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This study considers equilibrium problems, focusing on identifying finite solutions for feasible solution sequences. We introduce an innovative extension of the weak sharp minimum concept from convex programming to equilibrium problems, coining this as weak sharpness for solution sets. Recognizing situations where the solution set may not exhibit weak sharpness, we propose an augmented mapping approach to mitigate this limitation. The core of our research is the formulation of augmented weak sharpness for the solution set. This comprehensive concept encapsulates both weak sharpness and strong non-degeneracy within feasible solution sequences. Crucially, we identify a necessary and sufficient condition for the finite termination of these sequences under the premise of augmented weak sharpness for the solution set in equilibrium problems. This condition significantly broadens the scope of the existing literature, which often assumes the solution set to be weakly sharp or strongly non-degenerate, especially in mathematical programming and variational inequality problems. Our findings not only shed light on the termination conditions in equilibrium problems but also introduce a less stringent sufficient condition for the finite termination of various optimization algorithms. This research, therefore, makes a substantial contribution to the field by enhancing our understanding of termination conditions in equilibrium problems and expanding the applicability of established theories to a wider range of optimization scenarios. [ABSTRACT FROM AUTHOR]

The objective of this article is to introduce and study Itô type stochastic integrals with respect to tempered fractional Brownian motion (TFBM) of Hurst index H ∈ (1 2 , 1) and tempering parameter λ > 0 , by using the Wick product. The main tools are fractional calculus and Malliavin calculus. The Itô formula for this stochastic integral is established for the Itô type processes driven by TFBM. Based on this new Itô formula, we analyze the stability of stochastic differential equations driven by TFBM in the sense of p -th moment. A numerical example is given to illustrate our stability results. [ABSTRACT FROM AUTHOR]

Deer antlers are amazing appendages with the fastest growth rate among mammalian organs. Antler growth is driven by the growth center through a modified endochondral ossification process. Thus, identification of signaling pathways functioning in antler growth center would help us to uncover the underlying molecular mechanism of rapid antler growth. Furthermore, exploring and dissecting the molecular mechanism that regulates antler growth is extremely important and helpful for identifying methods to enhance long bone growth and treat cartilage- and bone-related diseases. In this study, we build a comprehensive intercellular signaling network in antler growth centers from both the slow growth stage and rapid growth stage using a state-of-art RNA-Seq approach. This network includes differentially expressed genes that regulate the activation of multiple signaling pathways, including the regulation of actin cytoskeleton, calcium signaling, and adherens junction. These signaling pathways coordinately control multiple biological processes, including chondrocyte proliferation and differentiation, matrix homeostasis, mechanobiology, and aging processes, during antler growth in a comprehensive and efficient manner. Therefore, our study provides novel insights into the molecular mechanisms regulating antler growth and provides valuable and powerful insight for medical research on therapeutic strategies targeting skeletal disorders and related cartilage and bone diseases.Key words: antler, rapid growth, RNA-Seq, differentially expressed genes, signaling pathways.Les bois de cerfs sont des appendices etonnants qui presentent le taux de croissance le plus eleve parmi tous les organes chez les mammiferes. La croissance des bois s'effectue a partir du centre de croissance via un processus modifie d'ossification endochondrale. Ainsi, l'identification des voies de signalisation qui operent au sein du centre de croissance des bois pourrait aider a comprendre les mecanismes moleculaires qui sous-tendent la croissance rapide des bois. De plus, l'exploration et la dissection du mecanisme moleculaire de cette croissance est extremement importante et utile pour identifier des methodes permettant d'augmenter la croissance des os longs et pour traiter les maladies touchant les cartilages et les os. Dans ce travail, les auteurs ont produit un reseau complet de la signalisation intercellulaire au sein des centres de croissance des bois, tant pendant le stade de croissance lente que pendant le stade de croissance rapide au moyen d'une analyes RNA-Seq a la fine pointe. Ce reseau inclus des genes exprimes de maniere differentielle qui regulent l'activation de plusieurs voies de signalisation, dont la regulation du cytosquelette d'actine, la signalisation via le calcium et les jonctions serrees. Ces voies de signalisation coordonnent plusieurs processus biologiques, dont la proliferation et la differenciation des chondrocytes, l'homeostasie de la matrice, des processus mecano-biologiques et le vieillissement, au cours de la croissance des bois de maniere complete et efficiente. Ainsi, cette etude apporte un eclairage nouveau sur les mecanismes moleculaires regulant la croissance des bois et procure des informations importantes et nouvelles en recherche medicale sur les strategies therapeutiques ciblant les desordres squelettiques et les maladies des cartilages et des os. [Traduit par la Redaction]Mots-cles : bois, croissance rapide, RNA-Seq, genes exprimes differentiellement, voies de signalisation., IntroductionDeer antler, an amazing appendage of deer species, is among the fastest growing organs in the animal kingdom (Picavet and Balligand 2016). The majority of deer start growing their first [...]