Mostrando recursos 1 - 20 de 27

  1. Semidualizing Module and Gorenstein Homological Dimensions

    Zhang, Zhen
    Let $C$ be a semidualizing module over any commutative ring $R$. We investigate the semidualizing module $C$ with finite injective dimension. In particular, we obtain some equivalent characterizations of $C$ under the trivial extension of $R$ by $C$. Moreover, we get that the supremum of the $C$-Gorenstein projective dimensions of all $R$-modules and the supremum of the $C$-Gorenstein injective dimensions of all $R$-modules are equal. Hence the $C$-Gorenstein global dimension of the ring $R$ is definable. At last, we consider the weak $C$-Gorenstein global dimension.

  2. A Locally Asymptotically Optimal Test With Application to Financial Data

    Lounis, Tewfik; Ngatchou-Wandji, Joseph
    A locally asymptotically optimal test is constructed for log-return processes. The behavior of the test statistic is studied under the null and under a sequence of local alternatives. A local asymptotic normality (LAN) result is previously established. Applying the test to log-return data, one rejects the hypothesis that they are independent and identically distributed (iid).

  3. Quasi-uniform Spaces and $\mathcal{U}$-startpoint

    Gaba, Yaé Ulrich
    In this note, we extend the idea of startpoint to a quasi-uniform space. We present two main results, first for single-valued maps and second for multi-valued maps.

  4. Attractors for a Cahn-Hilliard-Navier-Stokes Model with Delays

    Medjo, Theodore Tachim
    In this article, we study a coupled Cahn-Hilliard-Navier-Stokes model with delays in a two-dimensional domain. The model consists of the Navier-Stokes equations for the velocity, coupled with a Cahn-Hilliard model for the order (phase) parameter. We prove the existence of an attractor using the theory of pullback attractors.

  5. Semigroup and Blow-Up Dynamics of Attraction Keller-Segel Equations in Scale of Banach Spaces

    Iiyambo, David S. I.; Willie, Robert
    In this paper, we study the asymptotic and blow-up dynamics of the attraction Keller-Segel chemotaxis system of equations in scale of Banach spaces $E^\alpha_q = H^{2\alpha,q}(\Omega), −1 \le \alpha \le 1,1 \lt q \lt \infty$, where $\Omega \subset \mathbb{R}^N$ is a bounded spatial domain. We show that the system of equations is well-posed for a perturbed analytic semigroup, whenever $2\chi + a \lt \left( \frac{Ne\pi}{2} \right)^{\beta+\frac{\gamma}{2}-\frac{1}{2}}$, where $\chi$ is the chemical attractivity coefficient, $a$ is the rate of production of chemical, and $q, \beta, \gamma$ are of the scale spaces. Thus, as $t\nearrow\infty$, the asymptotic dynamics are captured in the...

  6. Graded Lie Agebroids of Poisson Almost Commutative Algebras

    Ngakeu, Ferdinand
    We introduce and study the notion of abelian groups graded Lie algebroid structures on almost commutative algebras $\mathcal A$ and show that any graded Poisson bracket on $\mathcal A$ induces a graded Lie algebroid structure on the $\mathcal A$-module of 1-forms on $\mathcal A$ as in the classical Poisson manifolds. We also derive from our formalism the graded Poisson cohomology.

  7. On Symplectic Dynamics

    Tchuiaga, Stéphane
    This paper continues to carry out a foundational study of Banyaga's topologies of a closed symplectic manifold $(M,\omega)$ [4]. Our intention in writing this paper is to work out several “symplectic analogues” of some results found in the study of Hamiltonian dynamics. By symplectic analogue, we mean if the first de Rham's group (with real coefficients) of the manifold is trivial, then the results of this paper reduce to some results found in the study of Hamiltonian dynamics. Especially, without appealing to the positivity of the symplectic displacement energy, we point out an impact of the $L^\infty-$version of Hofer-like length...

  8. About the Degenerate Spectrum of the Tension Field for Mappings into a Symmetric Riemannian Manifold

    Kourouma, Moussa
    Let $(M,g)$ and $(N,h)$ be compact Riemannian manifolds, where $(N,h)$ is symmetric, $v\in W^{1,2}((M,g),(N,h))$, and $\tau $ is the tension field for mappings from $(M,g)$ into $(N,h)$. We consider the nonlinear eigenvalue problem $\tau (u)-\lambda \exp _{u}^{-1}v=0$, for $u$ $\in W^{1,2}(M,N)$ such that $u_{\left\vert \partial M\right. }=v_{\left\vert \partial M\right.}$, and $\lambda \in \mathbb{R}$. We prove, under some assumptions, that the set of all $\lambda $, such that there exists a solution $(u,\lambda )$ of this problem and a non trivial Jacobi field $V$ along $u$, is contained in $\mathbb{R}_{+}$, is countable, and has no accumulation point in $\mathbb{R}$. This result...

  9. On Commutativity of Prime Γ-Rings with $θ$-Derivations

    Huang, Shuliang; Rehman, Nadeem ur
    Let $M$ be a prime $\Gamma-$ring, $I$ a nonzero ideal, $\theta$ an automorphism and $d$ a $\theta-$derivation of $M$. In this article we have proved the following result: (1) If $d([x,y]_{\alpha})=\pm([x,y]_{\alpha})$ or $d((x\circ y)_{\alpha})=\pm((x\circ y)_{\alpha})$ for $x, y\in I; \alpha\in \Gamma$, then $M$ is commutative. (2) Under the hypothesis $d\theta=\theta d$ and $Char M\neq2$, if $(d(x)\circ d(y))_{\alpha}=0$ or $[d(x),d(y)]_{\alpha}=0$ for all $x, y\in I;\alpha\in \Gamma$, then $M$ is commutative. (3) If $d$ acts as a homomorphism or an anti-homomorphism on $I$, then $d=0$ or $M$ is commutative. Moreover, an example is given to demonstrate that the primeness imposed on the...

  10. Existence of Solutions of Some Nonlinear $φ$-Laplacian Equations with Neumann-Steklov Nonlinear Boundary Conditions

    Goli, Charles Etienne; Adje, Assohoun
    We study the existence of solutions of the quasilinear equation $$(D(u(t))\phi(u'(t)))'=f(t,u(t),u'(t)),\qquad a.e. \;\;t\in [0,T],$$ subject to nonlinear Neumann-Steklov boundary conditions on $[0,T]$, where $\phi: (-a,a)\rightarrow \mathbb{R}$ (for $0 < a < \infty$) is an increasing homeomorphism such that $\phi(0)=0$, $f:[0,T]\times\mathbb{R}^{2} \rightarrow \mathbb{R}$ a $L^1$-Carathéodory function, $D$ : $\mathbb{R}\longrightarrow (0,\infty)$ is a continuous function. Using topological methods, we obtain existence and multiplicity results.

  11. Hammerstein Equations with Lipschitz and Strongly Monotone Mappings in Classical Banach spaces

    Diop, C.; Sow, T. M. M.; Djitte, N.; Chidume, C. E.
    Let $E$ be a Banach space either $l_p$ or $L_p$ or $W^{m,p}$, $1 < p < \infty$, with dual $E^*$, and let $F :E\mapsto E^*$, $K: E^*\mapsto E $ be Lipschitz and strongly monotone mappings with $D(K)=R(F)=E^*$. Assume that the Hammerstein equation $u+KFu=0$ has a unique solution $\bar u$. For given $u_1\in E$ and $v_1\in E^*$, let $\{u_n\}$ and $\{v_n\}$ be sequences generated iteratively by: $u_{n+1} = J^{-1}(Ju_n -\lambda(Fu_n-v_n)),\,\,\,n\geq 1$ and $v_{n+1} = J(J^{-1}v_n-\lambda(Kv_n+u_n)),\,\,\,n\geq 1$, where $J$ is the duality mapping from $E$ into $E^*$ and $\lambda$ is a positive real number in $(0,1)$ satisfying suitable conditions. Then it is...

  12. An Example Concerning Hamiltonian Groups of Self Product II

    Hu, S.; Lalonde, F.
    We describe the natural identification of $FH_*(X \times X, \triangle; \omega \oplus \omega)$ with $FH_*(X, \omega)$. Under this identification, we show that the extra elements in ${\rm Ham}(X \times X, \omega \oplus \omega)$ found in [3], for $X = (S^2 \times S^2, \omega_0 \oplus \lambda \omega_0)$ for $\lambda > 1$, do not define new invertible elements in $FH_*(X, \omega)$.

  13. An Example Concerning Hamiltonian Groups of Self Product I

    Hu, S.; Lalonde, F.
    We show that $(S^2\times S^2, \omega_0 \oplus \lambda\omega_0)$, with $\lambda > 1$, is an example of symplectic manifold $(X, \omega)$ such that the $\pi_1{\rm Ham}(X \times X, \omega\oplus \omega)$ contains extra elements than those from $\pi_1{\rm Ham}(X, \omega) \times \pi_1{\rm Ham}(X, \omega)$.

  14. KV-Cohomology and Differential Geometry of Affinely Flat Manifolds. Information Geometry

    Nguiffo Boyom, M.; Ngakeu, F.; Byande, P. M.; Wolak, R.
    This paper is devoted to the socalled twisted cohomology of Koszul-Vinberg algebras. We discuss relationships between the twisted cohomology of Koszul-Vinberg algebras and Chevalley-Eilenberg cohomology of the commutator algebra of these algebras. We also discuss some geometry applications of these relationships. For instance we obtain some homological criteria for hyberbolicity and for completeness of locally flat manifolds. We also discuss some topics which are related to twisted cohomology. In particular, we use some techniques of information geometry to discuss canonical representations of locally flat connections.

  15. Integration of Conformal Jacobi Fibrations and Prequantization of Poisson Fibrations

    Wade, A.
    We show that integrable conformal Jacobi fibrations are in onetoone correspondence with sourcesimply connected fibered conformal contact groupoids. We also prove that prequantizable Poisson fibrations give rise to Jacobi fibrations. In addition, sourcesimply connected symplectic groupoids associated to prequantizable and integrable Poisson fibrations are also prequantizable.

  16. Two Families of Affine Osserman Connections on 3-Dimensional Manifolds

    Diallo, A. S.; Hassirou, M.
    The aim of this note is to study the Osserman condition on two families affine connections. As applications, examples of affine Osserman connections which are Ricci flat but not flat are given.

  17. Three Approaches to Morse-Bott Homology

    Hurtubise, D. E.
    In this paper we survey three approaches to computing the homology of a finite dimensional compact smooth closed manifold using a Morse-Bott function and discuss relationships among the three approaches. The first approach is to perturb the function to a Morse function, the second approach is to use moduli spaces of cascades, and the third approach is to use the Morse-Bott multicomplex. With respect to an explicit perturbation (which can be used to derived the Morse-Bott inequalities), the first two approaches yield the same chain complex up to sign. The third approach is fundamentally different. It combines singular cubical chains...

  18. $\cal D$-Homothetic Warping and Applications to Geometric Structures and Cosmology

    Blair, D. E.
    It is a great pleasure for me to dedicate this paper to Professor Augustin Banyaga in recognition of both his collegiality and his many contributions to symplectic and contact geometry.

  19. Sasakian Metrics with an Additional Contact Structure

    Drăghici, T.; Rukimbira, P.
    The question of whether a Sasakian metric can admit an additional compatible ($K$)contact structure is addressed. In the complete case if the second structure is also assumed Sasakian, works of Tachibana-Yu and Tanno show that the manifold must be 3-Sasakian or an odd dimensional sphere with constant curvature. Some extensions of this result are obtained, mainly in dimensions 3 and 5.

  20. Sasakian Manifolds with Perfect Fundamental Groups

    Boyer, C. P.; Tønnesen-Friedman, C. W.
    Using the Sasakian join construction with homology 3-spheres, we give a countably infinite number of examples of Sasakian manifolds with perfect fundamental group in all odd dimensions $\geq 3$. These have extremal Sasaki metrics with constant scalar curvature. Moreover, we present further examples of both Sasaki-Einstein and Sasaki$\eta$Einstein metrics.

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