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)

We examine two different descriptions of the behavioral functions of the hippocampal system. One emphasizes spatially organized behaviors, especially those using cognitive maps. The other emphasizes memory, particularly working memory, a short-term memory that requires iexible stimulus-response associations and is highly susceptible to interference. The predictive value of the spatial and memory descriptions were evaluated by testing rats with damage to the hippocampal system in a series of experiments, independently manipulating the spatial and memory characteristics of a behavioral task. No (...) dissociations were found when the spatial characteristics of the stimuli to be remembered were changed; lesions produced a similar deficit in both spatial and nonspatial test procedures, indicating that the hippocampus was similarly involved regardless of the spatial nature of the task. In contrast, a marked dissociation was found when the memory requirements were altered. Rats with lesions were able to perform accurately in tasks that could be solved exclusively on the basis of reference memory. They performed at chance levels and showed no signs of recovery even with extensive postoperative training in tasks that required working memory. In one experiment all the characteristics of the reference memory and working memory procedures were identical except the type of memory required. Consequently, the behavioral dissociation cannot be explained by differences in attention, motivation, response inhibition, or the type of stimuli to be remembered. As a result of these experiments we propose that the hippocampus is selectively involved in behaviors that require working memory, irrespective of the type of material that is to be processed by that memory. (shrink)

A uniquely integrative work, this volume provides a much needed compilation of primary source material to researchers from basic neuroscience, psychology, developmental science, neuroimaging, neuropsychology and theoretical biology. * The ...

It is common for philosophers to claim that doxastic voluntarism, the view that an agent can form beliefs voluntarily, is false, and therefore that agents do not have the kind of control over their beliefs required for a straightforward application of deontological concepts such as obligation or duty in the domain of epistemology. The role that the denial of doxastic voluntarism plays in an argument to the effect that agents do not have obligations with respect to belief is simply this.

Quantum mechanics is not about 'quantum states': it is about values of physical variables. I give a short fresh presentation and update on the *relational* perspective on the theory, and a comment on its philosophical implications.

Alongside clinical practice, medical schools now confront mounting reasons to examine nontraditional approaches to ethics. Increasing awareness of systems of oppression and their effects on the experiences of trainees, patients, professionals, and generally on medical care, is pushing medical curriculum into an unfamiliar territory. While there is room throughout medical school to take up these concerns, ethics curricula are well-positioned to explore new pedagogical approaches. Feminist ethics has long addressed systems of oppression and broader structures of power. Some of its (...) established concepts can offer distinct value as medical climates change and adapt in response to increased awareness of the experiences of marginalized individuals and populations. In this essay, we offer a set of concepts from feminist ethics that have a fundamental role to play in medical school curriculum: relationality, relational autonomy, and epistemic justice. Though these concepts are not exhaustive, they can be taught in tandem with the concepts that have historically grounded ethics education in medical school, such as autonomy and beneficence. Ultimately, we contend that these concepts hold particular value in ethics curriculum insofar as they diversify mainstream ethical approaches, directly address the pervasiveness of systems of oppression in medicine, and recognize the voices and concerns that may be marginalized in standard approaches. (shrink)

Sebastian Luft presents and defends the philosophy of culture championed by the Marburg School of Neo-Kantianism. Following a historical trajectory from Hermann Cohen to Paul Natorp and through to Ernst Cassirer, this book makes a systematic case for the viability and attractiveness of a philosophical culture in a transcendental vein, in the manner in which the Marburgers intended to broaden Kant's approach.

Behind the images, the actual logical work iscarried out by reasoning-specific operations on these spatial layout models.