There is an extensive literature on the asymptotic order of Sudler's trigonometric product $P_N (\alpha) = \prod_{n=1}^N |2 \sin (\pi n \alpha)|$ for fixed or "typical" values $\alpha$. In present paper we establish a structural result, which given $\alpha$ characterizes those $N$ $P_N(\alpha)$ attains particularly large values. This characterization relies coefficients in its Ostrowski expansi...

We study the behaviour of a symmetric exclusion process in presence non-Markovian stochastic resetting, where configuration system is reset to step-like profile at power-law waiting times with an exponent $\alpha$. find that resetting leads rich for currents, as well density profile. show that, any finite system, $\alpha<1$, eventually becomes uniform while $\alpha >1$, eventual non-trivial sta...

inthis paper, the main aim is to introduce the class $mathcal{u}_p(lambda,alpha,beta,k_0)$ of $p$-harmonic mappings togetherwith its subclasses $mathcal{u}_p(lambda,alpha,beta,k_0)capmathcal {t}_p$ and $mathcal{u}_p(lambda,alpha,beta,k_0)capmathcal {t}_p^0$, andinvestigate the properties of the mappings in these classes. first,we give a sufficient condition for mappings to be in $mathcal{u}_p(l...

aim of this study is to determine the risk of adverse pregnancy outcome by maternal serum alpha-fetoprotein (msafp) level. we followed 295 pregnant women from msafp screening in the 14th to 22th week of gestation until the end of pregnancy and information on pregnancy outcome have been recorded in questionnaires. of 295 pregnant women, 270 had term labor and 25 had preterm labor. the frequencie...

objectives we aimed to investigate whether there is renal injury and its relationship with oxidative stress after intraperitoneal injection of α-ama in mice experimental poisoning models. materials and methods there were 37 male balb/c laboratory mice treated with α-ama, according to the study groups: control group (n = 7); low dose (0.2 mg/kg) (n = 10); moderate dose (0.6 mg/kg) (n = 10), and ...

conclusions the current report isolates, characterizes, and demonstrates the novel heat-adapted amylase-producing bacteria ss1, ss2 and ss3 from taptapani hot spring, indicating its potentiality and stability under acidic conditions. materials and methods bacterial strains were isolated by dilution plating method from the water samples collected from taptapani hot spring, odisha and screened fo...

for a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-armendariz ring, that is a generalization of both $pi$-armendariz rings, and $(alpha,delta)$-compatible skew armendariz rings. we first observe the basic properties of skew $pi$-armendariz rings, and extend the class of skew $pi$-armendariz rings through various ring extensions. we nex...

For a positive real number $\alpha$, let $\mathbb{N}_0[\alpha,\alpha^{-1}]$ be the semiring of all numbers $f(\alpha)$ for $f(x)$ lying in $\mathbb{N}_0[x,x^{-1}]$, which is Laurent polynomials over set nonnegative integers $\mathbb{N}_0$. In this paper, we study various factorization properties additive structure $\mathbb{N}_0[\alpha, \alpha^{-1}]$. We characterize when \alpha^{-1}]$ atomic. T...