An equivalence criterion for the generalized injectivity of modules with respect to algebraic classes of homomorphisms

2016 ◽  
Vol 15 (09) ◽  
pp. 1650166 ◽  
Author(s):  
Jorge E. Macías-Díaz ◽  
Siegfried Macías
Keyword(s):  
General Definition ◽  
Injective Modules ◽  
Equivalence Criterion ◽  
Definition Of ◽  
Injective Hulls ◽  
Essential Extensions ◽  
The Way

Departing from a general definition of injectivity of modules with respect to suitable algebraic classes of morphisms, we establish conditions under which two modules are isomorphic when they are isomorphic to submodules of each other. The main result of this work extends both Bumby’s criterion for the isomorphism of injective modules and the well-known Cantor–Bernstein–Schröder’s theorem on the cardinality of sets. In the way, various properties on essential extensions, injective modules and injective hulls are generalized. The applicability of our main theorem embraces the cases of [Formula: see text]-injective and pure-injective modules as particular scenarios. Many of the propositions which lead to the proof of the main result of this paper are valid for arbitrary categories.

scholarly journals Continuous homomorphisms and rings of injective dimension one

2012 ◽  
Vol 110 (2) ◽  
pp. 181
Author(s):  
Shou-Te Chang ◽  
I-Chiau Huang
Keyword(s):  
Power Series ◽  
Injective Dimension ◽  
One Dimensional ◽  
Injective Modules ◽  
Valuation Rings ◽  
Dimension One ◽  
Injective Hulls ◽  
Essential Extensions ◽  
Formal Power ◽  
The Ideal

Let $S$ be an $R$-algebra and $\mathfrak a$ be an ideal of $S$. We define the continuous hom functor from $R$-mod to $S$-mod with respect to the $\mathfrak a$-adic topology on $S$. We show that the continuous hom functor preserves injective modules iff the ideal-adic property and ideal-continuity property are satisfied for $S$ and $\mathfrak a$. Furthermore, if $S$ is $\mathfrak a$-finite over $R$, we show that the continuous hom functor also preserves essential extensions. Hence, the continuous hom functor can be used to construct injective modules and injective hulls over $S$ using what we know about $R$. Using the continuous hom functor we can characterize rings of injective dimension one using symmetry for a special class of formal power series subrings. In the Noetherian case, this enables us to construct one-dimensional local Gorenstein domains. In the non-Noetherian case, we can apply the continuous hom functor to a generalized form of the $D+M$ construction. We may construct a class of domains of injective dimension one and a series of almost maximal valuation rings of any complete DVR.

scholarly journals A remark on local fractional calculus and ordinary derivatives

2016 ◽  
Vol 14 (1) ◽  
pp. 1122-1124 ◽  
Author(s):  
Ricardo Almeida ◽  
Małgorzata Guzowska ◽  
Tatiana Odzijewicz
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Short Note ◽  
General Definition ◽  
Local Fractional Derivative ◽  
Fundamental Properties ◽  
Local Fractional Calculus ◽  
Definition Of

AbstractIn this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new concept and ordinary differentiation. Using such formula, most of the fundamental properties of the fractional derivative can be derived directly.

scholarly journals AB0677 REVISING THE DEFINITION OF REACTIVE ARTHRITIS AND DIFFERENTIATION FROM UNDIFFERENTIATED SPONDYLOARTHRITIS

2020 ◽  
Vol 79 (Suppl 1) ◽  
pp. 1633.2-1634
Author(s):  
F. Cosan ◽  
O. M. Gedar
Keyword(s):  
Causative Agent ◽  
Reactive Arthritis ◽  
Case Reports ◽  
Experimental Studies ◽  
Classification Criteria ◽  
General Definition ◽  
Parasitic Infections ◽  
Undifferentiated Spondyloarthritis ◽  
Classical Definition ◽  
Definition Of

Background:Reactive arthritis (ReA) is defined by 1999 ACR criteria as arthritis preceding a bacterial genitourinary (GUS) or gastrointestinal (GIS) infection in 3 days-6 weeks and evidence of triggering infection. Recently, ReA is classified as SpA and patients who do not fulfill SpA criteria are classified as undifferentiated spondyloarthritis (USpA) according to ASAS/EULAR SpA classification criteria.Objectives:In several case reports which are associated with other infective agents are reported and the definition is extended for some clinicians so that SpA which is occurred after any infection is called as ReA. On the other hand, some researchers still accept the classical definition of ReA. The problem with the heterogeneity of opinions and unstandardized definition of ReA hinders studies about pathogenesis and standardization of treatments. In this study, we aimed to determine the spectrum of the use of the definition of reactive arthritis in publications in PubMed between 2009-2019.Methods:The ReA keyword is searched in PubMed for the years between 2009-2019. 248 different publications have been identified and included in this research. 89 articles, 47 reviews, 108 case reports, 2 guidelines, and 2 editorials reviewed for the definition of ReA.Results:Only 42.7% (106 patients) of these publications meet the classical definition which suggests ReA after only GIS and GUS infections. In 4 (1.6%) of the publications ReA was defined after GIS, GUS and oropharyngeal infections; in 3 (1,2%) of the publications after any bacterial infection; in 9 (3.6%) of the publications after any infection. In 8 (3.2%) of the publications, ReA and USPA was used correspondingly. In 39 (15,7%) of the publications the term agent related, ReA was used without making a general definition for ReA. 79 publications (31,9%) have not defined ReA.According to causative agent and ReA relationship, in 64 (24,6%) general infective agents, in 75 (30,2%) classical agents, in 22 (8,9%) other bacterial agents, in 23 (9,3%) streptococcus, in 10(4%) intravesical BCG, in 6 (2.4%) HIV, in 6 (2.4%) tuberculosis, in 12 (4,8%) clostrudium difficle, in 2 (0.8%) parasites were reported. In 31 (12,5%) of the publications the causative agent for the ReA was unknown, the diagnosis was made clinically.Conclusion:In this study, it is aimed to draw attention terminology intricacy and the need for the standardization of the definition of ReA and USpA. It is clear that to standardize the definition of Rea and USpA is necessary. Between 2009-2019 there are reported cases diagnosed as ReA associated with bacterial infections (especially with Clostridium difficile, streptococcus and tuberculosis infections), and viral infections (by a majority with HIV), and parasitic infections. It is not clear if we need to define them classically or define them as USPA. Another important consideration is the necessity of extended laboratory investigations to find out the real causative agent even if the patient is clinically diagnosed with ReA. The requirement of the differentiation between ReA and USpA must be revealed for therapeutic researches.References:[1]A proposal for the classification of patients for clinical and experimental studies on reactive arthritis. Pacheco-Tena C, Burgos-Vargas R, Vázquez-Mellado J, Cazarín J, Pérez-Díaz JA. J Rheumatol. 1999 Jun;26(6):1338-46.[2]The Assessment of SpondyloArthritis International Society classification criteria for peripheral spondyloarthritis and for spondyloarthritis in general. Rudwaleit M, van der Heijde D, Landewé R, Akkoc N, Brandt J, Chou CT, Dougados M, Huang F, Gu J, Kirazli Y, et al. Ann Rheum Dis. 2011;70:25–31.Disclosure of Interests:None declared

scholarly journals What is a firm? A reply to Jean-Philippe Robé

2021 ◽  
pp. 1-11
Author(s):  
Simon Deakin ◽  
David Gindis ◽  
Geoffrey M. Hodgson
Keyword(s):  
Theory Of The Firm ◽  
Recent Book ◽  
Everyday Language ◽  
Modern Capitalism ◽  
Legal Foundations ◽  
Common Parlance ◽  
The Law ◽  
Business Entities ◽  
Definition Of ◽  
The Way

Abstract In his recent book on Property, Power and Politics, Jean-Philippe Robé makes a strong case for the need to understand the legal foundations of modern capitalism. He also insists that it is important to distinguish between firms and corporations. We agree. But Robé criticizes our definition of firms in terms of legally recognized capacities on the grounds that it does not take the distinction seriously enough. He argues that firms are not legally recognized as such, as the law only knows corporations. This argument, which is capable of different interpretations, leads to the bizarre result that corporations are not firms. Using etymological and other evidence, we show that firms are treated as legally constituted business entities in both common parlance and legal discourse. The way the law defines firms and corporations, while the product of a discourse which is in many ways distinct from everyday language, has such profound implications for the way firms operate in practice that no institutional theory of the firm worthy of the name can afford to ignore it.

scholarly journals A lattice-theoretic characterization of pure subgroups of Abelian groups

2021 ◽  
Author(s):  
M. Ferrara ◽  
M. Trombetti
Keyword(s):  
Abelian Group ◽  
Abelian Groups ◽  
Subgroup Lattice ◽  
General Definition ◽  
Short Paper ◽  
Theoretic Characterization ◽  
Definition Of

AbstractLet G be an abelian group. The aim of this short paper is to describe a way to identify pure subgroups H of G by looking only at how the subgroup lattice $$\mathcal {L}(H)$$ L ( H ) embeds in $$\mathcal {L}(G)$$ L ( G ) . It is worth noticing that all results are carried out in a local nilpotent context for a general definition of purity.

scholarly journals Proportional lumpability and proportional bisimilarity

2021 ◽  
Author(s):  
Andrea Marin ◽  
Carla Piazza ◽  
Sabina Rossi
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Upper And Lower Bounds ◽  
General Definition ◽  
Performance Indices ◽  
State Aggregation ◽  
Structural Regularity ◽  
Original Definition ◽  
Aggregation Technique ◽  
Definition Of

AbstractIn this paper, we deal with the lumpability approach to cope with the state space explosion problem inherent to the computation of the stationary performance indices of large stochastic models. The lumpability method is based on a state aggregation technique and applies to Markov chains exhibiting some structural regularity. Moreover, it allows one to efficiently compute the exact values of the stationary performance indices when the model is actually lumpable. The notion of quasi-lumpability is based on the idea that a Markov chain can be altered by relatively small perturbations of the transition rates in such a way that the new resulting Markov chain is lumpable. In this case, only upper and lower bounds on the performance indices can be derived. Here, we introduce a novel notion of quasi-lumpability, named proportional lumpability, which extends the original definition of lumpability but, differently from the general definition of quasi-lumpability, it allows one to derive exact stationary performance indices for the original process. We then introduce the notion of proportional bisimilarity for the terms of the performance process algebra PEPA. Proportional bisimilarity induces a proportional lumpability on the underlying continuous-time Markov chains. Finally, we prove some compositionality results and show the applicability of our theory through examples.

What Is Fatigue?

2002 ◽  
Vol 27 (1) ◽  
pp. 42-55 ◽  
Author(s):  
Brian R. Macintosh ◽  
Dilson E. Rassier
Keyword(s):  
Contractile Response ◽  
Initial Response ◽  
Calcium Sensitivity ◽  
General Definition ◽  
Light Chains ◽  
Posttetanic Potentiation ◽  
Tetanic Contraction ◽  
First Response ◽  
Definition Of ◽  
Regulatory Light Chain Phosphorylation

Fatigue and potentiation are two forms of force modulation. A general definition of fatigue is "a circumstance where less than the anticipated contractile response is obtained." Fatigue is associated with depressed Ca2+ release and possibly decreased Ca2+ sensitivity. Potentiation results from increased Ca2+ sensitivity due to regulatory light chain phosphorylation. Muscle fatigue and potentiation can coexist, making it difficult to quantify these processes. With repetitive 10 Hz stimulation, the developed tension first increases, then decreases. Is fatigue present when developed tension first begins to decrease or when it falls below the developed tension of the first response? Intermittent incompletely fused tetanic contractions for which peak developed tension first decreases, then increases, is another unusual example of fatigue. A third example is when twitch contractions following a tetanic contraction decrease to a level below the pretetanic twitch amplitude, indicating that fatigue may have been coexistent with posttetanic potentiation. These observations illustrate the complexity of detecting fatigue, based on the simple, but commonly accepted definition presented above. Care must be taken in interpreting "before vs. after" contractile responses. Even when the contraction amplitude is greater than the initial response, there is no guarantee that mechanisms associated with fatigue are not present. Key words: calcium sensitivity, staircase, posttetanic potentiation, myosin light chains, skeletal muscle

The Place of Interests in Hobbes’s Civil Science

2016 ◽  
Vol 29 (2) ◽  
pp. 105-128
Author(s):  
Elliott Karstadt
Keyword(s):  
The Political ◽  
Crucial Importance ◽  
Political Issue ◽  
Political Ideas ◽  
Form Of Government ◽  
Civil Science ◽  
Definition Of ◽  
The Impact ◽  
The Way

Many scholars argue that Hobbes’s political ideas do not significantly develop between The Elements of Law (1640) and Leviathan (1651). This article seeks to challenge that assumption by studying the way in which Hobbes’s deployment of the vocabulary of ‘interest’ develops over the course of the 1640s. The article begins by showing that the vocabulary is newly important in Leviathan, before attempting a ‘Hobbesian definition’ of what is meant by the term. We end by looking at the impact that the vocabulary has on two key areas of Hobbes’s philosophy: his theory of counsel and his arguments in favour of monarchy as the best form of government. In both areas, Hobbes’s conception of ‘interests’ is shown to be of crucial importance in lending a new understanding of the political issue under consideration.

scholarly journals General Definition of Gravitational Tension

2004 ◽  
Vol 2004 (05) ◽  
pp. 043-043 ◽  
Author(s):  
T Harmark ◽  
N.A Obers
Keyword(s):  
General Definition ◽  
Definition Of

Mean Diameters in Parallel-Flow and Counter-Flow Aerosol Systems

1976 ◽  
Vol 98 (2) ◽  
pp. 297-302 ◽  
Author(s):  
K. G. T. Hollands ◽  
K. C. Goel
Keyword(s):  
Mass Transfer ◽  
Continuous Phase ◽  
General Concept ◽  
Parallel Flow ◽  
General Definition ◽  
Single Pair ◽  
Counter Flow ◽  
Mean Diameter ◽  
The Mean ◽  
Definition Of

The general concept of the mean diameter of the disperse phase of an aerosol system, first introduced by Mugele and Evans in 1951, has proven to be a very useful one. In this concept, the proper mean diameter, xp,q, is characterized by a single pair of indices, p and q, which are dependent on the actual type of aerosol system under consideration. This paper re-examines the validity of this concept of mean diameter in heat and mass transfer aerosol systems. The concept is found to be applicable only under a very narrow range of conditions. Attention is then given to a more general definition of a mean diameter, applicable to aerosol heat or mass exchangers. Analyses of these devices shows that the more general mean diameter is a function of the capacity rate ratio, R, and effectiveness of the heat exchanger, ε. Solutions to the governing equations have permitted the mean diameter to be presented graphically as a function of these variables. These solutions are given for two types of particle size distributions, the Rosin-Rammler and the log-probability, and for both parallel-flow and counter-flow heat exchangers. The solutions are, however, restricted to cases where the resistance to heat or mass transfer lies exclusively in the continuous phase.

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