The linear discrepancy of a poset P is the least k such that there is a linear extension L of P such that if x and y are incomparable, then |hL(x)− hL(y)| ≤ k. Whereas the weak discrepancy is the least k such that there is a weak extension W of P such that if x and y are incomparable, then |hW (x)− hW (y)| ≤ k. This paper resolves a question of Tanenbaum, Trenk, and Fishburn on characterizing w...

We prove that if X is an infinite dimensional Banach lattice with a weak unit then there exists a probability space (Ω,Σ, μ) so that the unit sphere S(L1(Ω,Σ, μ) is uniformly homeomorphic to the unit sphere S(X) if and only if X does not contain l ∞’s uniformly.

There is a sizeable literature that tests for weak-form efficiency in commodity and energy spot and futures prices. While many studies now allow for multiple structural breaks to address the criticism that conventional unit root tests have low power to reject the unit root null in the presence of structural change, the extant literature overlooks the fact that conventional unit root tests are b...

In the present study relationship between shrimp catch per unit effort (CPUE) and satellite-based environmental parameters, chlorophyll-a (Chl-a) and sea surface temperature (SST), was investigated in 27 stations in Bushehr provincial waters in the geographical position from E 50˚ 44´ and N 28˚ 59´ to E 51˚ 40´ and N 27˚ 33´, in July 2017 and July 2018. SST and Chl-a data were extracted from +E...

‎it is well known that every (real or complex) normed linear space $l$ is isometrically embeddable into $c(x)$ for some compact hausdorff space $x$‎. ‎here $x$ is the closed unit ball of $l^*$ (the set of all continuous scalar-valued linear mappings on $l$) endowed with the weak$^*$ topology‎, ‎which is compact by the banach--alaoglu theorem‎. ‎we prove that the compact hausdorff space $x$ can ...

We extend the Larson–Sweedler theorem for weak Hopf algebras by proving that a finite dimensional weak bialgebra is a weak Hopf algebra iff it possesses a non-degenerate left integral. We establish the autonomous monoidal category of the modules of a weak Hopf algebra A and show the semisimplicity of the unit and the invertible modules of A. We also reveal the connection of these modules to lef...

The asymmetric unit of the title compound, 2C(8)H(9)N(2) (+)·C(10)H(6)O(6)S(2) (2-), contains a 2-methyl-benzimidazolium cation and one half of a naphthalene-1,5-disulfonate anion. The formula unit is generated by an inversion center. In the crystal, N-H⋯O hydrogen bonds link the components into chains along [001]. In addition, weak C-H⋯O hydrogen bonds and weak C-H⋯π inter-actions are observed...

We show that the unit ball of lp(Γ) in its weak topology is a continuous image of σ1(Γ) and we deduce some combinatorial properties of its lattice of open sets which are not shared by the balls of other equivalent norms when Γ is uncountable. For a set Γ and a real number 1 < p < ∞, the Banach space lp(Γ) is a reflexive space, hence its unit ball is compact in the weak topology and in fact, it ...

In the structure of the title salt, C(12)H(10)N(3)O(4) (+)·C(7)H(3)N(2)O(7) (-), the cations and the anions are linked by a single N(+)-H⋯O(carbox-yl) hydrogen bond, the discrete cation-anion unit having no inter-molecular associations other than weak cation-anion aromatic ring π-π inter-actions [ring centroid separation = 3.7320 (14) Å] and a number of weak inter-unit aromatic C-H⋯O contacts. ...