In this article we introduce a new sequence space denoted by
m(4u
v ; Á; p). We give some topological properties and inclusion relations
on this space. The results herein proved are analogous to those from [1].

In his work on Uzawa-Lucas model with unskilled labor, Robert-
son [6] asserts that his results do not substantially change if one relaxes
the assumption of a total utility function depending on the size of the
population, which means that the total utility depends only on the per
capita felicity discounted by the rate of time preference. In this paper,
Robertson's statement is proved analytically.

The Z¡eigenvalues, E¡eigenvalues and the corresponding
eigenvectors for the Berwald-Moor associated multilinear form in the case
m = n = 3, are computed by means of applying the method of resultants.
The complexity of the algorithm and further developments are discussed.

This paper provides a two-fold generalization of the logistic
population dynamics to a nonautonomous context. First it is assumed
the carrying capacity alone pulses the population behavior changing logis-
tically on its own. In such a way we get again the model of [10], numer-
ically computed by them, and we solve it completely through the Gauss
hypergeometric function. Furthermore, both the carrying capacity and
net growth rate are assumed to change simultaneously following two in-
dependent logistic dynamics. The population dynamics is then found in
closed form through a more di±cult integration, involving a (¿1; ¿2) exten-
sion of the Appell generalized hypergeometric function, [2]; a new analytic
continuation theorem has been proved about such an extension.


The classi¯cation of von Neumann algebras relative to a group
of automorphisms is introduced. It is shown that for certain classes of
groups of automorphisms of von Neumann algebras there exist mappings
similar to those of a centre valued G-trace. The G-dimension is introduced
and the equivalence of G-¯niteness and the existence of G-dimension func-
tion is studied. We introduce the theory with some articular cases, in more
general set up. Instead of considering group of automorphisms, we shall
consider groups of automorphisms under an action ®.

In this article, we introduce the de¯nition of a new type of the
wedge sum of two graphs. Also, we will deduce the fundamental group
of the folding on some types of the Dual graph. The relation between
the wedge sum of two dual graphs is obtained. The e®ect of folding on
the wedge sum of ¯nite numbers of graphs and their fundamental group
will be achieved. Theorems and corollaries governing these studies will be
achieved.c

We shall review the development of the notion of SpaceTime
and new challenges of theories of gravitation in the third millennium. We
shall stress the fundations of GR in the geometry and physics of XIX Cen-
tury and motivations leading to the Einstein paradigm. Then the math-
ematical structure of standard GR is brie°y reviewed and some possible
generalizations are considered. In particular the so-called alternative the-
ories of gravitation are considered. Their connection to dark matter/dark
energy problem is presented. Finally we shall brie°y review some open
problems of gravitational theories which lead to motivations for quantum
SpaceTimes and gravity.

This paper evaluates the dynamic e®ects of assuming a logis-
tic law hypothesis for population growth into the Mankiw, Romer, Weil
(hereafter MRW) neoclassical growth model [8]. Under this assumption,
the model is described by a three dimensional dynamical system, which
has a unique non-trivial steady state equilibrium that is a saddle point
with a two dimensional stable manifold. As a result, the speed of conver-
gence is determined by two stable roots, rather than only one as in the
basic MRW model, so that its transitional adjustment paths are enriched.

In this paper a criterion for L1- convergence of a certain co-
sine sums with twice quasi semi-convex coe±cients is obtained. Also a
necessary and su±cient condition for L1-convergence of the cosine series
is deduced as a corollary.

The object of this paper is to study ®-Kenmotsu manifolds
which can be derived from almost contact Riemannian manifolds satis-
fying some certain conditions. We ¯rst examine the generalized recur-
rent ®-Kenmotsu manifolds, and next we give some relations about Ricci
semi-symmetric and D-conformal curvature tensors. We show that Ricci
semi-symmetric ®-Kenmotsu manifolds are also Einstein manifolds. Fur-
thermore, we prove that the scalar curvature of ®-Kenmotsu manifolds
with ´-parallel Ricci tensors is constant. We conclude the paper with an
example on ®-Kenmotsu manifolds.

This paper is devoted to a discussion of speci¯c properties of
invariants in the theory of forms.

The paper is divided into two principal parts. In the ¯rst
one, we give the set of generalized inverses of a matrix A a structure of
a semigroup and study some algebraic properties like factorization and
commutativity. We also de¯ne an equivalence relation in order to estab-
lish an isomorphism between the quotient semigroup and the semigroup
of projectors on R(A). In the second part, we study a relation between
semigroups associated to equivalent matrices and establish a correspon-
dence between the set of matrices and the set of associated semigroups.
We also study some algebraic properties in this set like intersection and
partial order

In this paper we introduce the notion of generalized D¤-metric
space and prove some ¯xed point theorems in complete generalized D¤-
metric spaces.

In order to extend the notion of convergence of sequences, sta-
tistical convergence of sequences was introduced by Fast [5] and Schoen-
berg [26]. The main aim of this article is to study the concept of statistical
convergence from di®erence sequence spaces point of view which are de-
¯ned over real linear 2-normed spaces.

In this note, we propose an analytical solution to a nonlinear
second-order boundary value problem using the 4q-Boubaker Polynomials
Expansion Scheme (BPES). The results are plotted, and compared with
exact solutions proposed elsewhere, in order to evaluate accuracy.

One of the applied branches of mathematics is the entropy
of a dynamical system. In this paper we de¯ned the in¯nite partition of
an algebraic structure and then we introduce the entropy of a countable
partition of this structure. In this respect, we introduce the generators
of an m-preserving transformation of a discrete dynamical system. At
the end, we prove a version of Kolomogorov-Sinai theorem concerning the
entropy of a dynamical system.

In view of information geometry, the state space of thermody-
namic parameters S = f½j½ = Z¡1 expf¡Pn
i=1 ¯iFi;Tr ½ = 1g has been
investigated. Here the ®-geometric structures of the denormalization of
S called eS = fe½je½ = f(¿ )½; f(¿ ) > 0;Tr ½ = 1g is investigated. The co-
variant derivative and the ®-curvature tensor is studied. Therefore, the
relation of the ®-geometric structures between S and eS are obtained. The
results were obtained in [8] when ® = 0 and in [2] when f(¿ ) = 1./I>