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)

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)

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.

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)

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)

The Cartesian concept of nature, which has determined modern thinking until the present time, has become obsolete. It shall be shown that Hegel's objective-idealistic conception of nature discloses, in comparison to that of Descartes, new perspectives for the comprehension of nature and that this, in turn, results in possibilities of actualizing Hegel's philosophy of nature. If the argumentation concerning philosophy of nature is intended to catch up with the concrete Being-of-nature and to meet it in its concretion, then this is (...) impossible for the finite spirit in a strictly a priori sense – this is the thesis supported here which is not at all close to Hegel. As the argumentation rather has to consider the conditions of realization concerning the Being-of-nature, too, it is compelled to take up empirical elements – concerning the organism, for instance, system-theoretical aspects, physical and chemical features of the nervous system, etc. With that, on the one hand, empirical-scientific premises are assumed (e.g. the lawlikeness of nature), which on the other hand become (now close to Hegel) possibly able to be founded in the frame of a Hegelian-idealistic conception. In this sense, a double strategy of empirical-scientific concretization and objective-idealistic foundation is followed up, which represents the methodical basic principle of the developed considerations. In the course of the undertaking, the main aspects of the whole Hegelian design concerning the philosophy of nature are considered – space and time, mass and motion, force and law of nature, the organism, the pro-blem of evolution, psychic being – as well as Hegel's basic thesis concerning the philosophy of nature, that therein a tendency toward coherence and idealization manifests itself in the sense of a (categorically) gradually rising succession of nature: from the separateness of space to the ideality of sensation. In the sense of the double strategy of concretization and foundation it is shown that on the one hand possibilities of philosophical penetration concerning actual empirical-scientific results are opened, and on the other hand – in turn – a re-interpretation of Hegel's theorem on the basis of physical, evolution-theoretical and system-theoretical argumentation also becomes possible. In this mutual crossing-over and elucidation of empirical and Hegelian argumentation not only do perspectives of a new comprehension of nature become visible, but also, at the same time – as an essential consequence of this methodical principle – thoughts on the possibilities of actualizing Hegel's philosophy of nature. (shrink)

What is space? And why are questions of space important to social theory? Society, Action and Space is the first English translation of a book which has been widely recognized in Europe as a major contribution to the interface between geography and social theory. Benno Werlen focuses on the issues which are at the heart of the most important debates in human and social geography today. One of the most significant recent developments in social analysis has been (...) the increasing interchange among geographers, sociologists, anthropologists and social philosophers concerning "the spatial." This debate involves the work of Giddens, Foucault, Bourdieu, Lefebvre, Harvey, Gregory, Soja, and many others. From these new developments a whole series of new forms and empirical work, as well as theoretical innovations, have come into being. Spatial considerations are no longer confined to the realm of geography, but are now seen as fundamental to all forms of social theorizing, especially under conditions of late modernity and globalization. Society, Action and Space links discussions in the philosophy of social science with theories of action which have direct relevance to concepts of space. Benno Werlen provides a discussion of Popper's critical rationalism, and connects it to ideas drawn from phenomenology. This epistemological debate is linked with the sociological action theories of Pareto, Weber, Parsons, and Schutz. The book closes with an evaluation of how "the spatial" can be systematically integrated into action theory. Ambitious, original, and persuasive in its arguments, it raises exciting new implications for the study of space and social theory. (shrink)

Assembled here for the first time in English translation, Sigrid Weigel and Georgina Paul offer illuminating new insights into Benjamin's theory, combining impulses from post-structuralism, feminism, cultural anthropology and psychoanalysis.

‘Space does not exist fundamentally: it emerges from a more fundamental non-spatial structure.’ This intriguing claim appears in various research programs in contemporary physics. Philosophers of physics tend to believe that this claim entails either that spacetime does not exist, or that it is derivatively real. In this article, I introduce and defend a third metaphysical interpretation of the claim: reductionism about space. I argue that, as a result, there is no need to subscribe to fundamentality, layers of (...) reality and emergence in order to analyse the constitution of space by non-spatial entities. It follows that space constitution, if borne out, does not provide empirical evidence in favour of a stratified, Aristotelian in spirit, metaphysics. The view will be described in relation to two particular research programs in contemporary physics: wave function realism and loop quantum gravity. (shrink)

Presenting the history of space-time physics, from Newton to Einstein, as a philosophical development DiSalle reflects our increasing understanding of the connections between ideas of space and time and our physical knowledge. He suggests that philosophy's greatest impact on physics has come about, less by the influence of philosophical hypotheses, than by the philosophical analysis of concepts of space, time and motion, and the roles they play in our assumptions about physical objects and physical measurements. This way (...) of thinking leads to interpretations of the work of Newton and Einstein and the connections between them. It also offers ways of looking at old questions about a priori knowledge, the physical interpretation of mathematics, and the nature of conceptual change. Understanding Space-Time will interest readers in philosophy, history and philosophy of science, and physics, as well as readers interested in the relations between physics and philosophy. (shrink)

In this book, Lawrence Sklar demonstrates the interdependence of science and philosophy by examining a number of crucial problems on the nature of space and ...

Quality-space theory (QST) explains the nature of the mental qualities distinctive of perceptual states by appeal to their role in perceiving. QST is typically described in terms of the mental qualities that pertain to color. Here we apply QST to the olfactory modalities. Olfaction is in various respects more complex than vision, and so provides a useful test case for QST. To determine whether QST can deal with the challenges olfaction presents, we show how a quality space (QS) (...) could be constructed relying on olfactory perceptible properties and the olfactory mental qualities then defined by appeal to that QS of olfactory perceptible properties. We also consider how to delimit the olfactory QS from other modalities. We further apply QST to the role that experience plays in refining our olfactory discriminative abilities and the occurrence of olfactory mental qualities in non-conscious olfactory states. QST is shown to be fully applicable to and useful for understanding the complex domain of olfaction. (shrink)

In this book John Campbell shows that the general structural features of human thought can be seen as having their source in the distinctive ways in which we...

PREFACE: - BY his theory of relativity Albert Einstein has provoked a revolution of thought in physical science. The achievement consists essentially in this Einstein has succeeded in separating far more completely than hitherto the share of the observer and the share of external nature in the things we see happen. The perception of an object by an observer depends on his own situation and circumstances for example, distance will make it appear smaller and dimmer. We make allowance for this (...) almost unconsciously in interpreting what we see. But it now appears that the allowance made for the motion of the observer has hitherto been too crude a fact overlooked because in practice all observers share nearly the same motion, that of the earth. Physical space and time are found to be closely bound up with this motion of the observer and only an amorphous combination of the two is left inherent in the external world. When space and time are relegated to their proper source the observer the world of nature which remains appears strangely unfamiliar but it is in reality simplified, and the underlying unity of the principal phenomena is now clearly revealed. The deductions from this new outlook have, with one doubtful exception, been confirmed when tested by experiment. It is my aim to give an account of this work without intro ducing anything very technical in the way of mathematics, physics, or philosophy. The new view of space and time, so opposed to our habits of thought, must in any case demand unusual mental exercise. The results appear strange and the incongruity is not without a humorous side. For the first nine chapters the task is one of interpreting a clear-cut theory, accepted in all its essentials by a large and growing school of physicists although perhaps not everyone would accept the authors views of its meaning. Chapters x and xi deal with very recent advances, with regard to which opinion is more fluid. As for the last chapter, containing the authors specula tions on the meaning of nature, since it touches on the rudiments of a philosophical system, it is perhaps too sanguine to hope that it can ever be other than controversial. A non-mathematical presentation has necessary limitations and the reader who wishes to learn how certain exact result follow from Einsteins, or even Newtons, law of gravitation m bound to seek the reasons in a mathematical treatise. But thj limitation of range is perhaps less serious than the limitation of intrinsic truth. There is a relativity of truth, as there is a relativity of space. For is and IS-NOT though with Rule and Line And UP-AND-DOWK without, I could define, Alas It is not so simple. We abstract from the phenomena that which is peculiar to the position and motion of the observer but can we abstract that which is peculiar to the limited imagina tion of the human brain We think we can, but only in the symbolism of mathematics. As the language of a poet rings with a truth that eludes the clumsy explanations of his commentators, so the geometry of relativity in its perfect harmony expresses a truth of form and type in nature, which my bowdlerised version misses. But the mind is not content to leave scientific Truth in a dry husk of mathematical symbols, and demands that it shall be alloyed with familiar images. The mathematician, who handles x so lightly, may fairly be asked to state, not indeed the in scrutable meaning of a in nature, but the meaning which x conveys to him. Although primarily designed for readers without technical knowledge of the subject, it is hoped that the book may also appeal to those who have gone into the subject more deeply. A few notes have been added in the Appendix mainly to bridge the gap between this and more mathematical treatises, and to indicate the points of contact between the argument in the text and the parallel analytical investigation. It is impossible adequately to express my debt to con temporary literature and discussion... (shrink)

Our aim in this paper is to take quite seriously Heinz Post’s claim that the non-individuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry conditions. Using a different mathematical framework, namely, quasi-set theory, we avoid working within a label-tensor-product-vector-space-formalism, to use Redhead and Teller’s words, and get a more intuitive way of dealing with the formalism of quantum mechanics, although the underlying logic should be modified. We (...) build a vector space with inner product, the Q-space, using the non-classical part of quasi-set theory, to deal with indistinguishable elements. Vectors in Q-space refer only to occupation numbers and permutation operators act as the identity operator on them, reflecting in the formalism the fact of unobservability of permutations. Thus, this paper can be regarded as a tentative to follow and enlarge Heinsenberg’s suggestion that new phenomena require the formation of a new “closed” (that is, axiomatic) theory, coping also with the physical theory’s underlying logic and mathematics. (shrink)

In his argument for the possibility of knowledge of spatial objects, in the Transcendental Deduction of the B-version of the Critique of Pure Reason, Kant makes a crucial distinction between space as “form of intuition” and space as “formal intuition.” The traditional interpretation regards the distinction between the two notions as reflecting a distinction between indeterminate space and determinations of space by the understanding, respectively. By contrast, a recent influential reading has argued that the two notions (...) can be fused into one and that space as such is first generated by the understanding through an act of synthesis of the imagination. Against this reading, this article argues that a key characteristic of space as a form of intuition is its nonconceptual unity, which defines the properties of space and is as such necessarily independent of determination by the understanding through the transcendental synthesis of the imagination. The conceptual unity that the understanding prescribes to the manifold in intuition, by means of the categories, defines the formal intuition. Furthermore, this article argues that it is the sui generis, nonconceptual unity of space, when takenas a unity for the understanding by means of conceptual determination, that first enables geometric knowledge and knowledge of spatially located particulars. (shrink)

We live today within a system in which state and corporate power aim to render space flat, transparent, and uniform, for only then can it be truly controlled. The gaze of power and the commodity form are capable of infiltrating even the darkest of corners, and often, we invite them into our most private spaces. We do so as a matter of convenience, but also to placate ourselves and cope with the alienation inherent in our everyday lives. The resulting (...) dominant space can best be termed totalitarian. It is space stripped of uniqueness, deprived of the “spatial aura” necessary for authentic experience. In Totalitarian Space and the Destruction of Aura, Saladdin Ahmed sets out to help us grasp what has been lost before no trace remains. He draws attention to that which we might prefer not to see, but despite the bleakness of this indictment of reality, the book also offers a message of hope. Namely, it is only once we comprehend the magnitude of the threat to our spatial experience and our own complicity in sustaining this system that we can begin to resist the totalizing forces at work. (shrink)

Space, Time, and Stuff is an attempt to show that physics is geometry: that the fundamental structure of the physical world is purely geometrical structure. Along the way, he examines some non-standard views about the structure of spacetime and its inhabitants, including the idea that space and time are pointless, the idea that quantum mechanics is a completely local theory, the idea that antiparticles are just particles travelling back in time, and the idea that time has no structure (...) whatsoever. The main thrust of the book, however, is that there are good reasons to believe that spaces other than spacetime exist, and that it is the existence of these additional spaces that allows one to reduce all of physics to geometry. Philosophy, and metaphysics in particular, plays an important role here: the assumption that the fundamental laws of physics are simple in terms of the fundamental physical properties and relations is pivotal."--P. [4] of cover. (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.

Ian Stoner has recently argued that we ought not to colonize Mars because doing so would flout our pro tanto obligation not to violate the principle of scientific conservation, and there is no countervailing considerations that render our violation of the principle permissible. While I remain agnostic on, my primary goal in this article is to challenge : there are countervailing considerations that render our violation of the principle permissible. As such, Stoner has failed to establish that we ought not (...) to colonize Mars. I close with some thoughts on what it would take to show that we do have an obligation to colonize Mars and related issues concerning the relationship between the way we discount our preferences over time and projects with long time horizons, like space colonization. (shrink)