bluuebunny/crossref_metadata_2025 huggingface dataset:
Introduction And Method
Authors: Stewart Columba
Published: November 2023

Because the gospel speaks both individually to the heart and universally to the world, Christians have struggled since the day of Pentecost to integrate the believer’s quest for deepened faith with the Church’s communal witness. This integration becomes threatened when individuals or groups are convinced that Christ’s imperative, ‘Be perfect as my Father in heaven is perfect’, is addressed especially to them. Throughout the history of Christianity this has been the conviction of many of those who have sought to follow Christ by a renunciation of material possessions and a life of celibacy. Any claim to perfection and exclusivism invites notice and often sparks controversy. In every case the key question is the same: to what extent does an individual’s response to the Spirit depend upon or oblige participation in the larger Church?
The Stylistic Potential of Phraseological Units in the Light of Genre Analysis
Authors: Gläser Rosemarie
Published: November 2023

Phraseology as a subdiscipline of the linguistic system is an expanding field of research and has attracted interest from many sides. Scholarly attention has been focused on the semantic and syntactic properties of phraseological units, on various approaches to their synchronic and diachronic description, on their pragmatic function in discourse, and, quite recently, on cultural peculiarities of idioms and phrases in the light of a cross-cultural and contrastive approach. Several of these aspects are reflected in the range of topics represented in the present volume. This chapter will focus on stylistic properties of phraseological units and their textual environment—in short, their stylistic potential. This approach entails a number of subordinate aspects: the modification of the phraseological unit in certain contexts and its relation to a particular genre, punning with idioms in the light of intertextuality, and so on. At the outset, however, some key terms need to be explained and their related concepts defined.
Prefabricated Patterns in Advanced EFL Writing: Collocations and Formulae
Authors: Granger Sylviane
Published: November 2023

Since the mid-I98os, the use of prefabricated language (‘prefabs’) has become a major focus of interest in EFL, arguably for three main reasons. First, the emergence of the concept of lexico-grammar, inspired by Halliday and Sinclair, has promoted the syntagmatic investigation of lexis. The traditional association between syntagmatics and grammar, on the one hand, and paradigmatics and lexis, on the other, which was challenged by Michael Halliday as early as 1966, is now clearly a thing of the past. Secondly, corpus linguistics has played an important role, giving linguists the computational means to uncover and analyse lexical patterns. Abundant information about word-combinations can now be obtained with ease using text-retrieval software. Finally, pragmatics has become a major field of study in its own right, in linguistics, and now in EFL. Pragmatic competence has come to be viewed as an essential part of learners’ competence. The formulaic nature of many pragmalinguistic rules has necessarily contributed to bringing the study of prefabs to the fore.
Introduction
Authors: Gary Miller D
Published: November 2023

The term nonfinite, though potentially misleading, will encompass traditional infinitives, gerundials (gerunds, gerundives, supines), and participles. No theoretical significance is attached to any of these labels. They refer to slightly different clusters of features potentially constituting distinct formatives which may or may not have similar properties crosslinguistically. The non-discreteness of the categories and problems with (non)finiteness in the traditional sense have prompted some scholars to use the neutral term converb(see Haspelmath and Ko nig 1995; Auwera 1998). In English, infinitives are morphologically distinct from gerundials and the -ingparticiple, for which the traditional terms are convenient labels for the status of the formative as modifier/adjunct or argument. There are also aspectual and other differences. The fluidity of the feature content of these formatives in language change is an argument against the traditional labels, except that the changes are expositorily simpler to track with the standard terminology. The term nonfiniteis retained because prototypical infinitives, gerundials, and participles are in fact nonfinite in the traditional sense, that is, they have no subject person agreement. On the other hand, there is no simple feature [ ± finite] (in the traditional sense) that works crosslinguistically (cf. Haspelmath 1995: 4ff.; Ledgeway 1998: 58). Moreover, since nonfinite structures can have tense independent of the matrix tense (depending on the nature of the matrix predicate), and this infinitival tense can be manifested morphologically, a simple feature [ ± tense] also fails to distinguish finite and nonfinite structures.
Small Clauses and ECM
Authors: Gary Miller D
Published: November 2023

The term small clause(SC) is applied in the literature to many different structures. Essentially, SC will be used here to refer to a verbless clause that is semantically equivalent to a corresponding full clause with BE. The SC is clausal because it has the conventional subject/predicate geometry and semantic predication relation, and the core clausal properties of extraction.Two different theories of the SC are considered. One is that BE takes SC complements and assigns no theta role to the subject. The second is that BE is an inherent part of the SC. On this account, the subject originates in SpecVP, as in other clause types, which supposedly accounts for the theta-dependence of the subject on the SC-internal predicate. Some problems with this account lead me to adopt a variant of the first theory, in which the SC optionally merges (in the sense of Chomsky 1995) with BE in some languages.
The ECM Innovation in English
Authors: Gary Miller D
Published: November 2023

In earlier English, as in Modern, ECM was better with the verbs beand havethan with other verbs. Recent accounts of the history of ECM in English are first discussed, followed by a brief description of the Indo-European ancestry, where only SCs received structural object case from a matrix verb. A favored complement to reflective verbs in the ancient Indo-European languages, including Germanic, was the SC. SCs abounded also in Old English and by Late Old English could marginally merge with wesanor b-eon‘to be’. That is, the older scholarly tradition was essentially correct in seeing SC expansions as an early source of ECM in English. The Middle English continuation of these structures is sketched, and the final section shows that in Old English, as in Modern French, reflective verbs for the most part selected [ +Accord] infinitival complements.
English Gerundials
Authors: Gary Miller D
Published: November 2023

For heuristic reasons the following terminology is adopted (cf. Chomsky 1970): gerundrefers to nominal structures of the type the destroying of Rome; the clausal counterpart (destroying Rome (was easy)) is a gerundive. These are distinct from non-eventive nouns in -ing. I will also use Chomsky’s term (derived) nominalfor nouns of the type destructionas distinct from the gerundial destroying. The term gerundialwill encompass nominal gerunds and clausal gerundives. It is used when the distinction is not important.
The Verb Complement Construction in Historical Perspective with Special Reference to Cantonese
Authors: Yue Anne O
Published: November 2023

The present analysis concentrates on an aspect of Cantonese grammar different from standard Mandarin but reminiscent of the earlier history of the Chinese language-namely, a type of verb complement structure that is called the causative/resultative or the shichengshi nltrl in Chinese. I trace its history from the earliest documents extant down to the present time. The discussion is divided into two parts: the first part deals with the dating of the emergence of the causative/resultative structure. I argue that this happened during the Han dynasty. The second part deals with the reflexes of this causative/resultative struc ture in both modern and nineteenth-century Cantonese, which show residues of archaic and ancient features accumulated in several strata, temporally and spatially.
Development and Erosion of a Mixing Layer in a Stratified Flow
Authors: Walker S A , Hamill G A , Johnston H T
Published: November 2023

The temporal behaviour of a salt water impoundment due to a buoyant shear flow is presented. Mixing has been found to result in the formation of a third distinct layer, the characteristics of which change with time. Various fresh water velocities and depths combined with various salt water densities, were used to obtain a range of bulk Richardson numbers. Two regimes of interfacial layer behaviour have been identified. In the first regime the density of the layer decreases to a constant value, while in the second regime the density and thickness of the layer fluctuates as the layer is removed by sequential stripping. Transport rates across both boundaries of the interfacial layer are assessed from the change in density profile. Average transport rates for each test were obtained and found to best related to the bulk Richardson number.
Investigation of the Effect of Atmospheric Stability on Characteristic Decay Times of Tracer Concentrations in the Wake of an Isolated Obstacle
Authors: Mavroidis I , Griffiths R F
Published: November 2023

The effect of atmospheric stability on characteristic decay times of a gas tracer in the near-wake of an isolated obstacle has been investigated. Field experiments have been conducted in flat terrain using a model 2 m cube. Two cube orientations were considered, with the mean wind direction either normal or at 45 degrees to the cube. The experiments involved the release of a tracer gas upwind of the obstacle, with fast-response detectors measuring concentrations at various points in the obstacle wake, at a frequency of 100 Hz. Tracer gas was released continuously for a limited period in order to fill the wake. Thereafter, the source was switched off using a solenoid valve, and the concentration in the wake was found to decay in an exponential manner
The Effects of Stable Stratification on the Flow Around a Horizontal Circular Cylinder in a Channel of Finite Depth
Authors: Ozono* Shigehira , Aota** Noboru , Ohya* Yuji
Published: November 2023

This paper describes a numerical study of the two dimensional flow of linearly stably-stratified Boussinesq fluid around a circular cylinder in a channel of finite depth. The Reynolds number used is high enough for the vortex shedding to occur behind the cylinder in neutral flows. Attention was focused upon the interaction between the vortex shedding and internal gravity waves. The columnar disturbances and lee waves appear when parameter K is close to integers in conformity with linear theory.
Azomethine, carbonyl and thiocarbonyl ylides
Authors: Bartnik Romuald
Published: November 2023

Simple addition of a carbene or carbenoid to a C-N double bond would be expected to result in the formation of an azomethine ylide. This is consistent with electrophilic attack of the carbene at the nitrogen atom lone pair. Formation of ylides in this manner was reviewed by Padwa and Hornbuckle in 1991.

The reaction of carbenes with simple imines (Schiff bases) to form azomethine ylides, which then undergo 1,3-dipolar cycloaddition with a second molecule of imine, was first reported in 1972. Bartnik and Mloston subsequently extended this method by using various dipolarophiles. Catalytic decomposition of phenyldiazomethane with N-benzylidenemethylamine results in the formation of a trans-1,3-dipole which then undergoes [3+2]-cycloaddition with an available 1r-bond. This is illustrated by the synthesis of 1-methyl-2,5-diphenyl-3,4-dicarboxylic acid dimethyl ester 1 from phenyldiazomethane, N-benzylidenemethylamine and dimethyl maleate (Scheme 3.1.1). This reaction takes place in a highly diastereoselective manner giving only the r-2,t-3,t-4,t-5 isomer (Beilstein’s r,c,t-system).
Nomenclature
Authors: David Serge
Published: November 2023

Until now the topic of carbohydrate nomenclature has been deferred because of its rather tedious nature. But we hope the reader’s interest was sufficiently stimulated during the first three chapters for the reader to feel brave enough to tackle the present one. Only the nomenclature rules applicable to the work described in this book will be given. Knowing the correct terms will allow the reader to undertake reading of the primary literature and enable him or her to extrapolate these terms in unexpected situations due to a minimal sense of the general picture. These rules are extremely practical. The corresponding names are those utilized (in minute detail) in the tables of chemical compounds of the Chemical Substances Index of Chemical Abstracts. They are also the names used in the experimental sections of papers and theses, as paragraph headings describing procedures.
Feeding ecology
Authors: Fjeldså Jon
Published: November 2023

Grebes obtain most of their food by diving. Since their feeding is usually hidden to our eyes, finding out how they feed and what they eat presents a problem. Pertinent questions relate to hunting methods, depths, where they find their food, etc. We need to ask if a bird is a searcher or a pursuit hunter, a generalist or specialist? In addition to knowing the depth of the water where it feeds, we may want to know if it hunts near the surface, throughout the water column, around submergent vegetation, or at the bottom.
Behaviour and communication
Authors: Fjeldså Jon
Published: November 2023

Grebes are easy to watch, especially in areas where people do not harass them. Thus, the breeding behaviour of Silvery and Hooded Grebes, which breed on uninhabited Andean plateaus in Patagonia, could be watched from a few metres distance, with minimal need for using a hide (Erize 1981). Also in less remote places, some grebe pairs become habituated to people, and are easy to observe on close range.
Finitely generated groups and countably based groups
Authors: Wilson John S
Published: November 2023

We are concerned here with profinite groups whose topology has a countable base for its open sets. They may be characterized in various ways-they are, for example, the groups which are inverse limits of inverse systems of finite groups indexed by N. These groups, the countably based profinite groups, play a role similar to the role played by countable groups in abstract group theory. Examples are the profinite groups which are topologically finitely generated, and every countably based profinite group arises as a closed subgroup of a finitely generated profinite group. Indeed, for many classes C of finite groups, there exists a finitely generated pro-C group in which all countably based pro-C groups can be embedded.
Profinite groups of finite rank
Authors: Wilson John S
Published: November 2023

In this chapter we are concerned with profinite groups G for which there is an integer r such that every subgroup of G can be generated by r elements. Such groups are said to have finite rank. (This use of the term ‘rank’ should not be confused with its use in expressions such as ‘free group of rank r’.) The groups of finite rank play an important role in the theory of profinite groups and in applications to abstract group theory. After establishing the notation and some basic results, we study profinite soluble groups of finite rank and we give a number of characterizations of them.
Groups of finite cohomological dimension
Authors: Wilson John S
Published: November 2023

A profinite group G is said to have cohomological dimension at most n if Hr (G, A) is zero for all r > n and all discrete Z-torsion G-modules A. The groups of co omological dimension at most 1 are just the projective groups. Among other important groups which have finite cohomological dimension are the torsion-free profinite groups of finite rank and certain Galois groups Gal (K/k), where K is either a separable closure of k or the subfield of a separable closure generated by all finite Galois extensions of p-power degree.
Normal numbers
Authors: Harman Glyn
Published: November 2023

Definitions. Elementary properties. Alternative definitions. Metric theory. Borel-Cantelli lemmas. Borel’s normal number theorem. An important asymptotic formula ( Lemma 1.5). Why should there bezero one laws? Law of the iterated logarithm.
The integer parts of sequences
Authors: Harman Glyn
Published: November 2023

In the previous two chapters, we have begun to consider the distribution of [anα], anwhere a is a given sequence. In Chapter 6 it was a deliberate decision to restrict both numerator and denominator in our approximations. In Chapter 7 this was merely a technical device to avoid many fractions coinciding.
A single substance as a supercritical fluid
Authors: Clifford Tony
Published: November 2023

When two molecules approach each other in a fluid, at a temperature where their relative speed is likely to be low, their mutually attractive forces will bring about a temporary association between them. If there is a sufficient density of molecules, there is the possibility of condensation to a liquid. On the other hand, if the temperature and the probable relative speeds are high, the attractive force will be too weak to have more than a slight effect on the molecular velocities, and condensation cannot occur however high the molecular density. It is therefore reasonable to expect, on the basis of molecular behaviour, that for every substance there is a temperature below which condensation to a liquid (and evaporation to a gas) is possible, but above which these processes cannot occur. That there is a critical temperature above which a single substance can only exist as a fluid and not as either a liquid or gas was shown experimentally 170 years ago by Baron Charles Cagniard de la Tour (1822).
Geological History of Reefs
Authors: Tomascik Tomas , Mah Anmarie Janice , Nontji Anugerah , Moosa Mohammad Kasim
Published: November 2023

Reefs, the greatest structures made by life on earth, seem ageless, immovable and indestructible. Yet they are none of these things. Rather, they are the end products of a combination of geological and climatic events which have acted to change the face of the earth, as well as the products of an evolutionary process which started well before the appearance on earth of any fauna that we now recognize.— VERON 1986
Combinatorial Chemistry
Authors: Terrett Nicholas K
Published: November 2023

The field of combinatorial chemistry was instigated primarily in response to the need for large libraries of novel compounds to feed the high throughput screening facilities developed by biologists. Traditional methods of organic synthesis involving the sequential synthesis of individual molecules are simply orders of magnitude too slow to satisfy the demand for compounds. Combinatorial chemistry is still in its infancy, developing from the synthesis of large mixtures of compounds to the high speed parallel synthesis of large libraries of well characterized single compounds, with at the same time a shift in emphasis from solution phase to solid phase methodologies.
Interactions of PTPases with other proteins, peptides and macromolecules
Authors: Goldstein Barry J
Published: November 2023

Some of the most exciting work in cell signalling has been in the characterization of protein-protein intermolecular reactions. PTPases have been shown to be involved in a variety of interactions that hold promise in identifying associated cellular proteins, potential substrate targets and eventually to help elucidate the physiological roles of the various PTPase homologues (Table 12). The initial sequence characterization of several transmembrane PTPases revealed structural similarity in the extracellular domains to the NCAM family of cell adhesion molecules and to repeats of fibronectin type III (Fn-III) motifs [756, 891] suggesting that these domains might be regulated by homotypic cell-cell interactions [605, 901]. This hypothesis has been demonstrated to be true at least in the case of two of the receptor-type PTPases, RPTP-µ and RPTP-K;, where recombinant domains on inert spheres as well as in the surface of overexpressing eukaryotic cells have been shown to engage in homotypic aggregation [412, 421, 447, 1089].
The synthesis and applications of phosphines
Authors: Clarke Matthew L , Williams Jonathan M J
Published: November 2023

Phosphines are the most widely used ligands for transition metals because they are extremely versatile: It is possible to vary the size and the donating properties of the phosphine and to introduce either chiral or heteroatom groups. The steric bulk of a phosphine ligand is most often defined by its cone angle. This is a measure of how much volume the organic groups at phosphorus occupy. It is possible to vary widely the size of this angle by choice of organic groups (Scheme 1), and altering steric effects in this way can radically alter both how the phosphine binds to the metal and the reactivity of the metal itself.
Language and genes in the Americas
Authors: Ward Ryk
Published: November 2023

This paper will focus on a specific geographic region, the New World, and its original inhabitants, the Amerindians-a sub-group of our species that, in many respects, is quite recent in evolutionary terms. Despite this, Amerindians have developed a degree of cultural diversity which rivals that found in other, more ancient, regions of the world. They have also developed an appreciable degree of biological diversity.
Floating Numbers
Authors: Schatzman Michelle , Taylor John
Published: November 2023

The beginning of a course on numerical analysis naturally includes some fairly abstract considerations of how real numbers are represented in a computer, known as floating-point representation, and incidentally on systems of counting. To convince the reader that there is material here which is both surprising and thought-provoking, the following exercises are more effective than a long discourse. It is strongly recommended that the reader sharpens his or her mind by trying them. The level of mathematics and programming required is entirely elementary, though this does not spoil the fun of doing them.
Splines
Authors: Schatzman Michelle , Taylor John
Published: November 2023

Until now, we have studied two different approaches to polynomial approximation: interpolation and mean square approximation.
Gauss’s world
Authors: Schatzman Michelle , Taylor John
Published: November 2023

The objective is to find an equivalent system to eqn (9.0.1)1 that is1 one which has the same set of solutions as (9.0.1)1 but is triangular. As we saw in Section 3.11 such systems with triangular matrices are very easy to solve.
Projective spaces and algebraic varieties
Authors: Hirschfeld J W P
Published: November 2023

For any m = −1,0,1,2,... ,n, a subspace of dimension m, or m-space, of PG(n, K) is a set of points all of whose representing vectors form, together with the zero, a subspace of dimension m+1 of V = V(n 4+1, q); it is denoted by Πm A subspace of dimension zero has already been called a point; a subspace of dimension −1 is the empty set. Subspaces of dimension one, two, three are respectively a line, a plane, a solid. A subspace of dimension n −1 is a prime or hyperplane-, a subspace of dimension n−2 is a secundum. A subspace of dimension n −r is also referred to as a subspace of codimension r. The set of m-spaces is denoted PG(m)(n,q).
Canonical forms for varieties and polarities
Authors: Hirschfeld J W P
Published: November 2023

In each case, the form and the variety are degenerate if there is a change of coordinate system which reduces the form to one in fewer variables; otherwise, the form and the variety are non-degenerate.
Economic Aspects of Radio Channel Assignment
Authors: Leese Robert
Published: November 2023

The previous chapters in this volume have mainly addressed the radio engineering aspects of channel assignment. In particular, they have considered, in various settings, the relationship between the amount of spectrum allocated to a radio service and the interference that is experienced by users of the service. The aim in this final chapter is to demonstrate how economic modelling may be integrated into such frameworks, with the result that spectrum assignments may be evaluated not just in terms of engineering measures such as interference levels or span, but also in terms of economic measures such as operator and consumer surpluses. One then has a means of estimating the economic value of radio spectrum in light of the combined engineering and economic environments in which it is deployed.
The future
Authors: Solymar Laszlo
Published: November 2023

The easiest prediction is a simple extrapolation from existing trends. If the number of telephone subscribers has been increasing for the last 120 years then it is fairly safe to predict that it will keep on increasing for a while. At what rate? At the rate it increased in the last year. Can one make even better predictions? Mathematicians will say that it is necessary to look at the higher derivatives i.e. one needs to know not only the rate of change but also how in the course of last year the rate of change has changed, etc. This is the way professional forecasters, say those employed by telephone companies, are bound to proceed. At the same time their marketing people investigate the lilcely demand for some new services they intend to introduce, and then they extrapolate from the various surveys conducted. This kind of prediction envisages relatively slow change.
Dynamic Instability of Rapid Solidification Fronts
Authors: Alexandrov D V , Mansurov V V , Galenko P K
Published: November 2023

Planar front dynamic instability in the presence of rapid solidification is considered. Directional solidification of multi-component liquids often produces material with a laminated periodic ordered structure, especially under reduced gravity conditions when convection is hindered or prohibited. This structure has layers of abnormally high or low solute concentrations, roughly parallel to the crystallization front. This was detected by Stewart et al. [1] and is extensively discussed in [2)-[6). Different layered segregation patterns are characteristic of semiconductor crystals [7]-[10] and of metallic and organic materials [11]-[13].
2D Unsteady Temperature in a Boiler Shell by the Multistage-Multigroup Least Squares Method
Authors: Guzik A , Styrylska T , Taler J
Published: November 2023

he paper deals with the mathematical modelling of unsteady temperature fields using data subject to errors in the elements of technological systems. When the mathematical model contains measured results, using the adjustment procedure, we can verify its accuracy and obtain a more realistic solution from a statistical view point. The adjustment procedure is very often based upon the least squares principle. When numerical methods are used to get the solution, the coefficient matrix of the set of constraint equations is sparse and simplifications in the adjustment procedure are afforded. The multistage-multigroup approach to modelling of unsteady temperature fields has been derived. The efficiency of the algorithm allows on-line estimation of them. The procedure was employed for determining the unsteady temperature field in a boiler shell.
Heat Transfer and Gas Dynamics in Stirling Engines
Authors: Makhkamov Kh.Kh. , Ingham D B
Published: November 2023

Stirling Engines provide several advantages over existing types of engines. In particular their performance meets the demands for the efficient use of energy and environmental security. To realise the potential performance of a Stirling Engine it is important to accurately model its working process. In this paper the standard k-c: turbulence model has been used for the two-dimensional simulation of the heat transfer and gas dynamical processes on the external surface of the cavity-type heat receiver of a Stirling Engine for a Solar Power Plant.
Use of the Inverse Method to Measure Temperatures in Non-Newtonian Fluids
Authors: Tierney M J , Banim R S , Brett P N
Published: November 2023

High steady-state accuracy and a fast response are important requirements for most sensors. In mixers, temperature is an important variable with respect to automated process control and the resulting quality of output. However, fast sensor response and steady-state accuracy is difficult to achieve due to the strength requirements of probes penetrating the medium, steep temperature gradients and distributive variations within the batch. This paper describes multi-thermocouple probe techniques that are devised to reduce errors and are based on the design of existing probes. Here we describe several computational extrapolation techniques to process the sensory data on-line. It is shown that it is possible to estimate the temperature of the medium rather than that of the probe itself. The performance described is based on laboratory and industrial mixer trials and shows that the method can lead to a significant improvement in accuracy for determining the true fluid temperature.
Presentation of the Equations
Authors: Chemin Jean-Yves , Gallagher Isabelle , Iftimie Dragos
Published: November 2023

We want to describe the evolution of a perfect incompressible fluid between two times to and t1. A particle of fluid located at point x at time to will be located at point ψ 1(x) at time t1. The incompressibility of the fluid is translated into the fact that the function ψ1, assumed to be a diffeomorphism, is measure-preserving; that is to say, its Jacobian is of determinant 1.
Littlewood-Paley Theory
Authors: Chemin Jean-Yves , Gallagher Isabelle , Iftimie Dragos
Published: November 2023

The basic idea consists in localizing the frequencies with the help of a decomposition of their space into annuli of size 2q, q a natural number. The interesting aspect of this technique is in the behaviour of tempered distributions towards differentiation, when their Fourier transform is compactly supported. If the support of û is included in a ball of centre 0 and radius λ then a derivative costs no more than λ; if û is supported in a ring of centre 0, short radius r1λ and long radius r2λ, denoted by C(0, r1λ, r2λ), then a derivative costs exactly λ. More precisely, we have the following lemma.
The Case of Smooth Initial Data
Authors: Chemin Jean-Yves , Gallagher Isabelle , Iftimie Dragos
Published: November 2023

Throughout this section, we denote by II a bilinear operator defined on the set of pairs of vector fields in IRd with values in the set of vector fields on ℝ d. This operator II is assumed to verify the following tame estimate: for every r > 1 in the case of the first inequality and for every r ∈ (−1, 1) in the case of the second inequality, there exists a constant D(r) such that

(4.1)∥Π(v,w)∥r≤D(r)(∥v∥r∥w∥Lip+∥w∥r∥v∥Lip)∥Π(v,w)∥r≤D(r)min{∥v∥r∥w∥Lip,∥w∥r∥v∥Lip}
Constrained Generating Procedures
Authors: Holland John H
Published: November 2023

The Greeks, as mentioned in Chapter 1, already knew the benefits of describing diverse objects (machines) in terms of elementary mechanisms (the lever, the screw, and so on). This chapter develops a similar setting for describing the diverse systems that exhibit emergence.
Levels of Description and Reduction
Authors: Holland John H
Published: November 2023

We’ve seen repeatedly that much complexity can be generated in systems defined by a few well-chosen rules. When we observe emergent phenomena, we ought therefore to try to discover the rules that generate the phenomena. In the particular format we have developed, we need to find a constrained generating procedure that generates the emergent phenomena. In so doing, we will reduce our complex observations of emergence to the interactions of simple mechanisms.
Classical Problems and Indirect MethodS
Authors: Buttazzo Giuseppe , Giaquinta Mariano , Hildebrandt Stefan
Published: November 2023

In this first chapter we describe the classical indirect approach to solving variational problems. The first step of this method consists in deriving necessary conditions for a function to be a minimizer. Among these, the principal condition is the vanishing of the first variation of the functional to be minimized at the prospective minimizer.
Detecting adaptive radiation
Authors: Schluter Dolph
Published: November 2023

What is adaptive radiation? A working definition and the means to apply it are crucial to successful study of the process. Modern usage derives from Simpson (1953, p. 223): ‘adaptive radiation strictly speaking refers to more or less simultaneous divergence of numerous lines from much the same adaptive type into different, also diverging adaptive zones’. This definition is not fully operational by itself, but it incorporates two core processes that most researchers continue to regard as essential: a rise in the rate of appearance of new species and a concurrent increase in ecological and phenotypic diversity.
The ecological basis of speciation
Authors: Schluter Dolph
Published: November 2023

The rise of ecological and phenotypic diversity in adaptive radiation is accompanied by one or more episodes of speciation. Determining how the new species form, and why the pace of species formation is higher during some periods than others, is thus crucial to understanding the process. For organisms engaging in sexual reproduction, effort centres on the mechanisms that elevate levels of reproductive isolation between populations.
Collagen XVI
Authors: Ricard-Blum Sylvie , Dublet * Bernard , der Rest Michel van
Published: November 2023

Collagen XVI was discovered by screening of cDNA libraries from human skin fibroblasts [1018] and human placenta [1047].
Multivariate models
Authors: Lindsey J K
Published: November 2023

The first basic problem in constructing a multivariate distribution is deciding how to define an appropriate stochastic dependence. As we have seen in Section 2.3, one reason why the multivariate normal distribution is relatively simple to understand and to use is that all of the stochastic dependence structure among responses is contained in the covariance’s or correlations. Such a simple solution is not available in other cases.
Longitudinal discrete data
Authors: Lindsey J K
Published: November 2023

Categorical and count data observed over time can be modelled in a number of ways. For example, for categorical data, the multinomial probabilities of events may vary over time (or space), perhaps depending on the event(s) that occurred immediately previously, on the total number of previous such events that have already occurred, or on other time-varying covariates.
Event histories
Authors: Lindsey J K
Published: November 2023

In simple cases, the durations of successive periods, or waiting times, between events occurring to a unit, called life or event histories, involve events accumulated without any fundamental change in the unit: a point process. There may not be any fundamental evolution over time, as in a renewal process, or earlier events may influence the later ones, as for example in a birth process. In more complex situations, each event may induce a change of state for the unit, such as with a semi-Markov process (Section 3.1.2).
Modelling missing data and dropouts
Authors: Lindsey J K
Published: November 2023

Modelling missing values and dropouts is still in its infancy. Few plausible procedures are available, in part because studies are not often yet being designed to collect relevant intonation about the missingness or dropout process instead of viewing it as a nuisance. Hence, I can only look briefly at a few possible models.
Visions for future research in wildlife epidemiology
Authors: Grenfell B T , Amos W , Arneberg P , Bjornstad O N , Greenman J V , Harwood J , Lanfranchi P , McLean A R , Norman R A , Read A F , Skorping A
Published: November 2023

Prediction is a notoriously difficult task in any field of biology. The editors of this volume decided wisely to avoid this task, instead appointing as seers the doughty individuals who write below. Their prognostications are diverse, but share two common characteristics. The first is a call for more integration, both conceptually (§9.4) and across disciplines (§9.2). In particular, there is a clear message that the field should seek cross-discipline collaboration between field, theoretical, and laboratory-based epidemiologists and specialists in other fields (mathematicians, human geneticists, immunologists, etc.). This is true for both fundamental research problems (e.g. the measurement of immunocompetence; §9.3) and for applied questions (§9.6). In particular, in the modelling section the authors stress the need for a ‘meeting of minds’ between empiricists and theoreticians (§9.2; see also §9.6.2). The former often needs a better appreciation of the power and-especially-the limitations of theoretical approaches. The latter frequently need to understand more completely the importance of empirical data and expertise, the difficulties of collecting data, and the key skill of balancing mathematical elegance and tract- ability with biological realism and relevance.
Band Theory and Electronic Properties of Solids
Authors: Singleton John
Published: November 2023

This book provides an introduction to band theory and the electronic properties of materials at a level suitable for final-year undergraduates or first-year graduate students. It sets out to provide the vocabulary and quantum-mechanical training necessary to understand the electronic, optical and structural properties of the materials met in science and technology and describes some of the experimental techniques which are used to study band structure today. In order to leave space for recent developments, the Drude model and the introduction of quantum statistics are treated synoptically. However, Bloch's theorem and two tractable limits, a very weak periodic potential and the tight-binding model, are developed rigorously and in three dimensions. Having introduced the ideas of bands, effective masses and holes, semiconductor and metals are treated in some detail, along with the newer ideas of artificial structures such as super-lattices and quantum wells, layered organic substances and oxides. Some recent `hot topics' in research are covered, e.g. the fractional Quantum Hall Effect and nano-devices, which can be understood using the techniques developed in the book. In illustrating examples of e.g. the de Haas-van Alphen effect, the book focuses on recent experimental data, showing that the field is a vibrant and exciting one. References to many recent review articles are provided, so that the student can conduct research into a chosen topic at a deeper level. Several appendices treating topics such as phonons and crystal structure make the book a self-contained introduction to the fundamentals of band theory and electronic properties in condensed matter physics today.
Generalized subtractive algorithms
Authors: Schweiger Fritz
Published: November 2023

These algorithms were considered in Schweiger 1992. Let Δn+l = {b = (bo, b1, … , bn): bo ≥ bi ≥ … ≥ bn ≥ O}.We fix a number p with 1 ≤ p ≤ n and define
Fully subtractive algorithms
Authors: Schweiger Fritz
Published: November 2023

Let Δn+l = {b = (bo, b1, … , bn): bo ≥ bi ≥ … ≥ bn ≥ O}. We fix a number p with 1 ≤ p ≤ n and define p with 1 :S p ::S n and define There is a permutation π such that π σb Δn+l. The “bottom map” T is defined by the commutative diagram
Skew products
Authors: Schweiger Fritz
Published: November 2023

Let En := {0 < x1 ≤ 1, 0 ≤ x2 ≤ 1,…, 0 ≤ xn < 1}. These skew products are defined by the map T : En → En References are Ito 1986 and Schweiger 1989. Lemma 23 The digits are subject to the following conditions:
Periodic expansions
Authors: Schweiger Fritz
Published: November 2023

The multidimensional continued fraction of x is called periodic if there are numbers m ≥ 0, p ≥ I such that Tm+p x = Tmx. We need some well known results from linear algebra. Let A be an (n+1) x (n +1)matrix with real coefficients. A real or complex number ρ is called an eigenvalue of A if there is an (n + 1)-tuple υ = (υ0, υ1, … , υn) ≠ 0 such that Aυ= ρ υ.
Volume as a measure of approximation
Authors: Schweiger Fritz
Published: November 2023

As we have seen it is difficult to obtain positive results on simultaneous approximation for multidimensional continued fractions. For the Jacobi algorithm W. Schmidt 1958 made the interesting observation that for n = 2 the area of the triangle formed by the point x and two consecutive convergents is a much better generalization than simultaneous approximation. In Schweiger 1975c Schmidt’s result was obtained for the Jacobi algorithm for any n ≥ 1.
Dimension of exceptional sets
Authors: Schweiger Fritz
Published: November 2023

A basic feature of many results in Diophantine approximation and about onedimensional continued fractions is the fact that a certain property is either true for almost all points x or false for almost all points x. Clearly, the fact that mod 1 is an ergodic transformation with respect to Lebesgue measure is related to many theorems of this kind in dimension n = 1. But even if a certain property is valid only for a set of measure O these exceptional sets may be of quite different “size”. There are many devices to make the notion of “size” more precise. One of the most common notions concerns Hausdorff measure and Hausdorff dimension. We will not present the theory but we refer to standard text-books: Rogers 1970, Edgar 1990, say.
A Kuzmin theorem
Authors: Schweiger Fritz
Published: November 2023

The oldest problem in metric number theory is due to Gauss. Let be the map related to continued fractions. Then he considered the quantity and stated the theorem In the notation of Chapter 3 this means
One-way graphical representation of data matrices
Authors: Krzanowski W J
Published: November 2023

Having completed a preliminary look at some underlying geometrical concepts, we are now in a position to discuss the various techniques that are available for graphical representation of multivariate data. In keeping with the problem-orientated approach, the discussion will be structured according to the form in which the multivariate data are presented. Since all multivariate data can be presented in the form of a matrix, the most convenient classification will consider the entities that define the rows and columns of this matrix. It should be remembered that virtually any matrix of numbers can be input into any particular multivariate routine, and the computer will nearly always produce an answer. Whether or not this answer is sensible, however, will depend on whether or not the right type of matrix was input to the routine (mindful of the old computing adage: garbage in, garbage out). Care must therefore be exercised in deciding what sort of matrix one is faced with in any given application, what the objectives of the analysis are, and hence which set of techniques is appropriate for the problem in hand.
Reduction of dimensionality: inferential aspects of descriptive methods
Authors: Krzanowski W J
Published: November 2023

We now return to some of the techniques already described in Part I, and consider ways in which their purely descriptive use can be underpinned by statistical theory. Broadly speaking, the majority of these techniques comprise two main operations: finding a suitable small-dimensional space in which the sample can be embedded, and then inspecting the representation of sample members in this space for any evidence of pattern. Both of these operations carry associated statistical questions, which were hardly even alluded to earlier. In the first place, what is the ‘correct’ number of dimensions in which the sample is located? Given an r-dimensional representation of a p-variate sample, is this only an approximation, or have we identified the ·true’ dimensionality? Secondly, having obtained a small-dimensional representation, what effect will sampling variation have on the positions of the various entities in this space? For example, how far apart must be two points (or vectors, or curves) before we can safely assume that the entities they represent are genuinely different? In order to answer any of these questions we cannot rely simply on our geometrical model, but must also assume a statistical model for our initial multivariate sample. Hence consideration of these matters belongs properly to this part of the book. However, at this point we will break slightly with our problem-oriented philosophy. Since we have already devoted much space to the introduction and description of the various techniques earlier, it seems more natural to switch (in this chapter only) to a technique-oriented discussion, in which all aspects associated with statistical inference are summarized for each technique in turn.
Incorporating group structure: descriptive methods
Authors: Krzanowski W J
Published: November 2023

A common feature of all the situations considered thus far is an absence of any external information about the sample members prior to analysis of the data at hand. In other words, there is no external structure that must be imposed on the data matrix, so this matrix can be treated at face value for the purposes of analysis. Thus the descriptive methods of Part I presuppose an essentially homogeneous sample of individuals, and the same situation is more formally assumed for the inferential procedures of Part III. The possibility of heterogeneity is raised by those techniques in Chapters 2, 3, and 4 that enable a search to be made for any evidence of grouping among the sample members, but once again the starting point for these techniques is equivalent to a null hypothesis of ‘no structure’. Indeed, it was emphasized in Chapter 3 that a cluster analysis is not appropriate when we do have some information about structure of the units. Methods of incorporating such information into the analysis will occupy Part IV of this book.
Inferential aspects: more than two groups
Authors: Krzanowski W J
Published: November 2023

We now generalize the situation postulated at the start of Chapter 12, and suppose that the data matrix X is partitioned into g (>2) sections, the ith of which comprises n; rows and constitutes a random sample from a p-variate population πi (i = 1, ... , g). Inferences are sought about these populations, using the sample data in X as basis. Most of the techniques that are currently available require the assumption of multivariate normality, and are therefore only strictly applicable to continuous (or at least quantitative) data. In view of this restriction, we shall concentrate throughout the chapter on the multivariate normal model; a summary of available techniques for non-normal data will be given at the end of the chapter.
Explaining observed associations: latent-variable models
Authors: Krzanowski W J
Published: November 2023

The models considered in the previous chapter are ones linking the observed variables of a multivariate system. Their objective is explanation and prediction: by creating a model that adequately mimics the overall behaviour of the system, a better understanding can be gained into the mechanism of the system, and improved prediction of future behaviour is a natural consequence of such enhanced understanding. In order to make the model as accurate as possible, as much information as possible should be built into it. Given the observed associations between the variables of the system, therefore, it is natural these associations should be used in the model. In essence, the models of the previous chapter start from the observed associations and build outwards. It might be argued, however, that if we have a true understanding of the system then we should be able to predict reasonably accurately all aspects of the system, including the associations themselves. Thus a more fundamental model is one that explains the observed associations between variables, and considerable interest has been shown in such models in many fields of application. The impetus for this interest stemmed from the work of Psychologists involved in mental test theory at the turn of the century, and the pioneering ideas of Galton and Spearman provided fertile ground for the myriad developments (and no little controversy!) that have taken place in the succeeding eighty or ninety years.