bluuebunny/crossref_metadata_2025_split huggingface dataset:
Human evolution
Authors: Hein Jotun , Schierup Mikkel H , Wiuf Carsten 
Published: November 2023

Abstract
Humans are tremendously interested in human evolution and this topic gets more attention than the evolution of any other species. This is so for several reasons. Beyond the obvious, that we are interested in our own evolution, human evolution is tied up with the interpretation and understanding of diseases with a genetic component and is influenced by human demographic and cultural history of which much is known. For other species than our own less is known about demography and culture.
Until recently, longer term human evolution (thousands to millions of years) has mainly been investigated by comparisons of dated fossils and archaeology. Such analysis has brought much understanding of the time of origin of anatomically modern humans, the major migrations and colonisa- tion of the earth, and knowledge about demography. These studies have the advantage that they often use traits of direct interest such as brain volume, upright posture, and pathologies.
Convex polytopes
Authors: Webster Roger 
Published: November 2023

Abstract
The concept of a convex set is a simple one. A set in space is convex if whenever it contains two points, it also contains the line segment joining them. Elementary geometry abounds in convex sets: ellipses, triangles, parallelograms, balls, halfspaces, and cubes are convex. An annulus, a crescent, and the vertex set of a cube are examples of nonconvex sets. Convex and non-convex sets are illustrated in Fig. 2.1.
Classification and Construction of Buildings
Authors: Ronan Mark 
Published: November 2023

Abstract
The purpose of this article is to give some feeling for what a building is, to discuss their classification, their construction, and something of their local structure. For more details two recent books, [Br] and [R2], are available, both published in 1989, plus a survey article [R3] which contains an introductory treatment of the subject.As is well known, the theory of buildings was introduced, and has been largely developed, by Jacques Tits. Its original purpose was to provide an understanding of the analogues of the simple Lie groups, and particularly the exceptional groups, over an arbitrary field, and in this respect it has been brilliantly successful. The theory of spherical buildings and their classification [T2] was the result, but things by no means stop there. Work of lwahori and Matsumoto [IM] gave us affine buildings; the general theory of affine buildings was then developed by Bruhat and Tits [BT], and a classification was accomplished by Tits [T7].
Groups Acting Transitively on Locally Finite Classical Tits Chamber Systems
Authors: Meixner Thomas 
Published: November 2023

Abstract
Tits chamber systems admitting a transitive group of automorphisms have seen considerable interest in the last six or seven years. As a general reference I want to mention the surveys (lectures held at the Como conference in 1984) by Kantor ([61) and Timmesfeld ([28]). Some notions have been developed, some methods such as the “amalgam method” have proved to be very powerful instruments since then; different notions used, however, cause people to use different sets of hypotheses, and sometimes the interested reader might have trouble to see how the numerous papers written fit together and whether the results achieved give a completeclassification of the objects one is interested in.The purpose of this survey is to state the classification theorem that has been achieved since Como, to give the list of “types” allowed by the theorem together with explicit examples found by many authors, finally describe the systems of subgroups used in the literature with their various relationships. Thereby, I will have to repeat parts of Timmesfeld’s survey, but will do so in order to be as clear as possible.
Generalized Polygons and s-Transitive Graphs
Authors: Weiss Richard 
Published: November 2023

Abstract
Stabilizer Gacts transitively on the set of s-paths beginning at x.If, in addition, Gacts transitively on the vertex set off, and hence on the set of alls-paths in r, then f is called s-transitivewith respect to G.We will give here a brief survey of various efforts to extend and apply this and some related (but historically independent) results of Tits. As these developments include the entire theory of amalgams opened up byD. Goldschmidt’s seminal paper [8] on locally s-transitive trivalent graphs, our choice of results will, of necessity, be very selective. In general, we will describe results which are of a more graph theoretical nature. The reader is referred to (22] for an earlier report on s-transitive graphs.
Synthetic differential geometry
Authors: McLarty Colin 
Published: November 2023

Abstract
The synthetic differential geometry axioms (SDG) describe a topos in which each object has a differentiable structure, each arrow has a derivative, and the basic rules of calculus are simple calculations with infinitesimals. For this chapter we assume that we have a particular topos Spaces that satisfies the axioms. We refer to objects of Spaces as spaces, to its arrows as maps, and to global elements p: 1→.M aspoints of the space M.
Geometric Stability Theory
Authors: Pillay Anand 
Published: November 2023

Abstract
This book gives an account of the fundamental results in geometric stability theory, a subject that has grown out of categoricity and classification theory. This approach studies the fine structure of models of stable theories, using the geometry of forking; this often achieves global results relevant to classification theory. Topics range from Zilber-Cherlin classification of infinite locally finite homogenous geometries, to regular types, their geometries, and their role in superstable theories. The structure and existence of definable groups is featured prominently, as is work by Hrushovski. The book is unique in the range and depth of material covered and will be invaluable to anyone interested in modern model theory.
Stability theory
Authors: Pillay Anand 
Published: November 2023

Abstract
In this chapter, I survey the stability-theoretic results and notions required for the rest of the book. I include forking, canonical bases, ranks, orthogonality, and stable group theory. I give selective proofs. Hopefully this chapter will also provide a point of entry into general stability theory for the beginner, and thus I include a fairly thorough treatment of forking. I will be assuming knowledge of the basic ingredients of first-order model theory (languages, structures, elementary substructures, compactness, types, saturation, etc.). Such background can be found in Chang and Keisler’s book [CK] for example, and also in Hodges recent book [Ho], but notation will be consistent with my earlier book [Pl].Strictly speaking, a full grasp of stability theory is not required for understanding the ‘finite rank’ part of the theory, covered in Chapters 2, 3, 5, 6, and part of Chapter 4. For much of this material, simply dimension and canonical bases in strongly minimal sets or minimal sets are all that the reader has to understand. So the reader who so wishes can begin at Chapter 2 and refer back to various sections of Chapter 1 (on minimal sets, ranks, etc.) when necessary. On the other hand, general stability provides a unifying conceptual framework and language for the various topics covered in the book, as well as being an essential feature in Chapter 4, 7, and 8.
Quasifinite axiomatizability
Authors: Pillay Anand 
Published: November 2023

Abstract
We saw in Chapter 2 that totally categorical theories are not finitely axiomatizable. A slight extension of the proof yields non-finite axiomatizability of ω-categorical, ω-stable theories. At some point it was asked whether the only obstruction to the finite axiomatizability of, say, totally categorical theories was the non-finite expressibility of ‘there are infinitely many elements’, that is whether totally categorical theories could be finitely axiomatized modulo the ‘axiom of infinity’. In this chapter we see that this is true.
Solvable Groups
Authors: Borovik Alexandre , Nesin Ali 
Published: November 2023

Abstract
The structure theory of solvable groups of finite Morley rank is in a quite satisfactory state, though by no means as detailed as the theory available in the algebraic case [189). We obtain the conjugacy of Sylow subgroups for arbitrary primes (whereas the general theory of the next chapter works only for the prime 2) as well as the extensions of the Sylow theory due to Philip Hall (Section 9.9). Section 9.1 contains Zil’ber’s very useful technical result on the structure of certain actions of one abelian group on another, which leads to the theorem in Section 9.2 that the derived subgroup of a connected solvable group G of finite Morley rank is nilpotent. In the algebraic case there is also a representation of G as a semidirect product of an abelian group T acting on a nilpotent subgroup U. We would like such a result in our case, with at least U definable, but this problem is open. We discuss it in general in Section 9.3 and in the case of connected solvable groups of class 2 in Section 9.4. Specializing further in Section 9.5 to the case of rank 2, we obtain a detailed structure theory in the nonnilpotent case, and we make some further comments on the nilpotent case, motivated by the observation that in the study of solvable connected groups of finite Morley rank, nilpotent groups often arise in practice as the commutator subgroup of a given group. One candidate for the subgroup U above is the connected component of the Fitting subgroup, F (G)0 In Section 9.6 we show that the quotient G/ F(G)0 is divisible abelian (that it is abelian is already contained in the result of Section 9.2).
2-Sylow Theory
Authors: Borovik Alexandre , Nesin Ali 
Published: November 2023

Abstract
In this chapter we prove the conjugacy of Sylow 2-subgroups of groups of finite Morley rank and give some useful applications of this which are analogs of results on finite groups that play a major role in the classification of the finite simple groups (and which we apply subsequently in the same fashion). Since we do not have the ability to carry out counting arguments, the proof proceeds mainly by induction on rank. Sections 10.1 and 10.2 contain some general properties of involutions and their actions on invariant abelian subgroups, as well as an analog of the Brauer-Fowler theorem (Theorem 10.3). Section 10.3 contains the major result: Sylow 2-subgroups are conjugate. They are usually not definable, hence the notion of rank does not apply directly to them.
Geometries
Authors: Borovik Alexandre , Nesin Ali 
Published: November 2023

Abstract
This chapter contains results on various geometric structures related to groups of finite Morley rank. We will first look into some incidence geometries: the generalized n-gons and their flag-transitive automorphism groups. The generalized n-gons have been introduced by Tits [343] in 1959 in connection with certain group theoretic problems, and they generalize the projective planes. In Subsection 13.2, we will see that a bad group of Morley rank 3-which is not known to exist-acts sharply flag-transitively on a pseudoplane that looks very much like a projective plane (Theorem 13.16).
CN and CIT-Groups
Authors: Borovik Alexandre , Nesin Ali 
Published: November 2023

Abstract
In this chapter we will study two classes of groups: the CN and CIT-groups of finite Morley rank. CIT-groups are groups with involution where the centralizer of every involution is a 2-subgroup. CN-groups are groups where every centralizer is nilpotent. Note that simple bad groups are CN-groups. For this reason we have to assume that a CN-group has involutions. The classification of CN and CIT-groups in the context of finite groups uses character theory. Character theory is not available to us. We compensate this lack by computing in the group itself. Some of the computations that we need have been done in Subsection 11.5.5. In this chapter we will show that most of the CIT and CN-groups are split Zassenhaus groups and we will then apply the results of Subsection 11.5.5.
Effective representation systems
Authors: Smullyan Raymond M 
Published: November 2023

Abstract
In this chapter we apply the results of the last chapter to the representation systems of Chapter 4. For any positive n we define r n+1 (x,y 1, ... ,y n) to be the Gödel number of Ex(y 1,... ,y n). We call Z an effective representation system if: (1) for each positive n, the function r n+1(x,y 1, ... ,y n) is recursive; (2) the set of Gödel numbers of the sentences is recursive, and for each n, the set of Gödel numbers of predicates of degree n is recursive. Throughout this chapter Z will be assumed to be an effective representation system. We let r(x,y) be r 2(x,y) — thus r(x,y) is the Gödel number of Ex(y) and the diagonal function d(x) is r(x,x).
Synchronization and pairing functions
Authors: Smullyan Raymond M 
Published: November 2023

Abstract
In this chapter we consider a totally different approach to double and multiple fixed point properties. This approach is an outgrowth of the original form of the double recursion theorem[28] which involves a pairing function J(x, y) and its inverse functions K(x), L(x) for its very statement. We will deal with this in Part III of this chapter.
Applications of Sampling Theory to Combinatorial Analysis, Stirling Numbers, Special Functions and the Riemann Zeta Function
Authors: Butzer P L , Hauss M 
Published: November 2023

Abstract
The Shannon sampling theorem together with its version for not necessarily band-limited functions is essentially equivalent (in the sense that each can be deduced from any of the others by elementary means) to at least five fundamental theorems in four different fields of mathematics. namely to the Poisson summation formula of Fourier analysis, to a particular form of Cauchy’s integral formula of complex function theory, to the Euler-Maclaurin and Abel-Plana summation formulae of numerical analysis as well as to the celebrated functional equation of the Riemann zeta function of analytical number theory. Recall (Higgins 1996, pp. 90-96) and check Section 1.6 below.
Mathematical background I
Authors: Mason L J , Woodhouse N M J 
Published: November 2023

Abstract
In this chapter, we summarize the mathematical background to the Yang-Mills equations. In §2.l we give an informal overview of gauge theories and their relation to the anti-self-duality condition. In §2.2-§2.4 we give brief notes on the geometry of real and complex space-time, and on conformal transformations, followed in §2.5-§2.6 by a more formal discussion of bundles, connections, curvature and the Yang-Mills equations. These topics are covered more fully by Ward and Wells (1990).
Reduction to three dimensions
Authors: Mason L J , Woodhouse N M J 
Published: November 2023

Abstract
The ASD condition reduces to a system of equations in three dimensions when we take the quotient of a neighbourhood in space-time by the action of a one-dimensional group generated by a single conformal Killing vector. The general features of the various cases are determined by the properties of the generator: whether or not it is null, whether or not it is hypersurface orthogonal, and how it behaves near its zeros (the fixed points of the action). We shall see two significant phenomena in the case of a null translation. First, the invariants of the Higgs field are constant on the a-planes orthogonal to the generator: these ‘first integrals’ classify further reductions. Second, we find that the reduced system acquires an unexpected infinite-dimensional point symmetry group.
Twistor construction of hierarchies
Authors: Mason L J , Woodhouse N M J 
Published: November 2023

Abstract
In Chapter 8, we saw that a given solution to the ASDYM equation could be embedded in an infinite family of new solutions by moving it along the commuting flows of the ASDYM hierarchy. The lowest level flows in the hierarchy are the translations in space-time, from which the higher flows are generated by the recursion operator.
Finite p-groups acting uniserially
Authors: Leedharn-Green C R , McKay S 
Published: November 2023

Abstract
This chapter concentrates on the idea of a finite p-group G acting uniserially on a finite p-group N; that is to say, G acts on N, and the G-invariant subgroups of N are linearly ordered, there being precisely one of index pi in N for each i ≥ 1 with pi ≥ INI. This situation arises naturally in a finite p-group G of coclass r as the action of G on all but r of the sections of any normal series of G must be uniserial: see Lemma 4.1.15.
The proof of Conjecture A using powerful p-groups
Authors: Leedharn-Green C R , McKay S 
Published: November 2023

Abstract
At the heart of the basic techniques in p-group theory is the interplay between the commutators and the power structure. In particular, various classes of groups have been introduced in which some control is exerted over this interplay. The classic case is the class of regular p-groups introduced by P. Hall. These are described briefly in Section 1.2. More recently the class of powerful p-groups was introduced by A. Mann. Both classes contain the class of abelian p-groups, so in each case the properties obtained are to some extent generalizations of results for abelian groups.
Invariants Of Smooth Four-Manifolds
Authors: Donaldson S k. , Kronheimer P B 
Published: November 2023

Abstract
We turn now to the question which formed the second main thread of the topological discussion in Chapter 1, namely the question of distinguishing smooth four-manifolds having the same classical invariants. Our strategy is to define new invariants using the ASD moduli spaces. The ASD equations are not defined until a Riemannian metric g (or rather, a conformal class) is chosen; the space of solutions-the moduli spaces we have been studying-reflect accordingly many properties of the metric. In order to define differential-topological invariants, we must extract some piece of information from the moduli space which is insensitive to a change in the metric and therefore depends only on the underlying manifold.
Structure of H
g
Authors: Dwork Bernard 
Published: November 2023

Abstract
We consider the situation of Chapters 2 and 3, in particular hypothesis (2.4) but we shall not use hypotheses (2.5) and (2.6) until the second part of this chapter (§ 6.5 onwards). It will be shown later Lemma 9.1.1 that W^a is finite dimensional (and hence its adjoint space ℋ^a is dual) but this will not be used immediately. Our object is to find necessary and sufficient conditions under which for given u∈H^0 the map is an injective map of K^a into γ^−∘Xu The necessity of our condition is not established.
L-Functions and Representation Theory of p-Adic Groups
Authors: Shahidi Freydoon 
Published: November 2023

Abstract
The modern theory of automorphic forms as envisioned by Langlands (28, 30] gives an equal weight to representation theory of p-adic reductive groups as that of real groups. While representation theory of real groups is near perfection, a similar statement cannot be made about p-adic groups and in fact there is an abundance of unsolved problems of extreme depth, beauty, and importance that must be answered. The work of Harish-Chandra [11, 45] has already proved that a large part of the theory from real groups carries over, fairly precisely, to the p-adic case. Nothing like this can be said of their discrete series representations and in fact to this date our understanding of them remains poor, except for GLn and certain other classical groups (see the next paragraph).
Weak Forms of Amenability for Split Rank 1 p-Adic Groups
Authors: Valette Alain 
Published: November 2023

Abstract
Let F be a non-discrete locally compact field and let G be the group of F-rational points of a simple algebraic group defined over F. Let G have positive split rank, so that G is not compact in the locally compact topology coming from F. For example, G = SLn(F) when n ⩾ 2. It is then a classical fact that G is not amenable. We recall the proof below. However, if F is a local field and G has split rank 1 (for example, G = SL2(Q p ), or SL2(D), where D is a central division algebra over Q p ), then weak forms of amenability do hold. The aim of this paper is to survey weak forms of amenability.
A Motivated Introduction to the Langlands Program
Authors: Murty M Ram 
Published: November 2023

Abstract
This paper is partially expository and is intended as an introduction to the Langlands program for number theorists. The new theorem in the paper is that automorphic induction map for Hecke characters implies both the Artin conjecture and the Langlands reciprocity law. (See below for definitions.) In the last section, we describe some recent work with K. Murty [18] that applies the theory of base change to elliptic curves. The paper is not an exhaustive survey. We have tried to use some classical problems of number theory as motivation for discussion. For instance, we concentrate on GLnthough the functoriality conjecture predicts that this is not a limitation. Nevertheless, our discussion is sufficiently motivated from the number theoretic point of view that a non-specialist in the field can appreciate the depth and profundity of these ideas.
Ordered Factorizations for Integers and Arithmetical Semigroups
Authors: Knopfmacher A , Knopfmacher J , Warlimont R 
Published: November 2023

Abstract
The classical problems of “factorisatio numerorum” concern (i) the total number of ordered factorizations of a natural number n &gt; 1 into products of natural numbers larger than 1, and (ii) the corresponding total number of unordered factorizations of the same type. Results of this nature can be found, for example, in [l], [7], [12] and the references therein. Recently, in [8], the present authors considered the analogous problems within the context of additive arithmetical semigroups as treated in the monographs [10], [11].
Projection fro1n an Algebraic Quadratic Form to Rational Quadratic Forms
Authors: Cohn Harvey 
Published: November 2023

Abstract
0. Introduction. Class field theory, in its historical ongms, first centered on the study of conditions on a rational prime p which lead to its representation by a positive definite quadratic form in rational integers (0.1) p = ax2+bxy+cy2, (d=b2-4ac&lt;0), where (a, b,c) = 1, but the discriminant d need not be fundamental.
Model Theory and Computer Science: An Appetizer
Authors: Makowsky J A 
Published: November 2023

Abstract
The purpose of this chapter is to give an account of those aspects of model theory which we think are relevant to theoretical computer science. We start with a general outline of the evolution of model theory, which will serve as an exposition of the major themes. In the subsequent section we shall elaborate some of these themes and put them into the context of theoretical computer science.