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1
Vieira, Renata. "Definite description processing in unrestricted text". Thesis, University of Edinburgh, 1998. http://hdl.handle.net/1842/511.
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Noun phrases with the definite article the, that we call DEFINITE DESCRIPTIONS, following (Russell, 1905), are one of the most common constructs in English, and have been extensively studied by linguists, philosophers, psychologists, and computational linguists. In this dissertation we present an implemented model of definite description processing that is based on extensive empirical studies of definite description use and whose performance can be quantitatively measured. In almost all approaches to discourse processing and discourse representation, definite descriptions have been regarded as anaphoric1; and the models of definite description processing proposed in the literature tend to emphasise the role of common-sense inference mechanisms. Recent work on discourse interpretation (Carletta, 1996; Carletta et al., 1997; Walker and Moore, 1997) has claimed that the judgements on which a theory is based should be shared by more than one subject. On the basis of previous linguistics and corpus linguistics work, we developed several annotation schemes and ran two experiments in which subjects were asked to annotate the uses of definite descriptions in newspaper articles. We compared their annotations and used them to develop our system and to evaluate its performance. Quantitative evaluation has become an issue in other language engineering tasks such as parsing, and has shown its usefulness also for theoretical developments. Recently, evaluation techniques have been introduced for semantic interpretation as well, as is the case for the Sixth Message Understanding Conference (MUC-6) (Sundheim, 1995). However, in this case, the emphasis was on the engineering aspects rather than on a careful study of the phenomena. Our goal has been to develop methods whose performance could be evaluated, but that were based on a careful study of linguistic evidence. The empirical studies we present are evidence that definite descriptions are not primarily anaphoric; they are often used to introduce a new entity in the discourse. Therefore, in the model of definite description processing that we propose, recognising discourse new descriptions plays a role as important as identifying the antecedent of those used anaphorically. Unlike most previous models, our system does not make use of specific hand coded knowledge or common-sense reasoning techniques; the only lexical source we use is WordNet (Miller et al., 1993). As a consequence, our system can process definite descriptions in any domain; a drawback is that our coverage is limited. Nevertheless, our studies serve to reveal the kind of knowledge that is needed for resolving definite descriptions, especially the bridging cases. The system resulting from this work can be useful in applications such as semi-automatic coreference annotation in unrestricted domains.
2
COURA, MURILO FURTADO. "DEFINITE DESCRIPTIONS: GENERALITY WITHOUT UNIQUENESS". PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2012. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=21850@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
A presente tese defende uma teoria deflacionista de descrições definidas singulares. De acordo com essa teoria, um proferimento de uma frase da forma o F é G expressará simplesmente a proposição geral que pelo menos um F é G. A tese discorre sobre as teorias de descrições definidas de Russell e de Donnellan, com o propósito de mostrar que teorias unitárias (e quantificacionais) de descrições definidas são preferíveis a teorias da ambiguidade. A tese examina os principais argumentos em favor da interpretação semântica do uso referencial e conclui que eles são insatisfatórios. Apoiando-se em considerações gricianas, a tese também defende que teorias deflacionistas de descrições definidas são preferíveis a teorias inflacionistas e que a implicação de unicidade associada a descrições definidas é, em geral, de natureza pragmática. Em particular, a tese defende que há uma versão da teoria deflacionista que é superior àquelas propostas por Szabó e por Ludlow e Segal. A tese conclui que descrições definidas são expressões de quantificação que, pace Russell, não codificam unicidade.
The present thesis puts forward a deflationist theory of singular definite descriptions. According to this theory, an utterance of the F is G only expresses the proposition that at least one F is G. The thesis examines Russells theory of definite descriptions and Donnellans distinction between referential and attributive uses of definite descriptions and argues that Donnellan’s distinction is not at odds with a Russellian (i. e., unitarian and quantificational) approach to definite descriptions. Based on methodological considerations, the thesis claims that it is not necessary to postulate a distintic semantic interpretation for the referential use of definite descriptions and that these are best seen as a kind of pragmatic phenomena. However similar considerations suggest that the implication of uniqueness associated with some uses definite descriptions is not – in general - semantic either. Definite descriptions are quantificational expressions but there are no independent reasons for holding that uniqueness is part of their semantic content. Therefore an utterance of the F is G can be used to communicate that that there is at most one F despite the fact that this is not part of the proposition the utterance expresses.
3
Niedzialomski, Robert. "Extension of positive definite functions". Diss., University of Iowa, 2013. https://ir.uiowa.edu/etd/2595.
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Let $\Omega\subset\mathbb{R}^n$ be an open and connected subset of $\mathbb{R}^n$. We say that a function $F\colon \Omega-\Omega\to\mathbb{C}$, where $\Omega-\Omega=\{x-y\colon x,y\in\Omega\}$, is positive definite if for any $x_1,\ldots,x_m\in\Omega$ and any $c_1,\ldots,c_m\in \mathbb{C}$ we have that $\sum_{j,k=1}^m F(x_j-x_k)c_j\overline{c_k}\geq 0$.
Let $F\colon\Omega-\Omega\to\mathbb{C}$ be a continuous positive definite function. We give necessary and sufficient conditions for $F$ to have an extension to a continuous and positive definite function defined on the entire Euclidean space $\mathbb{R}^n$. The conditions are formulated in terms of strong commutativity of some certain selfadjoint operators defined on a Hilbert space associated to our positive definite function.
4
Martínez, Miraval Mihály y Cubas Agustín Curo. "Noción de integral definida: una mirada desde el enfoque instrumental". Universidad Peruana de Ciencias Aplicadas (UPC), 2017. http://hdl.handle.net/10757/624349.
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31 Reunión Latinoamericana de Matemática Educativa (Relme), evento desarrollado en la Universidad de Medellín, Colombia, del 31 Julio al 04 de Agosto de 2017.Esta investigación presenta el análisis de cómo se generó la génesis instrumental de la noción de integral definida en estudiantes universitarios desde el Enfoque instrumental, mediada por el Geogebra. Al contrastar los resultados esperados y obtenidos por medio de la Ingeniería didáctica, se observó que los estudiantes generaron esquemas de utilización de la integral definida al emplearla en la resolución de problemas matemáticos, evidenciando la instrumentalización e instrumentación de dicha noción matemática.
This research shows the analysis of how the instrumental genesis of definite-integral notion was generated by university students from the GeoGebra-based Instrumental Approach. When contrasting the expected results to the ones obtained by using Didactic Engineering, we could observe that the students generated schemes to use the definite integral by using it in solving mathematical problems, showing the instruments used and the instrumentation of this mathematical notion.
5
Moldovan, Andrei. "The Literal Meaning of Definite Descriptions". Doctoral thesis, Universitat de Barcelona, 2015. http://hdl.handle.net/10803/294262.
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This thesis focuses on the semantics of definite descriptions (DDs). In chapter 1 I introduce a framework for doing compositional semantics for natural language that follows Heim and Kratzer (1998) and Fintel and Heim (2011). I also address a number of issues concerning the methodology of natural language semantics, as well as the theoretical desiderata that we aim to achieve. In chapter 2 I offer a reconstruction within this theoretical framework of three classical theories of DDs: the Russellian theory, the Fregean theory, and the Barwise and Cooper (1981) theory. Chapter 3 focuses on incomplete DDs. The incompleteness problem affects not only the Russellian theory, but also the Fregean and B&C theories. I argue that the syntactic variable approach to QDR proposed by Stanley and Szabó (2000a) offers a solution to the incompleteness problem that is equally applicable to the three theories of DDs introduced. Chapter 4 focuses on the referential/attributive distinction. Although intuitions of singularity are not part of our methodology, I point out (following Neale (2004)) that there are independent reasons why the Russellian theory predicts that a DD is semantically a rigid designator when it is used referentially. I argue that this proposal is applicable not only to the Russellian theory, as Neale does, but also to the Fregean and the B&C theories. In Chapter 5 and 6 I look at non-denoting DDs (i.e. DDs for which either uniqueness or existence fails to be satisfied). In chapter 5 I address the phenomenon called ‘presupposition’ in the literature, distinguishing between various kinds of data that are usually treated under this heading. I argue that with respect to a certain characterization of presuppositions, the Fregean theory and the B&C theory have more explanatory power than the Russellian theory. Chapter 6 deals with the truth-value intuitions triggered by utterances of sentences containing improper DDs. With respect to failures of uniqueness, I discuss Ramachandran’s (1993) argument and offer an improved version of it, which provides a compelling objection against the Russellian theory. With respect to failures of existence, I argue that the Fregean and the B&C theorist are in a better position to account for the patter of data than the Russellian. In chapter 7 I address data concerning the embedding of DDs in propositional attitude verbs. I discuss in detail the objection proposed by Heim (1991) against the Russellian theory. Again, this poses an important problem to the Russellian theory, while the Fregean and the B&C theories are not affected by the objection. The overall conclusion that this discussion leads to is that the Russellian theory is in general less prepared to account for the kinds of truth-conditional data we have considered than the alternative proposals discussed. The conclusions of chapters 6 and 7, and partially those of chapter 5, all indicate that the Russellian theory is the worst of the three options considered. The main positive contribution of this thesis is to point out that the B&C theory, although generally ignored in the literature, has the same theoretical virtues as the Fregean theory with respect to accounting for the range of data considered.Esta tesis se centra en la semántica de las descripciones definidas (DDs). En el capítulo 1 introduzco un marco teórico para la semántica composicional del lenguaje natural que sigue la propuesta de Heim y Kratzer (1998) y Fintel y Heim (2011). En el capítulo 2 ofrezco una reconstrucción dentro de este marco de tres teorías clásicas de las DDs: la teoría de Russell, la teoría de Frege, y la propuesta de Barwise y Cooper (1981). El capítulo 3 tiene como enfoque las DDs incompletas y el capítulo 4 se centra en la distinción entre los usos referenciales y los usos atributivos. Argumento que ninguno de estos fenómenos nos permite elegir entre las tres teorías de las DDs introducidas. En los capítulos 5 y 6 analizo las DDs que no denotan. En el capítulo 5 sostengo que, con respecto a una determinada caracterización de las presuposiciones, la teoría de Frege y la de B&C tienen más poder explicativo que la teoría russelliana. El capítulo 6 trata de las intuiciones acerca de los valores de verdad de las oraciones que contienen DDs que no denotan. Discuto la objeción de Ramachandran (1993) a la teoría russelliana y ofrezco una versión mejorada de esta objeción. En el capítulo 7 analizo los datos provenientes de la inserción de DDs en el complemento de los verbos de actitud proposicional. Discuto la objeción propuesta por Heim (1991) contra la teoría russelliana. Una vez más, se trata de un problema importante para esta teoría que no afecta a las teorías de Frege y de B&C. La conclusión general de esta discusión es que la teoría de Russell es la menos preparada de las tres propuestas consideradas para dar cuenta de los tipos de datos lingüísticos analizados. Esta conclusión se sostiene sobre los resultados de los capítulos 6 y 7, y parcialmente los del capítulo 5. La principal contribución positiva de este trabajo es la de señalar que la teoría de B&C, aunque generalmente ignorada en la literatura relevante, tiene las mismas virtudes teóricas que la teoría de Frege con respecto a los datos que se han considerado aquí.
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Prieto-Cox, Juan Pablo. "Representations of positive definite Hermitian forms /". The Ohio State University, 1990. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487683401441982.
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Bainbridge, R. I. "A definite clause grammatical inversion of extended Montague semantics". Thesis, University of York, 1987. http://etheses.whiterose.ac.uk/10943/.
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Roehrs, Dorian. "Demonstratives and definite articles as nominal auxiliaries /". Amsterdam [u.a.] : Benjamins, 2009. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=017109235&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.
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Sinop, Ali Kemal. "Graph Partitioning and Semi-definite Programming Hierarchies". Research Showcase @ CMU, 2012. http://repository.cmu.edu/dissertations/145.
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Graph partitioning is a fundamental optimization problem that has been intensively studied. Many graph partitioning formulations are important as building blocks for divide-and-conquer algorithms on graphs as well as to many applications such as VLSI layout, packet routing in distributed networks, clustering and image segmentation. Unfortunately such problems are notorious for the huge gap between known best known approximation algorithms and hardness of approximation results. In this thesis, we study approximation algorithms for graph partitioning problems using a strong hierarchy of relaxations based on semi-definite programming, called Lasserre Hierachy.
Our main contribution in this thesis is a propagation based rounding framework for solutions arising from such relaxations. We present a novel connection between the quality of solutions it outputs and column based matrix reconstruction problem. As part of our work, we derive optimal bounds on the number of columns necessary together with efficient randomized and deterministic algorithms to find such columns. Using this framework, we derive approximation schemes for many graph partitioning problems with running times dependent on how fast the graph spectrum grows.
Our final contribution is a fast SDP solver for this rounding framework: Even though SDP relaxation has nO(r) many variables, we achieve running times of the form 2O(r) poly(n) by only partially solving the relevant part of relaxation. In order to achieve this, we present a new ellipsoid algorithm that returns certificate of infeasibility.
10
Sims, Kerry M. "Children's knowledge of indefinite and definite reference". Thesis, Durham University, 1990. http://etheses.dur.ac.uk/6233/.
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After reviewing previous theoretical and empirical investigations, the decision is made that an understanding of both "Familiarity' and 'Specificity' must be necessary for a full appreciation of indefiniteness/definiteness. Moreover, it is argued that knowledge of 'Specificity’ requires an ability to co-ordinate and integrate a number of linguistic and non-linguistic factors appropriately and for this reason, it is suggested that young children’s knowledge of indefinite/definite reference is incomplete.16 experiments are reported, most of which were designed to investigate children's knowledge of 'Familiarity' and 'Specificity' for indefinite/definite reference. Other areas of investigation include children’s ability to use both linguistic and non-linguistic factors in their understanding of definite reference and the way in which older children and adults use these factors for anaphoric reference. The results showed that whilst children from 3 ½ years of age are sensitive to the perceptual information given to listeners and will use their general knowledge to define ‘Familiarity’; they do not appreciate the need to consider the relative status of a referent in their choice of expression. It seems that young children will only consider 'Specificity' when the relative status and/or the identifying features of a referent are salient to them. The failure of the young child to appreciate the necessity of 'Specificity' for indefinite/definite reference may be explained as due to a failure to consider more than one possible interpretation of reference. By contrast, from about 8 years of age, children appear to be integrating contextual information about the number of available referents with their knowledge of linguistic constraints on reference. A model of the processing of definite anaphoric reference in children is proposed based on the 'weak' interactionist view of the effects of informational context on choice of definite construction.
11
Alsulaimani, Hamdan. "STRICT REGULARITY OF POSITIVE DEFINITE TERNARY QUADRATIC FORMS". OpenSIUC, 2016. https://opensiuc.lib.siu.edu/dissertations/1294.
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An integral quadratic form is said to be strictly regular if it primitively represents all integers that are primitively represented by its genus. The goal of this dissertation is to extend the systematic investigation of the positive definite ternary primitive integral quadratic forms and lattices that are candidates for strict regularity. An integer that is primitively represented by a genus, but not by some specific form in that genus, is called a primitive exception for that form. So, the strictly regular forms are those forms for which there are no primitive exceptions. Our computations of primitive exceptions for each of the 119 positive definite regular ternary forms which lie in multiple-class genera, and of the companion forms in their genera, show that there are 45 inequivalent such forms that are candidates for strict regularity. We provide a proof of the strict regularity of one of these candidates, bringing the total number of forms for which such proofs are known to 15, and prove partial results on the integers primitively represented by the other form in its genus. The theory of primitive spinor exceptional integers is used to analyze the primitive exceptions for the forms in two other genera known to contain a regular ternary form. In these cases, results are obtained relating the primitive representation of certain integers c by a given form in one of these genera to the primitive representation of the integers 4c and 9c by the forms in the genus.
12
Schiemann, Alexander. "Ternäre positiv definite quadratische Formen mit gleichen Darstellungszahlen". Bonn : [s.n.], 1994. http://catalog.hathitrust.org/api/volumes/oclc/31760889.html.
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Shantharam, Shubha Carleton University Dissertation Information and Systems Science. "Solving sparse positive definite systems on pipeline processors". Ottawa, 1985.
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Bannai, Etsuko. "Positive definite unimodular lattices with trivial automorphism groups /". The Ohio State University, 1988. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487588249823282.
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Icaza, P?erez Mar?ia In?es. "Effectiveness in representations of positive definite quadratic forms /". The Ohio State University, 1992. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487780393265363.
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Kerimo, Johannes. "Supergravities with positive definite potentials and AdS pp-waves". Texas A&M University, 2005. http://hdl.handle.net/1969.1/3782.
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Ten-dimensional superstring theory (or the conjectured nonperturbative Mtheory
in eleven dimensions) is the most promising candidate for a consistent quantum
theory of gravity capable of unifying all known forces of nature. An important
question concerning these fundamental theories is how they compactify to lower dimensions
and how to obtain a real four dimensional world? In this dissertation we
present new avenues for M/string theory to reduce to lower dimensions as well as to
four dimensions. For example, we show that by performing a generalized Kaluza-Klein
IR reduction on the low-energy field theory of the heterotic string, the resulting lower
dimensional theory compactifies spontaneously on S3 to give rise to (Minkowski)6
spacetime. Furthermore, a generalized reduction of M-theory on K3 Ã IR compacti-
fies spontaneously on S2 to give rise to a (Minkowski)4 spacetime.
The generalized Kaluza-Klein reduction gauges the Cremmer-Julia type global
symmetry and the homogeneous rescaling symmetry of the supergravity equations of
motion by giving the higher dimensional fields an additional dependence on the circle
coordinate. We apply the generalized reduction scheme to half-maximal supergravities
which are obtained from the heterotic string (or the NS-NS sector of the type-II
string) compactified on a (10 − D)-dimensional torus truncated to the pure supergravity
multiplet. This gives rise to new gauged supergravities in diverse dimensions
with supersymmetric Minkowski à sphere vacua.Since two large extra dimensions have received much attention recently, we make
a detailed study of the gauged D = 6, N = (1, 1) supergravity. In particular, we show
that this theory allows for a consistent sphere reduction on S2 to give rise to D = 4,
N = 2 supergravity coupled to a vector multiplet which can further be truncated to
N = 1 supergravity with a chiral multiplet.
We also investigate pp-waves in AdS backgrounds, i.e. pp-waves as solutions
of gauged supergravities with AdS vacua. These solutions generically preserve 1
4
of the supersymmetry. We demonstrate supernumerary supersymmetries for both
purely gravitational pp-waves and pp-waves supported by fields strengths. These new
backgrounds provide interesting novel features of the supersymmetry enhancement for
the dual conformal field theory in the infinite-momentum frame.
17
Valdinosi, Michele. "Utilizzo di un orchestratore per reti definite via software". Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/15855/.
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Nell'ultimo decennio il mondo delle Reti di Telecomunicazione ha avuto un'evoluzione accelerata, dovuta ai progressi del settore elettronico. I dispositivi hanno un ingombro sempre minore ed allo stesso tempo hanno mantenuto o addirittura aumentato la propria potenza di calcolo mentre calavano i costi di produzione ed acquisto (basti pensare ad un semplicissimo computer fisso degli anni 90 comparato ad uno smartphone dell'ultimo periodo, il quale ha una dimensione enormemente più piccola ed una potenza di calcolo maggiore).
Il settore delle Reti di Telecomunicazioni si è quindi dovuto adattare al nuovo cambiamento ed ha subito una vera e propria rivoluzione dei propri paradigmi che ha dato luogo alla creazione di nuovi metodi per l'utilizzo delle reti. Esempi importantissimi di questi nuovi metodi sono il “Cloud Computing” ed il “Software-Defined Networking” (abbreviato normalmente in SDN).
L'idea di utilizzare il Cloud Computing e l'SDN ha introdotto dei vantaggi, soprattutto dopo l'introduzione del Network Function Virtualization (NFV) che è il processo di virtualizzazione delle funzionalità di rete svolte da apparati di telecomunicazione fisici.
Nell'elaborato andremo a dare una definizione più specifica del significato di Cloud Computing, SDN e NFV passando anche dal protocollo OpenFlow per poi introdurre e spiegare cos'è un Overarching Orchestrator per reti SDN.
La parte finale riguarderà l'orchestrazione di reti Multi-Dominio, spiegando prima a cosa servono gli orchestratori di Dominio e Globali, e mostrando successivamente il funzionamento di un orchestratore globale tramite la sperimentazione di uno di questi sviluppato dal Politecnico di Torino chiamato Frog4.
18
Arafat, Hassan Mohammed Ahmed. "Mathematical Developments on Isotropic Positive Definite Functions on Spheres". Doctoral thesis, Universitat Jaume I, 2017. http://hdl.handle.net/10803/404050.
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In this thesis, three open problems related to the isotropic positive definite functions on the sphere have been solved. Firstly, we provide necessary and sufficient conditions for the equivalence of two Gaussian measures with two different covariance models with associated d-Schoenberg sequences. Secondly, we find the d-Schoenberg coefficients associated with an isotropic positive definite function on the sphere in terms of the Fourier coefficients on the circle. Thirdly, we drive the infimum of the second derivative at zero for the class of the locally supported isotropic positive definite functions on the sphere. Finally, we propose a new family of Markov processes in maximal compact subgroups of a semisimple Lie group.
19
Xie, Tailiang. "Positive definite matrix-valued functions and matrix variogram modeling". Diss., The University of Arizona, 1994. http://hdl.handle.net/10150/186727.
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In many applications in the physical and earth sciences there are multiple variables of interest which are correlated. In these cases, the spatial random function becomes vector-valued, in which spatial correlation and component (inter-variable) correlation come out simultaneously. We denote by Z(x) = (z₁(x), …, z(m)(x)ᵀ the vector-valued random function. Similarly the covariance and variogram structure of Z(x) play a central role in any prediction scheme. But the covariance function and variogram of Z(x) are no longer scalar functions. They are matrix-valued functions when m > 1 and have a positive (negative) definiteness property in a generalized sense. Any prediction technique for vector-valued spatial functions relies heavily on this property. Therefore, characterizing and modeling the matrix-valued covariance or variogram structure of Z(x) is extremely important in spatial statistics and become more difficult than in scalar cases. For instance, (a) there is a lack of standard models for the covariance function and variogram (23); (b) there is no efficient graphic aid for fitting models since the covariance function and variogram are matrix-valued functions; (c) there are many parameters need to be estimated. Even the basic analytic properties of matrix-valued positive definite functions are not clear. In this dissertation, we generalize the concept of (scalar) positive definite functions to matrix-valued functions which are related to correlations and variograms of vector-valued random functions, to analytically study matrix-valued (conditionally) positive definite functions beyond basic definitions, to create matrix-valued variogram models, to provide techniques for systematic variogram modeling.
20
Ho, Man-Kiu y 何文翹. "Iterative methods for non-hermitian positive semi-definite systems". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2004. http://hub.hku.hk/bib/B30289403.
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Heyfron, Peter. "Positive functions defined on Hermitian positive semi-definite matrices". Thesis, Imperial College London, 1990. http://hdl.handle.net/10044/1/46339.
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Mampitiya, M. A. Upali. "Spectral asymptotics for left-definite vector Sturm-Liouville problems". Thesis, University of Ottawa (Canada), 1988. http://hdl.handle.net/10393/5425.
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Kikonko, Mervis. "Some new results concerning general weighted regular Sturm-Liouville problems". Doctoral thesis, Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-59613.
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In this PhD thesis we study some weighted regular Sturm-Liouville problems in which the weight function takes on both positive and negative signs in an appropriate interval [a,b]. With such problems there is the possible existence of non-real eigenvalues, unlike in the definite case (i.e. left or right definite) in which only real eigenvalues exist. This PhD thesis consists of five papers (papers A-E) and an introduction to this area, which puts these papers into a more general frame. In paper A we give some precise estimates on the Richardson number for the two turning point case, thereby complementing the work of Jabon and Atkinson from 1984 in an essential way. We also give a corrected version of their result since there seems to be a typographical error in their paper. In paper B we show that the interlacing property, which holds in the one turning point case, does not hold in the two turning point case. The paper consists of a detailed presentation of numerical results of the case in which the weight function is allowed to change its sign twice in the interval (-1, 2). We also present some theoretical results which support the numerical results. Moreover, a number of new open questions are raised. We also observe that the real and imaginary parts of a non-real eigenfunction either have the same number of zeros in the interval (-1,2) or the numbers of zeros differ by two. In paper C, we obtain bounds on real and imaginary parts of non-real eigenvalues of a non-definite Sturm-Liouville problem, with Dirichlet boundary conditions, thus complementing the results obtained in a paper byBehrndt et.al. from 2013 in an essential way. In paper D we obtain a lower bound on the eigenvalue of the smallest modulus associated with a Dirichlet problem in the general case of a regular Sturm-Liouville problem. In paper E we expand upon the basic oscillation theory for general boundary problems of the form -y''+q(x)y=λw(x)y, on I = [a,b], where q(x) and w(x) are real-valued continuous functions on [a,b] and y is required to satisfy a pair of homogeneous separated boundary conditions at the end-points. Already in 1918 Richardson proved that, in the case of the Dirichlet problem, if w(x) changes its sign exactly once and the boundary problem is non-definite, then the zeros of the real and imaginary parts of any non-real eigenfunction interlace. We show that, unfortunately, this result is false in the case of two turning points, thus removing any hope for a general separation theorem for the zeros of the non-real eigenfunctions. Furthermore, we show that when a non-real eigenfunction vanishes inside I, then the absolute value of the difference between the total number of zeros of its real and imaginary parts is exactly 2.
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Berschneider, Georg J. [Verfasser]. "Conditionally Positive Definite Kernels : An Abstract Approach / Georg J Berschneider". Aachen : Shaker, 2010. http://d-nb.info/1106838777/34.
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Crestani, Giulio. "Implementazione di intercettazione telematica in reti virtuali definite via software". Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/12839/.
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Negli ultimi anni, all’interno delle reti, vengono effettuate delle azioni di controllo che, ormai, sono all’ordine del giorno. Per esempio, nel caso in cui ci fosse il sospetto di attività illecite da parte di un individuo, le autorità attuano delle intercettazioni su un router che si attesta nella zona limitrofa rispetto a dove si trova questo individuo, piuttosto che sulla rete mobile. Le installazioni di questi dispositivi avvengono mediante l’intervento fisico che agisce negli switch o nei router i quali si interpongono tra i vari flussi di traffico della rete e che quindi, vengono ritenuti significativi.
Dietro a tali operazioni vi sono questioni controverse, come il fatto che queste debbano essere autorizzate da qualcuno ed attuate rispettando certi termini e criteri. Quindi, l’azione gestionale di una rete fatta giorno per giorno e l’azione gestionale fatta con questi scopi di controllo, devono essere due processi completamente diversi. Ciò rimane invariato anche nel presente ma, stando ad una prospettiva futura in cui sopraggiungerà il paradigma SDN, saranno necessari maggiori analisi e controllo. Una possibile risposta a tutto questo potrebbe essere l’utilizzo delle tecnologie abilitanti la virtualizzazione di rete, le quali permettono a più soggetti in parallelo di gestire la rete fisica sottostante.
Più in particolare, si vuole fare in modo che un altro individuo possa eseguire azioni sul traffico gestito da uno di questi soggetti, in modo che non arrivi ad accorgersi della presenza dell’individuo. In pratica all’interno della rete è presente una sorta di superuser che può intervenire applicando azioni che normalmente gli altri utilizzatori non riescono a compiere come quelle di monitoraggio o di sicurezza.
Concludendo, l’obiettivo centrale della tesi è fare in modo di ottenere un sistema che riesca a controllare il flusso di dati di un particolare individuo all’interno di una rete SDN senza che nessun utilizzatore di quest’ultima ne sia a conoscenza.
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Nitt, Birgit [Verfasser] y Michael [Akademischer Betreuer] Schecker. "Definite Pronomina und Kontext bei Demenz vom Alzheimer Typ (DAT)". Freiburg : Universität, 2012. http://d-nb.info/1119805260/34.
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Shannon, John Francis. "Variability and the interlanguage production of the English definite article /". The Ohio State University, 1995. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487928649988355.
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Margutti, Pinto Paulo Roberto. "Wittgenstein and semantic presuppositions of definite descriptions in subject-position". Thesis, University of Edinburgh, 1992. http://hdl.handle.net/1842/1800.
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The purpose of this work is to characterize the problem of semantic presuppositions generated by definite descriptions in subject-position in the light of a reassessment of the semantic framework of the Russell/Strawson controversy and analyze what would be the early and the later Wittgenstein's solution to such a problem. In the first part, the Russell/Strawson controversy is characterized. On the basis of Strawson's account, a general concept of semantic presupposition against which other theories may be tested is constructed. This allows the formulation of the problem above mentioned. Further analysis of the accounts involved reveals that Frege's concept of a 'semantic prerequisite' generated by definite descriptions in subject-position is an instance of the general concept. But Frege also held the view that simple proper names do not generate semantic prerequisites. The Fregean referential dualism suggests that the Russell/Strawson controversy, as far as only these authors' accounts are involved, is undecidable at the purely semantic level. This is the semantic framework against which Wittgenstein's philosophies are tested in the second part. The "Tractatus" adopts a modified version of the Russellian Theory of Descriptions. Even so, the Tractarian account seems to be ultimately equivalent to Russell's. Further analysis reveals that the doctrine of simple signs in isolation, but not its conjunction with the picture theory, is consistent with the general concept of semantic presupposition. The "Investigations " adopts the programmatic principle of searching for the use of the words. But the question about the 'referring use' of descriptions in a specific language-game is consistent with, and in the spirit of, the "Investigations". The framework of the question involves the appeal to the Kripkean notions of 'semantic referent' and 'speaker's referent'. The analysis of the referring use in the language-game of reporting an event reveals that the later Wittgenstein tends to reject the semantic concept of presupposition. Further analysis reveals that he would tend to reject Russell's Theory of Descriptions and most of the variants of the pragmatic concept. The analysis seems to confirm that the Russell/Strawson dispute is idle at the purely semantic level. Even so, the later Wittgenstein's account of language is such that it is possible to imagine some particular language-games in which relationships occur that bear some analogies with the one of semantic presupposition.
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Kimber, Timothy. "Learning definite and normal logic programs by induction on failure". Thesis, Imperial College London, 2012. http://hdl.handle.net/10044/1/9961.
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This thesis presents two novel inductive logic programming (ILP) approaches, based on the notion of a connected theory. A connected theory contains clauses that depend on one another, either directly or via clauses in the background knowledge. Generalisation of such a theory is proved to be a sound and complete method for learning definite ILP hypotheses. The Induction on Failure (IOF) proof procedure, based on the connected theory generalisation method, adds secondary examples into the hypothesis, and generates auxiliary clauses to explain them. These concepts, novel to IOF, address the issues of incompleteness present in previous definite ILP methods. The concept of the connected theory is also applied to the non-monotonic, normal program setting. Thus, the method of generalisation of a normal connected theory is presented. Fundamental to this is the assertion that a partial non-monotonic hypothesis must include both positive and negative information, which the general hypothesis should preserve. This has resulted in, as far as the author is aware, the most complete semantic characterisation available of non-monotonic ILP using a bridge formula. It is proved that generalisation of such a formula to a set of completed definitions is a sound method of generating normal program hypotheses. In the course of establishing a completeness result for this latter approach, the semantics of the supported consequences of a normal program are defined, and the support tree method is presented and shown to be a sound and complete proof procedure for supported consequences. Using these results, it is shown that, for function-free programs, any correct hypothesis for which the examples are supported consequences of the learned program can be derived via a normal connected theory.
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Bagwell, Jeffrey N. "Reference and Presupposition". ScholarWorks@UNO, 2014. http://scholarworks.uno.edu/honors_theses/66.
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The topic of this paper is the logical analysis and translation of definite descriptions (structures of the form ‘the F’), in particular Bertrand Russell’s Theory of Descriptions, as put forth in “On Denoting” (1905). I argue in favor of an opposing theory, a presuppositional analysis of definite descriptions that fits in the tradition of Frege and Strawson, building upon the recent work of Heim and Elbourne. I argue that a definite description has a referential function that is supported by presuppositions of existence and uniqueness located outside of the analyzed sentence. Using a series of example sentences, I show that a presuppositional analysis handles the logic of ordinary language in a manner superior to a Russellian analysis, produces more natural readings of embedded sentences containing definite descriptions, explains why definite descriptions function in a consistent way across different types of sentences, and provides a much better account of the logical commitments of using referential terms. After providing background on Russell’s theory and its criticisms, I review and analyze Elbourne’s examples of sentences embedding definite descriptions in non-doxastic propositional attitudes or the antecedents of conditionals. I then present and analyze my own examples involving embedding within disjunctions and within two kinds of non-statement: questions and commands. I compare the effects of embedding sentences using proper names—another kind of referential term. I then analyze some logical consequences of Russellian analysis, and answer a potential Russellian objection.
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Böttcher, A. y S. M. Grudsky. "Estimates for the condition numbers of large semi-definite Toeplitz matrices". Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801238.
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This paper is devoted to asymptotic estimates for the condition numbers
$\kappa(T_n(a))=||T_n(a)|| ||T_n^(-1)(a)||$
of large $n\cross n$ Toeplitz matrices $T_N(a)$ in the case where
$\alpha \element L^\infinity$ and $Re \alpha \ge 0$ . We describe several classes
of symbols $\alpha$ for which $\kappa(T_n(a))$ increases like $(log n)^\alpha, n^\alpha$ ,
or even $e^(\alpha n)$ . The consequences of the results for singular values, eigenvalues,
and the finite section method are discussed. We also consider Wiener-Hopf integral
operators and multidimensional Toeplitz operators.
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McCarvel, Miranda Kelly. "Allomorphic Variation of Definite Articles in Jersey: a Sonority Based Account". The University of Montana, 2010. http://etd.lib.umt.edu/theses/available/etd-03082010-102529/.
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Allomorphic variation is a common linguistic phenomenon in Jersey (Jersey Norman French). Definite articles in Jersey each have at least two allomorphs. The occurrence of each allomorph has been attributed to the composition of word initial syllable following the article (Liddicoat 1994). Instead of using a ruled-based approach, this thesis examines the variation found among Jersey definite articles and uses sonority-based principles to analyze the allomorphic variation. Using Jersey phonotactics, this thesis first puts forth a Jersey specific sonority hierarchy and then utilizes that hierarchy and principles of syllabification to syllabify phrases containing definite articles. Then using sonority based principles, such as the Sonority Sequencing Principle and Syllable Contact Law, this thesis analyzes the syllabified phrases. The analysis identifies the sonority based conditions that trigger the allomorphic variation found in the data. This thesis contributes to the field of linguistics in several ways. It supports the use of both the Universal Sonority Hierarchy and language specific sonority hierarchies. This thesis also supports the practice of using available data sources for analysis. The analysis of a described but analyzed phenomenon contributes valuable information to the general knowledge of Jersey and sonority. Finally, this thesis also serves as an important resource for the study of Norman dialects in Europe such as Guernsey, Sark and Norman, as Jersey is a member of this linguistic group. This thesis contributes to both the field of Jersey linguistics and to the field of theoretical linguistics, while accounting for the allomorphic variation of Jersey definite articles.
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Roppert, Josef y Gerhard Derflinger. "On Some Definite Integrals of a certain Class of Logarithmic Functions". Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 1992. http://epub.wu.ac.at/504/1/document.pdf.
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Tsai, Wenyu Julie. "Neural computation of the eigenvectors of a symmetric positive definite matrix". CSUSB ScholarWorks, 1996. https://scholarworks.lib.csusb.edu/etd-project/1242.
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Murray, Joshua M. "No Definite Destination: Transnational Liminality in Harlem Renaissance Lives and Writings". Kent State University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=kent1461257721.
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Almeida, Francisco Wescley Cunha de. "Integral definida: uma abordagem para o ensino mÃdio com o auxÃlio do software GeoGebra". Universidade Federal do CearÃ, 2014. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=12328.
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nÃo hÃEste trabalho tem como objetivo principal inserir, no Ensino MÃdio, a ideia intuitiva da Integral Definida, o cÃlculo de Ãreas abaixo do grÃfico de funÃÃes positivas, limitadas pelo eixo das abscissas e por retas verticais, ou atà mesmo entre funÃÃes positivas em um intervalo determinado pelo domÃnio das mesmas, por exemplo. Para facilitar o entendimento dessas ideias, aliado ao estudo de funÃÃes, pode-se fazer o uso de um recurso computacional como o Geogebra, software utilizado como ferramenta de apoio a aprendizagem nas atividades sugeridas nesse trabalho. As atividades aqui propostas destinam-se a alunos do ensino mÃdio. Destaca-se a importÃncia da introduÃÃo dessas ideias por estimular a construÃÃo de conhecimentos mais sÃlidos sobre o comportamento de funÃÃes. Acredita-se que, assim, a longo prazo, os alunos que ingressarem no Ensino Superior nas disciplinas de CÃlculo terÃo condiÃÃes melhores de compreender os conceitos necessÃrios e, assim, os Ãndices de reprovaÃÃo nessas disciplinas serÃo reduzidos. O trabalho a seguir apresenta uma proposta de atividades sobre o ensino desses tÃpicos com auxÃlio do software GeoGebra. Verificou-se que à possÃvel abrir os horizontes no Ãmbito do ensino e aprendizagem de MatemÃtica no Ensino MÃdio, com as ideias intuitivas de CÃlculo, fazendo o uso de ferramentas diversas, como a utilizaÃÃo de tecnologias apropriadas e que à possÃvel, inclusive, proporcionar aos estudantes novas tÃcnicas de ensino que favoreÃam a aprendizagem desses e demais conceitos matemÃticos.
This work aims to incorporate in high school, the intuitive idea of the Definite Integral, calculation of areas below the positive functions, bounded by the x-axis and vertical lines, or even between positive graph functions in a certain range the area of the same, for example. To facilitate the understanding of these ideas, combined with the study of functions, you can make use of a computational resource such as Geogebra, software used to support learning activities suggested in this work tool. The activities proposed here are intended for high school students. Highlights the importance of introducing these ideas to stimulate the construction of more accurate information on the behavior of functions. It is believed that thus the term, students who enter higher education in the disciplines of calculation will be better able to understand the necessary and thus the failure rates in these disciplines will be reduced concepts. The following work presents a proposal of activities for teaching these topics with the help of GeoGebra software. It was found that you can open the horizons within the teaching and learning of Mathematics in Secondary Education, with intuitive ideas of Calculus, making the use of various tools such as the use of appropriate technologies and that is even possible to provide students new teaching techniques that encourage learning these and other mathematical concepts.
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Schneider, Michael [Verfasser] y Oliver [Akademischer Betreuer] Wendt. "New Challenges in Time-Definite Vehicle Routing / Michael Schneider. Betreuer: Oliver Wendt". Kaiserslautern : Technische Universität Kaiserslautern, 2012. http://d-nb.info/1027515819/34.
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Emslie, Hazel Carr. "Young children's use of the definite and indefinite articles in referring expressions". Thesis, Durham University, 1986. http://etheses.dur.ac.uk/6833/.
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It is argued that the theoretical framework used in earlier studies of children's use of the articles is inadequate, failing in some important ways to capture even normal adult usage. A new theory of article usage is proposed which is based on the concept of mental models. Previous psychological investigations are evaluated in the light of this theory and the major issues raised are investigated experimentally. Nine experiments involving approximately 310 three to seven-year old children and 65 parents are reported. The experiments were designed to investigate the effects of two main factors on children’s use of the articles, namely, the knowledge of the listener and the composition of the referential array. Different kinds of tasks were employed which required responses varying from article plus noun to single sentences and extended narratives. The results of the experiments showed that although young children can, and do, take into account the status of an object within a referential array, the over-riding factor in their choice of referring expression is their perception of the knowledge of the listener. When they judge that the listener's model does not contain the same number and kind of objects as their own (the listener is ignorant), children will use an indefinite description to introduce a referent regardless of the status of that referent in the array. However, when the listener is knowledgeable indefinite descriptions are reserved for one of several identical or similar objects and definite descriptions are used for objects which are known to be unique in the listener's model. Other factors which influence children’s use of the articles include the difficulty of the task, the child’s perception of the purpose of the task, and the range of descriptions in the child's linguistic repertoire.
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Pittsley, Jeremy. "To purify a people a definite design in the death of Christ /". Theological Research Exchange Network (TREN), 2008. http://www.tren.com/search.cfm?p086-0047.
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Jones, Mark Jonathon. "The phonetics and phonology of definite article reduction in northern English dialects". Thesis, University of Cambridge, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.615045.
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Kikonko, Mervis. "Qualitative and Spectral theory of some regular non-definite Sturm-Liouville problems". Licentiate thesis, Luleå tekniska universitet, Matematiska vetenskaper, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-18326.
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In this Licentiate thesis, we study some regular non-definite Sturm-Liouville problems. In this case, the weight function takes on both positive and negative signs on a given interval [a, b]. One feature of the non-definite Sturm-Liouville problem is the possible existence of non-real eigenvalues, unlike in the definite case (i.e. left or right definite) in which only real eigenvalues exist.This thesis consists of three papers (papers A-C) and an introduction to this area, which puts these papers into a more general frame.In paper A we give some precise estimates on the Richardson number for the two turning point case, thereby complementing the work of Jabon and Atkinson in an essential way. We also give a corrected version of their result since there seems to be a typographical error in their paper.In paper B we show that the interlacing property which holds in the one turning point case does not hold in the two turning point case. The paper consists of a detailed presentation of numerical results of the case in which the weight function is allowed to change its sign twice in the interval (−1, 2). We also present some theoretical results which support the numerical results.In paper C we extend results found in the paper by Jussi Behrndt et.al, in an essential way, to a case in which the weight function vanishes identically in a subinterval of [a, b]. In particular, we present some surprising numerical results on a specific problem in which the weight function is allowed to vanish identically on a subinterval of [−1, 2]. We also give some theoretical results which support these numerical examples.Godkänd; 2014; 20141110 (merkok); Nedanstående person kommer att hålla licentiatseminarium för avläggande av teknologie licentiatexamen. Namn: Mervis Kikonko Ämne: Matematik/Mathematics Uppsats: Qualitative and Spectral Theory of Some Regular Non-Definite Sturm-Liouville Problems Examinator: Professor Lars-Erik Persson, Institutionen för teknikvetenskap och matematik, Luleå tekniska universitet Diskutant: Professor Sten Kaijser, Matematiska Institutionen, Uppsala Universitet Tid: Fredag den 11 december 2014 kl 10,00 Plats: E243, Luleå tekniska universitet
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Bajracharya, Neeraj. "Level Curves of the Angle Function of a Positive Definite Symmetric Matrix". Thesis, University of North Texas, 2009. https://digital.library.unt.edu/ark:/67531/metadc28376/.
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Given a real N by N matrix A, write p(A) for the maximum angle by which A rotates any unit vector. Suppose that A and B are positive definite symmetric (PDS) N by N matrices. Then their Jordan product {A, B} := AB + BA is also symmetric, but not necessarily positive definite. If p(A) + p(B) is obtuse, then there exists a special orthogonal matrix S such that {A, SBS^(-1)} is indefinite. Of course, if A and B commute, then {A, B} is positive definite. Our work grows from the following question: if A and B are commuting positive definite symmetric matrices such that p(A) + p(B) is obtuse, what is the minimal p(S) such that {A, SBS^(-1)} indefinite? In this dissertation we will describe the level curves of the angle function mapping a unit vector x to the angle between x and Ax for a 3 by 3 PDS matrix A, and discuss their interaction with those of a second such matrix.
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Cavers, Ian Alfred. "Tiebreaking the minimum degree algorithm for ordering sparse symmetric positive definite matrices". Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/27855.
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The minimum degree algorithm is known as an effective scheme for identifying a fill reduced ordering for symmetric, positive definite, sparse linear systems, to be solved using a Cholesky factorization. Although the original algorithm has been enhanced to improve the efficiency of its implementation, ties between minimum degree elimination candidates are still arbitrarily broken. For many systems, the fill levels of orderings produced by the minimum degree algorithm are very sensitive to the precise manner in which these ties are resolved. This thesis introduces several tiebreaking enhancements of the minimum degree algorithm. Emphasis is placed upon a tiebreaking strategy based upon the deficiency of minium degree elimination candidates, and which can consistently identify low fill orderings for a wide spectrum of test problems. All tiebreaking strategies are fully integrated into implementations of the minimum degree algorithm based upon a quotient graph model, including indistinguishable sets represented by uneliminated supernodes. The resulting programs are tested on a wide variety of sparse systems in order to investigate the performance of the algorithm enhanced by the tiebreaking strategies and the quality of the orderings they produce.Science, Faculty of
Computer Science, Department of
Graduate
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Magolu, Monga-Made. "Sparse approximate block factorizations for solving symmetric positive (semi)definite linear systems". Doctoral thesis, Universite Libre de Bruxelles, 1992. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/212924.
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Hughes, Thomas James. "Grammar, ambiguity, and descriptions : a study in the semantics of definite descriptions". Thesis, Durham University, 2015. http://etheses.dur.ac.uk/11114/.
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The semantics of definite descriptions has been a central topic in philosophy of language ever since Russell’s landmark paper ‘On Denoting’(1905). Russell argued that definite descriptions should not be seen as referential expressions, but instead as quantificational expressions. In other words, a sentential utterance containing a definite description should be understood as expressing a general/object-independent proposition. A problem arises with the view once we consider the fact that definite descriptions are used frequently and consistently to refer to particular individuals. Through this observation, Donnellan (1966) argued that definite descriptions would be better understood as having two distinct uses, one referential and one attributive/quantificational. We can call this the ambiguity problem in definite descriptions. The following thesis will argue that the ambiguity problem disappears once we take seriously the grammar that underpins sentential utterances containing definite descriptions, and that the semantics of the definite article is determined in part by the grammatical topology of determiner phrases and in part by what grammatical environments determiner phrases can be felicitously placed. The thesis, therefore, is that the semantics of definite descriptions is grounded in grammatical facts.
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Elbourne, Paul. "The Semantics of Ellipsis". Universität Potsdam, 2005. http://opus.kobv.de/ubp/volltexte/2006/872/.
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There are four phenomena that are particularly troublesome for theories
of ellipsis: the existence of sloppy readings when the relevant pronouns cannot possibly be bound; an ellipsis being resolved in such a way that an ellipsis site in the antecedent is not understood in the way it was there; an ellipsis site drawing material from two or more separate antecedents; and ellipsis with no linguistic antecedent.
These cases are accounted for by means of a new theory that involves copying syntactically incomplete antecedent material and an analysis of silent VPs and NPs that makes them into higher order definite descriptions that can be bound into.
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Neretin, Yurii A. y neretin@main mccme rssi ru. "Matrix Balls, Radial Analysis of Berezin Kernels, and Hypergeometric". ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi974.ps.
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Birk, Sebastian [Verfasser]. "Deflated Shifted Block Krylov Subspace Methods for Hermitian Positive Definite Matrices / Sebastian Birk". Wuppertal : Universitätsbibliothek Wuppertal, 2015. http://d-nb.info/1073127559/34.
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Meroni, Luisa. "Putting children in context experimental studies on children's interpretation of definite noun phrases /". College Park, Md. : University of Maryland, 2005. http://hdl.handle.net/1903/2333.
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Thesis (Ph. D.) -- University of Maryland, College Park, 2005.Thesis research directed by: Linguistics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Mak, Lawrence. "The use and the omission of the Greek definite article with p̲n̲e̲u̲m̲a̲ h̲a̲g̲i̲o̲n̲". Theological Research Exchange Network (TREN), 1986. http://www.tren.com.
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