Using covariant derivatives and the operator definitions of quantum mechanics, gauge invariant Proca and Lehnert equations are derived and the Lorenz condition is eliminated in U(1) invariant electrodynamics. It is shown that the structure of the gauge invariant Lehnert equation is the same in an O(3) invariant theory of electrodynamics.

Nucleation and motion of kink pairs on partial dislocations are examined by elasticity theory for materials with a high Peierls stress. Two approaches are used: one considers the change in average stacking-fault energy due to alloying elements and the other considers the change in local SFE due to a nearby solute atom. Both approaches highlight the role of SFE on kink nucleation, propagation and annihilation and both furnish strain rate as a function of stress, temperature and SFE. Model predictions are (...) compared with yield stress data for two systems: firstly, an intermetallic, MoSi 2 , which softens for alloying elements that decrease the SFE and hardens for Re additions that increase the SFE; secondly, a ceramic oxide, MgO-Al 2 O 3 spinel, which softens with increasing addition of excess alumina and at the same time exhibits a decrease in SFE. The average SFE approach agrees qualitatively with the data while quantitative agreement is obtained with the local SFE approach. The possibility is considered that the model applies to other materials, such as TiAl, HfV 2 and Fe 3 Al, which show softening with certain alloying additions. One requirement is that the dislocations are dissociated more than a few atomic distances; otherwise kink nucleation occurs on the perfect dislocation . Hence the model does not apply to materials such as bcc metals which only have a core dissociation. Normal hardening effects of solutes from size and modulus misfits are additive with any softening effects from a decrease in SFE and so may mask the latter, as occurs for W additions to MoSi 2. (shrink)

This chapter describes the potential far‐reaching consequences of contemplative higher education for the fields of science and medicine.

The volume presents essays on the philosophical explanation of the relationship between body and soul in antiquity from the Presocratics to Galen. The title of the volume alludes to a phrase found in Plato, Aristotle and Plotinus, referring to aspects of living behaviour involving both body and soul, and is a commonplace in ancient philosophy, dealt with in very different ways by different authors.

© 2016 Regents of the University of California.The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 3,062 new measurements from 721 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. All the particle properties and search limits are listed in Summary Tables. We also give numerous (...) tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Among the 117 reviews are many that are new or heavily revised, including those on Pentaquarks and Inflation. The complete Review is published online in a journal and on the website of the Particle Data Group. The printed PDG Book contains the Summary Tables and all review articles but no longer includes the detailed tables from the Particle Listings. A Booklet with the Summary Tables and abbreviated versions of some of the review articles is also available. (shrink)

About one third of patients with epilepsy have seizures refractory to the medical treatment. Electrical stimulation mapping is the gold standard for the identification of “eloquent” areas prior to resection of epileptogenic tissue. However, it is time-consuming and may cause undesired side effects. Broadband gamma activity recorded with extraoperative electrocorticography during cognitive tasks may be an alternative to ESM but until now has not proven of definitive clinical value. Considering their role in cognition, the alpha and beta bands could further (...) improve the identification of eloquent cortex. We compared gamma, alpha and beta activity, and their combinations for the identification of eloquent cortical areas defined by ESM. Ten patients with intractable focal epilepsy participated in a delayed-match-to-sample task, where syllable sounds were compared to visually presented letters. We used a generalized linear model approach to find the optimal weighting of each band for predicting ESM-defined categories and estimated the diagnostic ability by calculating the area under the receiver operating characteristic curve. Gamma activity increased more in eloquent than in non-eloquent areas, whereas alpha and beta power decreased more in eloquent areas. Diagnostic ability of each band was close to 0.7 for all bands but depended on multiple factors including the time period of the cognitive task, the location of the electrodes and the patient’s degree of attention to the stimulus. We show that diagnostic ability can be increased by 3–5% by combining gamma and alpha and by 7.5–11% when gamma and beta were combined. We then show how ECoG power modulation from cognitive testing can be used to map the probability of eloquence in individual patients and how this probability map can be used in clinical settings to optimize ESM planning. We conclude that the combination of gamma and beta power modulation during cognitive testing can contribute to the identification of eloquent areas prior to ESM in patients with refractory focal epilepsy. (shrink)

The standard deduction theorem or introduction rule for implication, for classical logic is also valid for intuitionistic logic, but just as with predicate logic, other rules of inference have to be restricted if the theorem is to hold for weaker implicational logics.In this paper we look in detail at special cases of the Gentzen rule for and show that various subsets of these in effect constitute deduction theorems determining all the theorems of many well known as well as not well (...) known implicational logics. In particular systems of rules are given which are equivalent to the relevance logics E,R, T, P-W and P-W-I. (shrink)

In this article, an ethical analysis of an educational programme on renal replacement therapy options for patients and their social network is presented. The two main spearheads of this approach are: (1) offering an educational programme on all renal replacement therapy options ahead of treatment requirement and (2) a home-based approach involving the family and friends of the patient. Arguments are offered for the ethical justification of this approach by considering the viewpoint of the various stakeholders involved. Finally, reflecting on (...) these ethical considerations, essential conditions for carrying out such a programme are outlined. The goal is to develop an ethically justified and responsible educational programme. (shrink)