bluuebunny/crossref_metadata_2025 huggingface dataset:
Non-steady motion problems in two dimensions. I
Authors: Hill R
Published: November 2023

We now consider problems in which the stress and velocity at any fixed point are varying from moment to moment. To begin with, we restrict our attention to problems where the plastic region develops in such a way that the entire configuration remains geometrically similar. We have already encountered two examples, namely the expansion of a cylindrical or a spherical cavity from zero radius in an infinite medium; when the configuration at any moment is scaled down to a constant cavity radius the same distribution of stress is obtained. Other examples are the indenting of the plane surface of a semi-infinite block by a conical or pyramidal punch. For geometrical similarity it is necessary that the distortion should be initiated at a point or along a line, and that the specimen should be infinite in at least one dimension. Although either condition precludes the exact realization of similarity in practice, it is easily attained within experimental error. For example, Vickers pyramid hardness is observed to be effectively independent of the applied load, provided the specimen is large compared with the diameter and depth of the impression, and provided the impression is large compared with the grain size and the radius of curvature of the tip of the cone.
Non-steady motion problems in two dimensions. II
Authors: Hill R
Published: November 2023

We turn now to two-dimensional problems in which, for simplicity, it is necessary to restrict the analysis of the state of stress to the initial part of the loading path, when the total strain is still small. It will be assumed, in fact, that all changes in the external dimensions of the body are negligible, so far as the boundary conditions are concerned. The plastic strains being small, it is generally inaccurate, even for a calculation of the stress distribution, to suppose that the material is plastic-rigid; however, it will be shown that in certain circumstances the stress is independent of the value of Young’s modulus. We shall therefore carry out the analysis for a plastic-elastic material, and assume only that it has been pre-strained to a degree such that the work-hardening is negligible in the range of strain under consideration. When such a body is continuously loaded from a stress-free state the plastic and elastic components of the strain are at first comparable.
Miscellaneous Topics
Authors: Hill R
Published: November 2023

In the process of deep-drawing, a thin circular blank is formed into a cylindrical cup, open at the top and closed at the base. The blank is placed over a die with a circular aperture and rounded lip (Fig. 78a); usually a blank-holder is employed to minimize crinkling. † A punch is forced down on to the blank, drawing the outer annulus over the die to make the wall of the cup. Among the variables are the radius of the lip, the shape of the punch, the lubrication, the clearance between punch and die and between blank-holder and die. ‡ The following analysis is restricted to a calculation of the stress and strain in the outer annulus of the blank while it is being drawn radially towards the lip of the die.
Fundamental Notions
Authors: Jeffreys Harold
Published: November 2023

The fundamental problem of scientific progress, and a fundamental one of everyday life, is that of learning from experience. Knowledge obtained in this way is partly merely description of what we have already observed, but part consists of making inferences from past experience to predict future experience. This part may be called generalization or induction. It is the most important part; events that are merely described and have no apparent relation to others may as well be forgotten, and in fact usually are. The theory of learning in general is the branch of logic known as epistemology. A few illustrations will indicate the scope of induction.
Direct Probabilities
Authors: Jeffreys Harold
Published: November 2023

where by the likelihood we understand the probability that the observations should have occurred, given the hypothesis and the previous knowledge. The prior probability of the hypothesis has nothing to do with the observations immediately under discussion, though it may depend on previous observations. Consequently the whole of the information contained in the observations that is relevant to the posterior probabilities of different hypotheses is summed up in the values that they give to the likelihood. In addition, if the observations are to tell us much that we do not know already, the likelihood will have to vary much more between different hypotheses than the prior probability does. Special attention is therefore needed to the discussion of the probabilities of sets of observations given the hypotheses.
General Questions
Authors: Jeffreys Harold
Published: November 2023

Most of the present books on statistics, and of the longer papers in journals, include a careful disclaimer that the authors propose to use inverse probability, and emphasize its lack of logical foundation, which is supposed to have been repeatedly pointed out. In fact the continued mention of a principle that everybody is completely convinced is nonsense recalls the saying of the Queen in Hamlet: ‘The lady doth protest too much, methinks.’ Unfortunately some people that have examined the question have not been so convinced, and they include such first-rate logicians as W. E. Johnson, C. D. Broad, and F. P. Ramsey.
A Space-Time of Sufficient Generality
Authors: Chandrasekhar S
Published: November 2023

The black-hole solutions of general relativity are static and spherically symmetric (as the Schwarzschild and the Reissner-Nordstrom solutions are) or stationary and axisymmetric (as the Kerr and the Kerr-Newman solutions are). The perturbed state of these solutions, which are of equal concern to us, will be neither stationary nor axisymmetric. As a basis for the treatment of the various problems that are suggested in these latter contexts, it will be convenient to have on hand the Einstein and the Maxwell equations in a space-time of sufficient generality which will encompass the different situations we shall encounter in the course of our study. In this chapter, we shall consider a space-time which appears to have the requisite generality; and we shall provide expressions for the basic tensors which will enable us to write down, without any ado, the relevant equations appropriate to the different contexts.
The Gravitational Perturbations of the Kerr Black-Hole
Authors: Chandrasekhar S
Published: November 2023

This chapter is devoted to the theory of the gravitational perturbations of the Kerr black-hole. The subject is one of considerable complexity; and, in spite of the length of this chapter, the account, in large parts, is hardly more than an outline. When the Kerr black-hole is gravitationally perturbed, by the incidence of gravitational waves, for example, the quantities which vanish in the stationary state will, in general, cease to vanish and will become quantities of the first order of smallness; and the quantities which are finite in the stationary state will, likewise, experience first-order changes.
Spin -½Particles In Kerr Geometry
Authors: Chandrasekhar S
Published: November 2023

Considerations pertaining to the propagation of waves in Kerr geometry have so far been restricted to electromagnetic waves and gravitational waves-both massless and of integral spins (one and two). We now turn to a consideration of fields of spin-½, both massive and massless, such as the electrons and the two component neutrinos. On the mathematical side, the interest in these fields derives principally from the separability of Dirac’s equation in Kerr geometry. And on the physical side, the interest derives from the lack of super-radiance exhibited by the spin-½ waves.
Other Solutions; Other Methods
Authors: Chandrasekhar S
Published: November 2023

The treatment of the spin-½ particles in the last chapter concludes our study of the Schwarzschild and the Kerr solutions—the digression into the Reissner-Nordstrom solution in Chapter 5 was largely dictated by the consideration that its study enables a deeper understanding of the Schwarzschild solution and provides a convenient bridge to the Kerr solution. On these accounts, one might have thought that the Kerr-Newman solution—which stands in the same relation to the Kerr solution as the Reissner-Nordstrom solution to the Schwarzschild solution-will enable a similar deeper understanding of the Kerr solution. While the derivation of the Kerr-Newman solution (in §110) along the lines of the Kerr solution (in §54) does provide some useful generalizations of the underlying concepts, it does not appear that the methods developed in Chapter 9 for the treatment of the gravitational perturbations of the Kerr black-hole can be extended in any natural way to the treatment of the coupled electromagnetic and gravitational perturbations of the Kerr-Newman black-hole.
Spherical harmonics
Authors: Maxwell James Clerk
Published: November 2023

J 28.] The mathematical theory of spherical harmonics has been made the subject of several special treatises. The Handbuch <ler Kuge(functionen of Dr. E. Heine, which is the most elaborate work on the subject, has now (1878) reached a second edition in two volumes, and Dr. F. Neumann has published his Beitrage zur Theorie der Kugelfunctfonen (Leipzig, Teubner, 1878).
Electrostatic instruments
Authors: Maxwell James Clerk
Published: November 2023

On Electrostatic I nstrurnents.

The instruments which we have to consider at present may be divided into the following classes:

(1) Electrical machines for the production and augmentation of electrificat.ion.

(2) Multipliers, for increasing electrification in a known ratio.

(3) Electrometers, for the measurement of electric potentials and charges.
Current-sheets
Authors: Maxwell James Clerk
Published: November 2023

A current-sheet is an infinitely thin stratum of conducting matter, bounded on both sides by insulating media, so that electric currents may flow in the sheet, but cannot escape from it except at certain points called electrodes, where currents are made to enter or to leave the sheet.
Electromagnetic instruments,
Authors: Maxwell James Clerk
Published: November 2023

A galvanometer is an instrument by means of which an electric current is indicated or measured by its magnetic action.

When the instrument is intended to indicate the existence of a feeble current, it is called a sensitive galvanometer.
Ferromagnetism and diamagnetism explained by molecular currents
Authors: Maxwell James Clerk
Published: November 2023

We have seen (art. 380) that the action of magnets on one another can be accurately represented by the attractions and repulsions of an imaginary substance called ‘magnetic matter.’ we have shewn the reasons why we must not suppose this magnetic matter to move from one part of a magnet to another through a sensible distance, as at first sight it appears to do when we magnetize a bar, and we were led to poisson’s hypothesis that the magnetic matter is strictly confined to single molecules of the magnetic substance, so that a magnetized molecule is one in which the opposite kinds of magnetic matter are more or less separated towards opposite poles of the molecule, but so that no part of either can ever be actually separated from the molecule (art.430)
Grafting modalities onto substructural implication systems
Authors: Gabbay Dov M
Published: November 2023

When logical systems are used to formalise some application area, they may require the addition of modality to the language for a variety of reasons: to cater for changes of the system in time, or perhaps for the dependency of the system on the context, or even to bring metalevel notions into the object level. Be the reasons and motivations what they may, we must develop the logical capability of incorporating modalities into these systems, so adding a new dimension which can explicitly and naturally account for ‘accessibility ‘ relations involved in the processes that are being modelled.
An Isolated Case?
Authors: Schilthuizen Menno
Published: November 2023

When Charles Darwin first set foot on the Galapagos Islands, in September 1835, they must have seemed like paradise to him. He had spent the austral winter braving snowstorms and earthquakes in the barren mountains of the Andes, so the 26-year-old naturalist must have welcomed the tropical flora and fauna that the oceanic archipelago offered to him. In the five weeks that he and the crew of HMS Beagle spent there, Darwin took to unbounded collecting and experimentation. He was fascinated by the extreme tameness of the birds. In his report he wrote: ‘A gun is here almost superfluous; for with the muzzle, I pushed a hawk off the branch of a tree.’ The sea iguana appalled him on account of its being ‘hideous-looking’, ‘stupid’, and ‘sluggish’, and he even spent some time repeatedly hurling a particularly unlucky individual into the waves to see if it would eventually flee to sea (it never did, but doggedly kept returning to the shore).
Seductive Theories
Authors: Schilthuizen Menno
Published: November 2023

The male lyrebird of south-eastern Australia is as baroque as birds get. In the breeding season, it clears a circular mound of forest floor, and proceeds to put on its world-famous performance. It brings forward its two, long, lyre-shaped tail feathers and lowers them over its head, which is then completely obscured by the lacy fan of exceedingly delicate feathers in between. But the best part is yet to come: the concert.
Ecotone—Speciation Prone?
Authors: Schilthuizen Menno
Published: November 2023

Fish in cold arctic lakes and in muggy tropical ones have spawned new species because these biotopes offered more niches than a single fish could fill. Monophagous insects have done the same with the abundance of different host plants on offer. This is sympatric speciation in its purest form: first there was a homogeneous gene pool spread over a varied habitat, then the gene pool started to curdle and got lumpy.
Victoria s Blue Genes
Authors: Schilthuizen Menno
Published: November 2023

In the early nineteenth century, King Mwangonde walked from his home town to the village of Mwela to marry Mapunda. To do this, he crossed a plain that today lies submerged beneath the clear waters of Lake Malawi, the southern-most of the three large East African lakes, dubbed the Great Lakes. In 1894, a traveller named Swann saw gigantic trees growing in the water near the shores of the lake. And in 1983, the centenarian chief Moses Ngosi told a British diplomat that his grandparents used to talk about a sunken village that lay an hour’s walk lakewards from the present-day Ruasho River delta. Historical records like these confirm what geologists now know for a fact: the water level of Lake Malawi has risen by some 120 metres in the past two centuries.
Mystery? What Mystery?
Authors: Schilthuizen Menno
Published: November 2023

Douglas Futuyma, whose 1980 criticisms set off the second and fruitful wave of Rhagoletis investigations, as Chapter 6 recounts, once wrote that speciation is ‘more thoroughly awash in unfounded and often contradictory speculation than any other single topic in evolutionary theory’. We know a thing or two about that. In this book, we have had our share of contradiction and speculation. Just think of the debate about bottlenecks, the controversy surrounding sympatric speciation, and the speculations about instant speciation. In fact, speciation research has always had a strange and somewhat disturbing obsession with emphasizing and classifying the differences between the various theories, perhaps because the field emerged from taxonomy, the branch of biology whose business it is to name and classify things.
Integrable subsystems of Hamiltonian equations and Lax-integrable equations
Authors: Kuksin Sergei B
Published: November 2023

Quasilinear Hamiltonian PDEs with analytic coefficients have the form (2.1), where O  d usually equals the whole space Z  d and the gradient map ∇H is analytic of some order d  H for all sufficiently smooth spaces Z  d. The following three examples and their perturbations will be referred to constantly throughout the book.
Finite-gap manifolds for the KdV equation and theta formulas
Authors: Kuksin Sergei B
Published: November 2023

The approach to studying finite-gap manifolds we develop in this section is rather general. In the next section we apply it to the Sine–Gordon equation.
The Sine-Gordon equation
Authors: Kuksin Sergei B
Published: November 2023

In this chapter we consider the SG equation under periodic and even periodic boundary conditions (see Example 2.3 in Section 2.1). The results are parallel to the KdV case and our presentation is much shorter. Missing details can be found in McKean (1981), Belokolos et al. (1994), Bikbaev and Kuksin (1992), and Bobenko and Kuksin (1995a).
The normal form
Authors: Kuksin Sergei B
Published: November 2023

We continue to study the Hamiltonian equation (5.1) near an invariant manifold T  2n = Ф0(R × T  n which possesses the properties 1-5 as in Section 5.1.
Examples
Authors: Kuksin Sergei B
Published: November 2023

To get the result we used Theorem 8.1, its Amplification, and Theorem 8.2. The last theorem applies since the linearized KdV equation is uniformly well defined due to arguments in Example 1.6 (see (1.13)).
Linearized equations
Authors: Kuksin Sergei B
Published: November 2023

In this chapter we consider linearization of eqns (10.3) about any solution bo(t), constructed in Theorem 8.3, and prove in Theorem 8.4.
Forensic applications of microsatellite markers
Authors: Balding David
Published: November 2023

The application of microsatellite (or Short Tandem Repeat, STR) loci to problems in forensic science is reviewed, starting with a brief historical overview pointing out limitations of earlier forensic typing methods. The interpretation of STR profiles in terms of evidential weight is emphasized, leading to match probability calculations, which allow for relatedness and population genetic effects. The situation in which a single defendant is alleged to be the source of a crime scene STR profile is discussed in some detail, including a worked example typical of recent UK casework. In addition, there is a shorter discussion of more complex scenarios, in which paternity, or other relatedness, is investigated, or where the crime scene STR profile reflects the DNA of more than one individual (a so-called 'mixed' profile).
A hundred thousand reasons for being different
Authors: Little Peter
Published: November 2023

Even if Jeanne and Jean had possessed identical gene differences, the circumstances of their existence are so different that it is impossible to expect an equal outcome to both of their lives. But, of course, both Jean and Jeanne are not identical genetically and many DNA differences distinguish them; their cumulative effects will also contribute to their different future histories. These two influences are the reason why the life of one is a dream and that of the other a nightmare.
Genes and the mind
Authors: Little Peter
Published: November 2023

We can now begin to understand why Jeanne and Jean are physically so different—because both their gene differences and their environments have made them so. We could easily have spent a great deal of time discussing what is understood about how genes control our development and how this might be modulated by our environment and our gene differences, but this would really only tell us what we already know: that genes are important in defining our body plan.
Hierarchical Models for DNA Profiling Using Heterogeneous Databases
Authors: Dawid A Philip , Pueschel John
Published: November 2023

We consider forensic inference from DNA identification evidence, based on the “match probability”, for a genetically heterogeneous population. The genetic structure of the population is represented by a hierarchical model. Careful attention is given to the definition and use of the match probability, to the specification of appropriate parameters in its definition, and to the correct Bayesian method for inference about it. Errors in previously published analyses are identified. We reanalyse a UK database of DNA profiles, using MCMC methods, and compare the results of the correct and incorrect approaches.
Another Look at Conditionally Gaussian Markov Random Fields
Authors: Lavine Michael
Published: November 2023

This paper shows that a Markov random field prior on a lattice is identical to the posterior from a particular dynamic linear model updated with a particular data set Y. This opens the possibility of using dynamic linear model ideas, notably a computational algorithm, in the Markov random field setting.
Convergence Assessment for Reversible Jump MCMC Simulations
Authors: Brooks Stephen P , Giudici Paolo
Published: November 2023

The this paper we discuss the problem of assessing convergence of reversible jump MCMC algorithms on the basis of simulation output. We discuss the various direct approaches which could be employed, together with their associated drawbacks. Using the example of fitting a graphical Gaussian model via RJMCMC, we show how the simulation output for models which can be parameterised so that parameters of primary interest retain a coherent interpretation throughout the simulation, can be used to assess convergence. In the context of this example, we extend the work of Gelman and Rubin (1992) and Brooks and Gelman (1998), to provide convergence assessment procedures for graphical model determination problems, but which may be applied to any form of model choice problem and, indeed, MCMC simulations more generally.
Amygdala plasticity: the neurobiological implications of kindling
Authors: Weiss Susan R B , Li1 He , Sitcoske-O’Shea Martina , Post R M
Published: November 2023

In this chapter, we discuss how observations from the amygdala kindling model may offer clues about neuroplasticity in the amygdala and related limbic structures. Kindled seizures can be induced gradually and under precise experimental control, thus allowing detailed study of the emerging expression of what we believe to be a highly conserved neural plasticity. We suggest that delineation of the cellular mechanisms underlying kindling may reveal substrates of plasticity operative in non-epileptic situations ranging from normal memory formation to evolving, pathological neuropsychiatric conditions.
Myosins
Authors: Sellers James R
Published: November 2023

Myosins are a diverse superfamily of molecular motor proteins, which share the ability to reversibly bind actin and hydrolyse MgATP. They are capable of either translocating actin filaments or translocating vesicles or other cargo on fixed actin filaments. There are currently 15 distinct classes in the myosins superfamily, based on sequence homology. Myosin II and myosin I proteins are familiar and well studied; while Classes III-XV are less well characterized. All myosins examined to date are multimeric and appear to possess at least three functional domains, a head, neck, and tail. Myosins (second edition) explores the structure and functional properties of myosins, their regulation, and mutational analysis. It has been thoroughly updated since the first edition was published in 1995 including sections on the three additional classes defined by new sequences, information provided by the crystal structure of seven new Dicytostelium motor domains, and data from new techniques such as molecular imaging and tagging proteins with GFP 20. The three human diseases that are now known to be linked to mutations in different myosin heavy or light chains are also covered, including more than 50 mutations associated with hyperotrophic cardiomyopathy.
Some nonlinear PDE’s in the theory of flame propagation
Authors: Bcrestycki Henri
Published: November 2023

The modelling of flame propagation involves fluid mechanics equations, chemi cal kinetics, molecular diffusion and heat conductivity. Therefore, in view of the complexity of an exhaustive description, it is customary, even in practical situ ations, to consider simplified models where one aspect or another of the system is more particularly emphasized.
Propagation of cracks in elastic media
Authors: Friedman Avner
Published: November 2023

This result shows that the variational principle (for smooth cracks) is equivalent to the more traditional description of mode I and mode II cracks. The proof of Theorem 2.1 is based on new maximum principles for biharmonic functions in domains with corners, and some “blow up” arguments.
On the numerical solution of partial differential equations in unbounded domains
Authors: Friedman Avner
Published: November 2023

A longstanding issue in the numerical solution of partial differential equations concerns the reduction of an unbounded domain to a bounded domain by the imposition of nonreflecting boundary conditions at an artificial boundary. This issue arises, for example, in electromagnetic and acoustic scattering, computational fluid dynamics, crystal growth, astrophysics, elasticity, and computational chemistry. In this paper, we will briefly review recent progress in the development of fast integral equation methods for solving the most basic partial differential equations of mathematical physics: the canonical hyperbolic, parabolic and elliptic equations
Computational analysis of turbulence — description by low-pressure vortices
Authors: kida Shigeo
Published: November 2023

The dynamics of such complicated flows may be studied in two steps. First, the flow structure is watched carefully. Because explicit analytical solutions are known only for some simple cases, numerical solutions are indispensable to get a concrete picture of flow structure. Then, the dynamics is analysed based on the equations of motion. Understanding of the dynamics of fluid motion is extremely hard without knowledge of the structure.
What is quantum computation?
Authors: Popescu Sando
Published: November 2023

Only fifty years had passed from the first electronic computer, a monster weighting a couple of tonnes and capable of performing a few operations per second to a computer capable of competing with the best human being at chess. As you might recall, on this particular occasion Kasparov won, but only a year later Deep Blue defeated the world champion.
Quasi Monte Carlo methods for financial applications
Authors: Tezuka Shu
Published: November 2023

Monte Carlo simulations arc a common technique in finance, particularly in derivative pricing and in VaR (Value at Risk) computations, since they are sim ple to understand and to implement. In the area of derivative pricing, stochastic differential equations have been widely used as a modeling tool to describe the time evolution of the price of the underlying financial asset. The more com plex stochastic models become, the less available analytical solutions are. Thus, Monte Carlo simulations are viewed as a last resort for the computation involved in these applications.
Fluid Dynamics in 3-D Models of Cavopulmonary Connection with an Extracardiac Lateral Conduit
Authors: Migliavacca F , Leval M R de , Dubini G , Pietrabiss R , Fumero R
Published: November 2023

In recent years refinements of the Fontan procedure have been widely described. Since the original aorta-pulmonary conduit performed for the first time by Fontan and Baudet [1], modifications have included the insertion of an intraatrial lateral tubular PTFE baffle [2] with or without fenestration and, at the beginning of the nineties, the construction of a new form of a right bypass: inferior vena cava-pulmonary artery extracardiac conduit [3]. Computational fluid dynamics (CFD) have been used to evaluate the haemo dynamics of total cavopulmonary connection (TCPC) with an intraatrial tunnel and to refine the surgical procedure [4] and [5].
Experimental and Computational Modelling of Flow through an Arterial Bypass Graft
Authors: Bates C J , Williams D , O’Doherty D M
Published: November 2023

Distorted mean velocity and turbulence intensity profiles in the horizontal plane of a 30° Y junction at various Reynolds numbers show the significance of the graft geometry and flow conditions on the localisation of atherosclerosis and intimal hyperplasia. Fluctuating wall shear stresses in the graft, which are associated with disturbed flow, are believed to be important factors in the development and localisation of intimal hyperplasia. Atherosclerosis is a common disease in men and women over 60 years old. It is a disease that commences early in life. A study of American soldiers killed in action in Korea whose average age was 22.1 years old revealed that 77% of the hearts autopsied showed gross evidence of coronary atherosclerosis. Atherosclerosis results from the build up of plaques or fatty deposits, which can cause a critical reduction in the cross sectional area of the blood vessels. The result is a reduction in the circulation of blood to a symptomatic level. Symptoms of the disease include pain and ischemia. One example of this disease is plaque build up in the carotid arteries that reduces the flow of blood to the brain and eventually leads to a stroke. Similarly, obstruction of the blood flow through the coronary arteries can result in a heart attack. The surgical treatment of atherosclerosis includes angioplasty and arterial bypass grafts. Angioplasty is not a suitable treatment if there are more than three occluded vessels. In such patients, the surgeon can perform bypass surgery to improve the flow of blood through the artery. At present arterial bypass graft is a routine and effective re-constructive vascular surgery treating occlusive arterial disease.
Hemorheological Alterations After Percutaneous Transluminal Coronary Angioplasty
Authors: Kesmarky G , Toth K , Vajda* G , Habon* L , Halmosi R , Habon T , Roth E
Published: November 2023

Percutaneous transluminal coronary angioplasty (PTCA) is a widely used method for the treatment of coronary artery disease. During this procedure several changes in blood flow occur due to coronary stenosis, endothelial injury, and ischemia-reperfusion caused by the balloon inflation/deflation. In our study 20 patients (mean age 58 ± 9 years) undergoing PTCA were examined. Percutaneous transluminal coronary angioplasty (PTCA) is a widely used method in the treatment of significant coronary stenoses. The high (30-40%) ratio of reocclusion and restenosis is the main challenge of this procedure.
The Formalization of Intuitionistic Logic
Authors: Dummett Michael
Published: November 2023

A natural deduction system is a formalization of logic in which no formulas are axiomatically assumed as valid, but there are only rules of inference. To compensate for the lack of axioms, it is permitted to introduce any formula as a hypothesis at any stage. Most rules of inference will present the conclusion as depending on all hypotheses on which any of the premisses depends; but there will be some rules which discharge hypotheses (in the sense that the conclusion of the rule no longer depends on the hypothesis discharged).
Some Further Topics
Authors: Dummett Michael
Published: November 2023

So far we have discussed various principles which may be taken as axiomatic in intuitionistic mathematics, without attempting to delineate any actual formalizations of intuitionistic theories. This is appropriate to the subject. For the Hilbert school, and for formalists properly so called, formalization is integral to an exact treatment of mathematics; but the original impulse to formalization did not come from them, but from the logicists, for whom the formalization of a theory was a necessary means of identifying its basic principles, so that they could then show these to be derivable from pure logic. The intuitionists, on the other hand, were from the start hostile to formalization: for them, it is highly unlikely that the mental constructions intuitively recognizable as proving a statement of a given theory should be isomorphic to the formal proofs of any calculus, recognizable as such by a mechanical procedure making no appeal to meaning.
Why Did the Germans Not Make the Bomb?*
Authors: Perutz Max F
Published: November 2023

Did the German physicists make no atomic bombs during the Second World War because they wouldn’t or because they couldn’t? This is a question finally answered by the recent publication of the secretly recorded conversations between Heisenberg and the other German atomic physicists interned at Farm Hall, near Huntingdon, in England in the summer of 1945. Heisenberg’s leading role among German physicists stems from the revolutionary mathematical theory which he formulated at the age of 24.
The Battle Over Vitamin C*
Authors: Perutz Max F
Published: November 2023

Albert Szent-Györgyi was a flamboyant Hungarian biochemist, famous for having isolated vitamin C and for other important discoveries. He was born in Budapest in 1893, lived in Europe through two world wars, and then spent the remainder of his long life at Woods Hole on Cape Cod, where he died in October 1986. His name is the Hungarian for Saint George, whom he tried to emulate when he attempted single-handedly to save his country from the Nazi and Soviet dragons. Albert Szent-Gyorgyi was the son of a landowner who spent his time “thinking about the sheep, the hogs and manure” and of a sensitive, musical mother who was descended from a family of distinguished academics.
What Holds Molecules Together?
Authors: Perutz Max F
Published: November 2023

Like Michael Faraday, Linus Pauling was born poor; he struggled at menial jobs to support himself at high school and while studying for a degree in chemical engineering at the Oregon Agricultural College. All the same, he became interested in the electron theory of valence when he was only eighteen, and after this he “continued to hope that the empirical information about the properties of substances could eventually be encompassed in a theory of the structure of molecules:’ Fulfillment of his hope began to take shape in 1926 when he spent a postdoctoral year at Munich with Germany’s greatest teacher of theoretical physics, Arnold Sommer field, just as Erwin Schrodinger published his first papers on wave mechanics.
I Wish I’d Made You Angry Earlier
Authors: Perutz Max F
Published: November 2023

Fifty years ago, the great unsolved problem of biology seemed to be the structure of proteins. Bill Astbury, a physicist and X-ray crystallographer working for the Wool Research Association in Leeds (United Kingdom), discovered that the fibrous protein keratin, found in wool, horn, nails, and muscle, gave a common X-ray diffraction pattern consisting of just two reflections, a meridional one at 5.1 Å and an equatorial one at 9.8 Å
Dangerous Misprints*
Authors: Perutz Max F
Published: November 2023

Watson and Crick’s famous double helix showed how the genetic information is written on DNA and how it is copied every time cell divides. Some years after this, scientists also deciphered the genetic code. Occasionally, very rarely in fact, an error occurs in the copying of the message that makes up a gene. Even more rarely, such an error manifests itself in a malfunction or absence of the protein specified by that gene, and gives rise to a congenital disease. Such an error occurred in Queen Victoria who carried the gene for haemophilia which surfaced in some of her male descendants as a malfunctioning of a protein needed for the clotting of blood; consequently several of them bled to death.
A Deadly Inheritance*
Authors: Perutz Max F
Published: November 2023

This is the story of a Jewish paediatrician at the Harvard Medical School in Boston who saved the life of Dayem, a small Iranian Arab boy afflicted with a deadly inherited anaemia. In the course of 26 years of treatment David Nathan transformed the boy from a dwarfed, grotesquely hideous cripple to a good-looking, active, independent businessman and ban vivant. Dayem suffers from thalassaemia, a disease due to defective synthesis of haemoglobin, the protein of the red blood cells that transports oxygen from the lungs to the tissues and helps the return transport of carbon dioxide from the tissues back to the lungs. His red cells contained too little haemoglobin, and even that little haemoglobin was liable to precipitate and lead to the cells’ premature destruction.
By What Right Do We Invoke Human Rights?1
Authors: Perutz Max F
Published: November 2023

Scientists the world over are united by a common purpose, ideally to discover Nature’s secrets and put them to use for human benefit. Albert Szent-Györgyi, the discoverer of vitamin C, has said: “I feel closer to a Chinese colleague than to my own postman.” When a scientist who has committed no crime is imprisoned, we feel like the minister freeing the prisoners in Fidelio when he sings:
Swords into Ploughshares: Does Nuclear Energy Endanger Us? *
Authors: Perutz Max F
Published: November 2023

Here in Britain we are all criminals: guilty of conniving at a crime against humanity committed by a government that is polluting the Irish Sea, the British Isles, and the entire globe with the radioactive discharges from its nuclear plants at Sellafield, a village in northwest England on the Irish Sea. According to Marilynne Robinson, the author of the book Mother Country: Britain, the Welfare State and Nuclear Proliferation, “The earth has been under nuclear attack [from Sellafield] for almost half a century.”
Introduction
Authors: Ewald William
Published: November 2023

The first period gave us Aristotle and Euclid, Plato and Pythagoras, Zeno and Archimedes; irrational numbers, paradoxes of motion, mathematical proofs, axioms of geometry, syllogistic logic-indeed, it furnishes the groundwork for all that was to follow. This period has been intensively studied, and its contours are well known.
Colin MacLaurin (1698-1746)
Authors: Ewald William
Published: November 2023

Far the ablest reply to Berkeley’s Analyst was A treatise of fluxions (2 vols, 1742) by the Edinburgh mathematician and disciple of Newton, Colin MacLaurin. Until the appearance of Cauchy’s Cours d’analyse in 1821 (and apart from the researches of Bolzano, which were unknown) this work represented the high point of mathematical rigour in the foundations of the calculus.
Immanuel Kant (1724-1804)
Authors: Ewald William
Published: November 2023

Kant was the most influential philosopher of mathematics in modern times, and his Critique of pure reason to a considerable extent set the agenda for the philosophy of mathematics of the next century; the impact of his thought and of the reactions to it can be detected in most of the selections that follow.
Johann Heinrich Lambert (1728-1777)
Authors: Ewald William
Published: November 2023

Lambert’s principal contribution to the philosophy of mathematics is his discussion of the status of the Axiom of Parallels-a discussion which raises issues that will be encountered in the selections from Gauss, Riemann, von Helmholtz, Klein, Poincare, and Hilbert.
Bernard Bolzano (1781-1848)
Authors: Ewald William
Published: November 2023

Bolzano’s writing mark a turning-point in research on the foundations of mathematics-a transition from the mathematical style of the eighteenth century to that of the nineteenth.
Arthur Cayley (1821-1895)
Authors: Ewald William
Published: November 2023

Cayley was educated at Trinity College, Cambridge, which elected him to a Fellowship in 1842. He resigned after three years to enter Lincoln’s Inn; from 1849 to 1863 he practised law in London.
Georg Friedrich Bernhard Riemann (1826-1866)
Authors: Ewald William
Published: November 2023

The last few selections have dealt with algebra and its applications to logic, topics that were pursued largely by mathematicians in Britain and America. With Riemann we turn to the intellectual world of late nineteenth-century Germany, and to geometry. Previous selections-especially those from Kant, Lambert, Bolzano, and Gauss-have already broached the main traditional problems of the foundations of geometry.
Hermann von Helmholtz (1821-1894)
Authors: Ewald William
Published: November 2023

Helmholtz was the most celebrated scientist of late nineteenth-century Germany. As the director of major research laboratories, as Rector of the University of Berlin, and as a brilliant popular lecturer on scientific subjects, he had an immense influence on German and European intellectual life; his style of thought influenced several generations of scientists. He laid the foundations for modern physiological optics and acoustics; he was closely studied by Pavlov; his work in theoretical physics influenced Maxwell, Kelvin, Planck, Boltzmann, and Heinrich Hertz; his writings on the nature of space and on non-Euclidean geometry prepared the way for Einstein.
Christian Felix Klein (1849-1925)
Authors: Ewald William
Published: November 2023

Like Kronecker, Felix Klein was a major voice raising misgivings about the tendency in nineteenth-century mathematics known as the arithmetizing of the continuum. Gauss and Cauchy, Bolzano and Dirichlet, Weierstrass, Heine, Cantor, Dedekind, Peano, and others had laboured throughout the century to put the theory of real numbers on a strictly arithmetical.
Luitzen Egbertus Jean Brouwer (1881-1966)
Authors: Ewald William
Published: November 2023

Brouwer, the father of intuitionism, was the most eminent Dutch mathematician of the twentieth century; he lived in Holland all his life. He was educated at the University of Amsterdam, where he studied mathematics and philosophy, and where he obtained the degree of Doctor in Mathematics and Physics;
Animals and trees
Authors: Janse van Rensburg E J
Published: November 2023

In this chapter the limiting free energies and density functions of interacting models of lattice trees and animals will be considered.1 The first issues are the existence of growth constants, density functions and a pattern theorem. The adsorption of trees will also be considered, and finally the uniform embeddings of graphs, and their relations to walks and polygons in confined geometries will be discussed in Section 6.6.
Lattice vesicles and surfaces
Authors: Janse van Rensburg E J
Published: November 2023

In this chapter models of vesicles and surfaces will be examined. A general pattern theorem is not known for these models, although a very limited version of such a theorem has been proven [189]. This will be discussed in Section 7.5. In Section 7.2 two-dimensional models of vesicles are examined. These are square lattice polygons, counted by area, and lead naturally to the notion of a disk. Punctured disks are examined in Section 7.3, where the existence of growth constants, limiting free energies and density functions, and the asymptotic behaviour in these models are of particular interest.
The Hypergeometric Class Of Equations
Authors: Slavyanov Sergei yu. , Lay Wolfgang , Seeger Alfred
Published: November 2023

The hypergeometric class of second-order linear ODEs is generated by the Riemann equation-the Fuchsian equation with three singularities. It includes five types of equations which are considered mainly in their standard forms:

i. The generating hypergeometric equation (hE).

ii. Two types of confluent equations which we call the confluent hypergeometric equation (ChE) and biconfluent hypergeometric equation (BhE).

iii. Two types of reduced confluent equations which we caU reduced confluent hypergeometric equation (RChE) and reduced biconfluent hypergeometric equation (RBhE).
The fleeces of Spain
Authors: Wood Roger J , Orel Vítêzslav
Published: November 2023

Every lively debate on the nature of heredity taking place in the Brno Sheep Breeders’ Society, from its foundation in 1814 and for nearly three decades afterwards, owed its origin to a particular development in international trade. The entry of top quality Spanish Merino breeding stock into Moravia and neighbouring territories after 1775 had provided the essential basis on which production of fine woollen cloth could be greatly expanded there.
The sheep breeders’ legacy to Mendel
Authors: Wood Roger J , Orel Vítêzslav
Published: November 2023

We have presented C.C. Andre as an individual responsible for shaping an intellectual and organisational environment in which many others were able to express valuable talents. It was through his vision with its international scope that breeding began to emerge from an art to a science in Moravia.
Foundations
Authors: Darrigol Olivier
Published: November 2023

In the early nineteenth century electricity was already a wide research field, with diverse methods and multiple disciplinary connections. The oldest and best understood part of the subject was frictional electricity, especially its distribution over conductors and its mechanical effects. In his celebrated memoirs of the 1780s, Charles Coulomb, a military engineer, had founded quantitative electrostatics (later named so by Ampere). He posited two electric fluids, positive and negative, asserted the inverse square law by means of his celebrated torsion balance, and developed its consequences for the equilibrium of conductors in simple configurations. In 1812 Simeon Denis Poisson, one of the first polytechniciens, completed the mathematical apparatus of Coulomb’s theory. He borrowed from Lagrange’s and Laplace’s works on gravitation what we now call the potential (V), wrote the corresponding differential equation (ΔV + 4πρ = 0, where ρ is the charge density), solved it in simple cases, and improved the agreement of the theory with Coulomb’s experimental results.
German precision
Authors: Darrigol Olivier
Published: November 2023

Until the 1830s, most German physics consisted of an empirical, qualitative extension of major foreign discoveries such as Volta’s pile or Oersted’s effect. Favorite topics were the composition of the pile and the circumstances of the electromagnetic action. The most famous instrument then invented in Germany was Schweigger’s and Poggendorff’s ‘multiplicator,’ a coil that amplified the effect of the galvanic current on the magnetic needle. This device soon became an essential part of galvanometers–though not in the hands of its German inventors, who cared little about quantitative measurement.
British fields
Authors: Darrigol Olivier
Published: November 2023

In the first two decades of the nineteenth century, opinions on the nature of electric and magnetic actions still varied, especially in England and in Germany. There even were traces of the eighteenth century ‘atmospheres,’ invented to avoid direct action at a distance. After Ampere’s electrodynamics and its German extensions, however, the hegemony of Newtonian fluid theories spread from France to other countries. The penetration of the methods of French mathematical physics favored the most readily quantifiable representations of phenomena, and diverted attention from more qualitative notions.’
British Maxwellians
Authors: Darrigol Olivier
Published: November 2023

Maxwell’s electromagnetic theory remained a private enterprise until the early 1870s. The situation began to change after Maxwell’s appointment at the head of the new Cavendish Laboratory in 1871 and the publication of the Treatise in 1873. This was a slow process, because the Treatise was ‘a very hard nut to crack’ even to Cambridge wranglers, and because in his new capacity Maxwell could not effectively direct theoretical researches. Yet some English-speaking students of electromagnetism, in Cambridge and elsewhere, were now exposed to the new doctrine. Some of them became Maxwell’s disciples and apostles.1
Background Material
Authors: Joyce Dominic D
Published: November 2023

In this chapter we explain some background necessary for understanding the rest of the book. We shall assume that the reader is already familiar with the basic ideas of differential and Riemannian geometry (in particular, manifolds, tensors, and Riemannian metrics) and of algebraic topology (in particular, fundamental group, homology and cohomology).
The Calabi Conjecture
Authors: Joyce Dominic D
Published: November 2023

Let (M, J) be a compact, complex manifold, and g a Kähler metric on M , with Ricci form ρ From §4.6 we know that ρ is a closed (1,1)-form and [ρ] = 2π c1(M) ∈ H 2(M, R). It is natural to ask which closed (1,1)-forms can be the Ricci forms of a K ähler metric on M . The Calabi conjecture [49, 50] answers this question.