Expand all Collapse all | Results 1 - 25 of 459 |
1. CMB Online first
Cover products and Betti polynomials of graphs For disjoint graphs $G$ and $H$, with fixed
vertex covers
$C(G)$ and $C(H)$, their cover product is the graph $G
\circledast
H$ with vertex set
$V(G)\cup V(H)$ and edge set $E(G)\cup E(H)\cup\{\{i,j\}:i\in
C(G), j\in
C(H)\}$. We describe the graded Betti numbers of $G\circledast
H$ in terms of those of
$G$ and $H$. As applications we obtain: (i) For any positive
integer $k$ there
exists a connected bipartite graph $G$ such that $\operatorname{reg}
R/I(G)=\mu_S(G)+k$, where,
$I(G)$ denotes the edge ideal of $G$, $\operatorname{reg} R/I(G)$
is the Castelnuovo--Mumford
regularity of $R/I(G)$ and $\mu_S(G)$ is the induced or strong
matching number of
$G$; (ii) The graded Betti numbers of the complement of a tree
only depends upon
its number of vertices; (iii) The $h$-vector of $R/I(G\circledast
H)$ is described in
terms of the $h$-vectors of $R/I(G)$ and $R/I(H)$. Furthermore,
in a different
direction, we give a recursive formula for the graded Betti numbers
of chordal
bipartite graphs.
Keywords:Castelnuovo--Mumford regularity, chordal bipartite graph, edge ideal, graded Betti number, induced matching number, monomial ideal Categories:13D02, 05E45 |
2. CMB Online first
On the maximum curvature of closed curves in negatively curved manifolds Motivated by Almgren's work on the isoperimetric inequality,
we prove a sharp inequality relating the length and maximum curvature
of a closed curve in a complete, simply connected manifold of
sectional curvature at most $-1$. Moreover, if equality holds,
then the norm of the geodesic curvature is constant and the torsion
vanishes. The proof involves an application of the maximum principle
to a function defined on pairs of points.
Keywords:manifold, curvature Category:53C20 |
3. CMB Online first
On the Structure of Cuntz Semigroups in (Possibly) Nonunital C*-algebras We examine the ranks of operators in semi-finite $\mathrm{C}^*$-algebras
as measured by their densely defined lower semicontinuous traces.
We first prove that a unital simple $\mathrm{C}^*$-algebra whose
extreme tracial boundary is nonempty and finite contains positive
operators of every possible rank, independent of the property
of strict comparison. We then turn to nonunital simple algebras
and establish criteria that imply that the Cuntz semigroup is
recovered functorially from the Murray-von Neumann semigroup
and the space of densely defined lower semicontinuous traces.
Finally, we prove that these criteria are satisfied by not-necessarily-unital
approximately subhomogeneous algebras of slow dimension growth.
Combined with results of the first-named author, this shows that
slow dimension growth coincides with $\mathcal Z$-stability,
for approximately subhomogeneous algebras.
Keywords:nuclear C*-algebras, Cuntz semigroup, dimension functions, stably projectionless C*-algebras, approximately subhomogeneous C*-algebras, slow dimension growth Categories:46L35, 46L05, 46L80, 47L40, 46L85 |
4. CMB Online first
On domination of zero-divisor graphs of matrix rings We study domination in zero-divisor graphs of matrix rings over a
commutative ring with $1$.
Keywords:vector space, linear transformation, zero-divisor graph, domination, local ring Category:05C69 |
5. CMB Online first
On the largest dynamic monopolies of graphs with a given average threshold Let $G$ be a graph and $\tau$ be an assignment of nonnegative
integer thresholds to the vertices of $G$. A subset of vertices,
$D$ is said to be a $\tau$-dynamic monopoly, if $V(G)$ can be
partitioned into subsets $D_0, D_1, \ldots, D_k$ such that $D_0=D$
and for any $i\in \{0, \ldots, k-1\}$, each vertex $v$ in $D_{i+1}$
has at least $\tau(v)$ neighbors in $D_0\cup \ldots \cup D_i$.
Denote the size of smallest $\tau$-dynamic monopoly by $dyn_{\tau}(G)$
and the average of thresholds in $\tau$ by $\overline{\tau}$.
We show that the values of $dyn_{\tau}(G)$ over all assignments
$\tau$ with the same average threshold is a continuous set of
integers. For any positive number $t$, denote the maximum $dyn_{\tau}(G)$
taken over all threshold assignments $\tau$ with $\overline{\tau}\leq
t$, by $Ldyn_t(G)$. In fact, $Ldyn_t(G)$ shows the worst-case
value of a dynamic monopoly when the average threshold is a given
number $t$. We investigate under what conditions on $t$, there
exists an upper bound for $Ldyn_{t}(G)$ of the form $c|G|$, where
$c\lt 1$. Next, we show that $Ldyn_t(G)$ is coNP-hard for planar
graphs but has polynomial-time solution for forests.
Keywords:spread of influence in graphs, irreversible dynamic monopolies, target set selection Categories:05C69, 05C85 |
6. CMB Online first
The Contraction Principle for Multivalued Mappings on a Modular Metric Space with a Graph We study the existence of fixed points for contraction multivalued
mappings in modular metric spaces endowed with a graph. The
notion of a modular metric on an arbitrary set and the corresponding
modular spaces, generalizing classical modulars over linear spaces
like Orlicz spaces, were recently introduced. This paper can
be seen as a generalization of Nadler's and Edelstein's fixed
point theorems to modular metric spaces endowed with a graph.
Keywords:fixed point theory, modular metric spaces, multivalued contraction mapping, connected digraph. Categories:47H09, 46B20, 47H10, 47E10 |
7. CMB Online first
Spectral Properties of a Family of Minimal Tori of Revolution in Five-dimensional Sphere The normalized eigenvalues $\Lambda_i(M,g)$ of the Laplace-Beltrami
operator can be considered as functionals on the space of all
Riemannian metrics $g$ on a fixed surface $M$. In recent papers
several explicit examples of extremal metrics were provided.
These metrics are induced by minimal immersions of surfaces in
$\mathbb{S}^3$ or $\mathbb{S}^4$. In the present paper a family
of extremal metrics induced by minimal immersions in $\mathbb{S}^5$
is investigated.
Keywords:extremal metric, minimal surface Category:58J50 |
8. CMB Online first
Embedding theorem for inhomogeneous Besov and Triebel-Lizorkin spaces on RD-spaces In this article we prove the embedding theorem for inhomogeneous
Besov and Triebel-Lizorkin spaces on RD-spaces.
The crucial idea is to use the geometric density condition
on the measure.
Keywords:spaces of homogeneous type, test function space, distributions, CalderÃ³n reproducing formula, Besov and Triebel-Lizorkin spaces, embedding Categories:42B25, 46F05, 46E35 |
9. CMB Online first
A Fixed Point Theorem and the Existence of a Haar Measure for Hypergroups Satisfying Conditions Related to Amenability |
A Fixed Point Theorem and the Existence of a Haar Measure for Hypergroups Satisfying Conditions Related to Amenability In this paper we present a fixed point property for amenable
hypergroups which is analogous to Rickert's fixed point theorem
for semigroups. It equates the existence of a left invariant
mean on the space of weakly right uniformly continuous functions
to the existence of a fixed point for any action of the hypergroup.
Using this fixed point property, a certain class of hypergroups
are shown to have a left Haar measure.
Keywords:invariant measure, Haar measure, hypergroup, amenability, function translations Categories:43A62, 43A05, 43A07 |
10. CMB Online first
Vanishing of Massey products and Brauer groups Let $p$ be a prime number and $F$ a field containing a root of
unity of order $p$.
We relate recent results on vanishing of triple Massey products
in the mod-$p$ Galois cohomology of $F$,
due to Hopkins, Wickelgren, MinÃ¡Ä, and TÃ¢n, to classical
results in the theory of central simple algebras.
For global fields, we prove a stronger form of the vanishing
property.
Keywords:Galois cohomology, Brauer groups, triple Massey products, global fields Categories:16K50, 11R34, 12G05, 12E30 |
11. CMB Online first
Hyperplanes in the space of convergent sequences and preduals of $\ell_1$ The main aim of the present paper is to investigate various structural
properties
of hyperplanes of $c$, the Banach space of the convergent sequences.
In particular, we give an explicit formula for the projection
constants and we prove that an hyperplane of $c$ is isometric
to the whole space if and only if it is $1$-complemented. Moreover,
we obtain the classification
of those hyperplanes for which their duals are isometric to
$\ell_{1}$ and we give a complete description of the preduals
of $\ell_{1}$ under the assumption that the standard basis of
$\ell_{1}$
is weak$^{*}$-convergent.
Keywords:space of convergent sequences, projection, $\ell_1$-predual, hyperplane Categories:46B45, 46B04 |
12. CMB Online first
Almost Sure Global Well-posedness for Fractional Cubic SchrÃ¶dinger Equation on Torus In a previous paper, we proved that $1$-d periodic fractional
SchrÃ¶dinger equation with cubic nonlinearity is locally well-posed
in $H^s$ for $s\gt \frac{1-\alpha}{2}$ and globally well-posed for
$s\gt \frac{10\alpha-1}{12}$. In this paper we define an invariant
probability measure $\mu$ on $H^s$ for $s\lt \alpha-\frac{1}{2}$,
so that for any $\epsilon\gt 0$ there is a set $\Omega\subset H^s$
such that $\mu(\Omega^c)\lt \epsilon$ and the equation is globally
well-posed for initial data in $\Omega$. We see that this fills
the gap between the local well-posedness and the global well-posedness
range in almost sure sense for $\frac{1-\alpha}{2}\lt \alpha-\frac{1}{2}$,
i.e. $\alpha\gt \frac{2}{3}$ in almost sure sense.
Keywords:NLS, fractional Schrodinger equation, almost sure global wellposedness Category:35Q55 |
13. CMB Online first
On the Relation of Real and Complex Lie Supergroups A complex Lie supergroup can be described as a real Lie supergroup
with integrable almost complex structure. The necessary and
sufficient conditions on an almost complex structure on a real
Lie supergroup for defining a complex Lie supergroup are deduced.
The classification of real Lie supergroups with such almost
complex
structures yields a new approach to the known classification
of complex Lie supergroups by complex Harish-Chandra superpairs.
A universal complexification of a real Lie supergroup is
constructed.
Keywords:Lie supergroup, almost complex structure, Harish-Chandra pair, universal complexification Categories:32C11, 58A50 |
14. CMB Online first
Quantum unique ergodicity on locally symmetric spaces: the degenerate lift Given a measure $\bar\mu_\infty$ on a locally symmetric space $Y=\Gamma\backslash
G/K$,
obtained as a weak-{*} limit of probability measures associated
to
eigenfunctions of the ring of invariant differential operators,
we
construct a measure $\bar\mu_\infty$ on the homogeneous space $X=\Gamma\backslash
G$
which lifts $\bar\mu_\infty$ and which is invariant by a connected subgroup
$A_{1}\subset A$ of positive dimension, where $G=NAK$ is an Iwasawa
decomposition. If the functions are, in addition, eigenfunctions
of
the Hecke operators, then $\bar\mu_\infty$ is also the limit of measures
associated
to Hecke eigenfunctions on $X$. This generalizes results of the
author
with A. Venkatesh in the case where the spectral parameters
stay
away from the walls of the Weyl chamber.
Keywords:quantum unique ergodicity, microlocal lift, spherical dual Categories:22E50, 43A85 |
15. CMB Online first
Inequalities for partial derivatives and their applications We present various weighted integral inequalities for partial
derivatives acting on products and compositions of functions
which are applied to establish some new Opial-type inequalities
involving functions of several independent variables. We also
demonstrate the usefulness of our results in the field of partial
differential equations.
Keywords:inequality for integral, Opial-type inequality, HÃ¶lder's inequality, partial differential operator, partial differential equation Categories:26D10, 35A23 |
16. CMB Online first
Ground state solutions of Nehari-Pankov type for a superlinear Hamiltonian elliptic system on RN This paper is concerned with the following
elliptic system of Hamiltonian type
\[
\left\{
\begin{array}{ll}
-\triangle u+V(x)u=W_{v}(x, u, v), \ \ \ \ x\in {\mathbb{R}}^{N},
\\
-\triangle v+V(x)v=W_{u}(x, u, v), \ \ \ \ x\in {\mathbb{R}}^{N},
\\
u, v\in H^{1}({\mathbb{R}}^{N}),
\end{array}
\right.
\]
where the potential $V$ is periodic and $0$ lies in a gap of
the spectrum of $-\Delta+V$, $W(x, s, t)$ is
periodic in $x$ and superlinear in $s$ and $t$ at infinity.
We develop a direct approach to find ground
state solutions of Nehari-Pankov type for the above system.
Especially, our method is applicable for the
case when
\[
W(x, u, v)=\sum_{i=1}^{k}\int_{0}^{|\alpha_iu+\beta_iv|}g_i(x,
t)t\mathrm{d}t
+\sum_{j=1}^{l}\int_{0}^{\sqrt{u^2+2b_juv+a_jv^2}}h_j(x,
t)t\mathrm{d}t,
\]
where $\alpha_i, \beta_i, a_j, b_j\in \mathbb{R}$ with $\alpha_i^2+\beta_i^2\ne
0$ and $a_j\gt b_j^2$, $g_i(x, t)$
and $h_j(x, t)$ are nondecreasing in $t\in \mathbb{R}^{+}$ for every
$x\in \mathbb{R}^N$ and $g_i(x, 0)=h_j(x, 0)=0$.
Keywords:Hamiltonian elliptic system, superlinear, ground state solutions of Nehari-Pankov type, strongly indefinite functionals Categories:35J50, 35J55 |
17. CMB Online first
A note on planarity stratification of Hurwitz spaces One can easily show that any meromorphic function
on a complex closed Riemann surface can be represented as a
composition of a birational map of this surface to $\mathbb{CP}^2$ and
a projection of the image curve from an appropriate point
$p\in \mathbb{CP}^2$ to the pencil of lines through $p$. We introduce
a natural stratification of Hurwitz spaces according to the
minimal degree of a plane curve such that a given meromorphic
function can be represented in the above way and calculate the
dimensions of these strata. We observe that they are closely
related to a family of Severi varieties studied earlier by J. Harris,
Z. Ran and I. Tyomkin.
Keywords:Hurwitz spaces, meromorphic functions, Severi varieties |
18. CMB Online first
A specialisation of the Bump-Friedberg $L$-function We study the restriction of the Bump-Friedberg integrals to affine
lines $\{(s+\alpha,2s),s\in\mathbb{C}\}$.
It has a simple theory, very close to that of the Asai $L$-function.
It is an integral representation of the product
$L(s+\alpha,\pi)L(2s,\Lambda^2,\pi)$ which we denote by $L^{lin}(s,\pi,\alpha)$
for this abstract, when $\pi$ is a cuspidal automorphic
representation of $GL(k,\mathbb{A})$ for
$\mathbb{A}$ the adeles of a number field. When $k$ is even, we show
that for a cuspidal automorphic representation $\pi$,
the partial $L$-function $L^{lin,S}(s,\pi,\alpha)$ has a pole
at $1/2$, if and only if $\pi$ admits a (twisted) global
period, this gives a more direct proof of a
theorem of Jacquet and Friedberg, asserting
that $\pi$ has a twisted global period if and only if $L(\alpha+1/2,\pi)\neq
0$ and $L(1,\Lambda^2,\pi)=\infty$.
When $k$ is odd, the partial $L$-function is holmorphic in a
neighbourhood of $Re(s)\geq 1/2$ when $Re(\alpha)$ is
$\geq 0$.
Keywords:automorphic L functions Categories:11F70, 11F66 |
19. CMB Online first
Isometries and Hermitian Operators on Zygmund Spaces In this paper we characterize the isometries of subspaces of the little Zygmund space. We show that the isometries of these spaces are surjective and represented as integral operators. We also show that all hermitian operators on these settings are bounded.
Keywords:Zygmund spaces, the little Zygmund space, Hermitian operators, surjective linear isometries, generators of one-parameter groups of surjective isometries Categories:46E15, 47B15, 47B38 |
20. CMB Online first
Countable dense homogeneity in powers of zero-dimensional definable spaces We show that, for a coanalytic subspace $X$ of $2^\omega$, the
countable dense homogeneity of $X^\omega$ is equivalent to $X$
being Polish. This strengthens a result of HruÅ¡Ã¡k and Zamora
AvilÃ©s. Then, inspired by results of HernÃ¡ndez-GutiÃ©rrez,
HruÅ¡Ã¡k and van Mill, using a technique of Medvedev, we
construct a non-Polish subspace $X$ of $2^\omega$ such that $X^\omega$
is countable dense homogeneous. This gives the first $\mathsf{ZFC}$ answer
to a question of HruÅ¡Ã¡k and Zamora AvilÃ©s. Furthermore,
since our example is consistently analytic, the equivalence result
mentioned above is sharp. Our results also answer a question
of Medini and Milovich. Finally, we show that if every countable
subset of a zero-dimensional separable metrizable space $X$ is
included in a Polish subspace of $X$ then $X^\omega$ is countable
dense homogeneous.
Keywords:countable dense homogeneous, infinite power, coanalytic, Polish, $\lambda'$-set Categories:54H05, 54G20, 54E52 |
21. CMB Online first
Characterizing Distinguished Pairs by Using Liftings of Irreducible Polynomials Let $v$ be a henselian valuation of any rank of a field
$K$ and $\overline{v}$ be the unique extension of $v$ to a
fixed algebraic closure $\overline{K}$ of $K$. In 2005, it was studied properties
of those pairs $(\theta,\alpha)$ of elements of $\overline{K}$
with $[K(\theta): K]\gt [K(\alpha): K]$ where $\alpha$ is an element
of smallest degree over $K$ such that
$$
\overline{v}(\theta-\alpha)=\sup\{\overline{v}(\theta-\beta)
|\ \beta\in \overline{K}, \ [K(\beta): K]\lt [K(\theta): K]\}.
$$
Such pairs are referred to as distinguished pairs.
We use the concept of liftings of irreducible polynomials to give a
different characterization of distinguished pairs.
Keywords:valued fields, non-Archimedean valued fields, irreducible polynomials Categories:12J10, 12J25, 12E05 |
22. CMB Online first
Cohomogeneity one Randers metrics An action of a Lie group $G$ on a smooth manifold $M$ is called
cohomogeneity one if the orbit space $M/G$ is of dimension $1$.
A Finsler metric $F$ on $M$ is called invariant if $F$ is
invariant under the action of $G$. In this paper,
we study invariant
Randers metrics on cohomogeneity one manifolds. We first give a
sufficient and necessary condition for the existence of invariant
Randers metrics on cohomogeneity one manifolds. Then we obtain
some results on invariant Killing vector fields on the
cohomogeneity one manifolds and use that to deduce some
sufficient and necessary condition for a cohomogeneity one
Randers metric to be Einstein.
Keywords:cohomogeneity one actions, normal geodesics, invariant vector fields, Randers metrics Categories:53C30, 53C60 |
23. CMB Online first
Minimal Non-Self Dual Groups A group $G$ is self dual if every
subgroup
of $G$ is isomorphic to a quotient of $G$ and every quotient
of $G$ is isomorphic to
a subgroup of $G$. It is minimal non-self dual if every
proper subgroup of $G$
is self dual but $G$ is not self dual. In this paper, the structure
of minimal non-self dual groups is determined.
Keywords:minimal non-self dual group, finite group, metacyclic group, metabelian group Category:20D15 |
24. CMB Online first
On $s$-semipermutable or $s$-quasinormally embedded subgroups of finite groups Suppose that $G$ is a
finite group and $H$ is a subgroup of $G$. $H$ is said to be
$s$-semipermutable in $G$ if $HG_{p}=G_{p}H$ for any Sylow
$p$-subgroup $G_{p}$ of $G$ with $(p,|H|)=1$; $H$ is said to be
$s$-quasinormally embedded in $G$ if for each prime $p$ dividing the
order of $H$, a Sylow $p$-subgroup of $H$ is also a Sylow
$p$-subgroup of some $s$-quasinormal subgroup of $G$. We fix in
every non-cyclic Sylow subgroup $P$ of $G$ some subgroup $D$
satisfying $1\lt |D|\lt |P|$ and study the structure of $G$ under the
assumption that every subgroup $H$ of $P$ with $|H|=|D|$ is either
$s$-semipermutable or $s$-quasinormally embedded in $G$.
Some recent results are generalized and unified.
Keywords:$s$-semipermutable subgroup, $s$-quasinormally embedded subgroup, saturated formation. Categories:20D10, 20D20 |
25. CMB Online first
$L$-functions for Quadratic Characters and Annihilation of Motivic Cohomology Groups Let $n$ be a positive even integer, and let $F$ be a totally real
number field and $L$ be an abelian Galois extension which is totally
real or CM.
Fix a finite set $S$ of primes of $F$ containing the infinite primes
and all those which ramify in
$L$, and let $S_L$ denote the primes of $L$ lying above those in
$S$. Then $\mathcal{O}_L^S$ denotes the ring of $S_L$-integers of $L$.
Suppose that $\psi$ is a quadratic character of the Galois group of
$L$ over $F$. Under the assumption of the motivic Lichtenbaum
conjecture, we obtain a non-trivial annihilator of the motivic
cohomology group
$H_\mathcal{M}^2(\mathcal{O}_L^S,\mathbb{Z}(n))$ from the lead term of the Taylor series for the
$S$-modified Artin $L$-function $L_{L/F}^S(s,\psi)$ at $s=1-n$.
Keywords:motivic cohomology, regulator, Artin L-functions Categories:11R42, 11R70, 14F42, 19F27 |