bluuebunny/crossref_metadata_2025 huggingface dataset:
The Notion of a Shimura Variety
Authors: Murty V Kumar
Published: November 2023

The purpose of this note is to introduce the number theorist to Shimura varieties. These are a class of algebraic varieties associated to certain reductive algebraic groups, and studied extensively by G. Shimura over a period of many years. They embody deep arithmetic and geometric information. In recent years, Deligne has added some new insights and provided an intrinsic formulation. In this note, we shall introduce the terminology and give some examples. In particular, we barely scratch the surface of the theory, and we shall not discuss the deeper aspects such as canonical models, cohomology and L-functions. The reader interested in a more thorough discussion as well as references to the literature is advised to consult the article of Milne [Mi].
A Universal Format for Local/Global Theories
Authors: Feit Paul
Published: November 2023

The paper announces a proof of the existence of a category of global objects for any appropriate category of local structures. The proof is purely categorical, and does not require topological models. It applies equally well to examples whose present forms rely on topos theory.
Continued fractions of formal power series
Authors: Poorten A J van der
Published: November 2023

I will discuss continued fractions of formal power series, not for their own sake, but in terms of their use in obtaining explicit continued fraction expansions of classes of numbers. As we will see, the approach I outline accounts for essentially all the interesting examples of the past dozen years.
Class groups of exponent two in real quadratic fields
Authors: Louboutin S , Mollin R A , Williams H C
Published: November 2023

Moreover the solution in [10] provided applications to conjectures in the literature; viz., one of Chow la [l], one of Yokoi [15], one of Mollin [7], and three of Mollin-Williams [8,9]. Therefore this paper completes the task of determining all real quadratic fields of ERO-type having class group Cx of exponent eK ≤2, (with one possible exceptional value ruled out by the GRH). The next section provides notation and preliminary results needed to provide the proof of the ma.in result. A few remarks on our tables are given in Section 4.
The second limit problem in MPT
Authors: Grenander Ulf
Published: November 2023

This fundamental problem has generated an extensive literature motivated by problems in mathematical physics, especially the study of magnetism (see Note 10.1.1). It has been known for a long time that strange phenomena in P can occur for some values of the temperature.
Introduction
Authors: Reutenauer Christophe
Published: November 2023

The aim of this preliminary chapter is to show that the Lie algebra of Lie polynomials, which is introduced in Chapter 1 and which is the subject of this book, is indeed the free Lie algebra. Apart from some elementary universal constructions, two results are required: the Poincare-Birkhoff-Witt theorem (actually only its consequence, that a Lie algebra is embedded in its enveloping algebra), and the fact that the free Lie algebra is a free module. The first result will not be proved here, as it is included in many textbooks. The second one is proved in Section 0.3.
Scalar Spherical Harmonics
Authors: Freeden W , Gervens T , Schreiner M
Published: November 2023

The restriction to the unit sphere Ω of any homogeneous harmonic polynomial of degree nis called a spherical harmonic of order n.It turns out that any spherical harmonic is an eigenfunction of the Beltrami operator. On the sphere, spherical harmonics are the analogues of the exponential functions for Fourier analysis. They were introduced in the 1780s to study gravitational theory (cf. P.S. DE LAPLACE (1785), A.M. LEGENDRE (1785)). Early books on the theory of potentials and spherical harmonics are due to E. HEINE (1878) and F. NEUMANN (1887). Indeed, spherical harmonics are essential for the analysis of any phenomena with spherical symmetry, e.g. celestial mechanics, terrestrial magnetism, earthquakes, solar corona etc. The use of spherical harmonics in all geosciences for the purpose of representing fields is a well established technique. A great incentive came from the fact that global geomagnetic data became available in the first half of the last century (cf. C.F. GAUSS (1839)).
Green’s Functions With Respect To Iterated Beltrami Operators
Authors: Freeden W , Gervens T , Schreiner M
Published: November 2023

A fundamental question when approximating a function on the sphere by its truncated Fourier expansion (orthogonal expansion) in terms of spherical harmonics is the existence of a manageable error term. An adequate answer is the construction of integral formulae that will now be presented. It will be shown that the error term between a function and its truncated Fourier series expansion is explicitly available in integral form provided that sufficient smoothness is imposed on the function under consideration.
Spherical Radial Basis Functions
Authors: Freeden W , Gervens T , Schreiner M
Published: November 2023

In this chapter we deal with spherical radial basis functions, i.e. kernel functions depending only on the (spherical) distance between unit vectors. The importance of our considerations lies in the development of general Sobolev spaces ℋ and (invariant) pseudodifferential operators Λ in which it is possible that (i) the radial basis function is recognized as axisymmetric reproducing kernel function of ℋ and (ii) the kernel admits a Legendre expansion determined by the symbol {Λ^(n)} of a pseudodifferential operator Λ. Criteria are given for measuring the space-frequency localization of (radial basis) functions on the sphere. The trade off between space localization on the sphere and frequency localization in terms of spherical harmonics is described in form of an ‘uncertainty principle’.
Tensor Spherical Harmonics
Authors: Freeden W , Gervens T , Schreiner M
Published: November 2023

Many problems arising in geomathematics are of tensorial nature and spherical geometry. An important tool in dealing with such problems is the theory of tensor spherical harmonics. We present in this book a theory of tensor spherical harmonics generalizing in canonical way our approach to vector spherical harmonics. A striking point is that the tensor spherical harmonics are generated from the scalar ones by use of certain operators mapping scalar functions to tensor fields. As a matter of fact, these formulations (being as always independent of any choice of spherical coordinates) offer the possibility of extending all essential results known for scalar spherical harmonics to the tensorial case, including the definition of a tensorial Beltrami operator, the addition theorem, and tensorial versions of the Funk-Hecke formula. Furthermore, our appoach allows a straightforward transition of scalar approximation methods to the tensorial framework.
Provably Total Functions in Bounded Arithmetic Theories R, U and V
Authors: † Samuel R Buss*
Published: November 2023

Abstract

The outline of this paper is as follows: in section 2, we introduce the computational complexity classes using witness oracles and prove several fundamental closure properties for them. In section 3, we briefly review the fragments of Bounded Arithmetic needed and prove that various complexity classes of functions can be defined in these theories. In section 4, we review the witness predicate and prove the witnessing lemma and various corollaries for the first-order systems. Section 5 is a translation of the results of section 4 to the second-order systems. The reader who is interested primarily in first order-systems may safely omit all the sections that pertain to second-order objects and second order-systems (sections 2.2, 3.3 and 5). However, the reader interested in second-order systems must read the entire paper since we frequently omit proofs in the second-order case.
Using Herbrand-type theorems to separate strong fragments of arithmetic
Authors: Kaye Richard
Published: November 2023

Herbrand-type theorems to separate fragments of arithmetic. She, however, used truth definitions at the last step of her argument rather than the tricky combinatorics of Krajicek, Pudlak and Takeuti, or the direct recursion-theoretic argument I shall use here.
An Equivalence between Second Order Bounded Domain Bounded Arithmetic and First Order Bounded Arithmetic
Authors: Razborov Alexander A
Published: November 2023

But Bounded Arithmetic also gives an opportunity to directly interpret second order objects in a first order language. The antagonism “second order vs. first order” translates via this interpretation to “arbitrary integers vs. those “small” integers x for which f(x) exists” where f is a rapidly growing function whose existence is not provable in Bounded Arithmetic.
Rsuv Isomorphisms
Authors: Takeuti Gaisi
Published: November 2023

where by Con(S) we mean “the consistenc.r of S” and by BDCon(S) we mean the statement “there are no bounded proof to a contradiction”. (A proof P is bounded if no unbounded first order quantifiers occur in P.)
Feasible interpretability
Authors: Verbrugge* Rineke
Published: November 2023

Abstract

In PA, or even in 1.Δ.o  + EXP, we can define the concept of feasible interpretability. Informally stated, U feasibly interprets V iff: for some interpretation, U proves the interpretations of all axioms of V by proofs with Giidel numbers of length polynomial in the length of the Gödel numbers of those axioms.
Stochastic models for random sets of points
Authors: Kingman J F C
Published: November 2023

Figure 1.1 might represent the positions of visible stars in a patch of the sky, the positions (seen from above) of trees in an area of woodland, or those of certain archaeological sites. There is no clear pattern, the points are haphazardly distributed with no obvious regularity or trends in density. Similar situations can arise in three dimensions or in one, or in more complicated geometries. If we look at the whole sky, for example, the stars appear to be distributed over the surface of a sphere. Poisson processes are models of such phenomena, which use the theory of probability to describe this sort of highly random behaviour. Their characteristic feature is a property of statistical independence.
Poisson processes in general spaces
Authors: Kingman J F C
Published: November 2023

The state space S in which the points of a Poisson process sit is usually Euclidean space of some dimension d, or more generally (Chapter 7) a manifold which is locally equivalent to Rd. The theory does not, however, make use of the special properties of Euclidean space, but only needs a reasonable family of subsets to be used as test sets to count the random points. That is, we need sets for which the count function The natural way to do this is to suppose that S is a measurable space.
Deduction Systems Based on Resolution
Authors: Eisinger Norbert , Ohlbach Hans Jürgen
Published: November 2023

Statements about the real world or about Active or abstract worlds are often interrelated in that some of them follow from others. For example, given the statements: ‘Every cat eats fish’ ‘Garfield is a cat’ ‘Garfield eats fish’ one would agree that the third statement follows from the other two. Whenever we assume the first and the second statement to be true (in our considered world), we also have to accept the truth of the third statement.
Logical Features of Horn Clauses
Authors: Hodges Wilfrid
Published: November 2023

Horn clause logic is a part of first-order logic. It was first isolated by J. C. C. McKinsey (1943), who was working on decision problems. Between 1956 and 1970, Anatoliī Mal’tsev published a series of papers in which he showed that Horn clauses form the right setting for a large part of universal algebra—including the theory of presentations and initial models. Algebraic specification lies within this part of universal algebra.
Logical Basis for the Automation of Reasoning: Case Studies
Authors: Was Larry , Veroff Robert
Published: November 2023

With the availability of computers in the late 1950s, researchers began to entertain the possibility of automating reasoning. Immediately, two distinctly different approaches were considered as the possible basis for that automation. In one approach, the intention was to study and then emulate people; in the other, the plan was to rely on logic. In this chapter, we focus mainly on the latter, for logic has proved to provide an excellent basis for the automation of reasoning.
Handbook of Logic in Computer Science
Authors: Spurr Jane
Published: November 2023

The Handbook of Logic in Computer Science is a multi-volume work covering all major areas of application of logic to theoretical computer science. The Handbook comprises six volumes. Each volume contains five or six chapters giving an in-depth overview of one of the major topics in the field. It is the result of many years of co-operative effort by some of the most eminent frontline researchers in the area. It will no doubt be the standard reference work in logic and theoretical computer science for years to come - essential reading for all those interested in theoretical computer science and logic.
Designing a Theorem Prover
Authors: Paulson Lawrence C
Published: November 2023

Because many different forms of logic are applicable to computer science, a common question is — How do I write a theorem prover? This question can be answered with general advice. For instance, first do enough paper proofs to show that automation of your logic is both necessary and feasible. The question can also be answered with a survey of existing provers, as will be done in this chapter. But automatic theorem proving involves a combination of theoretical and coding skills that is best illustrated by a case study. So this chapter presents a toy theorem prover, called Folderol, highlighting the key design issues. Code fragments are discussed in the text; a full program listing appears at the end of the chapter.
Denotational Semantics
Authors: Tennent R D
Published: November 2023

Designers, implementers, and serious users of a programming language need a complete and accurate understanding of the semantics (the intended meaning) of every construct of that language. The semantic descriptions in reference manuals and language standards are almost always inadequate because they are based primarily on implementation techniques and intuition. A rigorous mathematical theory of the semantics of programming languages is needed to support correct description and implementation of their meanings, systematic development and verification of programs, analysis of existing programming languages, and design of new languages that are simpler and more regular.
Decidability in temporal logic
Authors: Gabbay Dov M , Hodkinson Ian , Reynolds Mark
Published: November 2023

This chapter is not intended as a survey of the huge field of decidability. There are many fine surveys, such as [Rabin, 1977] and [Gurevich, 1985], in the literature already. Rather, it is a discussion of the decidability of the temporal systems used in the rest of the book. In section 15.7 we will list these systems, and consider the decidability of each one. Most will turn out to be decidable, the main exceptions being the predicate systems of chapter 4 and the second-order systems of chapter 8. Some indications of the complexity of decision procedures will be given, but for a fuller treatment the reader is referred to the extensive literature on complexity, and to the second volume of this work.In the early part of this chapter we will amass some techniques for determining decidability.
Classical Logic
Authors: Chagrov Alexander , Zakharyaschev Michael
Published: November 2023

Classical propositional logic was created by Boole about 150 years ago (see Boole, 1947). It holds the central position among propositional logics not only due to its venerable age. In fact, it represents the simplest model of reasoning based upon the assumption that every proposition is either true or false. Many other logics are either contained in the classical one or built on its basis by enriching the language with new connectives.
Models for concurrency
Authors: Winskel Glynn , Nielsen Mogens
Published: November 2023

The purpose of this chapter is to provide a survey of the fundamental models for distributed computations used and studied within theoretical computer science. Such models have the nature of mathematical formalisms in which to describe and reason about the behaviour of distributed computational systems. Their purpose is to provide an understanding of systems and their behaviour in theory, and to contribute to methods of design and analysis in practice.
Strong Covering Lemma And Ch In V[R] [Sh g7]
Authors: Shelah Saharon
Published: November 2023

We prove a strengthening of the covering lemma, not using the fine structure theory (only some well known consequences, see Theorem 0.2). We prove it essentially in all cases in which the covering lemma holds. This, essentially, is Chapter XIII, sections 1 4 of “Proper Forcing” [Sh-b] (the other sections, 5, 6, are superseded by the other material in this book).
The Paraboloid Model and Heisenberg Geometry
Authors: Goldman William m.
Published: November 2023

In this chapter we describe how complex hyperbolic geometry degenerates into Heisenberg geometry on the absolute.
Underlying semantics for IDS worlds
Authors: Sandewall Erik
Published: November 2023

The definition of IDS worlds given in Chapter 1 was quite broad. More specific classes of worlds can be obtained in two ways: first by imposing various constraints according to the ontological characteristics, and then by specifying exactly the effects of actions using action laws. Conversely, from the point of view of logic, IDS’s provide a restriction on the classical set of models. Therefore, they can be used as an underlying semantics which defines the intended models or, equivalently, the intended conclusions from a given scenario description. In other words, there is a two-way relationship between the IDS ‘model’ and a logic of actions and change. Chapters 1 and 2 addressed this common topic from the IDS point of view; the preSCDt chapter will do it from the point of view of the logic.
Upper applicability bounds and assessment of soundness
Authors: Sandewall Erik
Published: November 2023

The assessments in earlier chapters have obtained lower bounds on the range of applicability. It is natural to also look for corresponding upper bounds for the same entailment criteria. Ideally, one would like to know that a certain chronicle family is both a lower bound and an upper bound, so that no additional improvement of the result is possible.
Future directions
Authors: Sandewall Erik
Published: November 2023

Chapter 3, subsection 3.1.5, proposed a long range strategy for the use of the systematic methodology. The idea was to proceed stepwise in the taxonomy of scenario descriptions which is defined by the ontological and epistemological characteristics. One should address successively larger and more difficult families in that taxonomy; at each step one defines the set of intended models for a given scenario description as the current variant of the function Σ, and uses it as the basis for assessment of entailment methods. The present volume has applied the proposed methodology to the chronicle family 𝒦-IA using the function 𝒦IA. Continuations of this work may address additional topics in the framework of SIA, or proceed to other families in the taxonomy.
Radial Basis Functions
Authors: Bishop Christopher M
Published: November 2023

The network models discussed in Chapters 3 and 4 are based on units which compute a non-linear function of the scalar product of the input vector and a weight vector. Here we consider the other major class of neural network model, in which the activation of a hidden unit is determined by the distance between the input vector and a prototype vector. An interesting and important property of these radial basis function networks is that they form a unifying link between a number of disparate concepts as we shall demonstrate in this chapter. In particular, we shall motivate the use of radial basis functions from the point of view of function approximation, regularization, noisy interpolation, density estimation, optimal classification theory, and potential functions.
Logic + Control Revisited: an Abstract Interpreter for GÖDEL Programs
Authors: Börger Egon , Riccobene Elvinia
Published: November 2023

We develop a simple interpreter for programs of the new logic programming language GODEL. The definition provides a clean interface between logical and control components for execution of GODEL programs. The construction is given in abstract terms which cover the general logic programming paradigm and allow for concurrency.
Schematic Consequence*
Authors: Aczel Peter
Published: November 2023

Nowadays we are well aware that there are many different logics. There are computer systems which are meant to be used to implement many logics. But there is no generally accepted account of what a logic is. Perhaps this is as it should be. We need imprecision in our vocabulary to mirror the flexible imprecision of our thinking. There are a number of related phrases that seem to have a similar imprecision e.g. formal system, language, axiom system, theory, deductive system, logical system, etc. … These are sometimes given technical meanings, often without adequate consideration of the informal notions.
On the Revision Of Conditional Belief Sets
Authors: Boutilier Craig , Goldszmidt Mois és
Published: November 2023

Both the dynamics of belief change and the process of reasoning by default can be captured with a conditional belief set, a set of ‘if-then’ rules held by a reasoning agent. In this paper we address the open problem of formalizing the revision of such a conditional belief set to incorporate new if-then rules, which may be interpreted as new default rules or new revision policies. We start by providing a purely semantic characterization, based on the semantics of conditional rules, which induces logical constraints on any such revision process. We then introduce logical (syntax-independent) and syntax-dependent techniques, and provide a precise characterization of the set of conditionals that hold after the revision. In addition to formalizing the dynamics of revising a default knowledge base, this work also provides some of the necessary formal tools for establishing the truth of nested conditionals and attacking the problem of learning new defaults.
Conditional Objects, Possibility Theory and Default Rules
Authors: Dubois Didier , Prade Henri
Published: November 2023

Conditioning is very often considered in connection with probability; both look strongly entwined in the usual notion of conditional probability. This connection has created a gap between probability theory and logic: while the former seems to ignore material implication when representing conditional knowledge, the latter has no genuine tool to account for conditioning. This chapter is an investigation of the relationship between conditional objects of the form q\p, obtained as a qualitative counterpart to conditional probabilities P(g|p), and non-monotonic reasoning. Viewed as an inference rule, the conditional object possesses properties of a well-behaved non-monotonic consequence relation. The basic tool is the 3-valued semantics of conditional objects that differs from the preferential semantics of Lehmann and colleagues and does not require probabilistic semantics. Semantic entailment of a conditional object q\p from a knowledge base made of conditional objects is equivalent to the inference of the conditional assertion p |˜ q in Lehmann’s system P.
Raman studies in heavily doped semiconductors
Authors: Castillo-Alvarado F L , Contreras-Puente, G S , Barrio R A
Published: November 2023

Heavily doped semiconductors have acquired enormous importance in recent years, mainly because of their use in technological applications, such as in tunnel diodes, strain gauges, or in magnetoresistance stable probes under nuclear radiation (Fistul 1969). These materials exhibit important physical properties due to their high impurity concentration leading to crystalline disorder. Therefore, these systems are considered to be semiconducting disorder alloys. These alloys have been studied experimentally by Raman spectroscopy. Contreras et al. (1985) have reported a softening of the Raman optical phonon in the Ge band of ultraheavily doped Ge with impurities like P and As. In previous papers (Castillo-Alvarado et al. 1988, 1989) we calculated the vibrational density of states of a Ge1 -xix alloy using a Bethe lattice in order to simulate the environment around the possible local surroundings of the various atoms in the alloy which are treated exactly. We have also presented a calculation of the Raman spectrum of Ge with P impurities (Castillo-Alvarado et al. 1989). In this work the observed softening of the Raman mode of ultraheavily doped Ge with P and As impurities is discussed in terms of the combined effects of the impurities and the disorder introduced by vacancies. In this chapter we continue to examine this problem and to apply the theory to other alloys.
The ageing of glass-forming liquids
Authors: Edwards S F
Published: November 2023

A key to the power of theoretical physics lies in the creation of models. One can set up a hierarchy:Complete description ->Simplified picture: the model ->Translation of the model into simple(r) mathematics -> Solution. This approach is not always followed or required; for example in quantum electrodynamics one can go, at least in a valid perturbation theory, directly to the solution. Also modern computing power allows one, in principle, to get the computer to circumvent the intermediate stage. However, the former exception is rare and the latter often difficult to interpret and to be acceptable in accuracy. So complicated problems require models, and modelling can often be simple. A good example was given in 1961 when Elliott and Chudley published a theory of the neutron scattering from liquids, in which they offered the model that molecules had two principal modes of motion-first, exploring a cage formed by their neighbours, and, second, hopping from one cage to another.
Magnetic impurity in an anisotropic ferromagnet
Authors: Djordjevii: B R , Djordjevic R
Published: November 2023

There has been much interest in the effect of impurities on the continuous energy spectrum of elementary excitations in solids. The perturbation produced by the impurity is characterized by its spatial extent and, for sufficiently small perturbations, the energy levels of the impurity-host system may be solved for exactly. The impurity and perturbed regions of the host form a complex with discrete energy levels that may lie within or outside the energy band of the host, virtual and localized states, respectively. The virtual levels decay into the band with a finite lifetime and may have a significant effect on the thermodynamic properties of the system. Localized levels have a long lifetime and, in general, are of less importance to the thermodynamic properties, but may have an important role in magneto-optical transitions. The literature on the effects of impurities in simple metals, crystals, and ferromagnetics is very extensive.
Spin glasses
Authors: Young Peter
Published: November 2023

The topic that I am going to discuss, spin glasses, combines two of Roger Elliott’s many interests: phase transitions and disordered systems. When I started research as Roger’s student, he suggested that I work on the theory of excitations in systems undergoing co-operative Jahn-Teller phase transitions. I immediately found phase transitions to be fascinating, and this fascination has stayed with me to this day. Although I did not work directly with Roger on disordered systems he had a big influence in convincing me that this too was a rich and challenging area. His lectures, given with the clarity for which he is noted, on topics such as percolation, random magnets, and localization played a big role in this. When interest in spin glasses exploded following the work of Edwards and Anderson (1975) I felt that this was an area in which I wanted to work in and, indeed, an area for which my background had prepared me well.
The Ising model in correlated random fields
Authors: Gonc;alves L L
Published: November 2023

The effect of an uncorrelated quenched random field on the critical behaviour of the ferromagnetic Ising model has been investigated by many authors since the work by Imry and Ma (1975). The controversies over the lower critical dimension below which long-range order cannot exist (Imry 1984; Imbrie 1986) and physical realizations of the system (Birgeneau et al. 1984; Cowley et al. 1986) have been the main reasons for the great interest in the model. Although there are some questions as far as the physical realizations of the model are concerned (Oliveira et al. 1988), the problem of the lower critical dimension has been settled by Bricmont and Kupiainen (1987), who have proved that d1c = 2 as predicted by Imry and Ma (1975).
Thermodynamic behaviour of two-dimensional vesicles*
Authors: Leib/er Stanislas , Singh, Rajiv R P , Fisher Michael E
Published: November 2023

Polymer physics is a field in which many results from the theory of random walks have been applied with marked success (see, for example, de Gennes 1979). Similarly, recent theoretical studies of random surfaces (reviewed by Frohlich 1985), largely motivated by high energy physics, may well find their most fruitful applications in describing the behaviour of flexible films or membranes (Meunier et al. 1987). Indeed, it is believed that fluid-like random-surface models may apply to amphiphilic films and bilayers (Helfrich 1973; Huse and Leibler 1988 and references therein), while solid-like models, such as the tethered-surface model (Kantor et al. 1986, 1987), should describe cross-linked membranes or polymer sheets.
Descartes’s Geometrie and revolutions in mathematics
Authors: Mancosu Paolo
Published: November 2023

In the aftermath of Kuhn’s book The structure of scientific revolutions (1962), there has been a lively debate on whether Kuhn’s picture of the growth of natural sciences can be applied to the growth of mathematics. Paradigm examples of such contributions are Crowe (1975), Mehrtens (1976), Dauben (1984), Dunmore (1989), and, of course, many of the chapters in this book. At the same time, Kuhn’s work spurred interest in the historical development and uses of the notion of revolution in science and mathematics, a topic which was pursued by Cohen (see e.g. Cohen 1985). Any position which takes seriously talk of revolutions in mathematics (either to assert or to deny their existence) must of course address the issue of whether Descartes’s Géométrie constitutes a revolution in mathematics.
Application of dynamic light scattering to polyelectrolytes in solution
Authors: Mandel Michel
Published: November 2023

Polyelectrolytes are macromolecules which, when dissolved in !l suitable polar solvent, spontaneously acquire a large number of electric charges or can be made to bear such charges by the addition of strong acids or bases. The behaviour and in particular the physical properties of solutions containing electrically charged chains can differ considerably from what is observed for the more conventional solutions of uncharged macromolecules. Specific aspects of polyelectrolyte solutions have recently been discussed. Even after as much as half a century of more or less intensive investigation, many aspects are still not well understood. It is thus important to study the behaviour of polyelectrolyte solutions by as many experimental techniques as possible, in particular those that have become available in more recent years. In fact it is only by confronting conclusions drawn from a variety of different methods of investigation that one can hope to gain a better quantitative understanding of polyelectrolytes.
Möbius’s modern legacy
Authors: Stewart Ian
Published: November 2023

M öbius is a household name—at least, it is in mathematical honse¬ holds—thanks to a topological toy. But August Mobius influenced mathematics on many levels. Specific ideas—his famous one-sided surface, his inversion formula, his number-theoretic function, his transformations of the complex plane, his geometrical nets—bear his name. But, in addition, and perhaps more importantly, Mobius was aware of the big ideas, the general principles, the major areas of research. What is M öbius’s modern legacy? It is a large part of today’s mathematical mainstream. The concepts that attracted his attention, and the methods that he helped to develop, play a central role in modern mathematics.
Climate And Habitat
Authors: Howell G , Steve N , Webb Sophie
Published: November 2023

Climate, both global and local, plays a major role in determining the distribution of vegetation types. The two main climatic factors in this respect are temperature and rainfall. Temperature in Mexico and northern Central America is determined largely by latitude and altitude, while precipitation depends on air currents, topography, ocean currents, and ocean temperature. However, while the climatic regimes of Middle America are easily described, their mechanics are far from understood.
Clubtail Dragonflies of Panama (Odonata: Anisoptera: Gomphidae)
Authors: Belle Jean , Arias Diomedes Quintero
Published: November 2023

Clubtail dragonflies (Gomphidae) are small to large (body length 25-85 mm) anisopterans, generally brightly patterned with black, green, and yellow stripes and spots. Most species have clear-hyaline wings; the occurrence of colours in the wings is restricted to some South American species (Belle 1984a). Adult gomphids are characterized by the following: Compound eyes widely set apart on top of the head (Fig. 6.1). Median lobe of labium without a median cleft on anterior margin (Fig. 6.2). Female lacks an ovipositor. Instead, the posterior margin of the sternum of abdominal segment 8 is prolonged to a bifid subgenital plate (vulvar lamina) (Fig. 6.3). Abdominal segments 8 and 9 (or 8-10) of male (and of the female in many species) markedly expanded, thus their common name of clubtails. Biologists may miss observing adult gomphids if they do not search at ‘the right time’ of the year. In Panama most adult gomphids fly during the early part of the rainy season (May to August), at which time they become locally common. At any other time of the year gomphid adults are difficult to find. We infer that this flight periodicity might be related predominantly to mating activities near bodies of water, after which adults take refuge in the forest. Adults generally prefer to perch in sunshine on objects near the ground or even on the ground, and do not ‘patrol’ (soar or hover in the open) as the more common libellulid dragonflies do. May (19 79) found that most of the gomphid species present on Barro Colorado Island (BCI), Panama, with the exception of Epigomphus Selys, were attracted to the lights of buildings during the evenings.
Behavioural ecology of the Giant Damselflies of Barro Colorado Island, Panama (Odonata: Zygoptera: Pseudostigmatidae)
Authors: Fincke Ola M
Published: November 2023

The Pseudostigmatidae is a small family of giant damselflies whose distribution is limited to New World lowland or montane forests (below 1200m) from Mexico to Bolivia (Table 7.1, see also Calvert 1908). The family is so named because the pterostigma (a thickened opaque spot along the costal margin of the wing) is either absent or is replaced by a pseudostigma, which is traversed by cross-veins and differs between fore-and hindwings (Davies and Tobin 1984). Their large size and graceful flight make these damselflies a notable attraction to both visitors (e.g. Calvert 1908, 1911, 1923) and natives (e.g. Geijskes 1975) of neotropical forests. The unusual biology of this family illustrates the potential of odonates to adapt to life in neotropical forests, where the standing water required by their aquatic larvae is often scarce (Note 1). Unlike their temperate counterparts, which are typically found in great numbers at breeding sites along streams or lakes, sexually mature pseudo stigmatids range widely and lay their eggs in water-filled plant containers such as treeholes and bromeliads randomly scattered throughout the forest. Adult pseudostigmatids feed on web-building spiders. Because one rarely encounters more than a dozen of them during a day’s search, studying these elusive insects presents a challenge to the field ecologist.
Stoneflies of Panama (Plecoptera)
Authors: Harper Pierre Paul
Published: November 2023

It is undoubtedly premature even to attempt to draw a preliminary list of the stoneflies of Panama. No paper has dealt directly with the local fauna, although scattered descriptions and records appear in the literature. Probably only the genus Anacroneuria Klapalek (Perlidae) occurs in the country, as is the case in most of Central America (Baumann 1982). The southernmost elements of the Nearctic fauna (Amphinemura Ris) reach just beyond Mexico City, and the northernmost Notogean species, Claudioperla tigrina Klapalek, does not extend beyond Ecuador, or perhaps Venezuela. Unfortunately the genus Anacroneuria is one of the least known in the order; a great number of specific names are available, but the descriptions are generally superficial and species recognition is on the whole impossible or at the most unreliable. Only recently have reliable characters been recognized for identification purposes (Zwick 19 71, 19 73) and synonymies established; the task has, however, just begun. The present paper is based on the examination of two small series of specimens: material collected mostly from light trap studies in recent years, now in the Museo de Invertebrados de la Universidad de Panama (MIUP), and sundry specimens, including some Jewett (1958) paratypes, in the United States National Museum of Natural History (NMNH) (Smithsonian Institution) in Washington DC.
Thrips of Panama: A biological catalogue and bibliography (Thysanoptera)
Authors: Mound Laurence A , Palmer Jenny M
Published: November 2023

The number of living insect species is at least equal to, and probably many times higher than, the number of species of all other living organisms taken together (Southwood 19 78; Erwin 1982). Indeed, the number of new species of insects described annually approaches the total number of known bird species (8500). A recent estimate of 30 million for the total number of species of terrestrial arthropods (Erwin 19 82), even if inaccurate by 50 per cent, is an indication of the diversity of the group and a measure of the logistic problems faced by biologists in attempting to record this diversity. The scientific manpower available to record and analyse the total diversity of the Insecta will continue to be inadequate, given that most entomologists must be concerned, in some way, with the relatively few species of known economic importance. One result of this is that our knowledge of an insect fauna is commonly a function of the pattern of life of particular entomologists - where they worked or went on holiday, and who their friends were. Data on most insect faunas have thus been collected both haphazardly and superficially. The insect order Thysanoptera, with about 5000 described species and probably three times that number throughout the world, is typical of this situation. Most thrips are tropical, but most thysanopterists are from temperate regions. The thrips fauna of Panama, judging from the number of papers published, is one of the best known in the tropics. But this knowledge is derived largely from one 6-week visit in 1933 by one man, Prof. J. D. Hood of Cornell University, albeit helped by his friends and relatives. James Zetek also collected thrips sporadically, particularly between 1913 and 1915, and L. A. Mound collected these insects for 12 days in 1983. The total time spent in serious field sampling of the thrips fauna in Panama by all workers, however, is probably less than 500 man hours, possibly much less, and this concentrated at only a few sites. All of the available records are from sites within a few miles of the ‘Canal Zone’. No collections seem to have been made from the highlands, or from the areas with either higher or lower rainfall.
Taxonomy and biology of Central American Robber Flies with an illustrated key to genera (Diptera: Asilidae)
Authors: Fisher Eric M , Hespenheide Henry A
Published: November 2023

The robber fly family Asilidae is one of the largest and most easily-recognized groups of Diptera. All robber flies are predaceous, and they possess adaptations for catching and eating other insects which give them a distinctive appearance. Characteristic features of the Asilidae include large eyes, which are usually flattened in front and protrude above the top of the head; a row or clump of setae (the mystax) located on the face between the mouth and antennae; stout, piercing-sucking mouthparts; and strong, spiny legs. Here we review the taxonomy and biology of all robber flies known to occur in Panama, Costa Rica, Nicaragua, Honduras, El Salvador, Belize, and Guatemala. Current knowledge of local faunal size, biogeography, seasonality, community ecology, prey selection, predators, mimicry, and foraging and courtship behaviour for regional asilids is summarized by Hespenehide in the first section. An overview of the taxonomy of Central American robber flies, including a key to 68 genera and an annotated list of about 315 species, is provided by Fisher in the second section.
Making sense out of scents: species differences in scent glands, scent-marking behaviour, and scent-mark composition in the Callitrichidae
Authors: Epple G , Belcher A M , Kilderling I , Zeller U , Scolnick L , Greenfield, K L , Smith III A B
Published: November 2023

In many mammals, chemical signals are of great importance in socio-sexual communication and in priming of reproductive functions. Such signals are contained in urine, faeces, genital discharge, saliva, and the secretion of specialized skin glands, of which several types may be present on an individual. Often, ingredients from several sources are combined to form complex mixtures. In addition, bacteria may act on substrates such as vaginal discharge or skin secretions to develop volatiles which carry signal function (see recent reviews by Albone 1984; Brown and Macdonald 1985; Duvall et al. 1986).
Flexibility and co-operation as unifying themes in Saguinus social organization and behaviour: the role of predation pressures
Authors: Caine Nancy G
Published: November 2023

For most of the history of behavioural primatology, New World monkeys were treated as the poor cousins of the Old World monkeys and apes. Despite some important and intriguing early research on captive (e.g. Hampton et al. 1966) and free-ranging (e.g. Carpenter 1934) platyrrhines, the data from these investigations figured only rarely in the development and testing of theory in primate behaviour. Considered to be primitive and simple, and difficult to observe in the wild, New World monkeys were not regarded as good candidates for most behavioural research. It seemed to be the general consensus (with important exceptions) that there was little to be gained from studying social organization and behaviour in species that were far removed from the human lineage in terms of both time and space (Kinzey 1986).
Predatory behaviour of the intertidal snail, Nucella lapillus, and its effect on community structure
Authors: Hughes Roger N , Burrows Michael T
Published: November 2023

Ecologists often seek generalizations about the structure and dynamics of communities in predator-prey interactions, because simple logic demands a causal relationship between the extent of predation and state of the prey population. In tightly coupled systems, such as those envisaged by the Lotka-Volterra equations, the relationship between predator and prey population is mutual, but with increasing polyphagy, the interaction becomes diffuse, with specific prey perhaps having little influence on the abundance of the predator. Either way, it is easy to imagine that details of predatory behaviour would have critical effects on the system. A predator that concentrates its effort where prey are dense will tend to have a population regulatory effect (Hassel 1978), and one that abandons a prey-type once it has become relatively rare will avoid driving any population to local extinction (Murdoch and Oaten 1975). If predators choose to eat the potential dominants, competitive exclusion among prey should be prevented (Paine 1966). These ideas are familiar to all ecologists and have been reviewed many times.
Discussion: predators, predation, and community structure: patterns and processes
Authors: Noakes David L G
Published: November 2023

The relationships between predators and prey have attracted the interest of human observers for as long as any aspect of ecology. Certainly, predation has been a fact of life for at least the past 110 million years, from direct evidence (Figs 8.1, 8.2), and not just the ghost of predation past (Connell 1980). The possibility of cycles of vertebrate predators and prey, the potential for control of pests by predators, and the possibility of regulation of consumers by producer species, are only a few of many well-known examples of human interest in predation (see Hassell and Anderson 1989). Of course, humans, as a predatory species, have presumably always been interested in predicting and regulating their harvest of other species. Our understanding of predators and predation continues to change, to become more refined, and (hopefully) more sophisticated. More importantly, we focus on the details of mechanisms, rather than just increasingly detailed descriptions of individual cases or of patterns, apparent or real (Schoener 1971; Huey and Pianka 1981; Dill 1983; Milinski 1984; Ydenberg and Dill 1986; May 1989; Lima and Dill 1990). Law and Watkinson (1989) remarked on an absence of progress in our understanding of competition in ecology, and noted a particular need for more empirical studies.
An extension of niche theory for complex interactions
Authors: Higashi Masahiko
Published: November 2023

No other concept in ecology has so strong an appeal and yet receives such diverse interpretations as that of ecological niche. The term tends to be very convenient as long as it is used in a loose fashion. This is why the concept is so appealing. But, such a loose usage of a term almost unavoidably generates and amplifies the ambiguity of the concept that the term should represent, and as a result, the single term comes to have many different meanings. Effort is then needed to separate the distinctive concepts that the single term embodies, and to sort out the relationships among those related but separable concepts. Such an effort is creative because it makes explicit those separate concepts that the term has accumulated with use over a period of time. There have been many excellent reviews and analyses of the notion of ecological niche, including recent ones by Abrams (1983), Schoener (1986), and Pianka (1988); more complete lists of relevant literature are already available in any of these reviews. An early definition of an organism’s (or a species’) niche is its status in the biotic environment (i.e. the community to which it belongs), or the relations that it has with its foods and enemies (Elton 1927). Hutchinson (1957) formulated the niche of an organism as a hypervolume in an Euclidian space with environmental factors as its axes; the hypervolume consists of points, each of which represents a specific state of the environment that allows the organism’s normal life. This definition represents an effort to formalize the concept on a quantitative basis. Hutchinson also introduced the notion of ‘realized niche’ of an organism, which is distinguished from the ‘fundamental niche’ of the organism, the realized niche of the organism when there is no other organism sharing the same habitat.