Abstract: In this work, we study cyclic codes that have generators as Fibonacci polynomials over finite fields. We show that these cyclic codes in most cases produce families of maximum distance separable and optimal codes with interesting properties. We explore these relations and present some examples. Also, we present applications of these codes to secret sharing schemes. PubDate: 2017-12-01

Abstract: We construct a metrical framed \(f(3,-1)\) -structure on the (1, 1)-tensor bundle of a Riemannian manifold equipped with a Cheeger–Gromoll type metric and by restricting this structure to the (1, 1)-tensor sphere bundle, we obtain an almost metrical paracontact structure on the (1, 1)-tensor sphere bundle. Moreover, we show that the (1, 1)-tensor sphere bundles endowed with the induced metric are never space forms. PubDate: 2017-12-01

Abstract: The aim of the article is to study the unsteady magnetohydrodynamic-free convection flow of an electrically conducting incompressible viscous fluid over an infinite vertical plate with ramped temperature and constant concentration. The motion of the plate is a rectilinear translation with an arbitrary time-dependent velocity. Closed-form solutions for the temperature, concentration and velocity fields of the fluid are obtained. The influence of transverse magnetic field that is fixed relative either to fluid or plate is studied. Furthermore, the effects of system parameters on the fluid velocity are analyzed through numerical simulations and graphical illustrations. PubDate: 2017-10-06

Abstract: In this paper, we introduce octadecic functional equation. Moreover, we prove the stability of the octadecic functional equation in multi-normed spaces by using the fixed point method. PubDate: 2017-09-30

Abstract: This work deals with concepts of non-differentiability and a non-integer order differential on timescales. Through an investigation of a local non-integer order derivative on timescales, a mean value theorem (a fractional analog of the mean value theorem on timescales) is presented. Then, by illustrating a vanishing property of this derivative, its objectivity is discussed. As a first-hand result, the potentials and capability of this fractional derivative connected to nonsmooth analysis, including non-differentiable paths and a class of self-similar fractals, are stated. It is stated that the non-integer order derivative never vanishes almost everywhere. It has been shown that with the help of changing the order of differentiability on a q-timescale, the non-differentiability disappears. PubDate: 2017-09-23

Abstract: Let G be a group and \(\omega (G)=\{o(g) g\in G\}\) be the set of element orders of G. Let \(k\in \omega (G)\) and \(s_k= \{g\in G o(g)=k\} \) . Let \(nse(G)=\{s_k k\in \omega (G) \}\) . In this paper, we prove that if G is a group and \(G_2 (4)\) is the Chevalley group such that \(nse(G)=nse(G_2 (4))\) , then \(G\cong G_2 (4)\) . PubDate: 2017-09-22

Abstract: Sub-Riemannian spaces are spaces whose metric structure may be viewed as a constrained geometry, where motion is only possible along a given set of directions, changing from point to point. The simplest example of such spaces is given by the so-called Heisenberg group. The characteristic constrained motion of sub-Riemannian spaces has numerous applications in robotic control in engineering and neurobiology where it arises naturally in the functional magnetic resonance imaging (FMRI). It also arises naturally in other branches of pure mathematics as Cauchy Riemann geometry, complex hyperbolic spaces, and jet spaces. In this paper, we review the use of the relationship between Heisenberg geometry and Cauchy Riemann (CR) geometry. More precisely, we focus on the problem of the prescription of the scalar curvature using techniques related to the theory of critical points at infinity. These techniques were first introduced by Bahri, Bahri and Brezis for the Yamabe conjecture in the Riemannian settings. PubDate: 2017-09-11

Abstract: A well-known result, due to Dirichlet and later generalized by de la Vallée–Poussin, expresses a relationship between the sum of fractional parts and the Euler–Mascheroni constant. In this paper, we prove an asymptotic relationship between the summation of the products of fractional parts with powers of integers on the one hand, and the values of the Riemann zeta function, on the other hand. Dirichlet’s classical result falls as a particular case of this more general theorem. PubDate: 2017-09-06

Abstract: For a sequence of positive numbers \(\beta =\{\beta _{n}\}_{n\in \mathbb {Z}}\) , the space \(L^2(\beta )\) consists of all \(f(z)=\sum _{-\infty }^\infty a_nz^n\) , \(a_n\in \mathbb {C}\) for which \(\sum _{-\infty }^\infty a_n ^2\beta _n^2<\infty \) . For a bounded function \(\varphi (z)=\sum _{-\infty }^\infty a_nz^n\) , the slant weighted Toeplitz operator \(A_\varphi ^{(\beta )}\) is an operator on \(L^2(\beta )\) defined as \(A_\varphi ^{(\beta )}=WM_\varphi ^{(\beta )}\) , where \(M_\varphi ^{(\beta )}\) is the weighted multiplication operator on \(L^2(\beta )\) and W is an operator on \(L^2(\beta )\) such that \(Wz^{2n}=z^n\) , \(Wz^{2n-1}=0\) for all \(n\in \mathbb {Z}\) . In this paper we show that for a trigonometric polynomial \(\varphi (z)=\sum _{n=-p}^q a_nz^n\) , \(A_\varphi ^{(\beta )}\) cannot be hyponormal unless \(\varphi \equiv 0\) . We also show that, for \(k \ge 2 \) the \(k^{th}\) order slant weighted Toeplitz operator \( U_{k,\varphi }^{(\beta )}\) cannot be hyponormal unless \(\phi \equiv 0 \) . Also the compression of \( U_{k,\varphi }^{(\beta )}\) to \(H^2(\beta )\) , denoted by \( V_{k,\varphi }^{(\beta )}\) , cannot be hyponormal unless \(\phi \equiv 0 \) . PubDate: 2017-09-05

Abstract: In this paper, we consider the problem of prescribing scalar curvature under minimal boundary conditions on the standard four-dimensional half sphere. We describe the lack of compactness of the associated variational problem and we give new existence and multiplicity results. PubDate: 2017-09-01

Abstract: We study the nonexistence of nontrivial solutions for the nonlinear elliptic system $$\begin{aligned} \left\{ \begin{array}{lll} (-\Delta _x)^{\alpha /2}u+ x ^{2\delta } (-\Delta _y)^{\beta /2}u+ x ^{2\eta } y ^{2\theta } (-\Delta _z)^{\gamma /2}u&{}=&{} v^p,\\ \\ (-\Delta _x)^{\mu /2}v+ x ^{2\delta } (-\Delta _y)^{\nu /2}v+ x ^{2\eta } y ^{2\theta } (-\Delta _z)^{\sigma /2}v&{}=&{} u^q, \\ \end{array} \right. \end{aligned}$$ where \((x,y,z)\in \mathbb {R}^{N_1}\times \mathbb {R}^{N_2}\times \mathbb {R}^{N_3}\) , \(0<\alpha ,\beta ,\gamma ,\mu , \nu , \sigma \le 2\) , \(\delta , \eta ,\theta \ge 0\) , and \(p,q>1\) . Here, \((-\Delta _x)^{\alpha /2}\) , \(0<\alpha <2\) , is the fractional Laplacian operator of order \(\alpha /2\) with respect to the variable \(x\in \mathbb {R}^{N_1}\) , \((-\Delta _y)^{\beta /2}\) , \(0<\beta <2\) , is the fractional Laplacian operator of order \(\beta /2\) with respect to the variable \(y\in \mathbb {R}^{N_2}\) , and \((-\Delta _z)^{\gamma /2}\) , \(0<\gamma <2\) , is the fractional Laplacian operator of order \(\gamma /2\) with respect to the variable \(z\in \mathbb {R}^{N_3}\) . Using a weak formulation approach, sufficient conditions are provided in terms of space dimension and system parameters. PubDate: 2017-09-01

Abstract: Let X be a simply connected CW-complex of finite type and \({\mathbb {K}}\) an arbitrary field. In this paper, we use the Eilenberg–Moore spectral sequence of \(C_*(\Omega (X), \mathbb K)\) to introduce a new homotopical invariant \(\textsc {r}(X, {\mathbb {K}})\) . If X is a Gorenstein space with nonzero evaluation map, then \(\textsc {r}(X, {\mathbb {K}})\) turns out to interpolate \(\mathrm {depth}(H_*(\Omega (X), {\mathbb {K}}))\) and \(\mathrm {e}_{{\mathbb {K}}}(X)\) . We also define for any minimal Sullivan algebra \((\Lambda V,d)\) a new spectral sequence and make use of it to associate to any 1-connected commutative differential graded algebra (A, d) a similar invariant \(\textsc {r}(A,d)\) . When \((\Lambda V,d)\) is a minimal Sullivan model of X, this invariant fulfills the relation \(\textsc {r}(X, {\mathbb {K}}) = \textsc {r}(\Lambda V,d)\) . PubDate: 2017-09-01

Abstract: In this paper, we characterize spaces such that their one-point compactification (resp., Herrlich compactification) is weakly submaximal. We also establish a necessary and sufficient condition on \(T_{0}\) -spaces in order to get their one-point compactification (resp., Herrlich compactification) \(T_{D}\) -spaces. PubDate: 2017-08-30

Abstract: In this paper, our aim is to deduce some sharp Turán type inequalities for the remainder q-exponential functions. Our results are shown to be generalizations of results which were obtained by Alzer (Arch Math 55, 462–464, 1990). PubDate: 2017-08-21

Abstract: In this paper, we prove the existence of at least one periodic solution for some nonlinear parabolic boundary value problems associated with Leray–Lions’s operators with variable exponents under the hypothesis of existence of well-ordered sub- and supersolutions. PubDate: 2017-08-19

Abstract: We obtain minimal dimension matrix representations for each of the Lie algebras of dimensions five, six, seven and eight obtained by Turkowski that have a non-trivial Levi decomposition. The key technique involves using the invariant subspaces associated to a particular representation of a semi-simple Lie algebra to help in the construction of the radical in the putative Levi decomposition. PubDate: 2017-08-17

Abstract: In this paper, we consider the problem of existence and multiplicity of conformal metrics on a Riemannian compact 4-dimensional manifold \((M^4,g_0)\) with positive scalar curvature. We prove a new existence criterium which provides existence results for a dense subset of positive functions and generalizes Bahri–Coron Euler–Poincaré type criterium. Our argument gives estimates of the Morse index of the founded solutions and has the advantage to extend known existence results. Moreover, it provides, for generic K Morse Inequalities at Infinity, which give a lower bound on the number of metrics with prescribed scalar curvature in terms of the topological contribution of its critical points at Infinity to the difference of topology between the level sets of the associated Euler–Lagrange functional. PubDate: 2017-05-02

Abstract: This paper is concerned with prescribing the fractional Q-curvature on the unit sphere \(\mathbb {S}^{n}\) endowed with its standard conformal structure \(g_0\) , \(n\ge 4\) . Since the associated variational problem is noncompact, we approach this issue with techniques passed by Abbas Bahri, as the well known theory of critical points at infinity, as well as some lesser known topological invariants that appear here as criteria for existence results. PubDate: 2017-04-18