Results 11 to 20 of about 46 (46)

The second coefficient of a function with all derivatives univalent

International Journal of Mathematics and Mathematical Sciences, Volume 5, Issue 2, Page 281-288, 1982., 1981
We consider the second coefficient of a class of functions, univalent and normalized, and with all derivatives univalent in the unit disk D, and improve on a known result. It is also shown that this bound is in a sense best possible.
A. Sathaye, S. M. Shah
wiley   +1 more source

Yet another characterization of the sine function

International Journal of Mathematics and Mathematical Sciences, Volume 4, Issue 2, Page 371-381, 1981., 1981
In this expository paper, it is shown that if an entire function of exponential type vanishes at least once in the complex plane and if it has exactly the same number of zeros (counting multiplicities) as its second derivative, then this function must take the form Asin(Bz + C).
Robert Gervais, Lee A. Rubel
wiley   +1 more source

Bounded index, entire solutions of ordinary differential equations and summability methods

International Journal of Mathematics and Mathematical Sciences, Volume 4, Issue 3, Page 417-434, 1981., 1981
A brief survey of recent results on functions of bounded index and bounded index summability methods is given. Theorems on entire solutions of ordinary differential equations with polynomial coefficients are included.
G. H. Fricke, Ranjan Roy, S. M. Shah
wiley   +1 more source

Efficacy of an oral chew containing fibre and Bacillus velezensis C‐3102 in the management of anal sac impaction in dogs

Veterinary Dermatology, Volume 36, Issue 1, Page 74-82, February 2025.
Background — Anal sac impaction is common in dogs and manual expression may be effective, yet recurrence remains a problem. To facilitate physiological emptying of the sacs, it is important to maintain a bulky stool consistency. Objectives — The study evaluated if supplementation with ProGlan, a complementary feed containing Bacillus velezensis C‐3102 ...
Marta Salichs, Shea Beasley, Josep Homedes   +2 more
wiley   +1 more source

Longitudinal evaluation of the cutaneous and rectal microbiota of German shepherd dogs with perianal fistulas undergoing therapy with ciclosporin and ketoconazole

Veterinary Dermatology, Volume 35, Issue 4, Page 375-385, August 2024.
Background – Perianal fistulas are painful ulcers or sinus tracts that disproportionately affect German shepherd dogs and are proposed as a spontaneous animal model of fistulising Crohn's disease. Objectives – To characterise the rectal and cutaneous microbiota in German shepherd dogs with perianal fistulas and to investigate longitudinal shifts with ...
Christine L. Cain, Ellen White, Lindsey E. Citron, Qi Zheng, Daniel O. Morris, Elizabeth A. Grice, Charles W. Bradley II   +6 more
wiley   +1 more source

Asymptotic expansions relating to the distribution of the length of longest increasing subsequences

Forum of Mathematics, Sigma
We study the distribution of the length of longest increasing subsequences in random permutations of n integers as n grows large and establish an asymptotic expansion in powers of $n^{-1/3}$ .
Folkmar Bornemann
doaj   +1 more source

The initial-value problem for a Gardner-type equation

Advanced Nonlinear Studies
Discussed here is a regularized version(0.1)ut+ux+uux+Au2ux−uxxt=0, $${u}_{t}+{u}_{x}+u{u}_{x}+A{u}^{2}{u}_{x}-{u}_{\mathit{xxt}}=0,$$ of the classical Gardner equationut+ux+uux+Au2ux+uxxx=0, $${u}_{t}+{u}_{x}+u{u}_{x}+A{u}^{2}{u}_{x}+{u}_{\mathit{xxx ...
Bona Jerry, Chen Hongqiu, Guerrero Pamela, Haidau Cristina, Pantic Sanja   +4 more
doaj   +1 more source

Integral mean estimates of Turán-type inequalities for the polar derivative of a polynomial with restricted zeros

Open Mathematics
In this article, we extend inequalities concerning the polar derivative of a polynomial to integral mean for the class of polynomials with s-fold zero at the origin and the remaining zeros inside some closed disk of radius kk for k≥1k\ge 1 and k≤1k\le 1,
Singha Nirmal Kumar, Chanam Barchand
doaj   +1 more source

Refinements of inequalities on extremal problems of polynomials

Open Mathematics
Let H(z) be a polynomial of degree n, and for any complex number α, let D α H(z) = nH(z) + (α − z)H′(z) denote the polar derivative of H(z) with respect to α.
Devi Maisnam Triveni, Singh Thangjam Birkramjit, Chanam Barchand   +2 more
doaj   +1 more source

Improved versions of certain Bernstein and Turán-type inequalities on polynomials

Open Mathematics
In this paper, we establish some new results on Bernstein and Turán-type inequalities for polynomials on the unit circle on the complex plane by using an improved Schwarz Lemma at the boundary recently proved by Mercer.
Laishangbam Raju, Soraisam Robinson, Chanam Barchand   +2 more
doaj   +1 more source