Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.

Measuring the Characteristic Function of the Work Distribution

We propose an interferometric setting for the ancilla-assisted measurement of the characteristic function of the work distribution following a time-dependent process experienced by a quantum system. We identify how the configuration of the effective interferometer is linked to the symmetries enjoyed by the Hamiltonian ruling the process and provide the explicit form of the operations to implement in order to accomplish our task. We finally discuss two physical settings, based on hybrid optomechanical-electromechanical devices, where the theoretical proposals discussed in our work could find an experimental demonstration.

Rational equivariant rigidity

We prove that if G is S1 or a profinite group, then all of the homotopical information of the category of rational G-spectra is captured by the triangulated structure of the rational G-equivariant stable homotopy category.

That is, for G profinite or S1, the rational G-equivariant stable homotopy category is rigid. For the case of profinite groups this rigidity comes from an intrinsic formality statement, so we carefully relate the notion of intrinsic formality of a differential graded algebra to rigidity.

A Characteristic Function Approach to Inconsistency Measures for Knowledge Bases.

Knowledge is an important component in many intelligent systems.
Since items of knowledge in a knowledge base can be conflicting, especially if
there are multiple sources contributing to the knowledge in this base, significant
research efforts have been made on developing inconsistency measures for
knowledge bases and on developing merging approaches. Most of these efforts
start with flat knowledge bases. However, in many real-world applications, items
of knowledge are not perceived with equal importance, rather, weights (which
can be used to indicate the importance or priority) are associated with items of
knowledge. Therefore, measuring the inconsistency of a knowledge base with
weighted formulae as well as their merging is an important but difficult task. In
this paper, we derive a numerical characteristic function from each knowledge
base with weighted formulae, based on the Dempster-Shafer theory of evidence.
Using these functions, we are able to measure the inconsistency of the knowledge
base in a convenient and rational way, and are able to merge multiple knowledge
bases with weighted formulae, even if knowledge in these bases may be
inconsistent. Furthermore, by examining whether multiple knowledge bases are
dependent or independent, they can be combined in different ways using their
characteristic functions, which cannot be handled (or at least have never been
considered) in classic knowledge based merging approaches in the literature.

Electroless nickel composite (Ni-P/SiC) coating - A study on interface and corrosion characteristic

Surface behaviour is of paramount importance as failure and degradation tend to initiate from the surface. Electroless composite coating (NiP/SiC) was developed using SiC as reinforcing particles. As heat treatment plays a vital role in electroless nickel coating owing to the changes in microstructure, phase structure and mechanical properties, an insight at the interface changes in chemistry and micromechanical behaviour was investigated using scanning electron microscopy (SEM) and energy dispersive X-ray (EDX) and microindentation techniques. Corrosion performance was analysed using electrochemical impedance spectroscopy (EIS). Absence of zinc and migration of copper at the interface was detected. Brittleness and microcracks was seen long the interface when indenting at load of 500 gf (Vickers). Corrosion performance is weaker than particles free coating. However, a thin blanket of NiP could enhance the resistance to corrosive medium.

Design characteristic of randomised controlled trials for geographic atrophy in age-related macular degeneration: selection of outcomes and sample size calculation

PurposeThe selection of suitable outcomes and sample size calculation are critical factors in the design of a randomised controlled trial (RCT). The goal of this study was to identify the range of outcomes and information on sample size calculation in RCTs on geographic atrophy (GA).MethodsWe carried out a systematic review of age-related macular degeneration (AMD) RCTs. We searched MEDLINE, EMBASE, Scopus, Cochrane Library, www.controlled-trials.com, and www.ClinicalTrials.gov. Two independent reviewers screened records. One reviewer collected data and the second reviewer appraised 10% of collected data. We scanned references lists of selected papers to include other relevant RCTs.ResultsLiterature and registry search identified 3816 abstracts of journal articles and 493 records from trial registries. From a total of 177 RCTs on all types of AMD, 23 RCTs on GA were included. Eighty-one clinical outcomes were identified. Visual acuity (VA) was the most frequently used outcome, presented in 18 out of 23 RCTs and followed by the measures of lesion area. For sample size analysis, 8 GA RCTs were included. None of them provided sufficient Information on sample size calculations.ConclusionsThis systematic review illustrates a lack of standardisation in terms of outcome reporting in GA trials and issues regarding sample size calculation. These limitations significantly hamper attempts to compare outcomes across studies and also perform meta-analyses.

Influencing effect of heat-treatment on radon emanation and exhalation characteristic of red mud

The reuse of industrial by-products is important for members of numerous industrial sectors. However, though the benefits of reuse are evident from an economical point of view, some compounds in these materials can have a negative effect on users' health.In this study, the radon emanation and exhalation features of red mud were surveyed using heat-treatment (100-1200 °C). As a result of the 1200°C-treated samples, massic radon exhalation capacity reduced from 75 ± 10 mBq kg^-1 h^-1 to 7 ± 4 mBq kg^-1 h^-1, approximately 10% of the initial exhalation rate.To find an explanation for internal structural changes, the porosity features of the heat-treated samples were also investigated. It was found that the cumulative pore volume reduced significantly in less than 100 nm, which can explain the reduced massic exhalation capacity in the high temperature treated range mentioned above.SEM snapshots were taken of the surfaces of the samples as visual evidence for superficial morphological changes. It was found that the surface of the high temperature treated samples had changed, proving the decrement of open pores on the surface.

Rational O(2)–Equivariant Spectra

The category of rational O(2)-equivariant cohomology theories has an algebraic model A(O(2)), as established by work of Greenlees. That is, there is an equivalence of categories between the homotopy category of rational O(2)-equivariant spectra and the derived category of the abelian model DA(O(2)). In this paper we lift this equivalence of homotopy categories to the level of Quillen equivalences of model categories. This Quillen equivalence is also compatible with the Adams short exact sequence of the algebraic model.

Meningeal alveolar soft part sarcoma confirmed by characteristic ASPCR1-TFE3 fusion

Sarcoma metastatic to the brain is uncommon and rarely occurs as the initial manifestation of tumor. Alveolar soft part sarcoma (ASPS) is a rare but well-studied subtype of sarcoma. A 39-year-old man presented with seizures due to a left temporal meningeal-enhancing lesion with striking brain edema on MRI. The patient underwent neurosurgical resection for suspected meningioma. Histology showed large tumor cells clustering and forming small nests, in places with pseudoalveolar pattern. Diastase-resistant periodic acid-Schiff revealed very rare granular and rod-like cytoplasmic inclusions. Immunohistochemistry showed convincing positivity only with vimentin and smooth muscle actin. The histological features were strongly suggestive of ASPS. At the molecular level RT-PCR and sequencing analysis demonstrated ASPCR1-TFE3 fusion confirming the histological diagnosis of ASPS. There was no evidence of primary extracranial tumor by physical examination and on chest and abdominal CT scan 11 months after presentation. ASPS typically arise from the soft tissues of the extremities and develop multiple metastatic deposits usually with a long clinical course. This case may represent primary meningeal ASPS although metastatic deposit from an undiscovered primary site cannot be entirely excluded.