1.
Local maximal operators on measure metric spaces - Lin, Chin-Cheng; Stempak, Krzysztof; Wang, Ya-Shu
The notion of local maximal operators and objects associated to them is introduced and systematically studied in the general setting of measure metric spaces. The locality means here some restrictions
on the radii of involved balls. The notion encompasses different definitions dispersed throughout the literature. One of the aims of the paper is to compare properties of the 'local' objects with the 'global'
ones (i.e. these with no restrictions on the radii of balls). An emphasis is put on the case of locality function of Whitney type. Some aspects of this specific case were investigated earlier by two out of
three authors of...
2.
Convexity of strata in diagonal pants graphs of surfaces - Aramayona, J.; Lecuire, C.; Parlier, H.; Shackleton, K. J.
We prove a number of convexity results for strata of the diagonal pants graph of a surface, in analogy with the extrinsic geometric properties of strata in the Weil-Petersson completion.
As a consequence, we exhibit convex flat subgraphs of every possible rank inside the diagonal pants graph.
3.
Flux limited generalized porous media diffusion equations - Caselles, V.
We study a class of generalized porous media type flux limited diffusion equations and we prove the existence and uniqueness of entropy solutions. We compute the Rankine-Hugoniot condition on the jump set
for solutions which are of locally bounded variation in space and time. We give also a
geometric characterization of the entropy conditions on the jump set for a restricted class of this type of equations.
4.
On the fixed-point set of an automorphism of a group - Wehrfritz, B. A. F.
Let $\phi$ be an automorphism of a group $G$. Under various finiteness or solubility
hypotheses, for example under polycyclicity, the commutator subgroup $[G, \phi]$ has finite index in $G$ if the fixed-point set $C_{G}(\phi)$ of $\phi$ in $G$ is finite, but
not conversely, even for polycyclic groups $G$. Here we consider a stronger, yet natural, notion of what it means for $[G, \phi]$ to have 'finite index' in $G$ and show that
in many situations, including $G$ polycyclic, it is equivalent to $C_{G}(\phi)$ being finite.
5.
Degree of the first integral of a pencil in \boldmath$\mathbb{P}^2$ defined by Lins Neto - Medina, Liliana Puchuri
Let $\mathcal{P}_4$ be the linear family of foliations of degree $4$ in $\mathbb{P}^2$ introduced by A. Lins Neto, whose set of parameter with first integral $I_p(\mathcal{P}_4)$
is dense and countable. In this work, we will compute explicitly the degree of the rational first integral of the
foliations in this linear family, as a function of the parameter.
6.
On rings whose modules have nonzero homomorphisms to nonzero submodules - Tolooei, Y.; Vedadi, M. R.
We carry out a study of rings $R$ for which $\operatorname{Hom}_R(M,N)\neq 0$ for all nonzero $ N\leq M_R$. Such rings are called
retractable. For a retractable ring, Artinian condition and having Krull dimension are equivalent. Furthermore, a right
Artinian ring in which prime ideals commute is precisely a right Noetherian retractable ring. Retractable rings are characterized
in several ways. They form a class of rings that properly lies between the class of pseudo-Frobenius rings, and the class of
max divisible rings for which the converse of Schur's lemma holds. For several types of rings, including commutative rings,
retractability is equivalent to semi-Artinian condition. We show...
7.
On the influence of transitively normal subgroups on the structure of some infinite groups - Kurdachenko, Leonid A.; Otal, Javier
A transitively normal subgroup of a group $G$ is one that is normal in
every subgroup in which it is subnormal. This concept is obviously related to the transitivity of normality because the latter holds in every subgroup of a group $G$ if and only if every
subgroup of $G$ is transitively normal. In this paper we describe the structure of a group whose cyclic subgroups (or a part of them) are transitively normal.
8.
A new characterization of Triebel-Lizorkin spaces on \boldmath$\mathbb R^n$ - Yang, Dachun; Yuan, Wen; Zhou, Yuan
In this paper, the authors characterize
the Triebel-Lizorkin space $\dot F^\alpha_{p,q}(\mathbb{R}^n)$
via a new square function
$$S_{\alpha,q}(f)(x)=\left\{\sum_{k\in\mathbb{Z}}
2^{k\alpha q}\left|\frac1{|B(x,2^{-k})|}\int_{B(x,2^{-k})}[f(x)-f(y)]\,dy
\right|^q \right\}^{1/q}$$
¶ where $f\in L^1_{\operatorname{loc}}({\mathbb R}^n)\cap \mathcal{S}'({\mathbb R}^n)$,
$x\in{\mathbb R}^n$, $\alpha\in(0,2)$ and $p, q\in(1,\infty]$.
Similar characterizations are also established for
Triebel-Lizorkin spaces $\dot F^\alpha_{p,q}(\mathbb{R}^n)$
with $\alpha\in(0,\infty)\setminus 2{\mathbb N}$ and $p,q\in(1,\,\infty]$,
and for Besov spaces $\dot B^\alpha_{p,q}(\mathbb{R}^n)$
with $\alpha\in(0,\infty)\setminus 2{\mathbb N}$,
$p\in(1,\infty]$ and $q\in(0,\infty]$.
9.
Two-weight norm inequalities for potential type and maximal operators in a metric space - Kairema, Anna
We characterize two-weight norm inequalities for potential type integral operators in terms of Sawyer-type testing conditions. Our result is stated in a space of homogeneous type
with no additional geometric assumptions, such as group structure or non-empty annulus property, which appeared in earlier works on the subject. One of the new ingredients
in the proof is the use of a finite collection of adjacent dyadic systems recently constructed by the author and
T. Hytönen. We further extend the previous Euclidean characterization of two-weight norm inequalities for fractional maximal functions into spaces of homogeneous type.
11.
On non-commuting sets in finite soluble CC-groups - Ballester-Bolinches, Adolfo; Cossey, John
Lower bounds for the number of elements of the largest non-commuting set of a finite soluble group with a CC-subgroup are considered in this paper
12.
On the Power Pseudovariety $\mathbf{PCS}$ - Auinger, K.
The pseudovariety $\mathbf{PCS}$ which is generated by all
power semigroups of finite completely simple semigroups is characterized in various ways. For example, the equalities
$$\mathbf{PCS}=\mathbf{J}\malcab \mathbf{CS} =\mathbf{BG}\malcab \mathbf{RB}$$
¶ are established. This resolves a problem raised by Kaďourek and leads to several transparent algorithms for deciding
membership in $\mathbf{PCS}$.
13.
A degree problem for two algebraic numbers and their sum - Drungilas, Paulius; Dubickas, Artūras; Smyth, Chris
For all but one positive integer triplet $(a,b,c)$ with $a\leqslant b\leqslant c$ and $b\leqslant 6$, we decide whether
there are algebraic numbers $\alpha$, $\beta$ and $\gamma$ of
degrees $a$, $b$ and $c$, respectively, such that
$\alpha+\beta+\gamma=0$. The undecided case $(6,6,8)$ will be included in another paper.
These results imply, for example, that the sum of two algebraic numbers
of degree $6$ can be of degree $15$ but cannot be of degree $10$.
We also show that if a positive integer triplet $(a,b,c)$ satisfies a certain triangle-like inequality with respect to
every prime number then there exist algebraic numbers $\alpha$, $\beta$, $\gamma$ of degrees $a$, $b$, $c$ such...
14.
Intermediaries in Bredon (Co)homology and Classifying Spaces - Dembegioti, Fotini; Petrosyan, Nansen; Talelli, Olympia
For certain contractible $G$-CW-complexes and $\mathfrak F$ a family of subgroups of $G$, we construct a spectral sequence converging to the
$\mathfrak F$-Bredon cohomology of $G$ with $\mathrm{E}_1$-terms given by the $\mathfrak F$-Bredon cohomology of the stabilizer subgroups.
As applications, we obtain several corollaries concerning the cohomological and geometric dimensions of the classifying space $E_{\mathfrak {F}}G$.
We also introduce, for any subgroup closed class of groups $\mathfrak F$, a hierarchically defined class of groups and show that if a group $G$ is
in this class, then $G$ has finite $\mathfrak F\cap G$-Bredon (co)homological dimension if and only if $G$ has jump $\mathfrak F\cap G$-Bredon...
15.
Un Théorème de Point Fixe sur les Espaces $L^p$ - Bourdon, Marc
We establish a fixed point theorem for group actions on $L^p$-spaces,
which generalizes a theorem of Żuk and of Ballmann-Świątkowski to the case $p \neq 2$.
16.
Elliptic obstacle problems with measure data: Potentials and low order regularity - Scheven, Christoph
We consider obstacle problems with measure data related to elliptic equations of
$p$-Laplace type, and investigate the connections between low order regularity properties of the solutions and non-linear
potentials of the data. In particular, we give pointwise estimates for the solutions in terms of Wolff potentials and address the
questions of boundedness and continuity of the solution.
17.
Thompson's group $T$ is the orientation-preserving
automorphism group of a cellular complex - Fossas, Ariadna; Nguyen, Maxime
We consider a planar surface $\Sigma$ of infinite type which has
Thompson's group $\mathcal{T}$ as asymptotic mapping class group.
We construct the asymptotic pants complex $\mathcal{C}$ of $\Sigma$ and
prove that the group $\mathcal{T}$ acts transitively by automorphisms on it.
Finally, we establish that the automorphism group of the complex
$\mathcal{C}$ is an extension of the Thompson group $\mathcal{T}$ by $\mathbb{Z}/2\mathbb{Z}$
18.
On $D(-1)$-Quadruples - Bonciocat, Nicolae Ciprian; Cipu, Mihai; Mignotte, Maurice
Quadruples $(a,b,c,d)$ of positive integers $a
19.
Boundedness of rough integral operators on Triebel-Lizorkin spaces - Al-Qassem, H. M.; Cheng, L. C.; Pan, Y.
We prove the boundedness of several classes of rough
integral operators on Triebel-Lizorkin spaces. Our results represent
improvements as well as natural extensions of many previously known results.
20.
Some non-amenable groups - Kar, Aditi; Niblo, Graham A.
We generalise a result of R. Thomas to establish the non-vanishing of the first $\ell^2$ Betti number for a class of finitely generated groups.
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