On the cubicity of bipartite graphs

A unit cube in k-dimension (or a k-cube) is defined as the Cartesian product R-1 x R-2 x ... x R-k, where each R-i is a closed interval on the real line of the form [a(j), a(i), + 1]. The cubicity of G, denoted as cub(G), is the minimum k such that G is the intersection graph of a collection of k-cubes. Many NP-complete graph problems can be solved efficiently or have good approximation ratios in graphs of low cubicity. In most of these cases the first step is to get a low dimensional cube representation of the given graph. It is known that for graph G, cub(G) <= left perpendicular2n/3right perpendicular. Recently it has been shown that for a graph G, cub(G) >= 4(Delta + 1) In n, where n and Delta are the number of vertices and maximum degree of G, respectively. In this paper, we show that for a bipartite graph G = (A boolean OR B, E) with |A| = n(1), |B| = n2, n(1) <= n(2), and Delta' = min {Delta(A),Delta(B)}, where Delta(A) = max(a is an element of A)d(a) and Delta(B) = max(b is an element of B) d(b), d(a) and d(b) being the degree of a and b in G, respectively , cub(G) <= 2(Delta' + 2) bar left rightln n(2)bar left arrow. We also give an efficient randomized algorithm to construct the cube representation of G in 3 (Delta' + 2) bar right arrowIn n(2)bar left arrow dimension. The reader may note that in general Delta' can be much smaller than Delta.

An upper bound for Cubicity in terms of Boxicity

An axis-parallel b-dimensional box is a Cartesian product R-1 x R-2 x ... x R-b where each R-i (for 1 <= i <= b) is a closed interval of the form [a(i), b(i)] on the real line. The boxicity of any graph G, box(G) is the minimum positive integer b such that G can be represented as the intersection graph of axis-parallel b-dimensional boxes. A b-dimensional cube is a Cartesian product R-1 x R-2 x ... x R-b, where each R-i (for 1 <= i <= b) is a closed interval of the form [a(i), a(i) + 1] on the real line. When the boxes are restricted to be axis-parallel cubes in b-dimension, the minimum dimension b required to represent the graph is called the cubicity of the graph (denoted by cub(G)). In this paper we prove that cub(G) <= inverted right perpendicularlog(2) ninverted left perpendicular box(G), where n is the number of vertices in the graph. We also show that this upper bound is tight.Some immediate consequences of the above result are listed below: 1. Planar graphs have cubicity at most 3inverted right perpendicularlog(2) ninvereted left perpendicular.2. Outer planar graphs have cubicity at most 2inverted right perpendicularlog(2) ninverted left perpendicular.3. Any graph of treewidth tw has cubicity at most (tw + 2) inverted right perpendicularlog(2) ninverted left perpendicular. Thus, chordal graphs have cubicity at most (omega + 1) inverted right erpendicularlog(2) ninverted left perpendicular and circular arc graphs have cubicity at most (2 omega + 1)inverted right perpendicularlog(2) ninverted left perpendicular, where omega is the clique number.

Socio-environmental impact of idol immersion: dimensions and directions

India possesses a diverse and rich cultural heritage and is renowned as a 'land of festivals'. These festivals attract massive community involvement paving way to new materials such as 'Plaster of Paris' being used for 'modernizing' the representation of idols with very little thought given to the issues of toxicity and environmental impacts. Another dimension to the whole issue is the plight of the artisans and the workers involved in the trade. Owing to the unorganized nature of the industry there is minimal or no guidelines pertaining-to the worker safety and health risks of the people involved. This paper attempts to address the complexities of the inherent hazards as a consequence of these socio-environmental issues and trace the scientific rationale in addressing them in a practical and pragmatic way.

Image-based midsole insert design and the material effects on heel plantar pressure distribution during simulated walking loads

The primary objective of this paper is to study the use of medical image-based finite element (FE) modelling in subjectspecific midsole design and optimisation for heel pressure reduction using a midsole plug under the calcaneus area (UCA). Plugs with different relative dimensions to the size of the calcaneus of the subject have been incorporated in the heel region of the midsole. The FE foot model was validated by comparing the numerically predicted plantar pressure with biomechanical tests conducted on the same subject. For each UCA midsole plug design, the effect of material properties and plug thicknesses on the plantar pressure distribution and peak pressure level during the heel strike phase of normal walking was systematically studied. The results showed that the UCA midsole insert could effectively modify the pressure distribution, and its effect is directly associated with the ratio of the plug dimension to the size of the calcaneus bone of the subject. A medium hardness plug with a size of 95% of the calcaneus has achieved the best performance for relieving the peak pressure in comparison with the pressure level for a solid midsole without a plug, whereas a smaller plug with a size of 65% of the calcaneus insert with a very soft material showed minimum beneficial effect for the pressure relief.

Buoyant Jet Discharges into Finite Ambient Waters

The paper presents the results of an experimental study regarding the effect of the lateral dimension of the receiving water on the spreading, mixing, and temperature decay of a horizontal buoyant surface jet. The widths of the ambient water in the experiments have been 240, 120, 90 and 60 times the diameter of the jet nozzle. Based on the experimental data, correlations are carried out and empirical equations for prediction of jet width, thickness in vertical direction and longitudinal temperature decay are obtained. The available data of earlier investigators are included to obtain generalized equations for the spreading and temperature decay. Similarity of temperature profiles in the lateral and vertical directions is observed. The longitudinal temperature decay is found to vary inversely with distance in the flow direction and ¼th power of the densimetric Froude number.

The Great Gatsby and Ned Kelly: Telling national iconic stories through a transnational lens

This chapter will examine how transnational film making allows national and iconic stories to shift outside their imposed national boundaries, freeing them from “nation building” constraints and predetermined ideological motivations. Each interpretation creates one more dimension to the story’s complexity and hybridity assuring its continuance and relevance into the future. Each new film version, and in the case of iconic stories, each new transnational film version, breathes new energy and life into the stories and also stops monolithic ownership of them. What is also of interest in this chapter is the judgement cast upon each of the retelling and adaptations of these iconic stories. Every adaptation is weighed up and judged against a mythic ideal, and as such, each always falls short of imagined expectations. But in a paradoxical fashion, it is this failure to capture that provides the impetus for the story’s future retellings.

Renormalization of the axial-vector current in QCD

Following the method of Ioffe and Smilga, the propagation of the baryon current in an external constant axial-vector field is considered. The close similarity of the operator-product expansion with and without an external field is shown to arise from the chiral invariance of gauge interactions in perturbation theory. Several sum rules corresponding to various invariants both for the nucleon and the hyperons are derived. The analysis of the sum rules is carried out by two independent methods, one called the ratio method and the other called the continuum method, paying special attention to the nondiagonal transitions induced by the external field between the ground state and excited states. Up to operators of dimension six, two new external-field-induced vacuum expectation values enter the calculations. Previous work determining these expectation values from PCAC (partial conservation of axial-vector current) are utilized. Our determination from the sum rules of the nucleon axial-vector renormalization constant GA, as well as the Cabibbo coupling constants in the SU3-symmetric limit (ms=0), is in reasonable accord with the experimental values. Uncertainties in the analysis are pointed out. The case of broken flavor SU3 symmetry is also considered. While in the ratio method, the results are stable for variation of the fiducial interval of the Borel mass parameter over which the left-hand side and the right-hand side of the sum rules are matched, in the continuum method the results are less stable. Another set of sum rules determines the value of the linear combination 7F-5D to be ≊0, or D/(F+D)≊(7/12). .AE

Disabled Revolutionary War Veterans and the Construction of Disability in the Early United States, c. 1776-1840

This thesis addresses the following broad research question: what did it mean to be a disabled Revolutionary War veteran in the early United States during the period from 1776 to roughly 1840? The study approaches the question from two angles: a state-centred one and an experiential one. In both cases, the theoretical framework employed comes from disability studies. Consequently, disability is regarded as a sociocultural phenomenon rather than a medical condition. The state-centred dimension of the study explores the meaning of disability and disabled veterans to the early American state through an examination of the major military pension laws of the period. An analysis of this legislation, particularly the invalid pension acts of 1793 and 1806, indicates that the early United States represents a key period in the development of the modern disability category. The experiential approach, in contrast, shifts the focus of attention away from the state towards the lived experiences of disabled veterans. It seeks to address the issue of whether or not the disabilities of disabled veterans had any significant material impact on their everyday lives. It does this through a comparison of the situation of 153 disabled veterans with that of an equivalent number of nondisabled veterans. The former group received invalid pensions while the latter did not. In comparing the material conditions of disabled and nondisabled veterans, a wide range of primary sources from military records to memoirs and letters are used. The most important sources in this regard are the pension application papers submitted by veterans in the early nineteenth century. These provide us with a unique insight into the everyday lives of veterans. Looking at the issue of experience through the window of the pension files reveals that there was not much difference in the broad contours of disabled and nondisabled veteran life. This finding has implications for the theorisation of disability that are highlighted and discussed in the thesis. The main themes covered in this study are: the wartime experiences of injured American soldiers, the military pension establishment of the early United States and the legal construction of disability, and the post-war working and family lives of disabled veterans. Keywords: disability, early America, veterans, military pensions, disabled people, Revolutionary War, United States, disability theory.

Dancing and Professional Dancers in Roman Egypt

The main aim of the study is to create a many-sided view of dancing in Roman Egypt (1st - early 4th centuries AD) and especially of the dancers who earned their living by dancing as hired performers. Even though dancers and other performers played a central part in many kinds of festivities throughout the ancient world, research on ancient professional dancers is rare and tends to rest on the ancient literature, which reflects the opinions of the elite. Documentary written sources (i.e., papyri, ostraka) the core of the present study are mentioned rather superficially, easily resulting in a stereotypical view of the dancers. This study will balance the picture of professional dancers in antiquity and of ancient dancing in a more general sense. The second aim characterizes this study as basic research: to provide a corpus of written sources from Greco-Roman Egypt on dancing and to discuss pictorial sources contemporary with the texts. The study also takes into account the theoretical discussion that centres on dancing as a nonverbal communicative mode. Dancers are seen as significant conveyors of social and cultural matters. This study shows that dancers were hired to perform especially in religious contexts, where the local associations on the village level also played an important part as the employers of the performers. These performers had a better standard of living in economic terms than the average hired worker, and dancers were better paid than other performers. In the Egyptian villages and towns, where the dancers performed and lived, the dancers do not seem to have been marginal because they were professionals or because of some ethnic or social background. However, their possible marginality may have occurred for reasons related to the practicalities of their profession (e.g., the itinerant life style). The oriental background of performers was a literary topos reflecting partly the situation in the centres of the empire, especially Rome, where many performers were of other than Roman origin. The connection of dancing, prostitution and slavery reflects the essential link between dance, body and gender: dancers are equated with such professions or socio-legal statuses where the body is the focus of attention, a commodity and a source of sensual pleasure; this dimension is clearly observable in ancient literature. According to the Egyptian documentary sources, there is no watertight evidence that professional dancers would have been engaged in prostitution and very little, if any, evidence that the disapproval of the professional dancers expressed by the ancient authors was shared by the Egyptians. From the 4th century onwards the dancers almost disappear from the documentary sources, reflecting the political and religious changes in the Mediterranean east.

The Saintly Madman : A Study of the Scholarly Reception History of Buile Shuibhne

This study examines the scholarly reception history of an early Irish text, Buile Shuibhne (The Frenzy of Suibhne), by focusing on the various theoretical and methodological presuppositions which have determined the scholars’ understanding of the text’s religious allegorical significance in the course of the 20th century. The reception-oriented inquiry takes the intersubjective aspect of literary interpretation as the basis for accentuating the importance of communally shared presumptions and reading strategies in the explication of interpretive variety. The materials of the study have been divided into four frameworks of interpretation: historical, pre-Christian, Christian and anthropological. This heuristic division does not denote mutually exclusive paradigms, but rather refers to perceived similarities within each group regarding the questions posed, and the evidence adduced, in textual analysis. The historical framework concentrates on the issues of the origins of the tale and the possible historicity of its main protagonist. The pre-Christian framework covers the theories of the shamanic, Indo-European and Celtic elements in the text, whereas the Christian framework includes readings emphasising the biblical, monastic and ascetic aspects of the tale. The anthropological framework in turn focuses on the parallels drawn between the narrative and the universal structure of the rites of passage. In addition to the examination of these four frameworks, the study also links the question of methodology with wider issues of authorship and textual integrity, and critically reconsiders the manner in which J.G. O'Keeffe's 1913 edition of the text has been reified in previous scholarship as a representation of a 12th century authorial original. The overall objective of the present case-study is to relate theoretical conceptions of literary theory, comparative religion and historiography to the study of early Irish narrative material by considering the communal and institutional dimension of meaning-making, and the implications of comparative methodology for historical research. In this aim, the prevailing methodological presuppositions informing the scholarly discourse on Buile Shuibhne are set against the wider context of Celtic Studies scholarship, in order to draw attention to the need to critically reflect upon the operations of knowledge production in future research.

Composite field approximations for ion traps with apertures on electrodes

This paper presents two approximate analytical expressions for nonlinear electric fields in the principal direction in axially symmetric (3D) and two dimensional (2D) ion trap mass analysers with apertures (holes in case of 3D traps and slits in case of 2D traps) on the electrodes. Considered together (3D and 2D), we present composite approximations for the principal unidirectional nonlinear electric fields in these ion traps. The composite electric field E has the form E = E-noaperture + E-aperture. where E-noaperture is the field within an imagined trap which is identical to the practical trap except that the apertures are missing and E-aperture is the field contribution due to apertures on the two trap electrodes. The field along the principal axis, of the trap can in this way be well approximated for any aperture that is not too large. To derive E-aperture. classical results of electrostatics have been extended to electrodes with finite thickness and different aperture shapes.E-noaperture is a modified truncated multipole expansion for the imagined trap with no aperture. The first several terms in the multipole expansion are in principle exact(though numerically determined using the BEM), while the last term is chosen to match the field at the electrode. This expansion, once Computed, works with any aperture in the practical trap. The composite field approximation for axially symmetric (3D) traps is checked for three geometries: the Paul trap, the cylindrical ion trap (CIT) and an arbitrary other trap. The approximation for 2D traps is verified using two geometries: the linear ion trap (LIT) and the rectilinear ion trap (RIT). In each case, for two aperture sizes (10% and 50% of the trap dimension), highly satisfactory fits are obtained. These composite approximations may be used in more detailed nonlinear ion dynamics Studies than have been hitherto attempted. (C) 2009 Elsevier B.V. All rights reserved.

Les formes d’adresse dans un corpus de films français et leur traduction en finnois

The use of forms of address in French films and their Finnish translations The use of forms of address constitutes an integral part of speakers’ communicative competence. In fact, they are not only used to assign to whom the speech is addressed, but also to construct the relationship between speakers. However, the choice of a suitable form is not necessarily evident in modern, pluralistic society. By the notion form of address, I refer to pronouns of address (tu vs. vous) and different nouns of address like names, titles (Monsieur, Madame, Mademoiselle), kinship terms, occupational terms, terms of endearment and insults. The purpose of the present thesis is, first, to study the semantic and pragmatic values of forms of address in dialogues of modern French films, and, second, their translation in Finnish subtitles. It is evident that film language is not spontaneous, but only a representation of authentic speech, and that subtitles are a written version of the original spoken language. Consequently, this thesis studies spoken fictive dialogues and their written translations. The methods applied in the study are the Interactional and Pragmatic Approach as well as Translatology. The role of forms of address in an interpersonal relationship is studied with dimensions of distance and power (Brown and Gilman 1960, Kerbrat-Orecchioni 1992), whereas the pragmatic dimension permits studying in particular the use of forms of address in speech acts (Kerbrat-Orecchioni 2001). The translation strategies are studied with the help of Venuti’s (1995) notions of foreignizing and domesticating strategies. The results of the thesis suggest that the pronoun use in the studied films is usually reciprocal. However, the relations of power have not disappeared, but are expressed in a more discrete manner with nouns of address (for instance vous + Docteur vs. vous + Anita). The use of the pronoun of address vous seems still to be common, but increased intimacy is expressed by accompanying familiar nouns of address like first names. The nominal forms of address accompany different speech acts, but not in a systematic manner. In a dialogue they appear usually in the first speech act, and more rarely in the response, but not in both. In addition, they have an important role in the mechanics of conversation. The translators here face multiple demands, and their translations seem mostly to be a compromise between foreignizing and domesticating strategies.

Elastic constants of sodium nitrate

Sodium nitrate is isostructural with calcite and crystallizes in the space group DQd. It is one of these substances whose physical properties have been widely investigated. However, a perusal of literature shows that the agreement between the elastic constants obtained by various investigators is not good.

Counter-figures : An Essay on Antimetaphoric Resistance: Paul Celan's Poetry and Poetics at the Limits of Figurality

Titled "An Essay on Antimetaphoric Resistance", the dissertation investigates what is here being called "Counter-figures": a term which has in this context a certain variety of applications. Any other-than-image or other-than-figure, anything that cannot be exhausted by figuration (and that is, more or less, anything at all, except perhaps the reproducible images and figures themselves) can be considered "counter-figurative" with regard to the formation of images and figures, ideas and schemas, "any graven image, or any likeness of any thing". Singularity and radical alterity, as well as temporality and its peculiar mode of uniqueness are key issues here, and an ethical dimension is implied by, or intertwined with, the aesthetic. In terms borrowed from Paul Celan's "Meridian" speech, poetry may "allow the most idiosyncratic quality of the Other, its time, to participate in the dialogue". This connection between singularity, alterity and temporality is one of the reasons why Celan so strongly objects to the application of the traditional concept of metaphor to poetry. As Celan says, "carrying over [übertragen]" by metaphor may imply an unwillingness to "bear with [mittragen]" and to "endure [ertragen]" the poem. The thesis is divided into two main parts. The first consists of five distinct prolegomena which all address the mentioned variety of applications of the term "counter-figures", and especially the rejection or critique of either metaphor (by Aristotle, for instance) or the concept of metaphor (defined by Aristotle, and sometimes deemed "anti-poetic" by both theorists and poets). Even if we restrict ourselves to the traditional rhetorico-poetical terms, we may see how, for instance, metonymy can be a counter-figure for metaphor, allegory for symbol, and irony for any single trope or for any piece of discourse at all. The limits of figurality may indeed be located at these points of intersection between different types of tropes or figures, and even between figures or tropes and the "non-figurative trope" or "pseudo-figure" called catachresis. The second part, following on from the open-ended prolegomena, concentrates on Paul Celan's poetry and poetics. According to Celan, true poetry is "essentially anti-metaphoric". I argue that inasmuch as we are willing to pay attention to the "will" of the poetic images themselves (the tropes and metaphors in a poem) to be "carried ad absurdum", as Celan invites us to do, we may find alternative ways of reading poetry and approaching its "secret of the encounter", precisely when the traditional rhetorical instruments, and especially the notion of metaphor, become inapplicable or suspicious — and even where they still seem to impose themselves.

Wipert von Blücher und Finnland : Alternativpolitik und Diplomatie im 'Dritten Reich'

This dissertation explores the role of the German minister to Helsinki, Wipert von Blücher (1883-1963), within the German-Finnish relations of the late 1930s and the Second World War. Blücher was a key figure – and certainly one of the constants – within German Finland policy and the complex international diplomacy surrounding Finland. Despite representing Hitler’s Germany, he was not a National Socialist in the narrower sense of the term, but a conservative civil servant in the Wilhelmine tradition of the German foreign service. Along with a significant number of career diplomats, Blücher attempted to restrict National Socialist influence on the exercise of German foreign policy, whilst successfully negotiating a modus vivendi with the new regime. The study of his political biography in the Third Reich hence provides a highly representative example of how the traditional élites of Germany were caught in an cycle of conformity and, albeit tacit, opposition. Above all, however, the biographical study of Blücher and his behaviour offers an hitherto unexplored approach to the history of the German-Finnish relations. His unusually long tenure in Helsinki covered the period leading up to the so-called Winter War, which left Blücher severely distraught by Berlin’s effectively pro-Soviet neutrality and brought him close to resigning his post. It further extended to the German-Finnish rapprochement of 1940/41 and the military cooperation of both countries from mid-1941 to 1944. Throughout, Blücher developed a diverse and ambitious set of policy schemes, largely rooted in the tradition of Wilhelmine foreign policy. In their moderation and commonsensical realism, his designs – indeed his entire conception of foreign policy – clashed with the foreign political and ideological premises of the National Socialist regime. In its theoretical grounding, the analysis of Blücher’s political schemes is built on the concept of alternative policy and indebted to A.J.P. Taylor’s definition of dissent in foreign policy. It furthermore rests upon the assumption, introduced by Wolfgang Michalka, that National Socialist foreign policy was dominated by a plurality of rival conceptions, players, and institutions competing for Hitler’s favour (‘Konzeptionen-Pluralismus’). Although primarily a study in the history of international relations, my research has substantially benefited from more recent developments within cultural history, particularly research on nobility and élites, and the renewed focus on autobiography and conceptions of the self. On an abstract level, the thesis touches upon some of the basic components of German politics, political culture, and foreign policy in the first half of the 20th century: national belonging and conflicting loyalties, self-perception and representation, élites and their management of power, the modern history of German conservatism, the nature and practice of diplomacy, and, finally, the intricate relationship between the ethics of the professional civil service and absolute moral principles. Against this backdrop, the examination of Blücher’s role both within Finnish politics and the foreign policy of the Third Reich highlights the biographical dimension of the German-Finnish relationships, while fathoming the determinants of individual human agency in the process.