1.
Matrix characterizations of Lipschitz operators on Banach spaces over Krull valued fields - Ochsenius, H.; Schikhof, W.H.
Let $K$ be a complete
infinite rank valued field and $E$ a $K$-Banach space with a
countable orthogonal base. In [9] and [10] we
have studied bounded (called Lipschitz) operators on $E$ and
introduced the notion of a strictly Lipschitz operator. Here we
characterize them, as well as compact and nuclear operators, in
terms of their (infinite) matrices. This results provide new
insights and also useful criteria for constructing operators with
given properties.
2.
Large deviations for compound Markov renewal processes with
dependent jump sizes and jump waiting times - Macci, Claudio
In [17] the author considered a compound Markov renewal
process $(\widetilde{S}_{N_t})$ where $((J_n,S_n))$ and $((\widetilde{J}_n,\widetilde{S}_n))$
are suitable independent Markov additive processes such that
$(S_n-S_{n-1})$ are positive random variables, and $N_t=\sum
_{n\geq 1}1_{S_n\leq t}$. In this paper we present the analogous
results for a more general situation where we consider a unique
Markov additive process $((J_n,Z_n))$ in place of $((J_n,S_n))$
and $((\widetilde{J}_n,\widetilde{S}_n))$, and $Z_n=(\widetilde{S}_n,S_n)$. Some further
results are also presented; in particular we relate in terms of
large deviations the sequence $((\widetilde{S} _n,S_n))$ and the process
$((\widetilde{S}_{N_t},N_t))$.
3.
On the number of orderings of n items - Omey, Edward; Van Gulck, Stefan
Suppose that consumers have to classify $n$ items or baskets of goods
according to their individual preferences or utility and such that ties are
allowed. In this paper we study the number of possible classifications or
outcomes $f(n)$.\ We obtain different representations for $f(n)$ and use
singularity analysis to determine the asymptotic behaviour of $f(n)$. We
also give a probabilistic interpretation of $f(n)$ and use a renewal
argument to study $f(n)$ as $n\rightarrow \infty $. Assuming that each of
the $f(n)$ outcomes has equal probability to occur, we study the random
variable $N_{n}$ where $N_{n}$ equals the number of most preferred items,
i.e. the number of items on the...
4.
Weyl's theorem for Algebraically class $A$ Operators - Mecheri, Salah
Let $A$ be a bounded linear operator acting on a Hilbert space $H$. In [32], A. Uchiyama
proved that Weyl's theorem holds for class A operators with the additional condition that $\ker A|_{[TH]}=0$ and he
showed that every class A operator whose Weyl spectrum equals to zero is compact and normal. In this paper we show
that Weyl's theorem holds for algebraically class $A$ operator without the additional condition $\ker A|_{[TH]}=0$. This
leads as to show that a class $A$ operator whose Weyl spectrum equals to zero is always compact and normal.
5.
Relaxing stratification - Forster , Thomas; Esser, Olivier
A number of ways of relaxing the stratification constraint for the
axioms of Quine's NF are reviewed. It is shown how most of them
result in inconsistency.
6.
Third order TVD scheme for hyperbolic conservation laws - Zahran, Yousef Hashem
A new third order finite difference scheme for the solution of initial value problems for hyperbolic
conservation laws is presented. The advantages of the scheme are its simplicity, third order accuracy and that it can be
used for large time steps which saves more time. The scheme is proved stable for initial and initial boundary value
problems for linear case. The technique of making the third order scheme oscillations free (TVD) is carried out. In this
paper we extend
TVD scheme to two dimension problems. The extension of the TVD scheme to nonlinear system of equations is illustrated by
solving shallow water equations. Numerical results are...
7.
D-homothetic transformations
for a generalization of contact metric manifolds - Cappelletti Montano, Beniamino; Di Terlizzi, Luigia
Curvature properties of some generalizations of contact metric
manifolds are studied, with special attention to
$\left(\kappa,\mu\right)$-nullity conditions in the framework of
$\cal S$-manifolds.
8.
Spectral Method for a Class of Systems of Generalized Zakharov Equations - Rashid, Abdur
In this paper, a Fourier spectral method for an initial boundary
value problem for a class of systems of generalized Zakharov
equations is proposed. Semi-discrete and fully discrete Fourier
spectral schemes are given. In fully discrete case we have
established a two level scheme which is convenient and saves time
in real computation. An energy estimation method is
used to obtain error estimates for approximate solutions.
9.
On the angular distribution of mass by Besov functions - Erlín Castillo, René; Ramos Fernández, Julio C.
Let $\Bbb D$ be the open unit disk in the complex plane. For $\varepsilon > 0$ we consider
the sector $\Sigma_{\varepsilon} = \{z\; : \; |\arg z | < \varepsilon \}$.
We will prove that for certain classes of functions $f$ in the
Besov's space $B_p\left(\Bbb D\right)$ such that $f(0)=0$, the $B_p$
norm
is obtained by integration over $f^{-1}(\Sigma_{\varepsilon})$.
10.
Lagrangian submanifolds attaining equality in the improved Chen's inequality - Bolton, J.; Vrancken, L.
In [7] Oprea gave an improved version of Chen's inequality for Lagrangian submanifolds of
$\mathbb CP^n(4)$. For minimal submanifolds this inequality coincides with a previous version proved in [5]. We
consider here those non-minimal $3$-dimensional Lagrangian submanifolds in $\mathbb CP^3 (4)$ attaining at all points
equality in the improved Chen inequality.
We show how all such submanifolds may be obtained starting from a minimal Lagrangian surface in $\mathbb CP^2(4)$.
11.
Short proof of a metrization theorem - Moll, S.; Sánchez Ruiz, L.M.
In this note we provide a new insight into trans-separable spaces,
i.e. those which are separable by seminorms. This approach enables getting
an easy proof of the fact that in a wide class of uniform spaces, containing
$(DF)$ and $(LM)$-spaces, precompact subsets are metrizable.
12.
Parallel surfaces in the motion groups $E(1,1)$ and $E(2)$ - Inoguchi, Jun-ichi; Van der Veken, Joeri
We give a classification of parallel surfaces in the groups of rigid
motions of Minkowski plane and Euclidean plane, equipped with a
general left-invariant metric. Our result completes the
classification of parallel surfaces in the eight three-dimensional
model geometries of Thurston and in three-dimensional unimodular Lie
groups with maximal isometry group.
13.
Punishing factors and Chua's conjecture - Avkhadiev, F. G.; Wirths, K.-J.
Let $\Omega $ and $\Pi $ be two simply connected domains in the complex plane $ \mathds{C}$ which are not equal to the
whole plane $\mathds{C}$. We are concerned with the set $A(\Omega,\Pi)$ of functions $f: \Omega\to\Pi$ holomorphic on
$\Omega$ and we prove estimates for $|f^{(n)}(z)|, f\in A(\Omega,\Pi), z \in \Omega$, of the following type. Let
$\lambda_{\Omega}(z)$ and $\lambda_{\Pi}(w)$ denote the density of the Poincar\'{e} metric of $\Omega$ at $z$ and of
$\Pi$ at $w$, respectively. Then for any pair $(\Omega,\Pi)$ where $\Omega$ is convex, $f\in A(\Omega,\Pi), z \in
\Omega$, and $n\geq 2$ the inequality
\[
\frac{|f^{(n)}(z)|}{n!}\leq (n+1) 2^{n-2}\frac{(\lambda_{\Omega}(z))^n}{\lambda_{\Pi}(f(z))}
\]
is valid.\\
For functions $f\in A(\Omega,\Pi)$, which are injective on...
15.
Almost Kenmotsu manifolds and local symmetry - Dileo, Giulia; Pastore, Anna Maria
We consider locally symmetric almost Kenmotsu manifolds
showing that such a manifold is a Kenmotsu manifold if and only if
the Lie derivative of the structure, with respect to the Reeb
vector field $\xi$, vanishes. Furthermore, assuming that for a
$(2n+1)$-dimensional locally symmetric almost Kenmotsu manifold
such Lie derivative does not vanish and the curvature satisfies
$R_{XY}\xi =0$ for any $X, Y$ orthogonal to $\xi$, we prove that
the manifold is locally isometric to the Riemannian product of an
$(n+1)$-dimensional manifold of constant curvature $-4$ and
a flat $n$-dimensional
manifold. We give an example of such a manifold.
16.
Functionals on normed function spaces and exponential
instability of linear skew-product semiflows - Megan, Mihail; Buliga, Larisa
The aim of this paper is to give necessary and
sufficient conditions for uniform exponential instability of
linear skew-product semiflows in terms of functionals on normed
function spaces. We obtain the versions of some results due to
Datko, Pazy, Neerven and Rolewicz for the case of instability of
linear skew-product semiflows.
17.
Geodesic Flow on Global Holomorphic Sections of ${TS}^2$ - Guilfoyle, Brendan; Klingenberg, Wilhelm
We study the geodesic flow on the global holomorphic sections of the bundle
$\pi:{\mbox{TS}}^2\rightarrow \mbox{S}^2$ induced by the neutral Kähler metric on the
space of oriented lines of ${\Bbb{R}}^3$, which we identify with ${\mbox{TS}}^2$. This flow is shown to be
completely integrable when the sections are symplectic, and the behaviour of the geodesics is
described.
18.
On the mathematical work of Jean Schmets - Bierstedt, Klaus D.; Bonet, José
In the introductory Section 0.
some of the most important points in the professional
curriculum vitae of Jean Schmets are given. Then
Section 1 is devoted to present (part of) the work
for which Schmets was very well known until 1990:
He has been the leading specialist in the world for
locally convex spaces $C(X)$ of continuous functions
with various topologies and for the corresponding
spaces $C(X,E)$ of vector valued continuous functions.
Finally, in Section 2 some results which Schmets
obtained in cooperation with Manuel Valdivia since
1990 are reviewed: work on domains of real analytic
existence, continuous linear right inverses for $C^\infty$-
functions and Whitney extensions for non quasianalytic
functions.
19.
Functionals that do not attain their norm - Acosta, María D.; Aizpuru, Antonio; Aron, Richard M.; García-Pacheco, Francisco J.
We study the set of non-norm-attaining functionals on a Banach
space, giving a sufficient condition for the density of this set. We
also find a large class of Banach spaces for which the set of
norm-attaining functionals is (dense-) lineable. In addition, among
other results, we provide a new proof of the fact that every real
Banach space can be equivalently renormed so that the set of
non-norm-attaining functionals is non-dense.
1.
