The gravitational equations were derived in general relativity using the assumption of their covariance relative to arbitrary transformations of coordinates. It has been repeatedly expressed an opinion over the past century that such equality of all coordinate systems may not correspond to reality. Nevertheless, no actual verification of the necessity of this assumption has been made to date. The paper proposes a theory of gravity with a constraint, the degenerate variants of which are general relativity and the unimodular theory of (...) gravity. This constraint is interpreted from a physical point of view as a sufficient condition for the adiabaticity of the process of the evolution of the space–time metric. The original equations of the theory of gravity with the constraint are formulated. On this basis, a unified model of the evolution of the modern, early, and very early Universe is constructed that is consistent with the observational astronomical data but does not require the hypotheses of the existence of dark energy, dark matter or inflatons. It is claimed that: physical time is anisotropic, the gravitational field is the main source of energy of the Universe, the maximum global energy density in the Universe was 64 orders of magnitude smaller the Planckian one, and the entropy density is 18 orders of magnitude higher the value predicted by GR. The value of the relative density of neutrinos at the present time and the maximum temperature of matter in the early Universe are calculated. The wave equation of the gravitational field is formulated, its solution is found, and the nonstationary wave function of the very early Universe is constructed. It is shown that the birth of the Universe was random. (shrink)

Let K be affine, that is, \\in {\mathbb {R}}^{n+m}: y_{1}=\cdots =y_{m}=0\}\). We compute the sharp constant of Hardy inequality related to the distance d for polyharmonic operator. Moreover, we show that there exists a constant \ such that for each \\), there holds $$\begin{aligned} \int _{{\mathbb {R}}^{n+m}}|\nabla ^{k} u|^{2}\mathrm{d}x\mathrm{d}y-c_{m,k}\int _{{\mathbb {R}}^{n+m}}\frac{u^{2}}{|y|^{2k}}\mathrm{d}x\mathrm{d}y\ge C\left ^{\frac{n+m-2k}{n+m}}, \end{aligned}$$where \, \}{n+m-2k}\), \p}{2}-n-m\) and \ is the sharp Hardy constant. These inequalities generalize the result of Maz’ya ) and Lu and the second author for polyharmonic operators). (...) In order to prove the main result, we establish some Poincaré–Sobolev inequalities on hyperbolic space which is of independent interest. (shrink)

In this paper we study computability of the solutions of the Korteweg-de Vries equation ut + uux + uxxx = 0. This is one of the open problems posted by Pour-El and Richards [25]. Based on Bourgain's new approach to the initial value problem for the KdV equation in the periodic case, we show that the periodic solution u of the KdV equation is computable if the initial data is computable.

The theory of Lebesgue and Sobolev spaces with variable integrability is experiencing a steady expansion, and is the subject of much vigorous research by functional analysts, function-space analysts and specialists in nonlinear analysis. These spaces have attracted attention not only because of their intrinsic mathematical importance as natural, interesting examples of non-rearrangement invariant function spaces but also in view of their applications, which include the mathematical modeling of electrorheological fluids and image restoration.The main focus of this book is (...) to provide a solid functional analytic background for the study of differential operators on spaces with variable integrability. It includes some novel stability phenomena which the authors have recently discovered.At the present time, this is the only book which focuses systematically on differential operators on spaces with variable integrability. The authors present a concise, natural introduction to the basic material and steadily move toward differential operators on these spaces, leading the reader quickly to current research topics. (shrink)

As is well known the derivative of a computable and C1 function may not be computable. For a computable and C∞ function f, the sequence {f} of its derivatives may fail to be computable as a sequence, even though its derivative of any order is computable. In this paper we present a necessary and sufficient condition for the sequence {f} of derivatives of a computable and C∞ function f to be computable. We also give a sharp regularity condition on an (...) initial computable function f which insures the computability of its derivative f′. (shrink)

Consumers’ engagement in morally-questionable behaviors poses a serious threat to firms. To further the understanding of consumers’ behavior, this study explores the association and conflicts between their ethical and legal judgments. In addition, it examines the way consumers’ judgments depend on their mind-sets and the legal liability criterion of action. In two experiments, participants were asked to judge the ethicality and legality of consumers’ morally-questionable behaviors. Behavior activity and participants’ mind-sets were manipulated. The results show that consumers are more likely (...) to judge a behavior to be legal when they consider it ethical than when they consider it unethical. Nevertheless, conflicts between ethical and legal judgments are prevalent. Furthermore, ethical judgments, legal judgments, and the occurrence of conflicts between them depend on activity and on consumers’ mind-sets. Finally, consumers report uncertainty about the ethicality and legality of a wide range of morally-questionable behaviors. Thus, the results paint a picture of individuals who perceive the law to be often beyond their reach or in conflict with their ethical principles. They portray both ethical and legal judgments as dynamically-changing, subjective, and context-dependent. Theoretical contribution and business applications are discussed. (shrink)

A major problem in the treatment of cancer is the specific targeting of anti‐tumor drugs to these abnormal cells. Ideally, such a drug should act over short distances to minimize damage to healthy cells, and target subcellular compartments that have the highest sensitivity to the drug. Photosensitizers, alpha‐emitting radionuclides and many other medicines could be considered as such drugs if they possessed cellular and subcellular specificity. The author describes a novel approach of using modular recombinant transporters to target photosensitizers and (...) alpha‐emitting radionuclides to the nucleus, where their action is most pronounced, of cancer cells. Photosensitizer‐transporter conjugates have up to 3000 times greater efficacy than free photosensitizers and display cell specificity in contrast to free photosensitizers. Alpha‐emitting radionuclides, conjugated with the modular transporters, acquired similar properties. The different modules of the transporters are interchangeable, meaning that they can be tailored for particular applications. BioEssays 30:278–287, 2008. © 2008 Wiley Periodicals, Inc. (shrink)

Space tourism is an emerging field where few people have direct experience. However, considering the potential in the near future, it is beneficial to better understand how related information influences people’s attitudes about this new form of tourism. Employing information-processing-based Bayesian Mindsponge Framework (BMF) analytics on a dataset of 361 respondents consuming content related to space tourism on Chinese social media, we found that induced happiness and impression are positively associated with willingness to try space tourism. Information (...) authenticity positively moderates these two associations. Our findings emphasize three aspects of information during the processes of reception and filtering: meaning, intensity, and trust. Since promotional materials for space tourism rely heavily on mental simulations rather than objective feedback, creative uses of digital technology are advantageous. However, precautions must be taken to prevent exploitation, such as false advertising, exaggeration, and emotional manipulation. (shrink)

Journal of Political Philosophy, EarlyView.

One of central problems in the theory of conditionals is the construction of a probability space, where conditionals can be interpreted as events and assigned probabilities. The problem has been given a technical formulation by van Fraassen (23), who also discussed in great detail the solution in the form of Stalnaker Bernoulli spaces. These spaces are very complex – they have the cardinality of the continuum, even if the language is finite. A natural question is, therefore, whether a technically (...) simpler (in particular finite) partial construction can be given. In the paper we provide a new solution to the problem. We show how to construct a finite probability space $$\mathrm {S}^\#=\left(\mathrm\Omega^\#,\mathrm\Sigma^\#,\mathrm P^\#\right)$$ S # = Ω #, Σ #, P # in which simple conditionals and their Boolean combinations can be interpreted. The structure is minimal in terms of cardinality within a certain, naturally defined class of models – an interesting side-effect is an estimate of the number of non-equivalent propositions in the conditional language. We demand that the structure satisfy certain natural assumptions concerning the logic and semantics of conditionals and also that it satisfy PCCP. The construction can be easily iterated, producing interpretations for conditionals of arbitrary complexity. (shrink)

The purpose of the two studies reported here was to develop an integrated model of the scientific reasoning process. Subjects were placed in a simulated scientific discovery context by first teaching them how to use an electronic device and then asking them to discover how a hitherto unencountered function worked. To do this task, subjects had to formulate hypotheses based on their prior knowledge, conduct experiments, and evaluate the results of their experiments. In the first study, using 20 adult subjects, (...) we identified two main strategies that subjects used to generate new hypotheses. One strategy was to search memory and the other was to generalize from the results of previous experiments. We described the former group as searching an hypothesis space, and the latter as searching an experiment space. In a second study, with 10 adults, we investigated how subjects search the hypothesis space by instructing them to state all the hypotheses that they could think of prior to conducting any experiments. Following this phase, subjects were then allowed to conduct experiments. Subjects who could not think of the correct rule in the hypothesis generation phase discovered the correct rule only by generalizing from the results of experiments in the experimental phase.Both studies provide support for the view that scientific reasoning can be characterized as search in two problem spaces. By extending Simon and Lea's (1974) Generalized Rule Inducer, we present a general model of Scientific Discovery as Dual Search (SDDS) that shows how search in two problem spaces (an hypothesis space and an experiment space) shapes hypothesis generation, experimental design, and the evaluation of hypotheses. The model also shows how these processes interact with each other. Finally, we interpret earlier findings about the psychology of scientific reasoning in terms of the SDDS model. (shrink)

The nature of matter was as intriguing a question for ancient philosophers as it is for contemporary physicists, and Matter, Space, and Motion presents a fresh and illuminating account of the rich legacy of the physical theories of the Greeks from the fifth century B.C. to the late sixth century A.D.

In Decision Space: Multidimensional Utility Analysis, first published in 2001, Paul Weirich increases the power and versatility of utility analysis and in the process advances decision theory. Combining traditional and novel methods of option evaluation into one systematic method of analysis, multidimensional utility analysis is a valuable tool. It provides formulations of important decision principles, such as the principle to maximize expected utility; enriches decision theory in solving recalcitrant decision problems; and provides in particular for the cases in which (...) an expert must make a decision for a group of people. The multiple dimensions of this analysis create a decision space broad enough to accommodate all factors affecting an option's utility. The book will be of interest to advanced students and professionals working in the subject of decision theory, as well as to economists and other social scientists. (shrink)

The geometry of the state space of a finite-dimensional quantum mechanical system, with particular reference to four dimensions, is studied. Many novel features, not evident in the two-dimensional space of a single spin, are found. Although the state space is a convex set, it is not a ball, and its boundary contains mixed states in addition to the pure states, which form a low-dimensional submanifold. The appropriate language to describe the role of the observer is that of (...) flag manifolds. (shrink)

The aim of this book is to give an account of Einstein's work without introducing anything very technical in the way of mathematics, physics, or philosophy.

Climate change is one of the most pressing issues facing humanity and has become an area of growing focus in Business & Society. Looking back and reviewing climate change discussion within this journal highlights the importance of time and space in addressing the climate crisis. Looking forward, we extend existing research by theorizing and politicizing the co-implication of time and space through the concept of “space-time.” To illustrate this, we employ the logical structure of “the trace” to (...) advance business and society scholarship on climate change by shifting the focus to a place-bound emphasis on climate impacts and directing scholarship toward climate change’s temporal markers and material effects. By operationalizing “the trace,” we contribute to Business & Society debates in three ways: reimagining complex stakeholder relations, advancing a performative understanding of climate risk, and foregrounding planetary systems and the physical environment. (shrink)

Quantum Theory, similar to Relativity Theory, requires a new concept of space-time, imposed by a universal constant. While velocity of lightcnot being infinite calls for a redefinition of space-time on large and cosmological scales, quantization of action in terms of a finite, i.e. non vanishing, universal constanthrequires a redefinition of space-time on very small scales. Most importantly, the classical notion of “time”, as one common continuous time variable and nature evolving continuously “in time”, has to be replaced (...) by an infinite manifold of transition rates for discontinuous quantum transitions. The fundamental laws of quantum physics, commutation relations and quantum equations of motion, resulted from Max Born’s recognition of the basic principle of quantum physics:To each change in nature corresponds an integer number of quanta of action. Action variables may only change by integer values ofh, requiring all other physical quantities to change by discrete steps, “quantum jumps”. The mathematical implementation of this principle led to commutation relations and quantum equations of motion. The notion of “point” in space-time looses its physical significance; quantum uncertainties of time, position, just as any other physical quantity, are necessary consequences of quantization of action. (shrink)

Many organisms possess multiple sensory systems, such as vision, hearing, touch, smell, and taste. The possession of multiple ways of sensing the world offers many benefits. However, combining information from different senses also poses many challenges for the nervous system. In recent years there has been dramatic progress in understanding how information from the different senses gets integrated in order to construct useful representations of external space. This volume brings together the leading researchers from a broad range of scientific (...) approaches to present the first overview of this central topic in cognitive neuroscience. (shrink)

Originally published in 1921, this book presents a concise study of time and space relations by the renowned British physicist Alfred Robb (1873-1936). The text is one of a series of works on the topic of special relativity written by Robb from 1911 onwards. An appendix section is included. This book will be of value to anyone with an interest in special relativity, the development of physics and the history of science.

Greenberger. Horne. Shimony, and Zeilinger gave a new version of the Bell theorem without using inequalities (probabilities). Mermin summarized it concisely; but Bohm and Hiley criticized Mermin's proof from contextualists' point of view. Using the branching space-time language, in this paper a proof will be given that is free of these difficulties. At the same time we will also clarify the limits of the validity of the theorem when it is taken as a proof that quantum mechanics is not (...) compatible with a deterministic world nor with a world that permits correlated space-related events without a common cause. (shrink)

Part I. Space and Time in the History of Philosophy. The Concept of Space in Antiquity / Max Jammer. -- Aristotle and the Sea Battle / G.E.M. Anscombe. -- Questions About Time / St. Augustine. -- Space and Matter / Renè Descartes. -- Absolute Space and Time / Isaac Newton. -- The Relational Theory of Space and Time / Gottfried Leibniz. -- Place, Extension and Duration / John Locke. -- Transcendental Ideality of Space and (...) Time / Immanuel Kant. -- Mirror Images / Immanuel Kant. -- Newton's Views of Time, Space and Motion / Ernst Mach. -- The Unreality of Space and time / F.H. Bradley. -- Duration and Intuition / Henri Bergson. -- The Problem of Infinity Considered Historically / Bertrand Russell. -- Part II. Geomoetry and Physics. What is Geometry? / A.S. Eddington. -- Space and Geometry / Ernest Nagel. -- Non-Eucledian Spaces / Hans Reichenbach. -- Geometry and Definition of Congruence / Hans Reichenbach. -- Geometry as a Branch of Physics / H.P. Robertson. -- Part III. Space-Time and Relativity. Relativity / R.E. Peierls. -- Autobiographical Notes / Albert Einstein. -- The Four-Dimensional World / Moritz Schlick. -- Space and Time / H. Minkowski. The Philosophical Retention of Absolute Space in Einstein's General Theory of relativity / Adolf Grünbaum. -- Part IV. Recent Philosophical Analyses. Ostensible Temporality / C.D. Croad. -- Time : A Treatment of Some Puzzles / J.N. Findlay. -- Time and Language, and the Passage fo Time / Nelson Goodman. -- Time / W.V. Quine. -- Geometrical Objects / W.V. Quine. -- Spatial and Temporal Ananlogies and the Concept of Identity / Richard Taylor. -- Time, Irreversible Processes, and the Physical Status of Becoming / Adolf Grünbaum. (shrink)

Hume’s discussion of space, time, and mathematics at T 1.2 appeared to many earlier commentators as one of the weakest parts of his philosophy. From the point of view of pure mathematics, for example, Hume’s assumptions about the infinite may appear as crude misunderstandings of the continuum and infinite divisibility. I shall argue, on the contrary, that Hume’s views on this topic are deeply connected with his radically empiricist reliance on phenomenologically given sensory images. He insightfully shows that, working (...) within this epistemological model, we cannot attain complete certainty about the continuum but only at most about discrete quantity. Geometry, in contrast to arithmetic, cannot be a fully exact science. A number of more recent commentators have offered sympathetic interpretations of Hume’s discussion aiming to correct the older tendency to dismiss this part of the Treatise as weak and confused. Most of these commentators interpret Hume as anticipating the contemporary idea of a finite or discrete geometry. They view Hume’s conception that space is composed of simple indivisible minima as a forerunner of the conception that space is a discretely (rather than continuously) ordered set. This approach, in my view, is helpful as far as it goes, but there are several important features of Hume’s discussion that are not sufficiently appreciated. I go beyond these recent commentators by emphasizing three of Hume’s most original contributions. First, Hume’s epistemological model invokes the “confounding” of indivisible minima to explain the appearance of spatial continuity. Second, Hume’s sharp contrast between the perfect exactitude of arithmetic and the irremediable inexactitude of geometry reverses the more familiar conception of the early modern tradition in pure mathematics, according to which geometry (the science of continuous quantity) has its own standard of equality that is independent from and more exact than any corresponding standard supplied by algebra and arithmetic (the sciences of discrete quantity). Third, Hume has a developed explanation of how geometry (traditional Euclidean geometry) is nonetheless possible as an axiomatic demonstrative science possessing considerably more exactitude and certainty that the “loose judgements” of the vulgar. (shrink)