Results 71 to 80 of about 16,410 (257)

Existence, Uniqueness and Asymptotic Behavior of Solutions for Semilinear Elliptic Equations

Mathematics
A class of semilinear elliptic differential equations was investigated in this study. By constructing the inverse function, using the method of upper and lower solutions and the principle of comparison, the existence of the maximum positive solution and ...
Lin-Lin Wang, Jing-Jing Liu, Yong-Hong Fan   +2 more
doaj   +1 more source

Asymptotic Formula for the Moments of Lebesgue’s Singular Function

Моделирование и анализ информационных систем, 2015
Recall Lebesgue’s singular function. Imagine flipping a biased coin with probability p of heads and probability q = 1 − p of tails. Let the binary expansion of ξ ∈ [0, 1]: ξ = ∑∞ k=1 ck2−k be determined by flipping the coin infinitely many times, that is ...
E. A. Timofeev
doaj   +1 more source

An asymptotic formula for the Chebyshev theta function [PDF]

Notes on Number Theory and Discrete Mathematics, 2019
Let $\{p_n\}_{n\ge 1}$ be the sequence of primes and $\vartheta(x) = \sum_{p \leq x} \log p$, where $p$ runs over the primes not exceeding $x$, be the Chebyshev $\vartheta$-function. In this note we derive lower and upper bounds for $\vartheta(p_n)/n$ by comparing it with $\log p_{n+1}$ and deduce that $\vartheta(p_n)/n=\log p_{n+1}\left(1-\frac{1 ...
openaire   +2 more sources

Artificial Neural Network Driven Computational Modeling of Naegleria fowleri Epidemics Using Variational Optimization

Advanced Physics Research, EarlyView.
ABSTRACT This study presents a mathematical framework to analyze the transmission dynamics of an amoeba‐induced central nervous system infection. The population is divided into compartments including susceptible, exposed, infected, quarantined, hospitalized, recovered, protected, and deceased.
Wakeel Ahmed, Areej Yaseen, Ghulamullah Saeedi, Shakeel Ahmed   +3 more
wiley   +1 more source

An Asymptotic Formula for a Trigonometric Sum of Vinogradov

Journal of Number Theory, 2001
The authors give a representation formula and an asymptotic formula for the trigonometric sum \[ f(m,n):= \sum_{k=1}^{m-1} \frac{|\sin ( \pi k n /m)|}{\sin ( \pi k /m)}. \] As an application they deduce from the representation formula the upper bound \[ f(m,n) < (4/ \pi^2) m \log m + (4/ \pi^2) ( \gamma - \log ( \pi /2) + 2 C_G) m + O(m/ \sqrt{\log m}),
Cochrane, Todd, Peral, J.C
openaire   +1 more source

The morphology of the oval window in Paranthropus robustus compared to humans and other modern primates

The Anatomical Record, EarlyView.
Abstract The oval window (OW) is an opening connecting the inner and middle ear. Its area has been shown to consistently scale with body mass (BM) in primates, and has been used alongside semi‐circular canal (SCC) size to differentiate Homo sapiens and fossil hominins, including Paranthropus robustus.
Ruy Fernandez, José Braga
wiley   +1 more source

Timelike asymptotics for global solutions to a scalar quasilinear wave equation satisfying the weak null condition

Forum of Mathematics, Sigma
We study the timelike asymptotics for global solutions to a scalar quasilinear wave equation satisfying the weak null condition. Given a global solution u to the scalar wave equation with sufficiently small $C_c^\infty $ initial data, we derive an
Dongxiao Yu
doaj   +1 more source

Asymptotic unboundedness of the norms of delayed matrix sine and cosine

Electronic Journal of Qualitative Theory of Differential Equations, 2017
In the paper, the asymptotic properties of recently defined special matrix functions called delayed matrix sine and delayed matrix cosine are studied. The asymptotic unboundedness of their norms is proved.
Zdenek Svoboda
doaj   +1 more source

Postnatal craniomandibular growth in Harbor seals (Phoca vitulina vitulina)

The Anatomical Record, EarlyView.
Postnatal ontogeny in Harbor seals (Phoca vitulina vitulina). Cranium and mandible grow rapidly until 5 years of age, followed by a deceleration and finally a stagnation. Abstract As secondarily aquatic carnivores, seals display several phenotypic differences compared to their terrestrial relatives.
Elisabeth Steinbach, Julia Schaar, Christine Böhmer   +2 more
wiley   +1 more source

A series transformation formula and related polynomials

International Journal of Mathematics and Mathematical Sciences, 2005
We present a formula that turns power series into series of functions. This formula serves two purposes: first, it helps to evaluate some power series in a closed form; second, it transforms certain power series into asymptotic series.
Khristo N. Boyadzhiev
doaj   +1 more source