bluuebunny/crossref_metadata_2025_split huggingface dataset:
Strong Solutions For Steady Navier–Stokes Equations Of Compressible Barotropic Flow And Small Data
Authors: Novotný A , Straškraba I 
Published: November 2023

Abstract
In this chapter we investigate strong solutions near equilibria of steady barotropic Navier–Stokes equations in bounded and exterior domains (all results can be relatively easily extended to a general viscous compressible heat-conducting gas). The functional framework and main results are formulated in Section 5.1. The main ideas of the proofs via the Helmholtz decomposition are explained in Section 5.2. In Section 5.3, we investigate several auxiliary problems resulting from the decomposition, i.e. we deal with the Dirichlet and Neumann problems for the Laplacian, with the Stokes problem, with the transport equation in a bounded or in an exterior domains and with the Oseen problem in an exterior domain.
π-type interactions
Authors: Jean Yves 
Published: November 2023

Abstract
In the preceding chapter, we derived the structure of the d block for several different MLn complexes in which the ligands were assumed to use only a single orbital to form the metal–ligand bond. This orbital was either nonbonding or essentially so, and oriented towards the metal centre. Since the overlap between this ligand orbital and a dorbital on the metal is of the axialtype, their interaction leads to the formation of a molecular orbital (MO) which characterizes a σ bond. As we have already seen in Chapter 1 (§ 1.5.2), some ligands have another orbital (or even two) that can in principle contribute to the bonding with the metal. The orientation of this orbital is usually perpendicular to the axis defined by the σ bond, so the resulting overlap with a d orbital on the metal is lateral, and the interaction of π type.
Elements of group theory and applications
Authors: Jean Yves 
Published: November 2023

Abstract
Examination of the geometries of isolated molecules shows that there are four types of symmetry elements: reflection planes, axes of rotation, inversion centres, and improper axes of rotation. A symmetry operationmoves a molecule from an initial configuration to another, equivalent configuration, either by leaving the position of the atoms unchanged, or by exchanging equivalent atoms. The ideas of symmetry element and symmetry operation are of course very closely linked, since a symmetry operation is defined with respect to a given element of symmetry, and, conversely, the presence of a symmetry element is established by the presence of one or more symmetry operations that are associated with that element.
In the Beginning
Authors: Hawley John F , Holcomb Katherine A 
Published: November 2023

Abstract
On a clear, moonless night, in a field far from city lights, the sky might be the cabinet of some celestial jeweller, displaying glittering points of light on a field of black velvet. A faint, irregular band meanders overhead, like a river of cosmic milk. On any particular night, noticeably bright stars might stand out among the others; on subsequent evenings, an observant watcher would find that these wandering lights had shifted their positions against the backdrop of stars. As the seasons change, so does the sky; some groups of stars visible in summer disappear during the winter, whereas others remain above the horizon all year.
Cosmology Becomes a Science
Authors: Hawley John F , Holcomb Katherine A 
Published: November 2023

Abstract
For thousands of years, the universe that occupied human minds was small, limited by human senses and abilities. The world seemed to end at the horizon, and few travelled far from the towns of their births. The heavens were the realm of gods, beyond the understanding of mortals. From such a narrow perspective, it is not surprising that the universe appeared to be dominated by the Earth. The stars were held to be eternally fixed in their positions on the celestial sphere.
The Special Theory of Relativity
Authors: Hawley John F , Holcomb Katherine A 
Published: November 2023

Abstract
In some faraway galaxy, an advanced civilization has mastered space travel. The crew of one of their starships discovers an asteroid on a collision course with one of their world’s space outposts, which would surely be destroyed if the asteroid collides with it. The asteroid is at a distance of 3,000,000 km, as measured by the sensors on the starship. The starship is flying toward the asteroid at nearly the speed of light as seen from the space station.
Black Holes
Authors: Hawley John F , Holcomb Katherine A 
Published: November 2023

Abstract
The death of supermassive stars must result in collapse; no known force can resist gravity in such stars once their nuclear fires have died. The result of this inevitable collapse is known as a black hole. The term black hole is nowadays bandied about so much, in science-fiction novels and movies, as well as in the occasional general-science articles of newspapers and magazines, that it would be difficult for any reasonably literate person to be unaware of the expression. Yet few understand why black holes exist, or what their properties really are.
The Expanding Universe
Authors: Hawley John F , Holcomb Katherine A 
Published: November 2023

Abstract
For at least as long as written history has existed, humanity has set its sights upon understanding the shape, scope, and history of the universe. To this task we bring our senses, our experience, and our reason. This was as true for ancient cosmologists as it is for modern scientists. Today, however, our senses are augmented by powerful tools, we benefit from the accumulated and recorded experience of many generations, and we have developed mathematical languages that provide an efficient means to systematize our reasoning.
Dark Matter and Large-Scale Structure
Authors: Hawley John F , Holcomb Katherine A 
Published: November 2023

Abstract
So far we have modeled the universe by treating it as mostly smooth and homogeneous, in keeping with the cosmological principle. In reality, the universe is not perfectly smooth; it contains stars, galaxies, clusters of galaxies, and even super clusters of galaxies. On the grandest scales, those appropriate to cosmological models, these local density enhancements can be averaged into a smooth background. Eventually, however, cosmologists must tackle the problem of the origin and evolution of structure in the universe.
The Edge of Time
Authors: Hawley John F , Holcomb Katherine A 
Published: November 2023

Abstract
In our journey through the universe, we have encountered many wonders. Once we leave behind the bounds of our Earthly velocities and distances, we realize that our cozy intuition is often wrong, our common sense does not apply. Special relativity seemed so strange at its introduction that even some of the most distinguished scientists of the day refused to accept it. General relativity had an easier time, but quickly gained such a formidable reputation that most people became convinced that none but the brightest genius could hope to grasp its concepts.
Comparisons with other methods
Authors: Sloan I H , Joe S 
Published: November 2023

Abstract
In Chapter 6 we saw theoretical evidence (based on the criterion P0:) that maximal rank lattice rules obtained by copying rank-I lattice rules are at least comparable in accuracy with rank-I rules of similar order. Also, we saw that such maximal rank lattice rules have two practical advantages. Firstly, computer searches to find good rules are computationally less demanding than searches for good rank-I rules, with this advantage increasing as the dimension s increases and being very substantial when s is large.
Introduction to Surface Physics
Authors: Prutton M 
Published: November 2023

Abstract
This text, aimed at final-year undergraduate students and new postgraduates in physics, provides a broad introduction to surface physics, covering key areas of surface studies. Techniques are described that are used to determine which atoms are present on a surface and in what quantities, and to determine their relative arrangement. New results and theoretical advances are included, which provide fresh insights into the phenomena that occur at surfaces. Selected case studies are presented with particular reference to the (lll) surface of elemental silicon to illustrate the application of relevant techniques to the electronic, vibrational, and adsoption properties of surfaces.
Surface structure
Authors: Prutton M 
Published: November 2023

Abstract
Having determined what types of atoms are present upon a surface, the next important problem is to discover their arrangements with respect to each other and with respect to the underlying atoms of the solid. There are two parts to this problem-the determination of the symmetry of the surface atomic arrangement and the determination of details of the atomic positions. In bulk investigations, the former is normally carried out by using simple observations of the diffraction pattern obtained when a beam of X-rays, neutrons, or electrons is scattered from a single crystal of the sample. These observations yield information about the symmetry of the repeating unit of the structure, the unit cell, and the size and shape of this cell. The latter involves measurements of the intensity of diffracted beams and the comparison of these intensities with those predicted from postulated models of the structure. If successful, the result is a complete description of where each kind of atom is situated within the unit cell.
Geometric Structures and Loop Variables in (2+l)-dimensional Gravity
Authors: Carlip Steven 
Published: November 2023

Abstract
In this chapter, I review the relationship between the metric formulation of (2+l)-dimensional gravity and the loop observables of Rovelli and Smolin. I emphasize the possibility of reconstructing the classical geometry, via the theory of geometric structures, from the values of the loop variables. I close with a brief discussion of implications for quantization, particularly for covariant canonical approaches to quantum gravity.
Rates of convergence in the central limit theorem
Authors: Petrov Valentin V 
Published: November 2023

Abstract
Let F(x) and G(x) be arbitrary distribution functions, and let f(t) and g(t) be the corresponding characteristic functions. If f(t) and g(t) are identically equal, then F;(x) and G(x) are identically equal. If, however, we know only that f(t) and g(t) are close to each other in some sense, then we may expect a certain nearness of F(x) and G(x). There are many results which elucidate this point. The following theorem of Esseen is one of the most useful of these.
Strong limit theorems: the law of the iterated logarithm
Authors: Petrov Valentin V 
Published: November 2023

Abstract
Theorem 7.1 is in some sense as sharp as possible. Namely, if we replace o by O in the condition (7.1), the assertion of the theorem may fail. Using the arguments that we employed in the proof of Theorem 7.1, we can prove the following proposition on the connection between an estimate of the remainder term in the central limit theorem and the law of the iterated logarithm, i.e. the relation (7.3).
Introduction
Authors: Karlsson Erik b. 
Published: November 2023

Abstract
All physical measurements must be based on some kind of interaction between the system to be studied and the measuring instrument via direct physical contact, via a force acting at a distance, or by some kind of radiation acting as a messenger. Therefore each measuring method in physics has its own specific limitations and possibilities, not only regarding accuracy and range of the parameters observed, but also because it observes the system from its own particular point of view.
Magnetism
Authors: Karlsson Erik b. 
Published: November 2023

Abstract
In this chapter, and in subsequent chapters up to Chapter 10, contributions to solid state physics using the DPAC, DPAD, and μ.SR methods are presented in the form of examples. In an attempt to put these case studies into perspective they are preceded by short general discussions of the specific physical problems to be investigated and to what extent such problems can be studied by other more conventional methods. As far as magnetism is concerned, these methods include macroscopic measurements (which can now be performed on samples of very limited size or thickness using superconducting quantum interference devices (SQUIDs)), scattering measurements using neutrons, laser light, or synchrotron radiation, and microscopic measurements using NMR and ESR to observe the magnetism of individual atoms in solids. It will be shown that PAC and μSR methods, which both belong to the last of those categories mentioned above, can sometimes make an essential contribution to the information obtained. One of the main reasons is their high sensitivity, which means that signals can be observed even from probe spins present in very high dilution, another is their time windows which allow certain important dynamical processes to be followed, and a third is their ability to record magnetic phenomena without applying any magnetic fields that might perturb the systems to be investigated.
Hydrogen on Metallic Surfaces and in Metallic Superlattices
Authors: Karlsson Erik b. 
Published: November 2023

Abstract
As indicated in the previous chapter, the absorption and desorption of hydrogen in metallic materials is strongly influenced by surface and interface conditions. In absorption from the gas phase the first step is a dissociation of H molecules which is followed by diffusion on the surface and into the bulk material. The probability for dissociation of an impinging H molecule depends strongly on the electronic properties of the surface layers. It is represented by a dissociation barrier, which may be very low for certain metals like Pd and Pt. For single crystals, it also means that the geometry of the external face exposed to the hydrogen is an essential parameter. It is also strongly dependent on the presence of impurity atoms on the surface.
The Formal Theory Of Potential Scattering
Authors: Fröbrich P , Lipperheide R 
Published: November 2023

Abstract
Since potential scattering describes solely elastic scattering it covers only a small, although important, aspect of nuclear collisions. For the treatment of general nuclear reactions like inelastic scattering or transfer of particles, a more general formalism is required. This formalism, formal theory of reactions, will now be developed.
The Coupled-Channel Description Of Direct Reactions
Authors: Fröbrich P , Lipperheide R 
Published: November 2023

Abstract
In the single-step approximation introduced in Section 5.4 and discussed in detail in Chapter 7, one assumes the reaction to proceed directly from the initial to the final state, and thus ignores the existence of any other than the entrance and exit channels. It was shown formally in Section 5.5 how the coupled-channel description allows one to go beyond this approximation. We shall now turn to the practical implementation of the coupled-channel method.
Compound-Nucleus Reactions
Authors: Fröbrich P , Lipperheide R 
Published: November 2023

Abstract
Compound-nucleus reactions occur whenever the reaction mechanism involves many degrees of freedom in the combined projectile-target system at close contact. This is not the case if the collision partners are both light nuclei. But when a light, low-energy projectile combines with a nucleus which is heavy, a large number of different transitory configurations may be formed, as discussed in Section 9.2.1. They give rise to narrow isolated resonances in the reaction cross section as a function of the incident energy. When energy and mass of the projectile increase, the number of these transitory states increases as well, their structure becomes more complicated, and the resonances begin to overlap. Eventually, and this is generally the case in collisions where both partners are heavy ions, the complexity of the compound nucleus becomes so high that the latter can no longer be described in terms of individual compound states but must be treated by statistical methods. This leads us to the statistical picture of the compound nucleus introduced by Niels Bohr (1936), which has already been invoked in the previous chapter.
Analysis Of Deep-Inelastic Collisions, Fusion, And Heavy-Ion Induced Fission
Authors: Fröbrich P , Lipperheide R 
Published: November 2023

Abstract
In Chapter 11 we introduced friction and fluctuations in order to describe the dissipative processes occuring in deep-inelastic collisions. For the calculation of these effects we derived the Langevin and Fokker-Planck equations. We studied these equations for several simple examples and discussed general methods of solving them.
Introduction
Authors: Malinowski Grzegorz 
Published: November 2023

Abstract
The vital part of the studies of logic seeks to determine structural criteria for propositional validity and deals with formal inference relations. A suitable starting point for any analysis of these problems consists in the selection of a set of propositions from among all grammatically well-formed sentences, the members of which satisfy some specified syntactical and semantical conditions. The assumption stating that to every proposition it may be ascribed exactly one of the two logical values, truth or falsity, called the principle of bivalence, constitutes the basis of classical logic. It determines both the subject matter and the scope of applicability of the logic, the main systems of which are the classical propositional calculus (CPC) and the (first-order) predicate calculus (quantifier calculus). CPC is a theory of all truth-functional propositional connectives, i.e. sentence-argument propositional functions having the property that the logical value of any complex sentence formed with their use is determined uniquely by the logical values of its components. The predicate calculus is formed by introducing to the language system, with its semantics adequately extended, the symbols of name-argument propositional functions representing the names of properties and relations and name quantifiers. It renders possible the profound analysis of propositions within the principle of bivalence paradigm.
Classical characterization of many-valued logics
Authors: Malinowski Grzegorz 
Published: November 2023

Abstract
Even the most radical authors of many-valued constructions devoted much attention to the classical logic. The matrix method inspired by truth-tables embodies a distinct shadow of two-valuedness in the division of the matrix universe into two subsets of designated and undesignated elements. Besides, it turned out that, by making use of some special, so-called standard, connectives, it is possible to map this division into the language as well as to describe consequence relations (operations) of some many-valued logics through appropriate sets of formulae and the consequence of the classical logic (see Chapter 8). In the 1970s the investigations of logical formalizations bore several descriptions of many-valued constructions in terms of zero-one valuations. Effectively, the interpretations associated with these descriptions shed new light on the problem of logical many-valuedness.
Intuitionism and the modal logics of Lewis
Authors: Malinowski Grzegorz 
Published: November 2023

Abstract
lntuitionistic logic and the modal logics of Lewis are the most important and best motivated non-classical logical constructions rendered axiomatically. Their creators were not guided by the idea of introducing supplementary logical values. However, it occurred that these logics can be characterized exclusively by means of infinite-valued matrices. On the other hand, non-matrix semantics formed to describe intuitionistic and modal logics became an important tool for interpreting and describing of all the non-classical logical constructions.
Resource Logics
Authors: Gabbay Dov M 
Published: November 2023

Abstract
This chapter will illustrate the use of the Metabox to define some known logics and a new class of logics called Resource Logics. We understand the term to cover all logics where it is important to know exactly from which assumptions and using which inference rules and at what order a conclusion is drawn. In this case the labels function as names to the assumptions (data) and the deductive process propagates the labels to the conclusion through an agreed labelling discipline.
Collisions, Quenching, and Particle Diffusion
Authors: Molisch Andreas F , Oehry Bernhard P 
Published: November 2023

Abstract
In this chapter, we deal with non-radiative processes that can create or destroy excited atoms.5 The theory of collisional excitation and de-excitation is extremely complicated. A thorough review of the work up to 1970 can be found in the five-volume book by Massey and Burhop (1968-1975). The work done after that time would probably fill another ten volumes. We will take here a mostly phenomenological point of view. The processes are described by effective cross-sections, and no investigation of the actual physical processes is done.
Formulation of the Classical Problem
Authors: Molisch Andreas F , Oehry Bernhard P 
Published: November 2023

Abstract
There are three principal mathematical approaches to describing trapping: the Holstein equation, the method of combining the equation of radiative transfer with the rate equation for the excited state atoms, and the multiple-scattering representation. Ultimately, these three descriptions are equivalent-as they should be, since they describe the same physical process. Their different formulations stem from different views of the trapping problem. Each method has its specific advantages and disadvantages for the evaluation, hence it is very helpful to fully understand all three formulations.
Macroirreversibility and microreversibility reconciled: the second law
Authors: Garrett A J M 
Published: November 2023

Abstract
There is a single consistent resolution of the reversible microdynamicsirreversible macrodynamics problem, stemming from better understanding of the role of probability in physics: the Bayesian viewpoint. The second law of thermodynamics arises on demanding that experiments on thermodynamic variables be reproducible though atomic microvariables differ from run to run. A general formulation for non-equilibrium statistical mechanics is outlined, based on Jaynes’ principle of maximum entropy, and the meaning of entropy is clarified using information theory. The conundrum facing the pioneers of kinetic theory in the late 19th century was to reconcile the reversible character of Hamiltonian atomic dynamics with the irreversibility of systems of atoms viewed on the large scale.
The Mathematical Formalism Of Quantum Mechanics
Authors: De Lange O L , Raab R E 
Published: November 2023

Abstract
Quantum mechanics was created mainly to account for microscopic phenomena that occur on a scale of order IO−10 m. It has turned out to be an astonishingly successful theory which applies on a scale down to at least 10−18 m. Quantum theory has become established as part of the essential core of physics. The purpose of this introductory chapter is twofold. Firstly, in Sections 1.1–1.7 we review the formalism of elementary nonrelativistic quantum mechanics. In this review we attempt to give enough of the terminology and basics of the subject so that a reader who is not already familiar with quantum mechanics will be able to follow the applications considered later in the book. For the reader who finds our discussion too brief, the literature on quantum mechanics is vast and we recommend in particular Refs 1–5. The second purpose of this chapter is to present the basic tools of operator methods as they are used in this book: thus in Sections 1.8–1.11 we discuss commutation relations, shift operators, and the virial, hypervirial, and Hellmann Feynman theorems.