Asymptotic approximation of central binomial coefficients with rigorous error bounds
OMS-Vol. 5 (2021), Issue 1, pp. 380 – 386 Open Access Full-Text PDF
Richard P. Brent
Abstract:We show that a well-known asymptotic series for the logarithm of the central binomial coefficient is strictly enveloping in the sense of Pólya and Szegö, so the error incurred in truncating the series is of the same sign as the next term, and is bounded in magnitude by that term. We consider closely related asymptotic series for Binet’s function, for \(\ln\Gamma(z+\frac12)\), and for the Riemann-Siegel theta function, and make some historical remarks.
Tail distribution estimates of the mixed-fractional CEV model
OMS-Vol. 5 (2021), Issue 1, pp. 371 – 379 Open Access Full-Text PDF
Nguyen Thu Hang, Pham Thi Phuong Thuy
Abstract:The aim of this paper is to study the tail distribution of the CEV model driven by Brownian motion and fractional Brownian motion. Based on the techniques of Malliavin calculus and a result established recently in [1], we obtain an explicit estimate for tail distributions.
Reachability results in labelled \(t\)-ary trees
OMS-Vol. 5 (2021), Issue 1, pp. 360 – 370 Open Access Full-Text PDF
Isaac Owino Okoth, Albert Oloo Nyariaro
Abstract:In this paper, we prove some new formulas in the enumeration of labelled \(t\)-ary trees by path lengths. We treat trees having their edges oriented from a vertex of lower label towards a vertex of higher label. Among other results, we obtain counting formulas for the number of \(t\)-ary trees on \(n\) vertices in which there are paths of length \(\ell\) starting at a root with label \(i\) and ending at a vertex, sink, leaf sink, first child, non-first child and non-leaf. For each statistic, the average number of these reachable vertices is obtained for any random \(t\)-ary tree.
Determination of heavy metals, macro and trace elements in selected medicinal plants from Central Market of San Salvador, El Salvador
OJC-Vol. 4 (2021), Issue 1, pp. 27 – 35 Open Access Full-Text PDF
Ulises G. Castillo, Sofía Hernández, Melissa Morataya, Keny Núñez, Freddy A. Carranza, Morena L. Martínez and Marvin J. Núñez
Abstract:Medicinal plant’s quality and safety are becoming a great interest topic worldwide, especially due to contamination with heavy metals. The main objective of this study is to determine the phytochemical composition and quantify the concentration of heavy metals, trace and macro elements in fourteen medicinal plants purchased in the Central Market of San Salvador. Samples were dried and fractionated, subsequently digested and analyzed at first by phytochemical screening and then by atomic absorption spectrometry. The concentration of twelve elements was determined, only Matricaria chamomilla exceeded the established World Health Organization limit for Cd and Cu. Acourtia nudicaulis and Turnera diffusa exceeded the permitted concentration of Ni. The concentration of these elements must be inspected in medicinal plants sold in the informal markets of El Salvador to ensure the safety and quality. To our knowledge, this is the first study of heavy metals in medicinal plants conducted in El Salvador.
A comprehensive review on biological impact of Anthocyanins on human life
OJC-Vol. 4 (2021), Issue 1, pp. 19 – 26 Open Access Full-Text PDF
Musarat Jabeen, Namra Hussain, Hira Noreen, Iqra Amjad, Amna Zia, Maria Manzoor, Komal Ashraf, Rabia Mehmood
Abstract:Due to the beneficial effects of anthocyanins on plants, animals and human beings, they have become the most interesting topic of research for scientists. They are being used in food industry as well as in pharmaceutical and cosmetic industries. Anthocyanins are present in red, blue, orange, purple, violet and intermediate color mostly. They are non-hazardous natural pigments that have positive impact on human health. They occur in nature since the evolution of flowering plants on earth. As humans were wild in ancient times, they consumed their large concentration through their diet and human digestive system is very active for their digestion. In this review, the chemistry and impact of anthocyanins on human health is discussed briefly.
Existence result for a semipositone fractional boundary value problem
OMA-Vol. 5 (2021), Issue 2, pp. 66 – 72 Open Access Full-Text PDF
Serife Müge Ege, Fatma Serap Topal
Abstract:This work deals with a boundary value problem for a nonlinear semipositone multi-point fractional differential equation. By using the Schauder fixed point theorem, we show the existence of one solution for this problem. Our result extend some recent works in the literature.
