Expand all Collapse all | Results 1 - 6 of 6 |
1. CMB 2014 (vol 57 pp. 277)
On Mutually $m$-permutable Product of Smooth Groups Let $G$ be a
finite group and $H$, $K$ two subgroups of G. A group $G$ is said to
be a mutually m-permutable product of $H$ and $K$ if $G=HK$ and
every maximal subgroup of $H$ permutes with $K$ and every maximal
subgroup of $K$ permutes with $H$. In this paper, we investigate the
structure of a finite group which is a mutually m-permutable product
of two subgroups under the assumption that its maximal subgroups are
totally smooth.
Keywords:permutable subgroups, $m$-permutable, smooth groups, subgroup lattices Categories:20D10, 20D20, 20E15, 20F16 |
2. CMB 2011 (vol 55 pp. 697)
Constructions of Uniformly Convex Functions We give precise conditions under which the composition
of a norm with a convex function yields a
uniformly convex function on a Banach space.
Various applications are given to functions of power type.
The results are dualized to study uniform smoothness
and several examples are provided.
Keywords:convex function, uniformly convex function, uniformly smooth function, power type, Fenchel conjugate, composition, norm Categories:52A41, 46G05, 46N10, 49J50, 90C25 |
3. CMB 2009 (vol 52 pp. 342)
On the X-ray Number of Almost Smooth Convex Bodies and of Convex Bodies of Constant Width The X-ray numbers of some classes of convex bodies are investigated.
In particular, we give a proof of the X-ray Conjecture as well as
of the Illumination Conjecture for almost smooth convex bodies
of any dimension and for convex bodies of constant width of
dimensions $3$, $4$, $5$ and $6$.
Keywords:almost smooth convex body, convex body of constant width, weakly neighbourly antipodal convex polytope, Illumination Conjecture, X-ray number, X-ray Conjecture Categories:52A20, 52A37, 52C17, 52C35 |
4. CMB 2007 (vol 50 pp. 356)
Existence of Positive Solutions for Nonlinear Noncoercive Hemivariational Inequalities In this paper we investigate the existence of positive solutions
for nonlinear elliptic problems driven by the $p$-Laplacian with a
nonsmooth potential (hemivariational inequality). Under asymptotic
conditions that make the Euler functional indefinite and
incorporate in our framework the asymptotically linear problems,
using a variational approach based on nonsmooth critical point
theory, we obtain positive smooth solutions. Our analysis also
leads naturally to multiplicity results.
Keywords:$p$-Laplacian, locally Lipschitz potential, nonsmooth critical point theory, principal eigenvalue, positive solutions, nonsmooth Mountain Pass Theorem Categories:35J20, 35J60, 35J85 |
5. CMB 2005 (vol 48 pp. 455)
On GÃ¢teaux Differentiability of Convex Functions in WCG Spaces It is shown, using the Borwein--Preiss variational principle
that for every continuous convex function $f$ on
a weakly compactly generated space $X$,
every $x_0\in X$ and every weakly compact convex symmetric set $K$ such that
$\cspan K=X$,
there is a point of G\^ateaux differentiability of $f$ in $x_0+K$.
This extends a Klee's result for separable spaces.
Keywords:GÃ¢teaux smoothness, Borwein--Preiss variational principle,, weakly compactly generated spaces Category:46B20 |
6. CMB 1998 (vol 41 pp. 497)
On the construction of HÃ¶lder and Proximal Subderivatives We construct Lipschitz functions such that for all $s>0$ they are
$s$-H\"older, and so proximally, subdifferentiable only on dyadic
rationals and nowhere else. As applications we construct Lipschitz
functions with prescribed H\"older and approximate subderivatives.
Keywords:Lipschitz functions, HÃ¶lder subdifferential, proximal subdifferential, approximate subdifferential, symmetric subdifferential, HÃ¶lder smooth, dyadic rationals Categories:49J52, 26A16, 26A24 |