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We introduce the weaker forms of the Scheepers property, namely almost Scheepers (${\sf aS}$), weakly Scheepers in the sense of Sakai (${\sf wS}$) and weakly Scheepers in the sense of Ko\v{c}inac (${\sf wS_k}$). We explore many topological…
Recent outer bounds on the capacity region of Gaussian interference channels are generalized to $m$-user channels with $m>2$ and asymmetric powers and crosstalk coefficients. The bounds are again shown to give the sum-rate capacity for…
Weak-type quasi-norms are defined using the mean oscillation or the mean of a function on dyadic cubes, providing discrete analogues and variants of the corresponding quasi-norms on the upper half-space previously considered in the…
Suppose we are given a set $\cal B$ of blue points and a set $\cal R$ of red points, all lying above a horizontal line $\ell$, in the plane. Let the weight of a given point $p_i\in {\cal B}\cup{\cal R}$ be $w_i>0$ if $p_i\in {\cal B}$ and…
Necessary and sufficient conditions for convexity and strong convexity, respectively, of sublevel sets that are defined by finitely many real-valued $C^{1,1}$-maps are presented. A novel characterization of strongly convex sets in terms of…
State convergence is essential in several scientific areas, e.g. multi-agent consensus/disagreement, distributed optimization, monotone game theory, multi-agent learning over time-varying networks. This paper is the first on state…
We study the relations between different regularity assumptions in the definition of weak solutions and supersolutions to the porous medium equation. In particular, we establish the equivalence of the conditions $u^m \in L^2_{\rm…
Let $L$ be a linear operator in $L^2(\mathbb{R}^n)$ which generates a semigroup $e^{-tL}$ whose kernels $p_t(x,y)$ satisfy the Gaussian upper bound. In this paper, we investigate several kinds of weighted norm inequalities for the conical…
Let $(Z,d,\mu)$ be a compact, connected, Ahlfors $Q$-regular metric space with $Q>1$. Using a hyperbolic filling of $Z$, we define the notions of the $p$-capacity between certain subsets of $Z$ and of the weak covering $p$-capacity of path…
By a formula of Farber the topological complexity TC(X) of a (p-1)-connected, m-dimensional CW-complex X is bounded above by (2m+1)/p+1. There are also various lower estimates for TC(X) such as the nilpotency of the ring $H^*(X\times…
This paper studies planar drawings of graphs in which each vertex is represented as a point along a sequence of horizontal lines, called levels, and each edge is either a horizontal segment or a strictly $y$-monotone curve. A graph is…
In this paper, we study the uplink of a cellular system using the linear deterministic approximation model, where there are two users transmitting to a receiver, mutually interfering with a third transmitter communicating with a second…
We consider the problem of estimating the states of weakly coupled linear systems from sampled measurements. We assume that the total capacity available to the sensors to transmit their samples to a network manager in charge of the…
We propose a graph-based process calculus for modeling and reasoning about wireless networks with local broadcasts. Graphs are used at syntactical level to describe the topological structures of networks. This calculus is equipped with a…
For each $p>1$ and each positive integer $m$ we use divided differences to give intrinsic characterizations of the restriction of the Sobolev space $W^m_p(R)$ to an arbitrary closed subset of the real line.
In this paper, we study on weak $I^K$-Cauchy condition as a generalization of weak $I^*$-Cauchy condition in a normed space. We investigate the relationship between weak $I$-Cauchy and weak $I^K$-Cauchy sequences using $AP(I,K)$-condition.…
We study the complexity of the reachability problem for Vector Addition Systems with States (VASSes) in fixed dimensions. We provide four lower bounds improving the currently known state-of-the-art: 1) \np-hardness for unary flat $4$-VASSes…
We establish analogs of sharp weighted weak-type bounds for $m$-sublinear operators satisfying sparse form domination, including multilinear Calder\'on-Zygmund singular integrals. Our results, which hold for general $\vec{p} \in…
We investigate the quasilinear elliptic system $-\Delta_{m} u&=u^{-p}v^{-q}$, $u>0 \quad\mbox{ in } \Omega$, $-\Delta_{m} v&=u^{r}v^{-s}$, $v>0 \quad\mbox{ in }\Omega$, $u=v=0 \quad\mbox{ on } \partial{\Omega}$, where $\Omega…
We prove that on a restricted contact type hypersurface the number of leaf-wise intersections is bounded from below by a certain cup-length.