Quantitative stability of linear infinite inequality systems under block perturbations with applications to convex systems

The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional) Banach spaces and that are indexed by an arbitrary fixed set J. Parameter perturbations on the right-hand side of the inequalities are required to be merely bounded, and thus the natural parameter space is l ∞(J). Our basic strategy consists of linearizing the parameterized convex system via splitting convex inequalities into linear ones by using the Fenchel–Legendre conjugate. This approach yields that arbitrary bounded right-hand side perturbations of the convex system turn on constant-by-blocks perturbations in the linearized system. Based on advanced variational analysis, we derive a precise formula for computing the exact Lipschitzian bound of the feasible solution map of block-perturbed linear systems, which involves only the system’s data, and then show that this exact bound agrees with the coderivative norm of the aforementioned mapping. In this way we extend to the convex setting the results of Cánovas et al. (SIAM J. Optim. 20, 1504–1526, 2009) developed for arbitrary perturbations with no block structure in the linear framework under the boundedness assumption on the system’s coefficients. The latter boundedness assumption is removed in this paper when the decision space is reflexive. The last section provides the aimed application to the convex case.

On a Class of Generalized Elliptic-type Integrals

The aim of this paper is to study a generalized form of elliptic-type integrals which unify and extend various families of elliptic-type integrals studied recently by several authors. In a recent communication [1] we have obtained recurrence relations and asymptotic formula for this generalized elliptic-type integral. Here we shall obtain some more results which are single and multiple integral formulae, differentiation formula, fractional integral and approximations for this class of generalized elliptic-type integrals.

Certain Properties of Fractional Calculus Operators Associated with Generalized Mittag-Leffler Function

Mathematics Subject Classification: 26A33, 33E12, 33C20.

Generalized Fractional Calculus, Special Functions and Integral Transforms: What is the Relation?

Виржиния С. Кирякова - В този обзор илюстрираме накратко наши приноси към обобщенията на дробното смятане (анализ) като теория на операторите за интегриране и диференциране от произволен (дробен) ред, на класическите специални функции и на интегралните трансформации от лапласов тип. Показано е, че тези три области на анализа са тясно свързани и взаимно индуцират своето възникване и по-нататъшно развитие. За конкретните твърдения, доказателства и примери, вж. Литературата.

Commutants of the Square of Differentiation on the Half-Line

MSC 2010: Primary: 447B37; Secondary: 47B38, 47A15

Elevated concentration of TNF-a induces trophoblast differentiation in mouse blastocyst outgrowths

Elevated expression of tumour necrosis factora (TNF-a) is associated with adverse pregnancy outcome. This study has examined the expression of TNF-a and its receptors (TNF-Rs) by mouse blastocysts and blastocyst outgrowths from day 4 to 9.5 of pregnancy and investigated the effects of elevated TNF-a on the inner cell mass (ICM) and trophoblast cells of blastocyst outgrowths. RTPCR demonstrated TNF-a mRNA expression from day 7.5 to 9.5, TNF-R1 from day 6.5 to 9.5 and TNF-R2 from day 5.5 to 7.5 of pregnancy, and in situ hybridisation revealed the trophoblast giant cells (TGCs) of the early placenta as the site of TNF-a expression. Day 4 blastocysts were cultured in a physiologically high concentration of TNF-a (100 ng/ml) for 72 h to the outgrowth stage and then compared to blastocysts cultured in media alone. TNF-a-treated blastocyst outgrowths exhibited a significant reduction in ICM cells (mean € SD 23.90€10.42 vs 9.37€7.45, t-test, P<0.0001) with no significant change in the numbers of trophoblast cells (19.97€8.14 vs 21.73€7.79, t-test, P=0.39). Within the trophoblast cell population, the TNF-a-treated outgrowths exhibited a significant increase in multinucleated cells (14.10€5.53 vs 6.37€5.80, t-test, P<0.0001) and a corresponding significant decrease in mononucleated cells (5.87€3.60 vs 15.37€5.87, t-test, P<0.0001). In summary, this study describes the expression of TNF-a and its receptors during the peri-implantation period in the mouse. It also reports that elevated TNF-a restricts ICM proliferation in the blastocyst and changes the ratio of mononucleated to multinucleated trophoblast cells. These findings suggest a mechanism by which increased

Structural differentiation and corporate venturing : the moderating role of formal and informal integration mechanisms

Research has suggested that corporate venturing is crucial to strategic renewal and firm performance, yet scholars still debate the appropriate organizational configurations to facilitate the creation of new businesses in existing organizations. Our study investigates the effectiveness of combining structural differentiation with formal and informal organizational as well as top management team integration mechanisms in establishing an appropriate context for venturing activities. Our findings suggest that structural differentiation has a positive effect on corporate venturing. In addition, our study indicates that a shared vision has a positive effect on venturing in a structurally differentiated context. Socially integrated senior teams and cross-functional interfaces, however, are ineffective integration mechanisms for establishing linkages across differentiated units and for successfully pursuing corporate venturing.

Multilineage differentiation potential of bone and cartilage cells derived from explant culture

To date, mesenchymal stem cells (MSCs) from various tissues have been reported, but the yield and differentiation potential of different tissue-derived MSCs is still not clear. This study was undertaken in an attempt to investigate the multilineage stem cell potential of bone and cartilage explant cultures in comparison with bone marrow derived mesenchymal stem cells (BMSCs). The results showed that the surface antigen expression of tissue-derived cells was consistent with that of mesenchymal stem cells, such as lacking the haematopoietic and common leukocyte markers (CD34, CD45) while expressing markers related to adhesion (CD29, CD166) and stem cells (CD90, CD105). The tissue-derived cells were able to differentiate into osteoblast, chondrocyte and adipocyte lineage pathways when stimulated in the appropriate differentiating conditions. However, compared with BMSCs, tissue-derived cells showed less capacity for multilineage differentiation when the level of differentiation was assessed in monolayer culture by analysing the expression of tissue-specific genes by reverse transcription polymerase chain reaction (RT-PCR) and histology. In high density pellet cultures, tissue-derived cells were able to differentiate into chondrocytes, expressing chondrocyte markers such as proteoglycans, type II collagen and aggrecan. Taken together, these results indicate that cells derived from tissue explant cultures reserved certain degree of differentiation properties of MSCs in vitro.

Stem cell regulatory gene expression in human adult dental pulp and periodontal ligament cells undergoing odontogenic/osteogenic differentiation

Introduction During development and regeneration, odontogenesis and osteogenesis are initiated by a cascade of signals driven by several master regulatory genes. Methods In this study, we investigated the differential expression of 84 stem cell–related genes in dental pulp cells (DPCs) and periodontal ligament cells (PDLCs) undergoing odontogenic/osteogenic differentiation. Results Our results showed that, although there was considerable overlap, certain genes had more differential expression in PDLCs than in DPCs. CCND2, DLL1, and MME were the major upregulated genes in both PDLCs and DPCs, whereas KRT15 was the only gene significantly downregulated in PDLCs and DPCs in both odontogenic and osteogenic differentiation. Interestingly, a large number of regulatory genes in odontogenic and osteogenic differentiation interact or crosstalk via Notch, Wnt, transforming growth factor β (TGF-β)/bone morphogenic protein (BMP), and cadherin signaling pathways, such as the regulation of APC, DLL1, CCND2, BMP2, and CDH1. Using a rat dental pulp and periodontal defect model, the expression and distribution of both BMP2 and CDH1 have been verified for their spatial localization in dental pulp and periodontal tissue regeneration. Conclusions This study has generated an overview of stem cell–related gene expression in DPCs and PDLCs during odontogenic/osteogenic differentiation and revealed that these genes may interact through the Notch, Wnt, TGF-β/BMP, and cadherin signalling pathways to play a crucial role in determining the fate of dental derived cell and dental tissue regeneration. These findings provided a new insight into the molecular mechanisms of the dental tissue mineralization and regeneration

'Anorexia Nervosa' : asceticism, differentiation, government

This paper looks at the severe fasting practices most commonly found among young women. Almost all explanations for this behaviour centre around the notion of the pathological condition 'anorexia nervosa'. However, food asceticism has a well-documented history, particularly when it concerns religious fasting. In ancient Greece, dietary asceticism constituted an important part of the means by which individuals constructed an acceptable 'self'. Ascetic fasting then later resurfaced at various historical moments and in various different places — such as amongst medieval religious women and, in a broader way, amongst contemporary young women. It is argued that these practices have traditionally formed part of the mechanisms by which differentiation by age and sex occurs. Overall, it is hoped that this analysis will permit not only a different focus on 'anorexia nervosa', but also on some of the ways in which young people become gendered.

Asceticism, differentiation, government : 'anorexia nervosa' as an achievement

As with the ancient Greeks, the `self' is not something to be discovered, it is something to be created. Practices such as ascetic fasting are not expressions of the struggle between the authentic self and the external world, they are the very practices by which a `self' is formed.