Abstract In this paper, we mainly consider the real interpolation spaces for variable Lebesgue defined by decreasing rearrangement function and corresponding martingale Hardy spaces. Let $$0&lt;q\le \infty $$ 0 &lt; q ≤ ∞ </mml:mat...

We derive exact results for correlations in the displacement fields $\{ \delta \vec{r} \} \equiv \{ r_{\mu = x,y} \}$ near-crystalline athermal systems two dimensions. analyze produced by different types of microscopic disorder, and show that disorder at scale gives rise to long-range with a dependence on system size $L$ given $\langle r_{\mu} r_{\nu} \rangle \sim c_{\mu \nu}(r/L,\theta)$. In a...

0. Introduction. Let X be a non-singular, connected, projective curve defined over an algebraically closed field k. Let U denote the set of isomorphism classes of stable vector bundles on X with given degree d and rank r. In the sixties, C.S. Seshadri and D. Mumford ([14], [17] and [18]) supplied U with a natural structure of quasi-projective variety, together with a natural compactification U ...

We study the wetting by water of complex "hydrophobic-hydrophilic" surfaces made of a hydrophobic substrate covered by a hydrophilic polymer brush. Polystyrene (PS) substrates covered with polystyrene- block-poly(acrylic acid) PS- b-PAA diblock copolymer layers were fabricated by Langmuir-Schaefer depositions and analyzed by atomic force microscopy (AFM) and ellipsometry. On bare PS substrate, ...

In this paper, we mainly announce the result: every Siegel-Hilbert cuspform of weight divisible by 4h and of square-free level relative to certain congruence subgroups is a linear combination of theta series. I N T R O D U C T I O N Theta series provides one of the two most explicit ways to construct holomorphic modular forms. The other way is by Eisenstein series. A virtue of theta series is t...

In this study, we investigate the long-time behavior of global solution anisotropic quasi-geostrophic equation, denoted by $$\theta $$ , where belongs to space $$C_b({\mathbb {R}}^+,H^s({\mathbb {R}}^2))$$ . Our results demonstrate that decays zero as time approaches infinity in $$L^p({\mathbb {R}}^2)$$ norm, with $$p\ge 2$$ Additionally, establish limit $$\Vert \theta (t)\Vert _{H^s}$$ t tends...

For $N\geq 3$, by the seminal paper of Brezis and V\'eron (Arch. Rational Mech. Anal. 75(1):1--6, 1980/81), no positive solutions $-\Delta u+u^q=0$ in $\mathbb R^N\setminus \{0\}$ exist if $q\geq N/(N-2)$; for $11$ $\theta\in \mathbb R$, we prove that nonlinear ell...

INTRODUCTION: Recombinant human erythropoietin (r-HuEPO) is used to treat symptomatic anaemia due to chemotherapy. A new r-HuEPO, Epoetin theta (Eporatio®), was investigated and compared to placebo and Epoetin beta in a randomised, double-blind clinical trial in adult cancer patients receiving platinum-based chemotherapy, using a fixed weekly starting dose of 20,000 IU Epoetin theta. The primar...