Sense Of Definition Research Articles

Closing a System in the Dynamic Input/Output Automata Model

By definition, an input/output (or I/O) automaton is closed if there are no input actions in its action signature, and open otherwise. The dynamic I/O automata (DIOA) model is a special kind of the I/O automata one in which automata can be created and destroyed dynamically, and automata action signatures can change from state to state. In this paper, we draw attention to the possibility that a DIOA model of a system is open in the sense of the above definition although it seems to the specifier to be closed. This can be the reason why some expected properties cannot be proved to hold for the system. We, therefore, introduce a restriction operator for DIOA to help obtain a closed model in which the expected system properties could be verified.

Erratum to: Existence and Regularity of Very Weak Solutions of the Stationary Navier–Stokes Equations

The purpose of this erratum is to correct some mistakes of Remark 1, Lemma 1 and their consequences in the paper [Arch Rational Mech Anal 193 (2009) 117–152]. The major contribution of the paper is to establish existence and regularity of very weak solutions in Lq( ) of the Dirichlet problem (NS) for the stationary Navier–Stokes equations with arbitrarily large boundary data g in W−1/q,q(∂ ). In particular, it is shown in Theorem 1, the main existence result, that there exists at least one very weak solution u ∈ Lq0( ) of (NS) in the sense of Definition 1 for the data f, k and g satisfying the very weak regularity (1). The proof of Theorem 1 is complete. Theorems 2 and 3, the main regularity results, are also correct. So are the corresponding results for the linear problems, i.e., Theorems 7, 9 and 10. However, due to the very weak regularity of f and k, the solution u neither satisfies (NS) in the usual distribution sense, nor does it have a well-defined trace, which contradicts the assertions in Remarks 2 and 3. In fact, Remarks 2 and 3 are wrong and should be corrected by imposing a stronger regularity assumption on f and k. Let X and Y be Banach spaces. Assume that X ↪→ Y , i.e., X ⊂ Y , and that there is a constant C > 0 such that ||x ||Y C ||x ||X for all x ∈ X . Then the restriction of each f ∈ Y ′ to X , denoted f |X , is a bounded linear functional on X ′ with the norm bounded by C || f ||Y ′ . Consider the space Y ′|X = { f |X : f ∈ Y ′} equipped with the quotient norm

Umgidi at the Mabambas': Gender, Practice and Performance Among Farm Workers in the Sundays River Valley

This article describes and analyses an umgidi, a celebratory feast that usually accompanies the final ‘coming out’ phase of circumcision, among farm workers in the Sundays River Valley, Eastern Cape. Anthropological monographs describing circumcision rituals among Xhosa-speakers appear not to discuss such a feast at all, despite this event being familiar to most rural and urban Xhosa-speakers, particularly in the western half of the Eastern Cape. In the absence of comparative information, this article introduces an umgidi feast as a multi-vocal event that comments on the spatial, performative and practice-oriented elements of life among workers in the Sundays River Valley. I show that farm workers have a definite sense of identity and place connected to the occupation of land as labour tenants and later as labourers. Their conservative rural values are closely associated with the memories of previous land occupation, but are also combined with experiences of displacement, so that memories of lost land directly inform the creation of current identities. An umgidi feast allows the unification of fragmented groups of kin and clan, and provides an opportunity for workers to articulate the pressures of modern farm employment. The prominence of female workers at umgidi feasts also heightens the use of domestic space as an idiom for commentary on experiences of disruption and labour domination. Broadly, the article contributes to an understanding of ritual among displaced communities in southern Africa, particularly labour tenants and farm workers on white farms.

Sovereignty and Socialism in Tanzania: The Historiography of an African State

Observers of the Tanzanian political scene would point out that the country makes its own decisions on matters of internal and international importance. The policy ofUjamaa Vijijini[African socialism in the villages], it would be argued, was formulated here and not at the dictate of any foreign power.In an edited volume entitledThe State in Tanzania, published in 1980 just before the precipitous denouement of President Julius Nyerere's philosophy of African socialism known asUjamaa, Haroub Othman began with the question of the sub-title, “Who Controls it and Whose Interest Does it Serve?” The cover featured a large black question mark on a red background. Provocatively Othman asked, “can one say in a specific and definite sense that Tanzania is building socialism?” Exhibiting a remarkable level of open criticism of the government in a one-party state, the essays framed their issues in the Marxist terms that were long predominant in literature on the Tanzanian state. The book dealt with an ongoing concern that Tanzania's ambitious goals for democracy and development were not being met and the overarching nationalist question of which sovereign defined those goals. It was a question that continues to vex political scientists of Africa today who seek to reconcile Westphalian concepts of sovereignty with the layered realities of African polities struggling to exert sovereign authority both internally and externally.Reviewing a representative sample of nearly fifty years of scholarship on the postcolonial Tanzanian state, one is struck by the tension enervating Othman's essays. Scholars are torn between the impulse to understand the theoretical implications of Tanzania's experience for socialism and a more pragmatic concern to evaluate the country's claim to sovereign authority.

Bifurcation control and chaos in a linear impulsive system

Bifurcation control and the existence of chaos in a class of linear impulsive systems are discussed by means of both theoretical and numerical ways. Chaotic behaviour in the sense of Marotto's definition is rigorously proven. A linear impulsive controller, which does not result in any change in one period-1 solution of the original system, is proposed to control and anti-control chaos. The numerical results for chaotic attractor, route leading to chaos, chaos control, and chaos anti-control, which are illustrated with two examples, are in good agreement with the theoretical analysis.

Interior and closure operators on texture spaces—II: Dikranjan–Giuli closure operators and Hutton algebras

In this work, we discuss interior and closure operators on textures in the sense of Dikranjan–Giuli. First, we define the category dfICL of interior–closure spaces and bicontinuous difunctions and show that it is topological over dfTex whose objects are textures and morphisms are difunctions. The category L- CLOSURE of L-closure spaces and Zadeh type powerset operators, and the counterparts of the Lowen functors have been presented by Wu–Neng Zhou in a fixed-basis setting. We consider the closure operators on a Hutton algebra L and, in a natural way, we define the category HCL of Hutton closure spaces taking the morphisms of the opposite category of HutAlg—the category of Hutton algebras (fuzzy lattices) and the mappings preserving arbitrary meets, joins and involution. In this case, the categories L- CLOSURE and H—the category of Hutton spaces and the morphisms in the sense of Definition 2.1—can be considered as a subcategory and a full subcategory of HCL, respectively. Using the fact that dfICL and HCL op are equivalent categories, we guarantee the existence of products and sums in HCL. Finally, we show that the generalized Lowen functor can be also given in a textural framework for [ 0 , 1 ] .

Gravitational collapse and the formation of black holes for the spherically symmetric Einstein-Vlasov system

We review results on the spherically symmetric, asymptotically flat Einstein-Vlasov system. We focus on a recent result where we found explicit conditions on the initial data which guarantee the formation of a black hole in the evolution. Among these data there are data such that the corresponding solutions exist globally in Schwarzschild coordinates. We put these results into a more general context, and we include arguments which show that the spacetimes we obtain satisfy the weak cosmic censorship conjecture and contain a black hole in the sense of suitable mathematical definitions of these concepts which are available in the literature.

Sequence stratigraphy hierarchy and the accommodation succession method

We propose a framework for the hierarchy of sedimentary units observed in stratigraphic data that is based entirely on the geometric relationship of the strata. This framework of geometries is assumed to result from repeated successions of accommodation creation and sediment fill (here named accommodation succession). We have modified existing hierarchal frameworks to describe depositional units resulting from accommodation successions of varying magnitude and duration, across a depositional profile. Each full succession consists of component partial succession sets that are, sequentially, lowstand—progradation to aggradational; transgressive—retrogradation; and highstand—aggradation to progradation to degradation. The terms “highstand” and “lowstand” as originally defined to label systems tracts relative to a shelf edge, and with an implied relationship between sea level and systems tracts, have been the root of confusion. We propose that these terms be used in the strict sense of the original definition, because their meaning has been lost when applied to the many depositional settings and high-resolution data sets to which the concepts of sequence stratigraphy are now applied. We propose that the concept of accommodation succession stacking be used in the interpretation of stratigraphic data within a hierarchal framework of depositional sequences, sequence sets, and composite sequences. This will allow an interpreter to accurately categorize observations, provide a basis for predictions away from control points, and develop a framework that allows revisions as higher-resolution data become available.

Inferentialism and the categoricity problem: reply to Raatikainen

It is sometimes held that rules of inference determine the meaning of the logical constants: the meaning of, say, conjunction is determined by either its introduction or its elimination rules, or both; similarly for the other connectives. In a recent paper, Panu Raatikainen argues that this view call it logical inferentialism is undermined by some Very little known' considerations by Carnap (1943) to the effect that 'in a definite sense, it is not true that the standard rules of inference' themselves suffice to 'determine the meanings of [the] logical constants' (Raatikainen 2000: 283). In a nutshell, Carnap showed that the rules allow for non-normal interpretations of negation and disjunction. Raatikainen concludes that 'no ordinary formalization of logic ... is sufficient to fully formalize all the essential properties of the logical constants' (2000: 283). We suggest that this is a mistake. Pace Raatikainen, intuitionists like Dummett and Prawitz need not worry about Carnap's problem. And although bilateral solutions for classical inferentialists as proposed by Timothy Smiley and Ian Rumfitt seem inadequate, it is not excluded that the classical inferentialists may be in a position to address the problem too.

Awareness of memory functioning, autobiographical memory and identity in early-stage dementia

Sense of identity is thought to be closely related to autobiographical memory. Theoretical models of awareness suggest that both may also be related to level of awareness of memory functioning among people with early-stage dementia. This study explores the relationships between autobiographical memory, identity and awareness in early-stage dementia. Thirty participants with Alzheimer's disease, or vascular or mixed dementia were assessed using the Autobiographical Memory Interview, with an additional section eliciting recall for the mid-life period, the Tennessee Self-Concept Scale, and the Memory Awareness Rating Scale. Lower levels of awareness of memory functioning were associated with poorer autobiographical recall for the mid-life period and with a more positive and definite sense of identity. Reduced awareness may serve a protective function against the threats to self posed by the onset and progression of dementia.

Making places: The role of attachment in creating the sense of place for traditional streets in Malaysia

Sense of place definition includes the point where the physical element, activity and meaning are intertwined in the people experience of place. In urban design and place quality research, much has been discussed on the significance of the physical elements and activities in creating the sense of place; however, the role of place attachment as a component that gives places meaning(s) has not been adequately explored. This article is based on the main findings of a doctoral research examining attachment to traditional shopping streets in the city centre of Kuala Lumpur. Surveys and face-to-face interviews were conducted with users of the streets to investigate place attachment and its influence on place identity. The finding demonstrates that attachment to the traditional streets is strong and it influences the users’ perception on the identity of the places. The streets were regarded as very important in sustaining the economic activities and meaningful in accentuating cultural diversity and self and group identity. The historical significance of the area as the earliest shopping locations in the city evoked personal and shared meanings to the long-term users who developed stronger place attachment. The paper concludes by establishing that place attachment has a significant contribution to the sense of place therefore should be considered in the design of urban places especially when redevelopment is one of the options.

Quasi-isometries between graphs and trees

Criteria for quasi-isometry between trees and general graphs as well as for quasi-isometries between metrically almost transitive graphs and trees are found. Thereby we use different concepts of thickness for graphs, ends and end spaces. A metrically almost transitive graph is quasi-isometric to a tree if and only if it has only thin metric ends (in the sense of Definition 3.6). If a graph is quasi-isometric to a tree then there is a one-to-one correspondence between the metric ends and those d-fibers which contain a quasi-geodesic. The graphs considered in this paper are not necessarily locally finite.

Emergence is coupled to scope, not level

AbstractSince its application to systems, emergence has been explained in terms of levels of observation. This approach has led to confusion, contradiction, and incoherence. When the concept of level is replaced by a framework of scope, resolution and state, this confusion is dissolved. We find that emergent properties are determined by the relationship between the scope of macrostate and microstate descriptions. This is formally demonstrated with mathematical examples, including the nonorientable, one sided and one edged emergent properties of the Mbius strip. Emergent properties are identified as nonlocal, because of spatially or temporally extended structure. This establishes normative definitions of emergent properties and emergence, which make sense of previous descriptive definitions of emergence. The central insight that emergence is coupled to scope means that emergence is objective, in the sense that it is independent of the knowledge of the observer. This framework is then used to identify fundamental limits to our ability to capture emergence in formal systems, and propose an alternative approach towards identifying system boundaries.© 2007 Wiley Periodicals, Inc. Complexity, 2007

Associated and Attached Primes of Some Graded Modules Over Semigroup Rings

In Helm and Miller (2003, Section 8), the authors posed the problem of which faces of a saturated affine semigroup Q correspond to prime ideals associated to the local cohomology module where ω R is the canonical module of the semigroup ring R = 𝕜[Q], 𝕜 a field, and I is a monomial ideal in R. In this article we will give a solution in the case that Q is simplicial. We will also consider a similar problem for attached primes of the local cohomology module where M is a squarefree module (in sense of Definition 2.7) and 𝔪 is the homogeneous maximal ideal of R. As a result, we will show that for a squarefree monomial ideal I in a normal simplicial semigroup ring R and each integer i ≥ 0, we have where d = dim R.

2006 Award of Merit acceptance speech

2006 Award of Merit acceptance speech

Infinitesimal deformations of basic tensor in generalized Riemannian space

At the beginning of the present work the basic facts on generalized Riemannian space (GRn) in the sense of Eisenhart's definition [Eis] and also on infinitesimal deformations of a space are given. We study the Lie derivatives and infinitesimal deformations of basic covariant and contravariant tensor at GRn.

Quantum-chemical study of the effects of noncovalent interactions on the nuclear magnetic screening constants of pyrimidine base associates

The effects of weak noncovalent interactions on the nuclear magnetic screening (NMS) constants (σ 1H), (σ 13C) and charge distribution (qt) on atoms in van der Waals model associates of unsubstituted and substituted pyrimidines and substituted uracil are considered. The NMS constants were calculated by the UB3LYP/6-31G(d,p) with GIAO functions. The correlation dependences of the 1H and 13C σ constants on the charge q on atoms whre constructed. It were shown that they can be represented as polynomials that include the terms that are linear and quadratic relative to the charge. The relations obtained in this way are similar in form and close in magnitude to the coefficients of the known Buckingham and Augspurger functions that describe the electric field effects on the nuclear magnetic screening constants. It was found that the coefficients in these polynomials have a definite physical sense in that they characterize nuclear magnetic screening and the “screening polarizability” tensor in the unperturbed molecule and associate, respectively. The NMS constants and charge distribution in pyrimidine base associates and accordingly the coefficients that reflect their values in polynomials depend on the form, size, and composition of the associate and can vary significantly depending on the position of the pyrimidine base in the associate.

Theodor Fontane und die Technik by Philipp Frank, and: Black Devil and Iron Angel: The Railway in Nineteenth-Century German Realism by Paul A. Youngman

MLR, I02.3, 2007 89I published text do not in any way depend on the careful examination of the source material in thepreceding parts of his book. Here it is worth repeating Fontane's own statement, so frequentlyquoted (see p. I I) and yet so frequently disregarded: 'Ich sehe klar ein, daB ich eigentlich erst bei dem 7oer Kriegsbuche und dann bei dem Schreiben meines Romans [Vor dem Sturm] ein Schriftsteller geworden bin d.h. einMann, der seinMetier als eine Kunst betreibt.' The corollary of this is surely thatwe should look for the differences between Der Krieg gegen Frankreich and its predecessors. Perhaps themost obvious is that the Franco-Prussian War did not readily lend itself to arrangement around a single de cisive battle, and its recalcitrantmaterial required amore subtle formof structuring. Comparison with themanuscript material shows in theMont-Valerien chapter, for instance, the late improvement of 'denZirkel' into 'den einschlieBenden Eisenzirkel' (p. I I3), which helps establish a parallel between Sedan and Paris, and so between books I and 2. The second major difference is the absence (at theauthor's insistence) of illustration. Pacholski seems to regret this,but a glance at theunpublished material he supplies makes Fontane's motives abundantly clear.At the editorial stage ofDer deutscheKrieg von i866 the finalcomments are those of the illustrator,usually requir ing the author to reorganize the text so as to accommodate an illustration, or recast a sentence so that itshould begin with a specific initial capital which, independently of the author, Burger had already supplied in elaborately decorated form.More empi rical inhis approach thanUwe Hebekus (Klios Medien (Tiibingen: Niemeyer, 2003), reviewed in MLR, 100 (2005), 558-59), Pacholski nevertheless chooses to emphasize the collaborative and multi-medial quality of thewar-books, whereas the tendency is clearly towards theprimacy of narrative. Pacholski's preference is reflected in thedetailed commentary on Burger's illustra tions, 'Exkurs iiberdas Bildwerk', the titleofwhich implicitly acknowledges a certain independence of the stated purpose of the study.Paradoxically, however, thisconsti tutes the second major contribution to the discussion of thewar-books. Because of thisand the manuscript material, Pacholski's book will have tohave a place alongside Fontane's published texts, which are unlikely ever tobe available in a critical edition. UNIVERSITY OFWARWICK JOHNOSBORNE Theodor Fontane und die Technik. By PHILIPP FRANK. (Epistemata Literaturwis senschaft, 526) Wiurzburg: Konigshausen & Neumann. 2005. 265 pp. E36. ISBN 978-3-8260-2965-3. Black Devil and IronAngel: The Railway in Nineteenth-Century German Realism. By PAULA. YOUNGMAN.Washington: Catholic University ofAmerica Press. 2005. xiii+ I73 pp. $49.95. ISBN 978-o-8I32-I4I6-0. In I977 the brilliantly eclectic Wolfgang Schivelbusch published his Geschichte der Eisenbahnreise (Frankfurt a.M.: Hanser). This impressionistic book, outlining the ef fectsof the railwaynetwork on nineteenth-century modes ofperception, set thepoints for a series of studies which looked at the symbolic import of thismost material of technological objects within thecultural history of the industrial age. There have been a number of anthologies (notablyWolfgang Minaty's Die Eisenbahn: Gedichte, Prosa, Bilder (Frankfurt a.M.: Insel, I984)) and also a number ofmonographs, inparticular by Johannes Mahr (Eisenbahnen in der deutschenDichtung (Munich: Fink, i982)), Gerhard Rademacher (Technik und industrielleArbeitswelt inder deutschenLyrik des I9. und 20. Jahrhunderts (Frankfurt a.M.: Peter Lang, I976)), and more recently, Alfred Heinimann (Technische Innovation und literarischeAneignung: Die Eisenbahn inder deutschen und englischenLiteratur des i9. Jahrhunderts (Bern: Francke, i992)), 892 Reviews followed byHarro Segeberg's seminal work Literatur im technischen Zeitalter (Darm stadt:Wissenschaftliche Buchgesellschaft, 1997). The two studies under considera tion here seek indifferentways tobuild on theseworks, although inboth cases there is a definite sense of dehaja vu for the reader already familiarwith the earlier books and inparticular with the literary texts that they (re-)examine. Common toboth studies is thework ofTheodor Fontane. While Paul Youngman devotes one chapter of his book on nineteenth-century 'realist' depictions of the train toFontane's Cecile and EffiBriest, Philipp Frank's methodical analysis isentirely de voted to the significance of technology in thewhole of Fontane's output, frompoems such as the early 'Junker Dampf' and the later 'Briuck'am Tay' through the reportage of his English journalism and wanderings through theMark Brandenburg to the 'Hauptwerk' that ishis...

Blow up solutions for one class of system of Pekar–Choquard type nonlinear Schrödinger equation

We prove that firstly the existence of stationary solutions of the Pekar–Choquard system with the form (PCS) i ϕ → t + Δ ϕ → + K ( ϕ → ) + | ϕ → | p - 2 ϕ → = 0 , secondly the solutions of Cauchy problem of (PCS) with initial data close to the stationary solution (in a suitable sense) must blow up at finite time; finally the standing wave relating to the stationary solution of (PCS) is strongly unstable in the sense of Definition 4.2.

Deep Matrix Algebras of Finite Type

Deep matrix algebras \(\varepsilon {\left( {X,A} \right)}\) based on a set \(X\) over a ring \(A\) are introduced and studied by McCrimmon when \(X\) has infinite cardinality. Here, we construct a new \(\varepsilon {\left( {X,A} \right)}\)-module that is faithful for \(X\) of any cardinality. For \(A=\mathbb{K}\) a field of arbitrary characteristic and \(2\le |X\,|<\infty\), \(\varepsilon {\left( {X,\mathbb{K}} \right)}\) is studied in depth. The algebra \(\varepsilon {\left( {X,\mathbb{K}} \right)}\) is shown to possess a unique proper non-zero ideal, isomorphic to \(Mat_{\infty}(\mathbb{K})\). This leads to a new and interesting simple algebra, \({\user1{\mathcal{A}}}{\left( {X,\,\mathbb{K}} \right)}\), the quotient of \(\varepsilon {\left( {X,\mathbb{K}} \right)}\) by its unique ideal. Both \(\varepsilon {\left( {X,\mathbb{K}} \right)}\) and the quotient algebra are shown to have centers isomorphic to \(\mathbb{K}\). Via the new faithful representation, all automorphisms of \(\varepsilon {\left( {X,\mathbb{K}} \right)}\) are shown to be inner in the sense of Definition 18.