are well known. When {Ij}j∈Z is the collection of dyadic intervals, i.e., I0 = {0} and Ij = sgn(j)[2 , 2) for |j| > 0, the estimate (1.2) is the classical Littlewood–Paley inequality which is valid (as well as the reverse estimate with ≥ in place of ≤) for all p ∈ (1,∞). If the Ij are disjoint intervals of equal length, then (1.2) holds if and only if p ∈ [2,∞); this was first proved by L. Carl...

Abstract The paper is devoted to the generalization of Vinberg theory homogeneous convex cones. Such a cone described as set “positive definite matrices” in commutative algebra ? n Hermitian T-matrices. These algebras are Euclidean Jordan and consist × matrices A = ( ij ), where ii ? ?, entry for i < j belongs some vector space V ; ????) $$ {a}_{ji}={a}_{ij}^{\ast }=\mathfrak{g}\left({a}_{ij...

1. Introduction. By a labeled graph we shall mean a finite (non-empty) graph Γ, without loops or multiple edges, each of whose edges is labeled by an integer greater than or equal to 2. Let the vertices of Γ be s 1 , s 2 ,. .. , s n , and let the label on an edge with endpoints s i and s j be m ij ≥ 2. Define ab m to be the word abab. .. of length m. Then the Artin group AΓ associated with the ...

For n ∈ , we consider the problem of partitioning the interval [0, n) into k subintervals of positive integer lengths `1, . . . , `k such that the lengths satisfy a set of simple constraints of the form `i ij `j where ij is one of <, >, or =. In the full information case, ij is given for all 1 ≤ i, j ≤ k. In the sequential information information case, ij is given for all 1 < i < k and j = i ± ...

The maximum cut problem this paper deals with can be formulated as follows. Given an undirected simple graph G = (V,E) where V and E stand for the node and edge sets respectively, and given weights assigned to the edges: (wij)ij∈E , a cut δ(S), with S ⊆ V is de ned as the set of edges in E with exactly one endnode in S, i.e. δ(S) = {ij ∈ E | |S ∩ {i, j}| = 1}. The weight w(S) of the cut δ(S) is...

Recommended by Lokenath Debnath In 1982 and 1970, Hdeib and Levine introduced the notions of ω-closed set and generalized closed set, respectively. The aim of this paper is to provide a relatively new notion of generalized closed set, namely, regular generalized ω-closed, regular generalized ω-continuous, a-ω-continuous, and regular generalized ω-irresolute maps and to study its fundamental pro...

We study the behavior of the Josephson current IJ flowing in a finite-size Josephson junction in a superconducting ring in the presence of an externally applied magnetic field H, taking into account the effect of the shielding currents. The set of self-consistent equations for the system can be solved explicitly for IJ in the small self-inductance coefficient limit for not negligible effective ...

A mixed graph is a that can be obtained from simple undirected by replacing some of the edges arcs in precisely one two possible directions. The Hermitian adjacency matrix $G$ order $n$ $n \times n$ $H(G)=(h_{ij})$, where $h_{ij}=-h_{ji}= \boldsymbol{\mathrm{i}}$ (with $\boldsymbol{\mathrm{i}} =\sqrt{-1})$ if there exists an arc $v_i$ to $v_j$ (but no $v_i$), $h_{ij}=h_{ji}=1$ edge (and arcs) b...

Water temperature controls the physiology, growth rate, distribution, and behavior of most plankton populations in sea thus affects energy transfer marine ecosystems. The present study focuses on influence seasonal changes surface phytoplankton size distribution copepods Arraial do Cabo Upwelling System (Brazil), where a wind-driven coastal upwelling can lead to multiple distinct bottom-up casc...