African Diaspora Journal of Mathematics Articles (Project Euclid)
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The latest articles from African Diaspora Journal of Mathematics on Project Euclid, a site for mathematics and statistics resources.en-usCopyright 2010 Cornell University LibraryEuclid-L@cornell.edu (Project Euclid Team)Thu, 05 Aug 2010 15:41 EDTThu, 21 Apr 2011 09:19 EDThttp://projecteuclid.org/collection/euclid/images/logo_linking_100.gifProject Euclid
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Intégrabilité algébrique : une introduction
http://projecteuclid.org/euclid.adjm/1270067485
<strong>Pol Vanhaecke</strong><p><strong>Source: </strong>Afr. Diaspora J. Math. (N.S.), Volume 9, Number 2, 1--16.</p>projecteuclid.org/euclid.adjm/1270067485_Thu, 05 Aug 2010 15:41 EDTThu, 05 Aug 2010 15:41 EDTExistence of $AP_{r}$-Almost Periodic Solutions For Some
Classes of Functional Differential Equationshttp://projecteuclid.org/euclid.adjm/1383677003<strong>C. Corduneanu</strong>, <strong>M. Mahdavi</strong><p><strong>Source: </strong>Afr. Diaspora J. Math. (N.S.), Volume 15, Number 2, 47--55.</p><p><strong>Abstract:</strong><br/>
This paper presents a couple of existence results, related to the classes of
functional equations of the form $x+k\ast x=f$, or $\frac{d}{dt}[\dot{x}+k\ast
x]=f$, with $f, x\in AP_r(R, \,{\mathcal{C}})=$ the space of almost periodic
functions defined by \[ AP_r(R,\, {\mathcal{C}})=\left\{f : f\simeq
\sum_{j=1}^{\infty} f_j\,e^{i\lambda_j t},\,f_j\in {\mathcal{C}},\lambda_j\in
R,\sum_{j=1}^{\infty}|f_j|^r \lt \infty\right\}, \] the norm being given by
$|f|_r= \left(\sum_{j=1}^{\infty}|f_j|^r\right)^{\frac{1}{r}}$, for each $r\in
[1, 2]$. The convolution product $k\ast x$, $k\in L^1(R,\, {\mathcal{C}})$,
$x\in AP_r(R,\, {\mathcal{C}})$ is defined by \[ (k\ast x)(t)=
\sum_{j=1}^{\infty} x_j\left( \int_R
k(s)\,e^{\lambda_j\,s}\,ds\right)\,e^{i\lambda_j\,t}, \] where $x(t)\simeq
\sum_{j=1}^{\infty} x_j\,e^{i\lambda_j\,t}$.
</p>projecteuclid.org/euclid.adjm/1383677003_Tue, 05 Nov 2013 13:43 ESTTue, 05 Nov 2013 13:43 ESTWeighted StepanovLike PseudoAlmost Periodic Functions in
Lebesgue Space with Variable Exponents $L^{p(x)}$http://projecteuclid.org/euclid.adjm/1387313355<strong>T. Diagana</strong>, <strong>M. Zitane</strong><p><strong>Source: </strong>Afr. Diaspora J. Math. (N.S.), Volume 15, Number 2, 56--75.</p><p><strong>Abstract:</strong><br/>
In this paper we introduce and study a new class of functions called
$S^{p,q(x)}$pseudo-almost periodic (or weighted Stepanov-like pseudo-almost
periodic functions with variable exponents), which generalizes the class of
weighted Stepanov-like pseudo-almost periodic functions. Basic properties of
these new spaces are established. The existence of weighted pseudo-almost
periodic solutions to some first-order differential equations with
$S^{p,q(x)}$pseudo-almost periodic coefficients will also be studied.
</p>projecteuclid.org/euclid.adjm/1387313355_Tue, 17 Dec 2013 15:49 ESTTue, 17 Dec 2013 15:49 ESTWeakly Almost Periodic Functions in Topological Vector
Spaceshttp://projecteuclid.org/euclid.adjm/1387313356<strong>S. M. Alsulami</strong>, <strong>L. A. Khan</strong><p><strong>Source: </strong>Afr. Diaspora J. Math. (N.S.), Volume 15, Number 2, 76--86.</p><p><strong>Abstract:</strong><br/>
Harald Bohr was the founder of the theory of almost periodicity. The theory of
almost periodic functions taking values in locally convex spaces was studied by
G.M. N'Guérékata in his papers [9, 10]. Khan and Alsulami [12] studied the
concept of almost periodicity in the general topological vector spaces. In this
paper, we pursue their study further and extend the concept of weakly almost
periodicity to topological vector spaces having non-trivial duals.
</p>projecteuclid.org/euclid.adjm/1387313356_Tue, 17 Dec 2013 15:49 ESTTue, 17 Dec 2013 15:49 ESTExistence and Attractivity Results for Some Fractional
Order Partial Integro-differential Equations with Delayhttp://projecteuclid.org/euclid.adjm/1388953704<strong>S. Abbas</strong>, <strong>M. Benchohra</strong>, <strong>T. Diagana</strong><p><strong>Source: </strong>Afr. Diaspora J. Math. (N.S.), Volume 15, Number 2, 87--100.</p><p><strong>Abstract:</strong><br/>
In this paper we study some existence, uniqueness, estimates and global
asymptotic stability results for some functional integro-differential equations
of fractional order with finite delay. To achieve our goals we make extensive
use of some fixed point theorems as well as the so-called Pachpatte techniques.
</p>projecteuclid.org/euclid.adjm/1388953704_Sun, 05 Jan 2014 15:28 ESTSun, 05 Jan 2014 15:28 ESTStrongly Nonlinear $p(x)$-Elliptic Problems with
$L^1$-Datahttp://projecteuclid.org/euclid.adjm/1413809899<strong>E. Azroul</strong>, <strong>A. Barbara</strong>, <strong>H. Hjiaj</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 16, Number 2, 1--22.</p><p><strong>Abstract:</strong><br/>
In this paper, we will study the existence of solutions in the sense of
distributions for the quasilinear $p(x)$-elliptic problem, $$ Au + g(x,u,\nabla
u) = f,$$ where $A$ is a Leray-Lions operator from $W_{0}^{1,p(\cdot)}(\Omega)$
into its dual, the nonlinear term $g(x,s,\xi)$ has a growth condition with
respect to $\xi$ and the sign condition with respect to $s.$ The datum
$\>f\>$ is assumed in the dual space $\>W^{-1,p'(\cdot)}(\Omega),\>$
and then in $\>L^{1}(\Omega).$
</p>projecteuclid.org/euclid.adjm/1413809899_20141020085820Mon, 20 Oct 2014 08:58 EDTOn Simultaneous Characterization of the Set of Elements of
Good Approximation in Metric Spaceshttp://projecteuclid.org/euclid.adjm/1413809900<strong>T. D. Narang</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 16, Number 2, 23--30.</p><p><strong>Abstract:</strong><br/>
If W is a subset of a metric space $(X,d)$ then for a given $\varepsilon>0$,
an element $y_0\in W$ is called a good approximation or
$\varepsilon-$approximation for $x\in X$ if $d(x,y_0)\leq d(x,W)+\varepsilon.$
We denote by $P_{W,\varepsilon}(x)$ the set of all such $y_0\in W$ i.e. $P_{W,\;
\varepsilon}(x)=\{y\in W:d(x,y)\leq d(x,W)+\varepsilon\}$. In particular, for
$\varepsilon=0$ we get the set of all best approximations to $x$ in W. Given a
subset M of W, what are the necessary and sufficient conditions in order that
every element $y_0\in M$ is an element of good approximation to $x$ by the
elements of W? The paper mainly deals with this problem of simultaneous
characterization of elements of good approximation in metric spaces. The proved
results extend and generalize several known results on the subject.
</p>projecteuclid.org/euclid.adjm/1413809900_20141020085820Mon, 20 Oct 2014 08:58 EDTLightlike Hypersurfaces in Lorentzian Manifolds with
Constant Screen Principal Curvatureshttp://projecteuclid.org/euclid.adjm/1413809901<strong>C. Atindogbe</strong>, <strong>M. M. Mahi</strong>, <strong>J. Tossa</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 16, Number 2, 31--45.</p><p><strong>Abstract:</strong><br/>
In this paper, we generalize the Cartan's fundamental formula on lightlike
hypersurfaces, then we use it to show that a screen conformal lightlike
hypersurface of a Lorentzian Euclidean space is locally a lightlike triple
product manifold.
</p>projecteuclid.org/euclid.adjm/1413809901_20141020085820Mon, 20 Oct 2014 08:58 EDTExistence of Stable Periodic Orbits for a Predatory-Prey
Model with Deddington-DeAngelis Functional Response and Delayhttp://projecteuclid.org/euclid.adjm/1413809902<strong>C. Duque</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 16, Number 2, 46--58.</p><p><strong>Abstract:</strong><br/>
In this paper a Beddington-DeAngelis predator-prey model with time lag for
predator is proposed and analyzed. Mathematical analysis regard to boundedness
of solutions, nature of equilibria, uniform persistence, and stability are
analyzed. We show that if the positive equilibrium is unstable, an orbitally
asymptotically stable periodic solution exists.
</p>projecteuclid.org/euclid.adjm/1413809902_20141020085820Mon, 20 Oct 2014 08:58 EDTOn a Non-classical Boundary Value Problem for the Heat
Equationhttp://projecteuclid.org/euclid.adjm/1413809903<strong>P. M. Fall</strong>, <strong>O. Nakoulima</strong>, <strong>A. Sene</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 16, Number 2, 59--71.</p><p><strong>Abstract:</strong><br/>
In this paper, we are concerned in a non-classical boundary value problem for
heat equation. More precisely, we study a linear heat equation without initial
condition but with a homogeneous Dirichlet condition on the whole boundary and a
nonhomogeneous Neumann condition on a part of the boundary. Under sufficient
conditions on the data, we prove that the problem has a unique solution. The
proof combines optimal control and controllability theories.
</p>projecteuclid.org/euclid.adjm/1413809903_20141020085820Mon, 20 Oct 2014 08:58 EDTTopological Structure of the Solutions Set of Impulsive Semilinear Differential
Inclusions with Nonconvex Right-Hand Sidehttp://projecteuclid.org/euclid.adjm/1413809904<strong>M. Benchohra</strong>, <strong>J. J. Nieto</strong>, <strong>A. Ouahab</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 16, Number 2, 72--91.</p><p><strong>Abstract:</strong><br/>
In this paper, we study the topological structure of solution sets for the
following first-order impulsive evolution inclusion with initial conditions: $$
\left\{ \begin{array}{rlll} y'(t)-Ay(t) &\in& F(t,y(t)), &\hbox{
a.e. } \, t\in J\backslash \{t_{1},\ldots,t_{m}\},\\
y(t^+_{k})-y(t^-_k)&=&I_{k}(y(t_{k}^{-})), &k=1,\ldots,m\\
y(0)&=&a\in E, \end{array} \right. $$where $J:=[0,b]$ and $0 = t_0 <
t_1 < \,... \,< t_m < b$, $A$ is the infinitesimal generator of a
$C_0-$semigroup of linear operator $T(t)$ on a separable Banach space $E$ and
$F$ is a set-valued map. The functions $I_k$ characterize the jump of the
solutions at impulse points $t_k$ ($k=1, \ldots ,m$). The continuous selection of
the solution set is also investigated.
</p>projecteuclid.org/euclid.adjm/1413809904_20141020085820Mon, 20 Oct 2014 08:58 EDTAnalytic Feller Semigroups via Hypergeometric
Serieshttp://projecteuclid.org/euclid.adjm/1413810098<strong>A. Favini</strong>, <strong>G.R. Goldstein</strong>, <strong>J.A. Goldstein</strong>, <strong>S. Romanelli</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 17, Number 1, 1--9.</p><p><strong>Abstract:</strong><br/>
We prove an alternative method in order to obtain generation and analyticity
results for the semigroups generated by some degenerate second order
differential operators linked to the hypergeometric equation.
</p>projecteuclid.org/euclid.adjm/1413810098_20141020090140Mon, 20 Oct 2014 09:01 EDTLe laplacien d'une quasi-bialgèbre de Liehttp://projecteuclid.org/euclid.adjm/1413810099<strong>M. Bangoura</strong>, <strong>I. Bakayoko</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 17, Number 1, 10--31.</p><p><strong>Abstract:</strong><br/>
Lie quasi-bialgebras are natural generalisations of Lie bialgebras introduced by
Drinfeld. To any finite-dimensional Lie quasi-bialgebra structure $(\mathcal{G},
\mu, \gamma, \phi)$ and a $\mathcal{D}$-module structure $M$, where
$\mathcal{D}$ is the double of the given Lie quasi-bialgebra, we associate one
operator $L_{M} =\partial_{\mu, M}d_{\gamma, M} + d_{\gamma, M}\partial_{\mu,
M}$ called the laplacien of the Lie quasi-bialgebra associated to the
$\mathcal{D}$-module structure. We establish the fondamentals properties of the
laplacian and give an explicit formula for $L_{M}$ by mean of adjoint characters
of $\mathcal{G}$ and $\mathcal{G^*}$.
</p>projecteuclid.org/euclid.adjm/1413810099_20141020090140Mon, 20 Oct 2014 09:01 EDTRicci Tensor for GCR-Lightlike Submanifolds of Indefinite
Nearly Kähler Manifoldshttp://projecteuclid.org/euclid.adjm/1413810100<strong>S. Kumar</strong>, <strong>R. Kumar</strong>, <strong>R. K. Nagaich</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 17, Number 1, 32--48.</p><p><strong>Abstract:</strong><br/>
We obtain the expression of Ricci tensor for a $GCR$-lightlike submanifold of
indefinite complex space form and discuss the properties of Ricci tensor on
totally geodesic $GCR$-lightlike submanifold of an indefinite complex space
form.
</p>projecteuclid.org/euclid.adjm/1413810100_20141020090140Mon, 20 Oct 2014 09:01 EDT$L$-Modules, $L$-Comodules and Hom-Lie
Quasi-Bialgebrashttp://projecteuclid.org/euclid.adjm/1413810101<strong>I. Bakayoko</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 17, Number 1, 49--64.</p><p><strong>Abstract:</strong><br/>
In this paper, we discuss $A$-modules and $L$-modules (resp. $L$-comodules) for
Hom-Lie algebras (resp. Hom-Lie coalgebras). We show that for a given
Hom-associative algebra $A$ (resp. Hom-coassociative coalgebra), the $A$-module
(resp. comodule) extends to $L(A)$-module (resp. comodule), where $L(A)$ is the
associated Lie algebra (resp. Lie coalgebra), with the same structure map. We
also prove that $L$-modules become $L_\alpha$-modules, where $L_\alpha$ is the
Hom-Lie algebra obtained from the Lie algebra $L$ by stwisting the Lie bracket.
Then we introduce Hom-Lie quasi-bialgebras and prove that a Lie quasi-bialgebra
turns to a Hom-Lie quasi-bialgebra by stwisting the Lie quasi-bialgebra
structure by an endomorphism. Moreover, we show that an exact Lie
quasi-bialgebra extends to an exact Hom-Lie quasi-bialgebra.
</p>projecteuclid.org/euclid.adjm/1413810101_20141020090140Mon, 20 Oct 2014 09:01 EDTAddendum to: "Quasicrystals, Almost Periodic Patterns, Mean
Periodic Functions and Irregular Sampling''http://projecteuclid.org/euclid.adjm/1413810102<strong>Yves Meyer</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 17, Number 1, 65--74.</p><p><strong>Abstract:</strong><br/>
This note completes [15]. Sharp results on Poisson summation formula and
irregular sampling are announced. In both cases tools from [15] are needed.
</p>projecteuclid.org/euclid.adjm/1413810102_20141020090140Mon, 20 Oct 2014 09:01 EDTInverse Problems and Approximations in Quantum Calculushttp://projecteuclid.org/euclid.adjm/1413810103<strong>S. Chefai</strong>, <strong>L. Dhaouadi</strong>, <strong>A. Fitouhi</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 17, Number 1, 75--84.</p><p><strong>Abstract:</strong><br/>
In this paper we study in quantum calculus the theory of inverse problem and
approximation in a large class of Hilbert spaces with reproducing kernels.
</p>projecteuclid.org/euclid.adjm/1413810103_20141020090140Mon, 20 Oct 2014 09:01 EDTPairing Rank in Rational Homotopy Grouphttp://projecteuclid.org/euclid.adjm/1413810104<strong>T. Yamaguchi</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 17, Number 1, 85--92.</p><p><strong>Abstract:</strong><br/>
Let $X$ be a simply connected CW complex of finite rational LS-category with
$\dim H_n(X;{\mathbb Q})<\infty$ for all $n$. The dimension of rational
Gottlieb group $G_*(X)\otimes {\mathbb Q}$ is upper-bounded by the rational
LS-category $cat_0(X)$ the inequation $\dim G_*(X)\otimes {\mathbb Q}\leq
cat_0(X)$ holds [2]. Then we introduce a new rational homotopical invariant
between them, denoted as the pairing rank $v_0(X)$ in the rational homotopy
group $\pi_*(X)\otimes {\mathbb Q}$ such that $\dim G_*(X)_{\mathbb Q}\leq
v_0(X)\leq cat_0(X)$. If $\pi_*(f)\otimes {\mathbb Q}$ is injective for a map
$f:X\to Y$, then we have $v_0(X)\leq v_0(Y)$. Also it has a good estimate for a
fibration $X{\to} E{\to} Y$ as $v_0(E)\leq v_0(X) +v_0(Y)$.
</p>projecteuclid.org/euclid.adjm/1413810104_20141020090140Mon, 20 Oct 2014 09:01 EDT$CR$-Submanifolds of a Nearly Trans-Hyperbolic Sasakian Manifold with a
Semi-Symmetric Non-Metric Connectionhttp://projecteuclid.org/euclid.adjm/1413810105<strong>M. Danish Siddiqi</strong>, <strong>M. Ahmad</strong>, <strong>J. P. Ojha</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 17, Number 1, 93--105.</p><p><strong>Abstract:</strong><br/>
In this paper, $CR$-submanifolds of a nearly trans-hyperbolic Sasakian manifold
with a semi-symmetric non-metric connection are studied. The parallel
distributions relating to $\xi$-vertical and $\xi$-horizontal $CR$-submanifolds
of nearly trans-hyperbolic Sasakian manifold with a semi symmetric non-metric
connection are obtained. Moreover, Nijenhuis tensor is calculated and
integrability conditions of the distributions on $CR$ submanifolds of nearly
trans-hyperbolic Sasakian manifold with a semi-symmetric non-metric connection
are discussed.
</p>projecteuclid.org/euclid.adjm/1413810105_20141020090140Mon, 20 Oct 2014 09:01 EDTFlot d'un systéme hyperboliquehttp://projecteuclid.org/euclid.adjm/1439297829<strong>Nadji Hermas</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 17, Number 2, 1--19.</p><p><strong>Abstract:</strong><br/>
In this paper, we study the existence of the flow of a hyperbolic system on some
functional spaces.
</p>projecteuclid.org/euclid.adjm/1439297829_20150811085711Tue, 11 Aug 2015 08:57 EDTAutomorphisms of Cotangent Bundles of Lie Groupshttp://projecteuclid.org/euclid.adjm/1439297830<strong>A. Diatta</strong>, <strong>B. Manga</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 17, Number 2, 20--46.</p><p><strong>Abstract:</strong><br/>
Let $G$ be a Lie group, ${\mathcal G}$ its Lie algebra and $T^*G$ its cotangent
bundle. On $T^*G,$ we consider the Lie group structure obtained by performing a
left trivialization and endowing the resulting trivial bundle $G\times {\mathcal
G}^*$ with the semi-direct product, using the co-adjoint action of $G$ on the
dual space ${\mathcal G}^*$ of ${\mathcal G}$. We investigate the group of
automorphisms of the Lie algebra ${\mathcal D}:=T^*{\mathcal G}$ of $T^*G.$ More
precisely, we fully characterize the Lie algebra of all derivations of
${\mathcal D},$ exhibiting a finer decomposition into components made of well
known spaces. Further, we specialize to the cases where $G$ has a bi-invariant
Riemannian or pseudo-Riemannian metric, with the semi-simple and compact cases
investigated as particular cases.
</p>projecteuclid.org/euclid.adjm/1439297830_20150811085711Tue, 11 Aug 2015 08:57 EDTOn the Completeness of the Root Vectors of Dissipative
Dirac Operators with Transmission Conditions.http://projecteuclid.org/euclid.adjm/1439297831<strong>H. Tuna</strong>, <strong>A. Eryilmaz</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 17, Number 2, 47--58.</p><p><strong>Abstract:</strong><br/>
In this article, we consider dissipative Dirac system in the limit-circle case.
Then using the Livsic's theorem, we prove the completeness of the system of root
vectors for dissipative Dirac system with transmission conditions.
</p>projecteuclid.org/euclid.adjm/1439297831_20150811085711Tue, 11 Aug 2015 08:57 EDTOn the Hilali Conjecture for Configuration Spaces of Closed Manifoldshttp://projecteuclid.org/euclid.adjm/1439297862<strong>Mohamed Rachid Hilali</strong>, <strong>My Ismail Mamouni</strong>, <strong>Hicham Yamoul</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 18, Number 1, 1--11.</p><p><strong>Abstract:</strong><br/>
The first author conjectured in 1990 (see [18]) that for any simply-connected elliptic space, the total dimension of the rational homotopy does not exceed that of its rational cohomology. Our main purpose in this paper is to investigate the following: does the Hilali conjecture holds for the configuration spaces of a rationally elliptic and simply connected topological space when it already holds for the space itself. We will prove that this statement is true for closed manifolds.
</p>projecteuclid.org/euclid.adjm/1439297862_20150811085742Tue, 11 Aug 2015 08:57 EDTBiharmonic Hypersurfaces in $E^5$ with Zero Scalar Curvaturehttp://projecteuclid.org/euclid.adjm/1439297863<strong> Deepika</strong>, <strong>R. S. Gupta</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 18, Number 1, 12--26.</p><p><strong>Abstract:</strong><br/>
We prove non-existence of proper biharmonic hypersurfaces of zero scalar curvature in Euclidean space $E^5$.
</p>projecteuclid.org/euclid.adjm/1439297863_20150811085742Tue, 11 Aug 2015 08:57 EDTOn Irreducibility of an Induced Representation of a Simply
Connected Nilpotent Lie Grouphttp://projecteuclid.org/euclid.adjm/1446472393<strong>Adjiey Jean-Luc Koffi</strong>, <strong>Kinvi Kangni</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 18, Number 2, 1--10.</p><p><strong>Abstract:</strong><br/>
Let $G$ be a simply connected nilpotent Lie group, $\mathcal{G}$ the
finite-dimensional Lie algebra of $G$, $\mathcal{V}$ a finite-dimensional vector
space over $\mathbb{C}$ or $\mathbb{R}$, and $H$ a connected Lie subgroup of $G$
such that the Lie algebra of $H$ is a subordinate subalgebra to an element $\pi
$ of $Hom\left( \mathcal{G},gl\left( \mathcal{V}\right) \right) $. In this work,
we construct an irreducible representation $\chi _{\pi }$ of $H$ such that the
induced of $ \chi _{\pi }$ on $G$ is irreducible.
</p>projecteuclid.org/euclid.adjm/1446472393_20151102085314Mon, 02 Nov 2015 08:53 ESTExistence of Solutions of IVPs for Differential Systems on Half Line with
Sequential Fractional Derivative Operatorshttp://projecteuclid.org/euclid.adjm/1446472405<strong>Yuji Liu</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 18, Number 1, 27--54.</p><p><strong>Abstract:</strong><br/>
In this article, we establish some existence results for solutions of a initial
value problem of a nonlinear fractional differential system on half line
involving the sequential Riemann-Liouville fractional derivatives. Our analysis
relies on the Schauder fixed point theorem. An efficiency example is presented
to illustrate the main theorem. As far as the author knows, the present work is
perhaps the first one that deals with such kind of initial value problems for
fractional differential systems on half line.
</p>projecteuclid.org/euclid.adjm/1446472405_20151102085328Mon, 02 Nov 2015 08:53 ESTSchläfli-type Mixed Modular Equations of Degrees $1$, $3$, $n$, and $3n$http://projecteuclid.org/euclid.adjm/1446472406<strong>M. S. Mahadeva Naika</strong>, <strong>N. P. Suman</strong>, <strong>S. Chandankumar</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 18, Number 1, 55--76.</p><p><strong>Abstract:</strong><br/>
In this paper, we establish several new Schläfli-type mixed modular equations of
composite degrees. These equations are analogous to those recorded by Ramanujan
in his second notebook. As an application, we establish several new explicit
values for the Ramanujan-Weber class invariant $G_{n}$ for $n=12, 48, 51, 57,
3/4, 3/16, 3/17$ and $3/19$.
</p>projecteuclid.org/euclid.adjm/1446472406_20151102085328Mon, 02 Nov 2015 08:53 ESTSome Inequalities for Power Series of Selfadjoint Operators in Hilbert Spaces Via
Wielandt and Reverses of Schwarz Inequalitieshttp://projecteuclid.org/euclid.adjm/1446472407<strong>S. S. Dragomir</strong>, <strong>Y. Seo</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 18, Number 1, 77--89.</p><p><strong>Abstract:</strong><br/>
In this paper we obtain some operator inequalities for functions defined by power
series with complex coefficients and, more specifically, with nonnegative
coefficients. In order to obtain these inequalities the classical Wielandt and
some reverses of the Schwarz inequality for vectors in inner product spaces are
utilized. Natural applications for some elementary functions of interest are
also provided.
</p>projecteuclid.org/euclid.adjm/1446472407_20151102085328Mon, 02 Nov 2015 08:53 ESTOn Quotient Hypermoduleshttp://projecteuclid.org/euclid.adjm/1446472408<strong>S. Ostadhadi-Dehkordi</strong>, <strong>B. Davvaz</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 18, Number 1, 90--97.</p><p><strong>Abstract:</strong><br/>
A hypermodule is a multivalued algebraic system satisfying the module like
axioms. In this paper, we construct quotient hypermodule. Let $M$ be a
hypermodule, $N$ be a subhypermodule of $M$ and $I$ be a hyperideal of $R$.
Then, $[M:N^{\ast}]$ is $R$-hypermodule and $[R:I^{\ast}]$-hypermodule, and
prove that when $N$ is normal subhypemodule, $[M:N^{\ast}]$ is a
$[R:I^{\ast}]$-module. Hence, the quotient hypermodules considered by Anvarieh
and Davvaz are modules.
</p>projecteuclid.org/euclid.adjm/1446472408_20151102085328Mon, 02 Nov 2015 08:53 ESTOn Jacobi Fields Along Eigenmappings of the Tension Field for Mappings into a
Symmetric Riemannian Manifoldhttp://projecteuclid.org/euclid.adjm/1446472409<strong>Moussa Kourouma</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 18, Number 1, 98--121.</p><p><strong>Abstract:</strong><br/>
We prove that the mean value (for some measure $\mu =\chi dx$ with $\chi \geq
0,dx=$ Riemannian measure) of the squared norm of the gradient of the unitary
direction of a Jacobi field along an eigenmapping $v$ (associated to an
eigenvalue $\lambda \geq 0$) of the tension field, for mappings from a compact
Riemannian manifold $(M,g)$ into a symmetric Riemannian manifold $(N,h)$ of
positive sectional curvature, is smaller than $c\lambda $, where $c>0$
depends only on the diameter and upper and lower curvature bounds of $(N,h)$.
For negative $\lambda $, we prove that there is no nonvanishing Jacobi field
along the eigenmappings, under the same assumptions on $(M,g)$ and $(N,h)$.
</p>projecteuclid.org/euclid.adjm/1446472409_20151102085328Mon, 02 Nov 2015 08:53 ESTTopology of Manifolds with Asymptotically Nonnegative Ricci Curvaturehttp://projecteuclid.org/euclid.adjm/1449496747<strong>Bazanfaré Mahaman</strong>, <strong>Mamadou Mboup</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 18, Number 2, 11--17.</p><p><strong>Abstract:</strong><br/>
In this paper, we study the topology of complete noncompact Riemannian manifolds
with asymptotically nonnegative Ricci curvature. We show that a complete
noncompact manifold $M$ with asymptotically nonnegative Ricci curvature and
sectional curvature $K(x)\ge \frac{C}{d_{p}(x)^{\alpha}}$ is diffeomorphic to
the Euclidean space $\mathbb{R}^n$ under some conditions on the density of rays
starting from the base point $p$ or on the volume growth of geodesic balls in
$M$.
</p>projecteuclid.org/euclid.adjm/1449496747_20151207085910Mon, 07 Dec 2015 08:59 ESTInequalities for the Growth and Derivatives of a Polynomialhttp://projecteuclid.org/euclid.adjm/1449496748<strong>Abdullah Mir</strong>, <strong>Mamadou Mboup</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 18, Number 2, 18--25.</p><p><strong>Abstract:</strong><br/>
In this paper, we present some inequalities for the growth and derivatives of a
polynomial with zeros outside a circle of arbitrary radius $k\gt 0$. Our results
provide improvements and generalizations of some well known polynomial
inequalities.
</p>projecteuclid.org/euclid.adjm/1449496748_20151207085910Mon, 07 Dec 2015 08:59 ESTRational Pairing Rank of a Maphttp://projecteuclid.org/euclid.adjm/1465472747<strong>Toshihiro Yamaguchi</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 19, Number 1, 1--11.</p><p><strong>Abstract:</strong><br/>
We define a rational homotopy invariant, the rational pairing rank $v_0(f)$ of a map $f:X\to Y$, which is a natural generalization of the rational pairing rank $v_0(X)$ of a space $X$ \cite{Y4}. It is upper-bounded by the rational LS-category $cat_0(f)$ and lower-bounded by an invariant $g_0(f)$ related to the rank of Gottlieb group. Also it has a good estimate for a fibration $X\overset{j}{\to} E\overset{p}{\to} Y$ such as $v_0(E)\leq v_0(j) +v_0(p)\leq v_0(X) +v_0(Y)$.
</p>projecteuclid.org/euclid.adjm/1465472747_20160609074548Thu, 09 Jun 2016 07:45 EDTA New Version of the Central Limit Theoremhttp://projecteuclid.org/euclid.adjm/1473854194<strong>Enrique Villamor</strong>, <strong>Pablo Olivares</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 19, Number 1, 12--20.</p><p><strong>Abstract:</strong><br/>
In this short note, we present a new version of the Central Limit Theorem whose
proof is based on Levy's characterization of Brownian motion. The method in the
proof may allow to extend the result to a more general context, e.g. to averaged
sums of properly compensated dependent random variables.
</p>projecteuclid.org/euclid.adjm/1473854194_20160914075637Wed, 14 Sep 2016 07:56 EDTMultidimensional BSDE with Poisson Jumps in Finite Time
Horizonhttp://projecteuclid.org/euclid.adjm/1473854195<strong>Yaya Sagna</strong>, <strong>Ahmadou Bamba Sow</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 19, Number 1, 21--36.</p><p><strong>Abstract:</strong><br/>
This paper is devoted to solve a multidimensional backward stochastic
differential equation with jumps in finite time horizon. Under weak monotonicity
condition on the generator and by means of suitable sequences, we prove
existence and uniqueness of solution.
</p>projecteuclid.org/euclid.adjm/1473854195_20160914075637Wed, 14 Sep 2016 07:56 EDTLeibniz Homology of the Affine Indefinite Orthogonal Lie
Algebrahttp://projecteuclid.org/euclid.adjm/1473854196<strong>Guy Roger Biyogmam</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 19, Number 1, 37--48.</p><p><strong>Abstract:</strong><br/>
In this paper, we construct several indefinite orthogonal invariants in terms of
balanced tensors and use Lodder's structure theorem to provide the Leibniz
(co)homology of the indefinite orthogonal Lie algebra in terms of these
invariants.
</p>projecteuclid.org/euclid.adjm/1473854196_20160914075637Wed, 14 Sep 2016 07:56 EDTA Note on Relations Between Hom-Malcev Algebras and
Hom-Lie-Yamaguti Algebrashttp://projecteuclid.org/euclid.adjm/1473854197<strong>Donatien Gaparayi</strong>, <strong>A. Nourou Issa</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 19, Number 1, 49--57.</p><p><strong>Abstract:</strong><br/>
A Hom-Lie-Yamaguti algebra, whose ternary operation expresses through its binary
one in a specific way, is a multiplicative Hom-Malcev algebra. Any
multiplicative Hom-Malcev algebra over a field of characteristic zero has a
natural Hom-Lie-Yamaguti structure.
</p>projecteuclid.org/euclid.adjm/1473854197_20160914075637Wed, 14 Sep 2016 07:56 EDTPseudo-Almost Periodic and Pseudo-Almost Automorphic Solutions of Class r Under the Light of Measure Theoryhttp://projecteuclid.org/euclid.adjm/1473854198<strong>Issa Zabsonre</strong>, <strong>Hamidou Toure</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 19, Number 1, 58--86.</p><p><strong>Abstract:</strong><br/>
The aim of this work is to present new approach to study weighted pseudo almost periodic and automorphic functions using the measure theory. We present a new concept of weighted ergodic functions which is more general than the classical one. Then we establish many interesting results on the functional space of such functions. We study the existence and uniqueness of $(\mu,\nu)$-pseudo almost periodic and automorphic solutions of class $r$ for some neutral partial functional differential equations in a Banach space when the delay is distributed using the spectral decomposition of the phase space developed in Adimy and co-authors. Here we assume that the undelayed part is not necessarily densely defined and satisfies the well-known Hille-Yosida condition, the delayed part are assumed to be pseudo almost periodic with respect to the first argument and Lipschitz continuous with respect to the second argument.
</p>projecteuclid.org/euclid.adjm/1473854198_20160914075637Wed, 14 Sep 2016 07:56 EDTConvergence Analysis on Quadrilateral Grids of a DDFV Method for Subsurface Flow Problems in Anisotropic Heterogeneous Porous Media with Full Neumann Boundary Conditionshttp://projecteuclid.org/euclid.adjm/1481338901<strong>A. Kinfack Jeutsa</strong>, <strong>A. Njifenjou</strong>, <strong>J. Nganhou</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 19, Number 2, 1--28.</p><p><strong>Abstract:</strong><br/>
Our purpose in this paper is to present a theoretical analysis of the Discrete Duality Finite Volume method (DDFV method) for 2D-flow problems in anisotropic heterogeneous porous media with full Neumann boundary conditions. We start with the derivation of the discrete problem, and then we give a result of existence and uniqueness of a solution for that problem. Their theoretical properties, namely stability and error estimates in discrete energy norms and $L^2$-norm are investigated. Numerical tests are provided.
</p>projecteuclid.org/euclid.adjm/1481338901_20161209220147Fri, 09 Dec 2016 22:01 ESTPeriodic Homogenization of Schrödinger Type Equations with Rapidly Oscillating Potentialhttp://projecteuclid.org/euclid.adjm/1481338902<strong>Lazarus Signing</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 19, Number 2, 29--45.</p><p><strong>Abstract:</strong><br/>
This paper is devoted to the homogenization of Shrödinger type equations with periodically oscillating coefficients of the diffusion term, and a rapidly oscillating periodic potential. One convergence theorem is proved and we derive the macroscopic homogenized model. Our approach is the well known two-scale convergence method.
</p>projecteuclid.org/euclid.adjm/1481338902_20161209220147Fri, 09 Dec 2016 22:01 ESTHammerstein Equations with Lipschitz and Strongly Monotone
Mappings in Classical Banach spaceshttp://projecteuclid.org/euclid.adjm/1494986432<strong>C. Diop</strong>, <strong>T. M. M. Sow</strong>, <strong>N. Djitte</strong>, <strong>C. E. Chidume</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 20, Number 2, 1--15.</p><p><strong>Abstract:</strong><br/>
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 proved that the sequence
$\{u_n\}$ converges strongly to $\bar u$, the sequence $\{v_n\}$ converges
strongly to $\bar v$, with $\bar{v}= F\bar{u}.$ Furthermore, our technique of
proof is of independent interest.
</p>projecteuclid.org/euclid.adjm/1494986432_20170516220033Tue, 16 May 2017 22:00 EDTExistence of Solutions of Some Nonlinear $φ$-Laplacian
Equations with Neumann-Steklov Nonlinear Boundary Conditionshttp://projecteuclid.org/euclid.adjm/1494986433<strong>Charles Etienne Goli</strong>, <strong>Assohoun Adje</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 20, Number 2, 16--38.</p><p><strong>Abstract:</strong><br/>
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.
</p>projecteuclid.org/euclid.adjm/1494986433_20170516220033Tue, 16 May 2017 22:00 EDTOn Commutativity of Prime Γ-Rings with
$θ$-Derivationshttp://projecteuclid.org/euclid.adjm/1494986434<strong>Shuliang Huang</strong>, <strong>Nadeem ur Rehman</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 20, Number 2, 39--44.</p><p><strong>Abstract:</strong><br/>
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
hypothesis of the various results is essential.
</p>projecteuclid.org/euclid.adjm/1494986434_20170516220033Tue, 16 May 2017 22:00 EDTAbout the Degenerate Spectrum of the Tension Field for
Mappings into a Symmetric Riemannian Manifoldhttp://projecteuclid.org/euclid.adjm/1494986435<strong>Moussa Kourouma</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 20, Number 2, 45--68.</p><p><strong>Abstract:</strong><br/>
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
generalizes a well known one about the spectrum of the Laplace-Beltrami
operator $\Delta $ for functions from $(M,g)$ into $\mathbb{R}$.
</p>projecteuclid.org/euclid.adjm/1494986435_20170516220033Tue, 16 May 2017 22:00 EDTPoisson Summation Formulae and the Wave Equation with a
Finitely Supported Measure as Initial Velocityhttp://projecteuclid.org/euclid.adjm/1495072816<strong>Jesus Ildefonso Diaz</strong>, <strong>Yves Meyer</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 20, Number 1, 1--13.</p><p><strong>Abstract:</strong><br/>
New Poisson summation formulae have been recently discovered by Nir Lev and
Alexander Olevskii since 2013. But some other examples were concealed in an old
paper by Andrew Guinand dating from 1959. This was observed by the second author
in 2016. In the present contribution a third approach is proposed. Guinand's
work follows from some simple observations on solutions of the wave equation on
the three dimensional torus. If the initial velocity is a Dirac mass at the
origin, the solution is Guinand's distribution. Using this new approach one can
construct a large family of initial velocities which give rise to crystalline
measures generalizing Guinand's solution.
</p>projecteuclid.org/euclid.adjm/1495072816_20170517220018Wed, 17 May 2017 22:00 EDTOn Symplectic Dynamicshttp://projecteuclid.org/euclid.adjm/1496800891<strong>Stéphane Tchuiaga</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 20, Number 2, 69--94.</p><p><strong>Abstract:</strong><br/>
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 in the investigation of the symplectic nature of
the $C^0 -$limit of a sequence of symplectic maps. This yields a symplectic analogue of
a result that was proved by Hofer-Zehnder [10] (for compactly supported Hamiltonian
diffeomorphisms on $\mathbb{R}^{2n}$); then reformulated by Oh-Müller [14] for
Hamiltonian diffeomorphisms in general. Furthermore, we show that Polterovich's
regularization process for Hamiltonian paths extends over the whole group of symplectic
isotopies, and then use it to prove the equality between the two versions of Hofer-like
norms. This yields the symplectic analogue of the uniqueness result of Hofer's geometry
proved by Polterovich [13]. Our results also include the symplectic analogues of some
approximation lemmas found by Oh-Müller [14]. As a consequence of a result of this
paper, we prove by other method a result found by McDuff-Salamon [12].
</p>projecteuclid.org/euclid.adjm/1496800891_20170606220135Tue, 06 Jun 2017 22:01 EDTGraded Lie Agebroids of Poisson Almost Commutative Algebrashttps://projecteuclid.org/euclid.adjm/1515467141<strong>Ferdinand Ngakeu</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 20, Number 2, 95--107.</p><p><strong>Abstract:</strong><br/>
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.
</p>projecteuclid.org/euclid.adjm/1515467141_20180108220544Mon, 08 Jan 2018 22:05 ESTSemigroup and Blow-Up Dynamics of Attraction Keller-Segel Equations in Scale of Banach Spaceshttps://projecteuclid.org/euclid.adjm/1520391703<strong>David S. I. Iiyambo</strong>, <strong>Robert Willie</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 21, Number 1, 1--31.</p><p><strong>Abstract:</strong><br/>
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 limit set $\mathcal{M}\cup \{0\}$, where $\mathcal{M} = |\Omega|L^1 -$spatial average solutions. The constants for the sharp space embedding $E^\alpha_q \subset L ^\Theta(\Omega) (1\lt\Theta\le\infty)$ indicate that for either the application of Banach fixed point theorem, or the global existence of solutions, no need of either the time for a contraction mapping, nor the initial data of the system of equations, to be small, respectively. In blow-up dynamics, we prove that the solutions blow-up at the borderline scale spaces $E^\alpha_q, \alpha = \frac{N}{2q}$, independent of time $t > 0$, if the chemo-attractivity coefficient dominates the Moser-Trudinger threshold value. An analysis of the finite time bounds for blow-up of solutions in norm of $L^{2p}(\Omega),1 \le p \le 6$ and $\Omega \subset \mathbb{R}^N,N = 2, 3$, is also furnished.
</p>projecteuclid.org/euclid.adjm/1520391703_20180306220148Tue, 06 Mar 2018 22:01 ESTAttractors for a Cahn-Hilliard-Navier-Stokes Model with Delayshttps://projecteuclid.org/euclid.adjm/1520391704<strong>Theodore Tachim Medjo</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 21, Number 1, 32--52.</p><p><strong>Abstract:</strong><br/>
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.
</p>projecteuclid.org/euclid.adjm/1520391704_20180306220148Tue, 06 Mar 2018 22:01 ESTQuasi-uniform Spaces and $\mathcal{U}$-startpointhttps://projecteuclid.org/euclid.adjm/1523412026<strong>Yaé Ulrich Gaba</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 21, Number 1, 53--56.</p><p><strong>Abstract:</strong><br/>
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.
</p>projecteuclid.org/euclid.adjm/1523412026_20180410220034Tue, 10 Apr 2018 22:00 EDTA Locally Asymptotically Optimal Test With Application to Financial Datahttps://projecteuclid.org/euclid.adjm/1523412027<strong>Tewfik Lounis</strong>, <strong>Joseph Ngatchou-Wandji</strong>. <p><strong>Source: </strong>African Diaspora Journal of Mathematics, Volume 21, Number 1, 57--72.</p><p><strong>Abstract:</strong><br/>
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).
</p>projecteuclid.org/euclid.adjm/1523412027_20180410220034Tue, 10 Apr 2018 22:00 EDT