Recursos de colección
Project Euclid (Hosted at Cornell University Library) (204.217 recursos)
African Diaspora Journal of Mathematics
African Diaspora Journal of Mathematics
Yamaguchi, Toshihiro; Yokura, Shoji
The well-known Hilali conjecture stated in [9] is one claiming that if $X$ is a simply connected elliptic space, then $ \dim \pi_*(X)\otimes {\mathbb Q} \leq \dim H_*(X; {\mathbb Q})$. In this paper we propose that if $f:X \to Y$ is a continuous map of simply connected elliptic spaces, then $\dim {\rm Ker} \ \pi_*(f)_{\mathbb Q}\leq \dim {\rm Ker}\ H_*(f; {\mathbb Q})+1$, and we prove this for certain reasonable cases. Our proposal is a relative version of the Hilali conjecture and it includes the Hilali conjecture as a special case.
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.
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).
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.
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.
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...
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.
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...
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...
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...
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.
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...
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 $FH_*(X, \omega)$.
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 $FH_*(X, \omega)$.
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 $\pi_1{\rm Ham}(X, \omega) \times \pi_1{\rm Ham}(X, \omega)$.
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 $\pi_1{\rm Ham}(X, \omega) \times \pi_1{\rm Ham}(X, \omega)$.
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.
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.
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.
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.