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...

Abstract We study linear subset regression in the context of high-dimensional overall model $y = \vartheta +\theta ' z + \epsilon $ with univariate response y and a d -vector random regressors , independent $\epsilon . Here, “high-dimensional” means that number available explanatory variables is much larger than n observations. consider simple submodels where regressed on set p given by $x M'z$...

The Hot (homolog of theta) protein of bacteriophage P1 can substitute for the Escherichia coli DNA polymerase III theta subunit, as evidenced by its stabilizing effect on certain dnaQ mutants that carry an unstable polymerase III epsilon proofreading subunit (antimutator effect). Here, we show that Hot can also cause an increase in the mutability of various E. coli strains (mutator effect). The...

The partial theta function is the sum of series \medskip\centerline{$\displaystyle\theta (q,x):=\sum\nolimits _{j=0}^{\infty}q^{j(j+1)/2}x^j$,}\medskip\noi where $q$is a real or complex parameter ($|q|<1$). Its name due to similaritieswith formula for Jacobi function$\Theta (q,x):=\sum _{j=-\infty}^{\infty}q^{j^2}x^j$. $\theta$ has been considered in Ramanujan's lost notebook. Itfinds applic...

It is shown that if $\gamma: [a,b] \to S^2$ $C^3$ with $\det(\gamma, \gamma', \gamma'') \neq 0$, and $A \subseteq \mathbb{R}^3$ a Borel set, then $\dim \pi_{\theta} (A) \geq \min\left\{ 2,\dim A, \frac{ \dim A}{2} + \frac{3}{4} \right\}$ for a.e. $\theta \in [a,b]$, where $\pi_{\theta}$ denotes projection onto the orthogonal complement of $\gamma(\theta)$ ``$\dim$'' refers to Hausdorff dimensio...

The cycles of a graph give natural cyclic ordering to their edge-sets, and these orderings are consistent in that two edges adjacent one cycle if only they every which appear together. An orderable matroid is whose set circuits admits such ordering. In this paper, we consider the question determining matroids orderable. Although able answer for non-binary matroids, it remains open binary matroi...

Let $$\Omega _+$$ be either the open unit disc or upper half plane right plane. In this paper, we compute norm of basic operator $$A_\alpha =\Pi _\Theta T_{b_\alpha }|_{\mathcal {H}(\Theta )}$$ in vector valued model space $$\mathcal )=H^m_2 \ominus \Theta H^m_2$$ associated with an $$m\times m$$ matrix inner function $$\Theta $$ and show that is attained. Here $$\Pi denotes orthogonal projecti...

Computing the theta series of an arbitrary lattice, and more specifically a related quantity known as the flatness factor, has been recently shown to be important for lattice code design in various wireless communication setups. However, the theta series is in general not known in closed form, excluding a small set of very special lattices. In this article, motivated by the practical applicatio...

This study was performed to evaluate the alterations of glomerular filtration barrier characteristics following acute renal ischemia-reperfusion (I/R). Ischemia was induced in anesthetized rats by unilateral renal artery occlusion for either 20 or 60 min, followed by reperfusion during 20 or 60 min, respectively, with the contralateral kidney serving as control. Sieving coefficients (theta) wer...