Contributions of flow cytometry to the molecular study of spermatogenesis in mammals

Mammalian testes are very heterogeneous organs, with a high number of different cell types. Testicular heterogeneity, together with the lack of reliable in vitro culture systems of spermatogenic cells, have been an obstacle for the characterization of the molecular bases of the unique events that take place along the different spermatogenic stages. In this context, flow cytometry has become an invaluable tool for the analysis of testicular heterogeneity, and for the purification of stage-specific spermatogenic cell populations, both for basic research and for clinical applications. In this review, we highlight the importance of flow cytometry for the advances on the knowledge of the molecular groundwork of spermatogenesis in mammals. Moreover, we provide examples of different approaches to the study of spermatogenesis that have benefited from flow cytometry, including the characterization of mutant phenotypes, transcriptomics, epigenetic and genome-wide chromatin studies, and the attempts to establish cell culture systems for research and/or clinical aims such as infertility treatment

Constant Sign Solutions to Linear Fractional Integral Problems and Their Applications to the Monotone Method

This manuscript provides some results concerning the sign of solutions for linear fractional integral equations with constant coefficients. This information is later used to prove the existence of solutions to some nonlinear problems, together with underestimates and overestimates. These results are obtained after applying suitable modifications in the classical process of monotone iterative techniques. Finally, we provide an example where we prove the existence of solutions, and we compute some estimates.This research was partially supported by grant numbers MTM2016-75140-P (AEI/FEDER, UE) and ED431C 2019/02 (GRC Xunta de Galicia)S

Existence of solution to a periodic boundary value problem for a nonlinear impulsive fractional differential equation

We study the existence of solution to a periodic boundary value problem for nonlinear impulsive fractional differential equations by using Schaeffer’s fixed point theorem

Applications of Contractive-like Mapping Principles to Fuzzy Equations

We recall a recent extension of the classical Banach fixed point theorem to partially ordered sets and justify its applicability to the study of the existence and uniqueness of solution for fuzzy and fuzzy differential equations. To this purpose, we analyze the validity of some properties relative to sequences of fuzzy sets and fuzzy functions.We recall a recent extension of the classical Banach fixed point theorem to partially ordered sets and justify its applicability to the study of the existence and uniqueness of solution for fuzzy and fuzzy differential equations. To this purpose, we analyze the validity of some properties relative to sequences of fuzzy sets and fuzzy functions

Existence of extremal solutions for quadratic fuzzy equations

Some results on the existence of solution for certain fuzzy equations are revised and extended. In this paper, we establish the existence of a solution for the fuzzy equation , where , , , and are positive fuzzy numbers satisfying certain conditions. To this purpose, we use fixed point theory, applying results such as the well-known fixed point theorem of Tarski, presenting some results regarding the existence of extremal solutions to the above equation.Research partially supported by Ministerio de Educación y Ciencia and FEDER, Projects BFM2001 – 3884 – C02 – 01 and MTM2004 – 06652 – C03 – 01, and by Xunta de Galicia and FEDER, Project PGIDIT02PXIC20703PNS

Krasnosel'skii type compression-expansion fixed point theorem for set contractions and star convex sets

This is a post-peer-review, pre-copyedit version of an article published in Journal of Fixed Point Theory and Applications. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11784-020-00799-0In this paper, we give or improve compression-expansion results for set contractions in conical domains determined by balls or star convex sets. In the compression case, we use Potter’s idea of proof, while the expansion case is reduced to the compression one by means of a change of variable. Finally, to illustrate the theory, we give an application to the initial value problem for a system of implicit first order differential equations.Cristina Lois-Prados and Rosana Rodríguez-López acknowledge the support of the research grant MTM2016-75140-P (AEI/FEDER, UE). The research of Cristina Lois-Prados has been partially supported by grant ED481A-2018/080 from Xunta de Galicia.S

Prólogo

Prólogo al volumen II, por Rosana Paula Rodríguez