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Simple Proof for Global Existence of Bohmian Trajectories  [PDF]
Stefan Teufel,Roderich Tumulka
Physics , 2004, DOI: 10.1007/s00220-005-1302-0
Abstract: We address the question whether Bohmian trajectories exist for all times. Bohmian trajectories are solutions of an ordinary differential equation involving a wavefunction obeying either the Schroedinger or the Dirac equation. Some trajectories may end in finite time, for example by running into a node of the wavefunction, where the law of motion is ill-defined. The aim is to show, under suitable assumptions on the initial wavefunction and the potential, global existence of almost all solutions. We provide a simpler and more transparent proof of the known global existence result for spinless Schroedinger particles and extend the result to particles with spin, to the presence of magnetic fields, and to Dirac wavefunctions. Our main new result are conditions on the current vector field on configuration-space-time which are sufficient for almost-sure global existence.
GOAL: What Have We Learned?
Timothy Leek
Allergy, Asthma & Clinical Immunology , 2005, DOI: 10.1186/1710-1492-1-3-117
Abstract: To fully appreciate the study, it is necessary to highlight two previous hypothesis-generating studies [2,3] that led to the development of the GOAL trial protocol. In the first of the two studies, the authors pooled data from eight trials using inhalers containing combined salmeterol and fluticasone propionate [2]. The data were reanalyzed with a new endpoint based on a composite measurement of asthma control as defined in guidelines published by the Global Initiative for Asthma (GINA). This was the first time a composite endpoint based on current asthma guidelines was used, as opposed to the majority of asthma studies to date, which have selected single-variable endpoints. The results of this analysis indicated that guideline-defined asthma control can be achieved and led to the development of a prospective protocol using the composite measure as the endpoint. The second hypothesis-generating study also indicated that improved quality of life was realized as the level of control improved, control again being defined by a guideline-based composite measure [3]. A significant observation across both studies was that similar proportions of individuals were achieving the same levels of asthma control [2,3] and improvements in quality of life [3] in the populations studied, regardless of the severity of asthma. This suggests that patients with more severe asthma should be taught to expect the same level of control and the same quality of life as those with milder asthma.The GOAL trial was then developed as a "proof of concept" that asthma control according to the GINA guideline-based definition is achievable. The primary objective of the study was to compare the proportion of individuals who achieved a composite guideline-based measure of well-controlled asthma by using an inhaled corticosteroid alone with the proportion of those who achieved the same by using an inhaled corticosteroid in combination with a long-acting β agonist. The patients were stratified before rand
An Elementary Proof That Symplectic Matrices Have Determinant One  [PDF]
Donsub Rim
Mathematics , 2015,
Abstract: We give one more proof of the fact that symplectic matrices over real and complex fields have determinant one. While this has already been proved many times, there has been lasting interest in finding in an elementary proof. Our result is restricted to the real and complex case due to its reliance on field-dependent spectral theory, however in this setting we obtain a proof which is more elementary in the sense that it is direct and requires only well-known facts. Finally, an explicit formula for the determinant of conjugate symplectic matrices in terms of its square subblocks is given.
Examples of factors which have no Cartan subalgebras  [PDF]
Yusuke Isono
Mathematics , 2012,
Abstract: We consider some conditions similar to Ozawa's condition (AO), and prove that if a non-injective factor satisfies such a condition and has the W*CBAP, then it has no Cartan subalgebras. As a corollary, we prove that $\rm II_1$ factors of universal orthogonal and unitary discrete quantum groups have no Cartan subalgebras. We also prove that continuous cores of type $\rm III_1$ factors with such a condition are semisolid as a $\rm II_\infty$ factor.
Have we Overtreated Children with Vesicoureteric Reflux?
J Lazarus
African Journal of Urology , 2010,
Abstract: Urinary tract infections (UTI) are the most common serious bacterial infections in young children. These UTIs have a high association with vesicoureteric reflux (VUR). The pathophysiology of VUR’s renal sequelae, its investigation and management is presently undergoing a reassessment. This review documents these changes focusing on compelling new data. With regard to the need for and benefit of imaging procedures in children with UTIs we present an algorithm for investigation that is tailored to the African context. The value of continuous antibiotic prophylaxis is questioned and the role of injectable ureteric bulking is discussed with reference to the Swedish Reflux Trial. Key Words: Vesicoureteric reflux, children, etiology, pathophysiology, investigation, managment
We have time because we shall never know  [PDF]
Reza Tavakol,Edward Anderson
Physics , 2015,
Abstract: We argue against current proposals concerning the non-existence of time. We point out that a large number of these proposals rely, at least implicitly, on the assumption of `closure' (or `partial closure') of the laws of Physics. I.e. the assumption that laws of Physics as they are known today are either complete (and hence closed) or that they possess features that a hypothetical future `complete' theory must share (and hence are partially closed). Given that the assumption of closure of laws of Physics can never be verified operationally, it cannot justifiably be used to support the claim for non-existence of time. Some approaches against time are `timeless' at the primary level for the universe as a whole. In these approaches time arises at a secondary level, mostly in the sense of `time being abstracted from change'. On the other hand, there are other approaches that deny the existence of time altogether. We argue that metaphysical arguments of this type - similar to those based on closure - by implicitly implying the absence of history, are by their nature circular.
MicroRNAs and cancer: what we know and what we still have to learn
George A Calin
Genome Medicine , 2009, DOI: 10.1186/gm78
Abstract: The organizers of the 2009 Keystone Symposia on MicroRNAs and Cancer assembled a fine panel of speakers, and the audience of more than 300 participants consisted mainly of young scientists, including graduate students, postdoctoral fellows and early career researchers, all fully convinced that the microRNA (miRNA) revolution in the field of cancer research has already arrived! The meeting had double the number of delegates of the previous meeting two years ago, proof that the scientific community is focused on understanding the roles of these small regulatory RNAs in human tumors. The meeting was organized in plenary sessions centered on the main research avenues, such as 'Regulation of development by miRNAs', 'Gene regulation by non-coding RNAs', 'MicroRNAs in cancer', 'Roles of small RNAs in cancer', and 'MicroRNAs as diagnostics and therapeutics'. In addition, workshops were held based on the most interesting posters and focusing on new topics related to clinical translation, such as 'Bench to bedside: translating miRNA discoveries into clinical applications', 'Hot topics in miRNA research' or 'Emerging ideas and technologies in small RNAs'. As proved by the previous enumeration, two new research directions were wisely selected by the organizers to be presented and discussed extensively - firstly, the clinical applications of the already overwhelming number of mechanistic discoveries related to miRNAs and, secondly, the involvement of other short or long non-coding RNAs (ncRNAs) in human cancers and their potential use for patients. Clearly proving this research tendency was the selection, as Keynote address, of the seminal contribution of Joan Massague (Memorial Sloan-Kettering Cancer Center, New York, NY, USA) on understanding the mechanisms of metastasis and of miRNA involvement in late-stage tumorigenesis.The translational implications of miRNA research for cancer patients certainly represents one of the most exciting avenues of research due to its great diag
An elementary proof of uniqueness of Markoff numbers which are prime powers  [PDF]
Ying Zhang
Mathematics , 2006,
Abstract: We present a very elementary proof of the uniqueness of Markoff numbers which are prime powers or twice prime powers, in the sense that it uses neither algebraic number theory nor hyperbolic geometry.
A simple proof of uniqueness of the particle trajectories for solutions of the Navier-Stokes equations  [PDF]
Masoumeh Dashti,James C. Robinson
Mathematics , 2007, DOI: 10.1088/0951-7715/22/4/003
Abstract: We give a simple proof of the uniqueness of fluid particle trajectories corresponding to: 1) the solution of the two-dimensional Navier Stokes equations with an initial condition that is only square integrable, and 2) the local strong solution of the three-dimensional equations with an $H^{1/2}$-regular initial condition i.e.\ with the minimal Sobolev regularity known to guarantee uniqueness. This result was proved by Chemin & Lerner (J Diff Eq 121 (1995) 314-328) using the Littlewood-Paley theory for the flow in the whole space $\R^d$, $d\ge 2$. We first show that the solutions of the differential equation $\dot{X}=u(X,t)$ are unique if $u\in L^p(0,T;H^{(d/2)-1})$ for some $p>1$ and $\sqrt{t}\,u\in L^2(0,T;H^{(d/2)+1})$. We then prove, using standard energy methods, that the solution of the Navier-Stokes equations with initial condition in $H^{(d/2)-1}$ satisfies these conditions. This proof is also valid for the more physically relevant case of bounded domains.
A Proof that Thompson's Groups have Infinitely Many Relative Ends  [PDF]
Daniel Farley
Mathematics , 2007,
Abstract: We show that each of Thompson's groups F, T, and V have infinitely many ends relative to certain subgroups. We go on to show that T and V both have Serre's property FA, i.e., any action of T or V on a tree will have a fixed point. (The proof of the latter statement was originally due to Ken Brown, and our proof is based on his notes.)
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