equations Of Fractional Order With Perturbation Term In Weighted $L_P$-Spaces On ${\Mathbb{R}}^+$, Mohamed M. A. Metwali

Turkish Journal of Mathematics

This article deals with the solvability of Gripenberg's equations of fractional order with a perturbation term in weighted Lebesgue spaces on ${\mathbb{R}}^+=[0,\infty)$ via the fixed point hypothesis and the measure of noncompactness. The uniqueness of the solutions for the studied problem is discussed. An example is included to validate our results. The results presented in the article extend and generalize some former results in the available literature.

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Some Notes On Crossed Semimodules, Sedat Temel Jan 2022

Some Notes On Crossed Semimodules, Sedat Temel

Turkish Journal of Mathematics

In this paper, we introduce the notion of lifting via a homomorphism of monoids for a crossed semimodule and give some properties. Further, we characterize actions and coverings of Schreier internal categories in the category Mon of monoids and prove the natural equivalence between their categories. Then, we prove that liftings of a certain crossed semimodule are naturally equivalent to the actions of Schreier internal category in Mon, where the Schreier internal category corresponds to the crossed semimodule. Finally, we give a relation between crossed semimodules and simplicial monoids.

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A Köthe-Toeplitz Dual Of A Generalized Cesaro Difference Sequence Space, A Degenerate Lorentz Space, Their Corresponding Function Spaces And Fpp, Veysel Nezi̇r, Ni̇zami̇ Mustafa Jan 2022

A Köthe-Toeplitz Dual Of A Generalized Cesaro Difference Sequence Space, A Degenerate Lorentz Space, Their Corresponding Function Spaces And Fpp, Veysel Nezi̇r, Ni̇zami̇ Mustafa

Turkish Journal of Mathematics

In 1970, Cesaro sequence spaces was introduced by Shiue. In 1981, Kızmaz defined difference sequence spaces for ${\ell }^{\infty }$, ${\mathrm{c}}_0$ and $\mathrm{c}$. Then, in 1983, Orhan introduced Cesaro difference sequence spaces. Both works used difference operator and investigated the Köthe-Toeplitz dual for the new Banach spaces they introduced. Later, various authors generalized these new spaces, especially the one introduced by Orhan. In this study, first we discuss the fixed point property for these spaces and for the corresponding function space of the Köthe-Toeplitz dual. Moreover, we consider another generalized space which is a degenerate Lorentz space because the spaces …

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The Arens-Michael Envelopes Of Laurent Ore Extensions, Petr Kosenko Jan 2022

The Arens-Michael Envelopes Of Laurent Ore Extensions, Petr Kosenko

Turkish Journal of Mathematics

For an Arens-Michael algebra $A$ we consider a class of $A$-$\hat{\otimes}$-bimodules which are invertible with respect to the projective bimodule tensor product. We call such bimodules topologically invertible over $A$. Given a Frechet-Arens-Michael algebra $A$ and a topologically invertible Frechet $A$-$\hat{\otimes}$-bimodule $M$, we construct an Arens-Michael algebra $\widehat{L}_A(M)$ which serves as a topological version of the Laurent tensor algebra $L_A(M)$. Also, for a fixed algebra $B$ we provide a condition on an invertible $B$-bimodule $N$ which allows us to explicitly describe the Arens-Michael envelope of $L_B(N)$ as a topological Laurent tensor algebra. In particular, we provide an explicit description of …

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Small Genus-$4$ Lefschetz Fibrations On Simply-Connected $4$-Manifolds, Tüli̇n Altunöz Jan 2022

Small Genus-$4$ Lefschetz Fibrations On Simply-Connected $4$-Manifolds, Tüli̇n Altunöz

Turkish Journal of Mathematics

We consider simply connected $4$-manifolds admitting Lefschetz fibrations over the $2$-sphere. We explicitly construct nonhyperelliptic and hyperelliptic Lefschetz fibrations of genus $4$ on simply-connected $4$-manifolds which are exotic symplectic $4$-manifolds in the homeomorphism classes of $\mathbb{C} P^{2}\#8\overline{\mathbb{C} P^{2}}$ and $\mathbb{C} P^{2}\#9\overline{\mathbb{C} P^{2}}$, respectively. From these, we provide upper bounds for the minimal number of singular fibers of such fibrations. In addition, we prove that this number is equal to $18$ for $g=3$ when such fibrations are hyperelliptic. Moreover, we discuss these numbers for higher genera.

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Gradient Estimates Of A Nonlinear Elliptic Equation For The $V$-Laplacian On Noncompact Riemannian Manifolds, Deng Yihua Jan 2022

Gradient Estimates Of A Nonlinear Elliptic Equation For The $V$-Laplacian On Noncompact Riemannian Manifolds, Deng Yihua

Turkish Journal of Mathematics

In this paper, we consider gradient estimates for positive solutions to the following equation $$\triangle_V u+au^p\log u=0$$ on complete noncompact Riemannian manifold with $k$-dimensional Bakry-Emery Ricci curvature bounded from below. Using the Bochner formula and the Cauchy inequality, we obtain upper bounds of $ \nabla u $ with respect to the lower bound of the Bakry-Emery Ricci curvature.

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Existence And Multiplicity Of Solutions For P(.)-Kirchhoff-Type Equations, Rabi̇l Ayazoğlu, Sezgi̇n Akbulut, Ebubeki̇r Akkoyunlu Jan 2022

Existence And Multiplicity Of Solutions For P(.)-Kirchhoff-Type Equations, Rabi̇l Ayazoğlu, Sezgi̇n Akbulut, Ebubeki̇r Akkoyunlu

Turkish Journal of Mathematics

his paper is concerned with the existence and multiplicity of solutions of a Dirichlet problem for $p(.)$-Kirchhoff-type equation% \begin{equation*} \left\{ \begin{array}{c} M\left( \int_{\Omega }\frac{\left\vert \nabla u\right\vert ^{p(x)}}{p(x)}% dx\right) \left( -\Delta _{p(x)}u\right) =f(x,u),\text{ in }\Omega , \\ u=0,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{on }\partial \Omega .% \end{array}% \right. \end{equation*}% Using the mountain pass theorem, fountain theorem, dual fountain theorem and the theory of …

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Quasilinear Systems With Unpredictable Relay Perturbations, Mehmet Onur Fen, Fatma Fen Jan 2022

Quasilinear Systems With Unpredictable Relay Perturbations, Mehmet Onur Fen, Fatma Fen

Turkish Journal of Mathematics

It is rigorously proven under certain assumptions that a quasilinear system with discontinuous right-hand side possesses a unique unpredictable solution. The discontinuous perturbation function on the right-hand side is defined by means of an unpredictable sequence. A Gronwall-Coppel type inequality is utilized to achieve the main result, and the stability of the unpredictable solution is discussed. Examples with exponentially asymptotically stable and unstable unpredictable solutions are provided.

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Representation Variety Of Free Or Surface Groups And Reidemeister Torsion, Fati̇h Hezenci̇, Yaşar Sözen Jan 2022

Representation Variety Of Free Or Surface Groups And Reidemeister Torsion, Fati̇h Hezenci̇, Yaşar Sözen

Turkish Journal of Mathematics

For $G \in \left\{ \mathrm{GL}(n,\mathbb{C}) , \mathrm{SL}(n,\mathbb{C})\right\} ,$ we consider $G-$valued representations of free or surface group with genus $ >1.$ We establish a formula for computing Reidemeister torsion of such representations in terms of Atiyah-Bott-Goldman symplectic form for $G.$ Furthermore, we apply the obtained results to hyperbolic 3-manifolds.

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On Sharpening And Generalization Of Rivlin's Inequality, Prasanna Kumar, Gradimir Milovanovic Jan 2022

On Sharpening And Generalization Of Rivlin's Inequality, Prasanna Kumar, Gradimir Milovanovic

Turkish Journal of Mathematics

n inequality due to T. J. Rivlin from 1960 states that if $P(z)$ is a polynomial of degree $n$ having no zeros in $ z

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Arf Numerical Semigroups With Multiplicity $11$ And $13$, Hali̇l İbrahi̇m Karakaş, Sedat İlhan, Meral Süer Jan 2022

Arf Numerical Semigroups With Multiplicity $11$ And $13$, Hali̇l İbrahi̇m Karakaş, Sedat İlhan, Meral Süer

Turkish Journal of Mathematics

Parametrizations are given for Arf numerical semigroups with multiplicity up to 10. In this work, we give parametrizations of Arf numerical semigroups with multiplicity $11$ and $13$, and combining these results with previous results about the number of Arf numerical semigroups with multiplicity $2, 3, 5, 7$, we share some observations about the set of Arf numerical semigroups with prime multiplicity.

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On Slack $2$-Geodesic Convex Set And Geodesic $E$-Pseudoconvex Function With Application, Akhlad Iqbal, Praveen Kumar, Izhar Ahmad Jan 2022

On Slack $2$-Geodesic Convex Set And Geodesic $E$-Pseudoconvex Function With Application, Akhlad Iqbal, Praveen Kumar, Izhar Ahmad

Turkish Journal of Mathematics

We introduce a new class of sets named, slack $2$-geodesic convex set on Riemannian manifolds and verify by a nontrivial example. We define a geodesic $E$-pseudoconvex function with a suitable example. Some properties of geodesic $E$-quasiconvex function are discussed. We establish some relationships between slack $2$-geodesic convex set, geodesic $E$-pseudoconvex function and geodesic $E$-quasiconvex function. Moreover, an application of geodesic $E$-quasiconvex function to a nonlinear programming problem is also presented.

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Tensor Products Of Graded-Simple $\Mathfrak{Sl}_2(\Mathbb{C})$-Modules, Yuri Bahturin, Abdallah Shihadeh Jan 2022

Tensor Products Of Graded-Simple $\Mathfrak{Sl}_2(\Mathbb{C})$-Modules, Yuri Bahturin, Abdallah Shihadeh

Turkish Journal of Mathematics

In our paper [3] we have constructed the first example of simple graded torsion-free $\mathfrak{sl}_2(\mathbb{C})$-module denoted by $ M^{C}_{λ}$. Here we examine tensor product of $ M^{C}_{λ}$ with finite dimensional simple $\mathfrak{sl}_2(\mathbb{C})$-modules.

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Jordan Maps And Zero Lie Product Determined Algebras, Matej Bresar Jan 2022

Jordan Maps And Zero Lie Product Determined Algebras, Matej Bresar

Turkish Journal of Mathematics

Let $A$ be an algebra over a field $F$ with $(F)\ne 2$. If $A$ is generated as an algebra by $[[A,A],[A,A]]$, then for every skew-symmetric bilinear map $\Phi:A\times A\to X$, where $X$ is an arbitrary vector space over $F$, the condition that $\Phi(x^2,x)=0 $ for all $x\in A$ implies that $\Phi(xy,z) +\Phi(zx,y) + \Phi(yz,x)=0$ for all $x,y,z\in A$. This is applicable to the question of whether $A$ is zero Lie product determined and is also used in proving that a Jordan homomorphism from $A$ onto a semiprime algebra $B$ is the sum of a homomorphism and an antihomomorphism.

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Invariants Of Symplectic And Orthogonal Groups Acting On $Gl(N,Cc)$-Modules, Vesselin Drensky, Elitza Hristova Jan 2022

Invariants Of Symplectic And Orthogonal Groups Acting On $Gl(N,Cc)$-Modules, Vesselin Drensky, Elitza Hristova

Turkish Journal of Mathematics

Let $GL(n) = GL(n, CC)$ denote the complex general linear group and let $G \subset GL(n)$ be one of the classical complex subgroups $OO(n)$, $SO(n)$, and $Sp(2k)$ (in the case $n = 2k$). We take a finite dimensional polynomial $GL(n)$-module $W$ and consider the symmetric algebra $S(W)$. Extending previous results for $G=SL(n)$, we develop a method for determining the Hilbert series $H(S(W)^G, t)$ of the algebra of invariants $S(W)^G$. Our method is based on simple algebraic computations and can be easily realized using popular software packages. Then we give many explicit examples for computing $H(S(W)^G, t)$. As an application, we …

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