1. CMB Online first
 Bu, Shangquan; Cai, Gang

HÃ¶lder continuous solutions of degenerate differential equations with finite delay
Using known operatorvalued Fourier multiplier results on vectorvalued
HÃ¶lder continuous function spaces $C^\alpha (\mathbb R; X)$, we completely
characterize the $C^\alpha$wellposedness of the first order
degenerate differential equations with finite delay $(Mu)'(t)
= Au(t) + Fu_t + f(t)$ for $t\in\mathbb R$
by the boundedness of the $(M, F)$resolvent of $A$ under suitable
assumption on the delay operator $F$, where $A, M$ are closed
linear
operators on a Banach space $X$ satisfying $D(A)\cap D(M) \not=\{0\}$,
the delay operator $F$ is a bounded linear operator
from $C([r, 0]; X)$ to $X$ and $r \gt 0$ is fixed.
Keywords:wellposedness, degenerate differential equation, $\dot{C}^\alpha$multiplier, HÃ¶lder continuous function space Categories:34N05, 34G10, 47D06, 47A10, 34K30 

2. CMB 2014 (vol 58 pp. 7)
 Boulabiar, Karim

Characters on $C(X)$
The precise condition on a completely regular space $X$ for every character on
$C(X) $ to be an evaluation at some point in $X$ is that $X$ be
realcompact. Usually, this classical result is obtained relying heavily on
involved (and even nonconstructive) extension arguments. This note provides a
direct proof that is accessible to a large audience.
Keywords:characters, realcompact, evaluation, realvalued continuous functions Categories:54C30, 46E25 

3. CMB 2012 (vol 57 pp. 61)
 Geschke, Stefan

2dimensional Convexity Numbers and $P_4$free Graphs
For $S\subseteq\mathbb R^n$ a set
$C\subseteq S$ is an $m$clique if the convex hull of no $m$element subset of
$C$ is contained in $S$.
We show that there is essentially just one way to construct
a closed set $S\subseteq\mathbb R^2$ without an uncountable
$3$clique that is not the union of countably many convex sets.
In particular, all such sets have the same convexity number;
that is, they
require the same number of convex subsets to cover them.
The main result follows from an analysis of the convex structure of closed
sets in $\mathbb R^2$ without uncountable 3cliques in terms of
clopen, $P_4$free graphs on Polish spaces.
Keywords:convex cover, convexity number, continuous coloring, perfect graph, cograph Categories:52A10, 03E17, 03E75 

4. CMB 2011 (vol 55 pp. 449)
 Bahreini, Manijeh; Bator, Elizabeth; Ghenciu, Ioana

Complemented Subspaces of Linear Bounded Operators
We study the complementation of the space $W(X,Y)$ of weakly compact operators, the space $K(X,Y)$ of compact operators, the space $U(X,Y)$ of unconditionally converging operators, and the space $CC(X,Y)$ of completely continuous operators in the space $L(X,Y)$ of bounded linear operators from $X$ to $Y$.
Feder proved that if $X$ is infinitedimensional and $c_0
\hookrightarrow Y$, then $K(X,Y)$ is uncomplemented in
$L(X,Y)$. Emmanuele and John showed that if $c_0 \hookrightarrow
K(X,Y)$, then $K(X,Y)$ is uncomplemented in $L(X,Y)$.
Bator and Lewis showed that if $X$ is not a Grothendieck space and
$c_0 \hookrightarrow Y$, then $W(X,Y)$ is uncomplemented in
$L(X,Y)$. In this paper, classical results of Kalton and separably
determined operator ideals with property $(*)$ are used to obtain
complementation results that yield these theorems as corollaries.
Keywords:spaces of operators, complemented subspaces, compact operators, weakly compact operators, completely continuous operators Categories:46B20, 46B28 

5. CMB 2011 (vol 55 pp. 623)
 Pan, Jiaqing

The Continuous Dependence on the Nonlinearities of Solutions of Fast Diffusion Equations
In this paper, we consider the Cauchy problem
$$
\begin{cases}
u_{t}=\Delta(u^{m}), &x\in{}\mathbb{R}^{N}, t>0, N\geq3,
\\
% ^^ here
u(x,0)=u_{0}(x), &x\in{}\mathbb{R}^{N}.
\end{cases}
$$
We will prove that:
(i) for
$m_{c}
Keywords:fast diffusion equations, Cauchy problem, continuous dependence on nonlinearity Categories:35K05, 35K10, 35K15 

6. CMB 2010 (vol 53 pp. 466)
 Dubarbie, Luis

Separating Maps between Spaces of VectorValued Absolutely Continuous Functions
In this paper we give a description of separating or disjointness preserving linear bijections on spaces of vectorvalued absolutely continuous functions defined on compact subsets of the real line. We obtain that they are continuous and biseparating in the finitedimensional case. The infinitedimensional case is also studied.
Keywords:separating maps, disjointness preserving, vectorvalued absolutely continuous functions, automatic continuity Categories:47B38, 46E15, 46E40, 46H40, 47B33 

7. CMB 2010 (vol 53 pp. 360)
 Porter, Jack; Tikoo, Mohan

Separating Hsets by Open Sets
In an Hclosed, Urysohn space, disjoint Hsets can be separated by disjoint open sets. This is not true for an arbitrary Hclosed space even if one of the Hsets is a point. In this paper, we provide a systematic study of those spaces in which disjoint Hsets can be separated by disjoint open sets.
Keywords:Hset, Hclosed, θcontinuous Categories:54C08, 54D10, 54D15 

8. CMB 2008 (vol 51 pp. 217)
 Filippakis, Michael E.; Papageorgiou, Nikolaos S.

A Multivalued Nonlinear System with the Vector $p$Laplacian on the SemiInfinity Interval
We study a second order nonlinear system driven by the vector
$p$Laplacian, with a multivalued nonlinearity and defined on
the positive time semiaxis $\mathbb{R}_+.$ Using degree
theoretic techniques we solve an auxiliary mixed boundary value
problem defined on the finite interval $[0,n]$ and then via a
diagonalization method we produce a solution for the original
infinite timehorizon system.
Keywords:semiinfinity interval, vector $p$Laplacian, multivalued nonlinear, fixed point index, Hartman condition, completely continuous map Category:34A60 

9. CMB 2008 (vol 51 pp. 15)
10. CMB 2007 (vol 50 pp. 632)
 Zelenyuk, Yevhen; Zelenyuk, Yuliya

Transformations and Colorings of Groups
Let $G$ be a compact topological group and let $f\colon G\to G$ be a
continuous transformation of $G$. Define $f^*\colon G\to G$ by
$f^*(x)=f(x^{1})x$ and let $\mu=\mu_G$ be Haar measure on $G$. Assume
that $H=\Imag f^*$ is a subgroup of $G$ and for every
measurable $C\subseteq H$,
$\mu_G((f^*)^{1}(C))=\mu_H(C)$. Then for every measurable
$C\subseteq G$, there exist $S\subseteq C$ and $g\in G$ such that
$f(Sg^{1})\subseteq Cg^{1}$ and $\mu(S)\ge(\mu(C))^2$.
Keywords:compact topological group, continuous transformation, endomorphism, Ramsey theoryinversion, Categories:05D10, 20D60, 22A10 

11. CMB 2005 (vol 48 pp. 267)
 Rodman, Leiba; Šemrl, Peter; Sourour, Ahmed R.

Continuous Adjacency Preserving Maps on Real Matrices
It is proved that every adjacency preserving continuous map
on the vector space of real matrices of fixed size, is either a
bijective affine tranformation
of the form $ A \mapsto PAQ+R$, possibly followed by the transposition if
the matrices are of square size, or its range is contained
in a linear subspace consisting of matrices of rank at most one
translated by some matrix $R$. The result
extends previously known
theorems where the map was assumed to be also injective.
Keywords:adjacency of matrices, continuous preservers, affine transformations Categories:15A03, 15A04. 

12. CMB 2003 (vol 46 pp. 268)
 Puls, Michael J.

Group Cohomology and $L^p$Cohomology of Finitely Generated Groups
Let $G$ be a finitely generated, infinite group, let $p>1$, and let
$L^p(G)$ denote the Banach space $\{ \sum_{x\in G} a_xx \mid \sum_{x\in
G} a_x ^p < \infty \}$. In this paper we will study the first
cohomology group of $G$ with coefficients in $L^p(G)$, and the first
reduced $L^p$cohomology space of $G$. Most of our results will be for a
class of groups that contains all finitely generated, infinite nilpotent
groups.
Keywords:group cohomology, $L^p$cohomology, central element of infinite order, harmonic function, continuous linear functional Categories:43A15, 20F65, 20F18 

13. CMB 1999 (vol 42 pp. 118)
 Rao, T. S. S. R. K.

Points of Weak$^\ast$Norm Continuity in the Unit Ball of the Space $\WC(K,X)^\ast$
For a compact Hausdorff space with a dense set of isolated points, we
give a complete description of points of weak$^\ast$norm continuity
in the dual unit ball of the space of Banach space valued functions
that are continuous when the range has the weak topology. As an
application we give a complete description of points of weaknorm
continuity of the unit ball of the space of vector measures when
the underlying Banach space has the RadonNikodym property.
Keywords:Points of weak$^\ast$norm continuity, space of vector valued weakly continuous functions, $M$ideals Categories:46B20, 46E40 

14. CMB 1998 (vol 41 pp. 261)