Ramanujan theta functions and birth and death processes

This paper discusses birth and death processes that are related to the celebrated Ramanujan’s theta functions. The pertinent transient system size probabilities are calculated numerically via a truncation of continued fractions.     

Comparison of Certain Complexes of Modules of Generalized Fractions and Čech Complexes

We establish an explicit quasi-isomorphism of complexes, which is homogeneous in graded situation, from a given ?ech complex to a certain complex of modules of generalized fractions. This leads to characterizations of local cohomology and ideal transforms of a module. Also, in this note, we study the behavior of generalized fraction formation along exact sequences and vanishing of modules of generalized fractions in certain cases.     

Hausdorff Dimension of the Exceptional Set in Engel Continued Fractions北大核心CSCD

For any real number x ∈ (0,1), there exists a unique Engel continued fractions of x. In this paper, we mainly discuss the exceptional set which the logarithms of the partial quotients grow with non-linear rate. We completely characterize the Hausdorff dimension of the relevant exceptional set. © 2022 Chinese Academy of Sciences. All rights reserved.     

Some results related to Hurwitz stability of combinatorial polynomials

Many important problems are closely related to the zeros of certain polynomials derived from combinatorial objects. The aim of this paper is to observe some results and applications for the Hurwitz stability of polynomials in combinatorics and study other related problems.We first present a criterion for the Hurwitz stability of the Turán expressions of recursive polynomials. In particular, it implies the q-log-convexity or q-log-concavity of the original polynomials. We also give a criterion for the Hurwitz stability of recursive polynomials and prove that the Hurwitz stability of any palindromic polynomial implies its semi-γ-positivity, which illustrates that the original polynomial with odd degree is unimodal. In particular, we get that the semi-γ-positivity of polynomials implies their parity-unimodality and the Hurwitz stability of polynomials implies their parity-log-concavity. Those results generalize the connections between real-rootedness, γ-positivity, log-concavity and unimodality to Hurwitz stability, semi-γ-positivity, parity-log-concavity and parity-unimodality (unimodality). As applications of these criteria, we derive some Hurwitz stability results occurred in the literature in a unified manner. In addition, we obtain the Hurwitz stability of Turán expressions for alternating run polynomials of types A and B and the Hurwitz stability for alternating run polynomials defined on a dual set of Stirling permutations.Finally, we study a class of recursive palindromic polynomials and derive many nice properties including Hurwitz stability, semi-γ-positivity, non-γ-positivity, unimodality, strong q-log-convexity, the Jacobi continued fraction expansion and the relation with derivative polynomials. In particular, these properties of the alternating descents polynomials of types A and B can be implied in a unified approach.     

Biological activities from andiroba (Carapa guianensis Aublet.) and its biotechnological applications: A systematic review

Carapa guianensis is a tree from Meliaceae family traditionally known as andiroba that has a wide range of biological properties, including therapeutic effects, antioxidant activities, insecticidal and repellent effects that can be used in biotechnological approaches to medicine, agriculture, and cosmetic products. Therefore, we aim to explore the biological activities exhibited by this species and their respective biotechnological applications of interest. For this, a systematic review was carried out following the PRISMA guidelines dated from 1993 to 2022 through the Scopus, Web of Science and Agricultural Research Database (Base de Dados da Pesquisa Agropecuária - BDPA), screened for biological activity/bioactive compounds. A total of 129 studies were included in the PRISMA flow analysis. Biological properties and major bioactive compounds, as well as biotechnological approaches could be identified. The biological activity from C. guianensis could be observed in different vegetative parts through diverse methods of extractions. These activities are mainly due to the unsaturated fatty acids and bioactive compounds, such as the limonoids and a small fraction of phenolic compounds. Gedunin-type limonoids, like gedunin and its derivatives, represent the class of compounds that show the highest bioactivities in different applications.