Open Access. Powered by Scholars. Published by Universities.®

Physical Sciences and Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

2019

Discipline
Institution
Keyword
Publication
Publication Type
File Type

Articles 12751 - 12780 of 15722

Full-Text Articles in Physical Sciences and Mathematics

Synthesis And Antimicrobial Activity Of 1-(Benzo[B]Thiophen-4-Yl)-4-(2-(Oxo, Hydroxyl, And Fluoro)-2-Phenylethyl)Piperazine And 1-(Benzo[D]Isothiazole-3-Yl)-4-(2-(Oxo, Hydroxy, And Fluoro)-2-Phenylethyl)Piperazine Derivatives, Vaibhav Mishra, Tejpal Singh Chundawat Jan 2019

Synthesis And Antimicrobial Activity Of 1-(Benzo[B]Thiophen-4-Yl)-4-(2-(Oxo, Hydroxyl, And Fluoro)-2-Phenylethyl)Piperazine And 1-(Benzo[D]Isothiazole-3-Yl)-4-(2-(Oxo, Hydroxy, And Fluoro)-2-Phenylethyl)Piperazine Derivatives, Vaibhav Mishra, Tejpal Singh Chundawat

Turkish Journal of Chemistry

Twenty-two compounds in a series of 1-(benzo[$b$]thiophen-4-yl)-4-(2-(oxo, hydroxy, and fluoro)-2-phenylethyl) piperazine and 1-(benzo[$d$]isothiazole-3-yl)-4-(2-(oxo, hydroxy, and fluoro)-2-phenylethyl)-piperazine derivatives were synthesized through nucleophilic substitution reaction of phenacyl bromides with hetero arylpiperazine, reduction, and then fluorination. Compound K2 showed potent activity against gram-negative bacterial stain P. aeruginosa with minimum inhibitory concentration (MIC) value of 12.5 μg/mL. This compound showed better inhibitory activity than the standard drug chloramphenicol. K4 against S. aureus, H2 against P. aeruginosa, and F4 against E. coli showed good inhibitory activity with MIC values of 62.5 μg/mL. Compounds K1, K2, K4, K8, F1, and F3 showed good inhibitory activity against …

Go to article

Improving The Mechanical And Thermal Properties Of Chlorinated Poly(Vinyl Chloride) By Incorporating Modified Caco$_{3}$ Nanoparticles As A Filler Jan 2019

Improving The Mechanical And Thermal Properties Of Chlorinated Poly(Vinyl Chloride) By Incorporating Modified Caco$_{3}$ Nanoparticles As A Filler

Turkish Journal of Chemistry

Chlorinated poly(vinyl chloride) (CPVC)/calcium carbonate nanocomposites were successfully prepared by the incorporation of calcium carbonate (CaCO$_{3})$ nanoparticles into the CPVC matrix. The compatibility between the two phases was obtained by surface modification of the CaCO$_{3}$ nanoparticles with stearic acid, leading to improved material performance. The effects of the addition of different amounts of CaCO$_{3}$ nanoparticles to the CPVC on the thermal, mechanical, and morphological characteristics of the CPVC/CaCO$_{3}$ nanocomposites were investigated. The thermal stability of the CPVC/CaCO$_{3}$ nanocomposites was evaluated by thermogravimetric analysis~and differential scanning calorimetry. In addition, the surface texture of the CPVC and the dispersion of the CaCO$_{3}$ …

Go to article

Electrochemical Oxidation Of Curcuminoids: An Experimental And Computational Investigation, Zeynep Kalaycioğlu, Nurgül Karadaş, Mehmet Emi̇n Çinar, Si̇bel Ayşil Özkan, Duri̇şehvar Özer Ünal, Ayşegül Gölcü, Fatma Bedi̇a Eri̇m Jan 2019

Electrochemical Oxidation Of Curcuminoids: An Experimental And Computational Investigation, Zeynep Kalaycioğlu, Nurgül Karadaş, Mehmet Emi̇n Çinar, Si̇bel Ayşil Özkan, Duri̇şehvar Özer Ünal, Ayşegül Gölcü, Fatma Bedi̇a Eri̇m

Turkish Journal of Chemistry

Curcuminoids, reported to have important biological properties, such as antioxidant, anti-Alzheimer, and antidiabetic properties, comprise curcumin (CRM; 1,7-bis [4-hydroxy-3-methoxyphenyl]-1,6-heptadiene-3,5-dione) and its derivatives demethoxycurcumin (DMC; (E,6E)-1-(3,4-dimethoxy-cyclohexyl)-7-(3,4-dimethoxyphenyl)hepta-1,6-diene-3,5-dione) and bisdemethoxycurcumin (BDMC; 1,7-bis[4-hydroxyphenyl]-1,6-heptadiene-3,5-dione). Their electrochemical oxidations are thoroughly explored by applying cyclic and differential pulse voltammetric techniques. The dependence of current intensities and potentials on pH, concentration, scan rate, and nature of the buffer was investigated. The outcome is supported by density functional theory computations indicating the transfer of 4-e$^{-}$/H$^{+}$, 6-e$^{-}$/H$^{+}$, and 8-e$^{-}$/H$^{+}$ couples involved in the oxidation mechanisms of CRM, DMC, and BDMC, respectively, leading to the formation of the same oxidized product.

Go to article

Bisbenzoxazole Derivatives Had An Antiinflammatory Effect On In Vitro Stimulated Macrophages, Furkan Ayaz, Rusmeenee Kheeree, Qadar Ahmed Isse, Ronak Haj Ersan, Özteki̇n Algül Jan 2019

Bisbenzoxazole Derivatives Had An Antiinflammatory Effect On In Vitro Stimulated Macrophages, Furkan Ayaz, Rusmeenee Kheeree, Qadar Ahmed Isse, Ronak Haj Ersan, Özteki̇n Algül

Turkish Journal of Chemistry

Benzoxazoles are DNA base bioisosteres and studies suggest that their derivatives have antiproliferative activities. Based on their antiproliferative activities they have been mostly studied as new generation anticancer drugs. In our study we exploited their antiproliferative effect, aiming to delineate bisbenzoxazole derivatives' (RHE 231 and RHE 238) potential antiinflammatory effect on mouse macrophages that are activated in vitro through danger signal LPS stimulation. RAW 267.4 mammalian macrophages were activated in the presence of our derivatives with or without danger mimic E. coli derived LPS. We present data that support the strong antiinflammatory activity of the bisbenzoxazole derivatives RHE 231 and …

Go to article

On The Cover Ideals Of Chordal Graphs, Nursel Erey Jan 2019

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.

Go to article

On A Class Of Nonself-Adjoint Multidimensional Periodic Schrödinger Operators, Oktay Veli̇ev Jan 2019

On A Class Of Nonself-Adjoint Multidimensional Periodic Schrödinger Operators, Oktay Veli̇ev

Turkish Journal of Mathematics

We investigate the Schrödinger operator $L(q)$ in $L_{2}\left( \mathbb{R}^{d}\right) \ (d\geq1)$ with the complex-valued potential $q$ that is periodic with respect to a lattice $\Omega.$ Besides, it is assumed that the Fourier coefficients $q_{\gamma}$ of $q$ with respect to the orthogonal system $\{e^{i\left\langle \gamma x\right\rangle }:\gamma\in\Gamma\}$ vanish if $\gamma$ belongs to a half-space, where $\Gamma$ is the lattice dual to $\Omega.$ We prove that the Bloch eigenvalues are $\mid\gamma+t\mid^{2}$ for $\gamma\in\Gamma,$ where $t$ is a quasimomentum and find explicit formulas for \ the Bloch functions. Moreover, we investigate the multiplicity of the Bloch eigenvalue and consider necessary and sufficient conditions …

Go to article

Almost Symmetric Numerical Semigroups With High Type, Pedro A. Garcia-Sanchez, Ignacio Ojeda Jan 2019

Almost Symmetric Numerical Semigroups With High Type, Pedro A. Garcia-Sanchez, Ignacio Ojeda

Turkish Journal of Mathematics

We establish a one-to-one correspondence between numerical semigroups of genus $g$ and almost symmetric numerical semigroups with Frobenius number $F$ and type $F-2g$, provided that $F$ is greater than or equal to $4g-1$.

Go to article

The Exponential Diophantine Equation $(3am^2-1)^X+(A(A-3)M^2+1)^Y=(Am)^Z$, Nai-Juan Deng, Dan-Yao Wu, Ping-Zhi Yuan Jan 2019

The Exponential Diophantine Equation $(3am^2-1)^X+(A(A-3)M^2+1)^Y=(Am)^Z$, Nai-Juan Deng, Dan-Yao Wu, Ping-Zhi Yuan

Turkish Journal of Mathematics

Let $a,\ m$ be positive integers such that $am\not\equiv0\pmod{3}, 2\nmid a$, and $a>3$. We prove that the exponential Diophantine equation $(3am^2-1)^x+(a(a-3)m^2+1)^y=(am)^z$ has only the positive integer solution $(x,y,z)=(1,1,2)$.

Go to article

On Factorials In Perrin And Padovan Sequences, Nuretti̇n Irmak Jan 2019

On Factorials In Perrin And Padovan Sequences, Nuretti̇n Irmak

Turkish Journal of Mathematics

Assume that $w_n$ is the $n$th term of either Padovan or Perrin sequence. In this paper, we solve the equation $w_n=m!$ completely.

Go to article

Ricci-Yamabe Maps For Riemannian Flows And Their Volume Variation And Volume Entropy, Si̇nem Güler, Mircea Crasmareanu Jan 2019

Ricci-Yamabe Maps For Riemannian Flows And Their Volume Variation And Volume Entropy, Si̇nem Güler, Mircea Crasmareanu

Turkish Journal of Mathematics

The aim of this short note is to produce new examples of geometrical flows associated to a given Riemannian flow $g(t)$. The considered flow in covariant symmetric $2$-tensor fields will be called Ricci-Yamabe map since it involves a scalar combination of Ricci tensor and scalar curvature of $g(t)$. Due to the signs of considered scalars the Ricci-Yamabe flow can be also a Riemannian or semi-Riemannian or singular Riemannian flow. We study the associated function of volume variation as well as the volume entropy. Finally, since the two-dimensional case was the most commonly addressed situation we express the Ricci flow equation …

Go to article

On Congruences For $Q$-Analogues Of Ballot Numbers, Si̇bel Koparal Jan 2019

On Congruences For $Q$-Analogues Of Ballot Numbers, Si̇bel Koparal

Turkish Journal of Mathematics

In this paper, we examine some congruences with $q$-analogues of ballot numbers. For example, for $n>1$ and $% d=0,1,...,n-1$, \begin{eqnarray*} &&\sum\limits_{k=1}^{n-d}q^{k}B_{k,d}^{q}\equiv -2+\left( -1\right) ^{n-d}\left( \frac{n-d+1}{3}\right) q^{-\frac{1}{3}\binom{n-d}{2}}-\left( \frac{n-d-1% }{3}\right) q^{d+1-\frac{1}{3}\binom{n-d-2}{2}} \pmod{\Phi _{n}\left( q\right)} , \end{eqnarray*}% with the Legendre symbol $\left( \frac{.}{3}\right) ,~$the$~q$-analogue of ballot number $B_{n,d}^{q}$, and the $n$th cyclotomic polynomial $% \Phi _{n}\left( q\right) $.

Go to article

Unbounded Absolutely Weak Dunford-Pettis Operators, Nazi̇fe Erkurşun Özcan, Ni̇yazi̇ Anil Gezer, Omid Zabeti Jan 2019

Unbounded Absolutely Weak Dunford-Pettis Operators, Nazi̇fe Erkurşun Özcan, Ni̇yazi̇ Anil Gezer, Omid Zabeti

Turkish Journal of Mathematics

In the present article, we expose various properties of unbounded absolutely weak Dunford?Pettis and unbounded absolutely weak compact operators on a Banach lattice E. In addition to their topological and lattice properties, we investigate relationships between M-weakly compact operators, L-weakly compact operators, and order weakly compact operators with unbounded absolutely weak Dunford-Pettis operators. We show that the square of any positive uaw-Dunford-Pettis (M-weakly compact) operator on an order continuous Banach lattice is compact. Many examples are given to illustrate the essential conditions.

Go to article

On Composition Factors In Modules Over Some Group Rings, Martyn Russell Dixon, Leonid Andreevich Kurdachenko, Igor Yakov Subbotin Jan 2019

On Composition Factors In Modules Over Some Group Rings, Martyn Russell Dixon, Leonid Andreevich Kurdachenko, Igor Yakov Subbotin

Turkish Journal of Mathematics

The aim of this paper is to prove the following result: Let G be an FC-hypercentral group and let A have a finite FG-composition series. Then A contains two FG-submodules B,C such that A = B ⊕ C, where each FG-composition factor of B has finite F -dimension and each FG-composition factor of C has infinite F -dimension. Thishasconsequencesfor FG-modules whose proper submodules all have finite F -dimensionandforthose FG-modules whose proper quotients all have finite F -dimension.

Go to article

Minimal Free Resolutions Of The Tangent Cones For Gorenstein Monomial Curves, Pinar Mete, Esra Emi̇ne Zengi̇n Jan 2019

Minimal Free Resolutions Of The Tangent Cones For Gorenstein Monomial Curves, Pinar Mete, Esra Emi̇ne Zengi̇n

Turkish Journal of Mathematics

We study the minimal free resolution of the tangent cone of Gorenstein monomial curves in affine 4-space. We give the explicit minimal free resolution of the tangent cone of noncomplete intersection Gorenstein monomial curve whose tangentcone has fiveminimal generators and showthat the possible Betti sequences are (1,5,6,2) and (1,5,5,1). Moreover, we compute the Hilbert function of the tangent cone of these families as a result.

Go to article

Zeros Of The Extended Selberg Class Zeta-Functions And Of Their Derivatives, Ramunas Garunkstis Jan 2019

Zeros Of The Extended Selberg Class Zeta-Functions And Of Their Derivatives, Ramunas Garunkstis

Turkish Journal of Mathematics

Levinson and Montgomery proved that the Riemann zeta-function ζ(s) and its derivative have approximately the same number of nonreal zeros left of the critical line. Spira showed that ζ'(1/2+it) = 0 implies that ζ(1/2+it) = 0. Here we obtain that in small areas located to the left of the critical line and near it the functions ζ(s) and ζ'(s) have the same number of zeros. We prove our result for more general zeta-functions from the extended Selberg class S. We also consider zero trajectories of a certain family of zeta-functions from S.

Go to article

Compactness Of The Commutators Of Intrinsic Square Functions On Weighted Lebesgue Spaces, Xiaomei Wu, Xiao Yu Jan 2019

Compactness Of The Commutators Of Intrinsic Square Functions On Weighted Lebesgue Spaces, Xiaomei Wu, Xiao Yu

Turkish Journal of Mathematics

The aim of this paper is to study the compactness for the commutators of intrinsic square functions, including the intrinsic $g_{\lambda}^*$-function and the intrinsic Littlewood-Paley g-function. Using a weighted version of the Frech\'{e}t-Kolmogorov-Riesz theorem, the compactness for their commutators generated with the CMO functions is obtained on the weighted Lebesgue spaces.

Go to article

Inclusion Properties Of Lucas Polynomials For Bi-Univalent Functionsintroduced Through The $\Mathfrak{Q}$-Analogue Of The Noor Integral Operator, Şahsene Altinkaya Jan 2019

Inclusion Properties Of Lucas Polynomials For Bi-Univalent Functionsintroduced Through The $\Mathfrak{Q}$-Analogue Of The Noor Integral Operator, Şahsene Altinkaya

Turkish Journal of Mathematics

In this paper, by using the $(\mathbf{P},\mathbf{Q})$-Lucas polynomials and the $\mathfrak{q}$-analogue of the Noor integral operator, we aim to build a bridge between the theory of geometric functions and that of special functions.

Go to article

Some General Results On Fractional Banach Sets, Faruk Özger Jan 2019

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.

Go to article

Covariant Differential Calculus On ${\Cal Sp}_H^{2, Sali̇h Çeli̇k, İlknur Temli̇ Jan 2019

Covariant Differential Calculus On ${\Cal Sp}_H^{2, Sali̇h Çeli̇k, İlknur Temli̇

Turkish Journal of Mathematics

The $h$-deformed symplectic superspaces via a contraction of the $q$-deformed symplectic superspaces are introduced and a covariant differential calculus on the quantum symplectic superspace ${\cal SP}_h^{2 1}$ is presented.

Go to article

Study On The Existence Of Solutions To Two Specific Types Of Differential-Difference Equations, Qiong Wang, Qiongyan Wang Jan 2019

Study On The Existence Of Solutions To Two Specific Types Of Differential-Difference Equations, Qiong Wang, Qiongyan Wang

Turkish Journal of Mathematics

This paper concerns the description of the entire or meromorphic solutions to two certain types of differential-difference equations under some certain conditions. The significance of our results lies in that we find the entire solutions of the second type equation with the form $f=Ae^{Bz}$, where $A,B$ are constants that are completely determined only by coefficients and correlated indices. Our results are accurate in a certain sense and are supplemented by an example. In particular, our results generalize and improve a result of Zhang and Huang, and they are closely related to recent results by Dong and Liao.

Go to article

Inverse Problem For Sturm-Liouville Differential Operators With Two Constant Delays, Mohammad Shahriari Jan 2019

Inverse Problem For Sturm-Liouville Differential Operators With Two Constant Delays, Mohammad Shahriari

Turkish Journal of Mathematics

In this manuscript, we study nonself-adjoint second-order differential operators with two constant delays. We investigate the properties of the spectral characteristics and the inverse problem of recovering operators from their spectra. An inverse spectral problem is studied of recovering the potential from spectra of two boundary value problems with one common boundary condition. The uniqueness theorem is proved for this inverse problem.

Go to article

On The Divisors Of Shifted Primes, Jean Marie De Koninck, Imre Katai Jan 2019

On The Divisors Of Shifted Primes, Jean Marie De Koninck, Imre Katai

Turkish Journal of Mathematics

Let $\tau(n)$ stand for the number of positive divisors of $n$. Given an additive function $f$ and a real number $\alpha\in [0,1)$, let $\displaystyle{h_n(\alpha):= \frac 1{\tau(n)} \sum_{d\mid n \atop \{f(d)\}

Go to article

Global Dynamics Of Perturbation Of Certain Rational Differenceequation, Sabina Hrustic, Mustafa Kulenovic, Samra Moranjkic, Zehra Nurkanovic Jan 2019

Global Dynamics Of Perturbation Of Certain Rational Differenceequation, Sabina Hrustic, Mustafa Kulenovic, Samra Moranjkic, Zehra Nurkanovic

Turkish Journal of Mathematics

We investigate the global asymptotic stability of the difference equation of the form \begin{equation*} x_{n+1}=\frac{A x_{n}^{2}+F}{a x_{n}^{2}+e x_{n-1}}, \quad n=0,1,\ldots, \end{equation*}% with positive parameters and nonnegative initial conditions such that $x_0 + x_{-1}>0$. The map associated to this equation is always decreasing in the second variable and can be either increasing or decreasing in the first variable depending on the parametric space. In some cases, we prove that local asymptotic stability of the unique equilibrium point implies global asymptotic stability.

Go to article

On Wiener's Tauberian Theorems And Convolution For Oscillatory Integral Operators, Luis Pinheiro De Castro, Rita Correia Guerra, Nguyen Minh Tuan Jan 2019

On Wiener's Tauberian Theorems And Convolution For Oscillatory Integral Operators, Luis Pinheiro De Castro, Rita Correia Guerra, Nguyen Minh Tuan

Turkish Journal of Mathematics

The main aim of this work is to obtain Paley--Wiener and Wiener's Tauberian results associated with an oscillatory integral operator, which depends on cosine and sine kernels, as well as to introduce a consequent new convolution. Additionally, a new Young-type inequality for the obtained convolution is proven, and a new Wiener-type algebra is also associated with this convolution.

Go to article

Some Unpublished Reclaw Theorems And Their Applications To Baire-Star-One Functions, Tomasz Natkaniec, Waldemar Sieg Jan 2019

Some Unpublished Reclaw Theorems And Their Applications To Baire-Star-One Functions, Tomasz Natkaniec, Waldemar Sieg

Turkish Journal of Mathematics

Lunina's 7-tuples $\langle E^1,\ldots, E^7\rangle$ of sets of pointwise convergence, divergence to $\infty$, divergence to $-\infty$, etc. for sequences of Baire-star-one functions are cha\-racterized. Generalization on ideal convergence of such sequences is discussed. Limits and ideal limits of sequences of Baire-star-one functions are considered in the last part of the article.

Go to article

A Short Note On Some Arithmetical Properties Of The Integer Part Of $\Alpha P$, Yildirim Akbal Jan 2019

A Short Note On Some Arithmetical Properties Of The Integer Part Of $\Alpha P$, Yildirim Akbal

Turkish Journal of Mathematics

Let $\alpha>0$ be an irrational number. We study some of the arithmetical properties of $\{ \fl{\alpha p}\}_{p=2}^{\infty}$, where $p$ denotes a prime number and $\fl{x}$ denotes the largest integer not exceeding $x$.

Go to article

The Cissoid Of Diocles In The Lorentz-Minkowski Plane, Şenay Baydaş, Bülent Karakaş Jan 2019

The Cissoid Of Diocles In The Lorentz-Minkowski Plane, Şenay Baydaş, Bülent Karakaş

Turkish Journal of Mathematics

This article presents the cissoid of Diocles and the cissoid of two circles with respect to origin in the Lorentz-Minkowski plane.

Go to article

A New General Subclass Of Analytic Bi-Univalent Functions, Serap Bulut Jan 2019

A New General Subclass Of Analytic Bi-Univalent Functions, Serap Bulut

Turkish Journal of Mathematics

In a very recent work, Şeker [Seker B. On a new subclass of bi-univalent functions defined by using Salagean operator. Turkish Journal of Mathematics 2018; 42: 2891-2896] defined two subclasses of analytic bi-univalent functions by means of Salagean differential operator and he obtained the initial Taylor-Maclaurin coefficient estimates for functions belonging to these classes. The main purpose of this paper is to improve the results obtained by Şeker in the aforementioned study. For this purpose, we define a general subclass of bi-univalent functions.

Go to article

Converse Theorems In Lyapunov's Second Method And Applications For Fractional Order Systems, Javier Gallegos, Manuel Duarte-Mermoud Jan 2019

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 …

Go to article

Some Ergodic Properties Of Multipliers On Commutative Banach Algebras, Heybetkulu Mustafayev, Hayri̇ Topal Jan 2019

Some Ergodic Properties Of Multipliers On Commutative Banach Algebras, Heybetkulu Mustafayev, Hayri̇ Topal

Turkish Journal of Mathematics

A commutative semisimple regular Banach algebra $A$ with the Gelfand space $ \Sigma _{A}$ is called a Ditkin algebra if each point of $\Sigma _{A}\cup \left\{ \infty \right\} $ is a set of synthesis for $A$. Generalizing the Choquet-Deny theorem, it is shown that if $T$ is a multiplier of a Ditkin algebra $A,$ then $\left\{ \varphi \in A^{\ast }:T^{\ast }\varphi =\varphi \right\} $ is finite dimensional if and only if \textnormal{card}$\mathcal{F}_{T}$ is finite, where $\mathcal{F}_{T}=\left\{ \gamma \in \Sigma _{A}:\widehat{T}\left( \gamma \right) =1\right\} $ and $ \widehat{T}$ is the Helgason-Wang representation of $T.$

Go to article

First Prev Next Last