We establish sharp bounds for the second moment of symmetric-square $L$-functions attached to Hecke Maass cusp forms $u_j$ with spectral parameter $t_j$, where is a sum over $t_j$ in short interval. At central point $s=1/2$ $L$-function, our interval smaller than previous known results. More specifically, $|t_j|$ size $T$, $T^{1/5}$, while best was $T^{1/3}$ from work Lam. A little higher up on...

An estimator is said to be of order s > 0 if its bias has magnitude n−s, where n is the sample size. We give delta estimators and jackknife estimators of order four for smooth functions of the parameters of a multinomial distribution. An unbiased estimator is given for its density function. We also give a jackknife estimator of any order for smooth functions of the binomial parameter. The jackk...

This article is devoted to nonlinear ordinary differential equations with additive or multiplicative terms consisting of Dirac delta functions or derivatives thereof. Regularizing the delta function terms produces a family of smooth solutions. Conditions on the nonlinear terms, relating to the order of the derivatives of the delta function part, are established so that the regularized solutions...

Motivated from studies on anomalous diffusion, we show that the memory function $M(t)$ of complex materials, their creep compliance follows a power law, $J(t)\sim t^q$ with $q\in \mathbb{R}^+$, is fractional derivative Dirac delta function, $\frac{\mathrm{d}^q\delta(t-0)}{\mathrm{d}t^q}$ \mathbb{R}^+$. This leads to finding inverse Laplace transform $s^q$ for any \mathbb{R}^+$ $\frac{\mathrm{d}...

The homothallic, filamentous ascomycete Sordaria macrospora is self-fertile and produces sexual fruiting bodies (perithecia) without a mating partner. Even so, S. macrospora transcriptionally expresses two pheromone-precursor genes (ppg1 and ppg2) and two pheromone-receptor genes (pre1 and pre2). The proteins encoded by these genes are similar to alpha-factor-like and a-factor-like pheromones a...

In cystic fibrosis, the absence of functional CFTR results in thick mucous secretions in the lung and intestines, as well as pancreatic deficiency. Although expressed at high levels in the kidney, mutations in CFTR result in little or no apparent kidney dysfunction. In an effort to understand this phenomenon, we analyzed Delta F508 CFTR maturation and function in kidney cells under conditions t...

MOTIVATION We describe algorithms implemented in a new software package, RNAbor, to investigate structures in a neighborhood of an input secondary structure S of an RNA sequence s. The input structure could be the minimum free energy structure, the secondary structure obtained by analysis of the X-ray structure or by comparative sequence analysis, or an arbitrary intermediate structure. RESUL...

New types of connectedness in $ S $-proximity spaces, named as an $-$\delta$-connectedness, local $-$ \delta $-connectedness are introduced. Also, their inter-relationships studied. In space (X, \delta_{X}) $, the a subset U X with respect to \delta_{X} may not be same its subspace proximity \delta_{U} $. Further, $-component and $-treelike spaces also defined number results given.

The equilibrium binding to the synthetic RNA poly(U) of a series of oligolysines containing one, two, or three tryptophans has been examined as a function of pH, monovalent salt concentration (MX), temperature, and Mg2+. Oligopeptides containing lysine (K) and tryptophan (W) of the type KWKp-NH2 and KWKp-CO2 (p = 1-8), as well as peptides containing additional tryptophans or glycines, were stud...