Let X be a Banach space. Suppose that for all p ∈ (1,∞) a constant Cp,X depending only on X and p exists such that for any two Xvalued martingales f and g with tangent martingale difference sequences one has E‖f‖ ≤ Cp,XE‖g‖ p (∗). This property is equivalent to the UMD condition. In fact, it is still equivalent to the UMD condition if in addition one demands that either f or g satisfy the so-ca...

Let V be a vector space over a field F . If G≤GL(V, F ), the central dimension of G is the F -dimension of the vector space V/CV (G). In [DEK] and [KS], soluble linear groups in which the set Licd(G) of all proper infinite central dimensional subgroups of G satisfies the minimal condition and the maximal condition, respectively, have been described. On the other hand, in [MOS], periodic locally...

Let X be a Banach space. Suppose that for all p ∈ (1,∞) a constant Cp,X depending only on X and p exists such that for any two X-valued martingales f and g with tangent martingale difference sequences one has E‖f‖ ≤ Cp,XE‖g‖ p (∗). This property is equivalent to the UMD condition. In fact, it is still equivalent to the UMD condition if in addition one demands that either f or g satisfy the so-c...

For a graph $G$, let $P(G,lambda)$ denote the chromatic polynomial of $G$. Two graphs $G$ and $H$ are chromatically equivalent if they share the same chromatic polynomial. A graph $G$ is chromatically unique if any graph chromatically equivalent to $G$ is isomorphic to $G$. A $K_4$-homeomorph is a subdivision of the complete graph $K_4$. In this paper, we determine a family of chromatically uni...

This study reports the pathogen Perkinsus beihaiensis in oysters of the genus Crassostrea on the coast of the State of Bahia (Brazil), its prevalence, infection intensity and correlation with salinity. Oysters (n = 240) were collected between October and December 2014 at eight sampling stations between latitudes 13°55'S and 15°42'S. The laboratory procedures included macroscopic analysis, histo...

The aim of the current paper is to present the path-wise and moment estimates for solutions to stochastic functional differential equations with non-linear growth condition in the framework of G-expectation and G-Brownian motion. Under the nonlinear growth condition, the pth moment estimates for solutions to SFDEs driven by G-Brownian motion are proved. The properties of G-expectations, Hölder'...

in this paper, we investigate a problem of finding natural condition to assure the product of two graphs to be hamilton-connected. we present some sufficient and necessary conditions for $gbox h$ being hamilton-connected when $g$ is a hamilton-connected graph and $h$ is a tree or $g$ is a hamiltonian graph and $h$ is $k_2$.

in this paper we proved that every g-riesz basis for hilbert space $h$ with respect to $k$ by adding a condition is a riesz basis for hilbert $b(k)$-module $b(h,k)$. this is an extension of [a. askarizadeh,m. a. dehghan, {em g-frames as special frames}, turk. j. math., 35, (2011) 1-11]. also, we derived similar results for g-orthonormal and orthogonal bases. some relationships between dual fram...

Given a 2-connected graph G on n vertices, let G∗ be its partially square graph, obtained by adding edges uv whenever the vertices u, v have a common neighbor x satisfying the condition NG(x) ⊆ NG[u] ∪ NG[v], where NG[x] = NG(x) ∪ {x}. In particular, this condition is satisfied if x does not center a claw (an induced K1,3). Clearly G ⊆ G∗ ⊆ G, where G is the square of G. For any independent tri...