Laminar compressible boundary layer flow at a three-dimensional stagnation point with vectored mass transfer

The effect of surface mass transfer velocities having normal, principal and transverse direction components (‘vectored’ suction and injection) on the steady, laminar, compressible boundary layer at a three-dimensional stagnation point has been investigated both for nodal and saddle points of attachment. The similarity solutions of the boundary layer equations were obtained numerically by the method of parametric differentiation. The principal and transverse direction surface mass transfer velocities significantly affect the skin friction (both in the principal and transverse directions) and the heat transfer. Also the inadequacy of assuming a linear viscosity-temperature relation at low-wall temperatures is shown.     

Experiments with an interactive paired comparison simplex method for molp problems

In this paper, an interactive paired comparison simplex based method formultiple objective linear programming (MOLP) problems is developed and compared to other interactive MOLP methods. The decision maker (DM)’s utility function is assumed to be unknown, but is an additive function of his known linearized objective functions. A test for ‘utility efficiency’ for MOLP problems is developed to reduce the number of efficient extreme points generated and the number of questions posed to the DM. The notion of ‘strength of preference ’ is developed for the assessment of the DM’s unknown utility function where he can express his preference for a pair of extreme points as ‘strong ’, ‘weak ’, or ‘almost indifferent ’. The problem of ‘inconsistency of the DM’ is formalized and its resolution is discussed. An example of the method and detailed computational results comparing it with other interactive MOLP methods are presented. Several performance measures for comparative evaluations of interactive multiple objective programming methods are also discussed. All rights reserved. This study, or parts thereof, may not be reproduced in any form without written permission of the authors.     

Universal properties of stable states of a free energy model with small parameters

We consider the problem of minimizing functionals of the form , for small , subject to the constraint . (Here is typically a double well potential.) We study structural properties of minimizers that are shared by all minimizers of the problem, for sufficiently small values of . It is shown that the average ‘mass’ and ‘energy’ of minimizers, over intervals of length , is almost uniformly distributed (depending on ), for all sufficiently small . Here is a constant depending on the degree of ‘uniformity’, but independent of . Received May 5, 1996 / Accepted October 28, 1996     

Artistic Expression Goes Green

The paper is a critical discussion of the rich and insightful final chapter of Mitchell Green’s Self-Expression. There, Green seeks to elucidate the compelling, but inchoate intuition that when we’re fully and most expertly expressing ourselves, we can ‘push out’ from within not just our inner representations, but also the ways that we feel. I question, first, whether this type of ‘qualitative expression’ is really distinct from the other expressive forms that Green explores, and also whether it’s genuinely ‘expressive’. I then scrutinize the nature of the ‘qualitative congruences’ that lie at the heart of Green’s theory; and I wonder whether they can play the role Green claims they can in providing a novel account of artistic expression.     

Convergence analysis of a conforming adaptive finite element method for an obstacle problem

The adaptive algorithm for the obstacle problem presented in this paper relies on the jump residual contributions of a standard explicit residual-based a posteriori error estimator. Each cycle of the adaptive loop consists of the steps ‘SOLVE’, ‘ESTIMATE’, ‘MARK’, and ‘REFINE’. The techniques from the unrestricted variational problem are modified for the convergence analysis to overcome the lack of Galerkin orthogonality. We establish R-linear convergence of the part of the energy above its minimal value, if there is appropriate control of the data oscillations. Surprisingly, the adaptive mesh-refinement algorithm is the same as in the unconstrained case of a linear PDE—in fact, there is no modification near the discrete free boundary necessary for R-linear convergence. The arguments are presented for a model obstacle problem with an affine obstacle χ and homogeneous Dirichlet boundary conditions. The proof of the discrete local efficiency is more involved than in the unconstrained case. Numerical results are given to illustrate the performance of the error estimator.     

On some properties of a class of spearman rank statistics with applications

Summary The object of the present investigation is to study some properties of a class of Spearman rank statistics and to apply these results in studying the properties of a sequential procedure proposed in Section 3. The problem is one of bounded length confidence intervals for simple regression coefficients in linear models where both variables are subject to error. It is shown that the proposed procedure is asymptotically ‘consistent’ and ‘efficient’ in the sense of Chow and Robbins [3].     

Pro-torus actions on Poincaré duality spaces

In this paper, it is shown that some of the results of torus actions on Poincaré duality spaces, Borel’s dimension formula and topological splitting principle to local weights, hold if ‘torus’ is replaced by ‘pro-torus’.     

On Estimating a Dynamic Function of a Stochastic System with Averaging

We consider a two-scaled diffusion system, when drift and diffusion parameters of the ‘slow’ component are contaminated by the ‘fast’ unobserved component. The goal is to estimate the dynamic function which is defined by averaging the drift coefficient of the ‘slow’ component w.r.t. the stationary distribution of the ‘fast’ one. We apply a locally linear smoother with a data-driven bandwidth choice. The procedure is fully adaptive and nearly optimal up to a log log factor. This revised version was published online in June 2006 with corrections to the Cover Date.     

Cohomological stratification of diagram algebras

The class of cellularly stratified algebras is defined and shown to include large classes of diagram algebras. While the definition is in combinatorial terms, by adding extra structure to Graham and Lehrer’s definition of cellular algebras, various structural properties are established in terms of exact functors and stratifications of derived categories. The stratifications relate ‘large’ algebras such as Brauer algebras to ‘smaller’ ones such as group algebras of symmetric groups. Among the applications are relative equivalences of categories extending those found by Hemmer and Nakano and by Hartmann and Paget, as well as identities between decomposition numbers and cohomology groups of ‘large’ and ‘small’ algebras.     

Three-dimensional Tollmien-Schlichting waves generated by sound in the boundary layer on an elastic surface at transonic free-stream velocities

Within the framework of the triple-deck theory, the effect of surface elasticity on three-dimensional packets of Tollmien-Schlichting waves generated by acoustic disturbances induced near the boundary layer at transonic free-stream velocities is investigated. It is shown that the elasticity of the surface considerably weakens the most unstable oblique waves but does not change the characteristic horseshoe shape of wave packets with two disturbance peaks propagating at an angle to the incoming flow.     

Constructing greedy linear extensions by interchanging chains

A natural way to prove that a particular linear extension of an ordered set is ‘optimal’ with respect to the ‘jump number’ is to transform this linear extension ‘canonically’ into one that is ‘optimal’. We treat a ‘greedy chain interchange’ transformation which has applications to ordered sets for which each ‘greedy’ linear extension is ‘optimal’.     

Potential,value, and coalition formation

In this paper, a simple probabilistic model of coalition formation provides a unified interpretation for several extensions of the Shapley value. Weighted Shapley values, semivalues, weak (weighted or not) semivalues, and the Shapley value itself appear as variations of this model. Moreover, some notions that have been introduced in the search of alternatives to Shapley’s seminal characterization, as ‘balanced contributions’ and the ‘potential’ are reinterpreted from this point of view. Natural relationships of these conditions with some mentioned families of ‘values’ are shown. These reinterpretations strongly suggest that these conditions are more naturally interpreted in terms of coalition formation than in terms of the classical notion of ‘value.’      

Isotonic tests for spread and tail

Summary One-sample test problem for ‘stochastically more (or less) spread’ is defined and a family of tests with isotonic power is given. The problem is closely related to that for ‘longer (or shorter) tail’ in the reliability theory and the correspondence between them is shown. To characterize the tests three spread preorders inR ⁿ and corre-sponding tail preorders inR ₊ ⁿ are introduced. Functions which are ‘monotone’ in these orders, and subsets which are ‘centrifugal’ or ‘centripetal’ with respect to these orders are studied. These notions generalize the Schur convexity. The Institute of Statistical Mathematics     

Moral coherence,moral worth and explanations of moral motivation

Moral internalism and moral externalism compete over the best explanation of the link between judgment and relevant motivation but, it is argued, they differ at best only verbally. The internalist rational-conceptual nature of the link’ as accounted by M. Smith in The Moral Problem is contrasted to the externalist, also rational, link that requires in addition support from the agent’s psychological-dispositional profile; the internalist link, however, is found to depend crucially on a, similarly to the externalist, psychologically ‘loaded’ profile. It is also argued that the differentiation of the two competing explanations is insufficient partly because they both fail to consider crucial quantitative parameters of the judgment-motivation link. Such parameters become very important particularly in the light of Smith’s claim that this link is grounded on the observable “striking fact” where changes in the set of one’s moral beliefs systematically bring about changes in one’s moral behavior. Examples of algorithms measuring moral coherence and moral worth are provided to serve as evidence for what it comes down to, vis-à-vis the alleged fact, only a verbal dispute between the two camps. Finally, the ‘misfiring’ of these explanations is understood in connection to the irreducibility of concepts such as ‘moral worth’, and/or, ‘moral sensitivity’.     

Roof duality,complementation and persistency in quadratic 0–1 optimization

The paper is concerned with the ‘primal’ problem of maximizing a given quadratic pseudo-boolean function. Four equivalent problems are discussed—the primal, the ‘complementation’, the ‘discrete Rhys LP’ and the ‘weighted stability problem of a SAM graph’. Each of them has a relaxation—the ‘roof dual’, the ‘quadratic complementation,’ the ‘continuous Rhys LP’ and the ‘fractional weighted stability problem of a SAM graph’. The main result is that the four gaps associated with the four relaxations are equal. Furthermore, a solution to any of these problems leads at once to solutions of the other three equivalent ones. The four relaxations can be solved in polynomial time by transforming them to a bipartite maximum flow problem. The optimal solutions of the ‘roof-dual’ define ‘best’ linear majorantsp(x) off, having the following persistency property: if theith coefficient inp is positive (negative) thenx _i=1 (0) in every optimum of the primal problem. Several characterizations are given for the case where these persistency results cannot be used to fix any variable of the primal. On the other hand, a class of gap-free functions (properly including the supermodular ones) is exhibited.     

Quaternion Polar Representation with a Complex Modulus and Complex Argument Inspired by the Cayley-Dickson Form

We present a new polar representation of quaternions inspired by the Cayley-Dickson representation. In this new polar representation, a quaternion is represented by a pair of complex numbers as in the Cayley-Dickson form, but here these two complex numbers are a complex ‘modulus’ and a complex ‘argument’. As in the Cayley-Dickson form, the two complex numbers are in the same complex plane (using the same complex root of −1), but the complex phase is multiplied by a different complex root of −1 in the exponential function. We show how to calculate the ‘modulus’ and ‘argument’ from an arbitrary quaternion in Cartesian form.     

Test of symmetry of a one-dimensional distribution against positive biasedness

Summary Definitions of different strengths are given to the notion of ‘a positively biased random variable’. This notion is related to that of ‘a stochastically larger component of a two-dimensional random vector’, which was introduced previously by the authors. Properties of common rank tests of symmetry about zero against our specification of alternatives are studied in detail. The positive biasedness is extended to ‘positively more biased’. Test of symmetry of a two-dimensional random vector is also referred to.     

On over-reflection of acoustic-gravity waves incident upon a magnetic shear layer in a compressible fluid

A study is made of over-reflection of acoustic-gravity waves incident upon a magnetic shear layer in an isothermal compressible electrically conducting fluid in the presence of an external magnetic field. The reflection and transmission coefficients of hydromagnetic acoustic-gravity waves incident upon magnetic shear layer are calculated. The invariance of wave-action flux is used to investigate the properties of reflection, transmission and absorption of the waves incident upon the shear layer, and then to discuss how these properties depend on the wavelength, length scale of the shear layers, and the ratio of the flow speed and phase speed of the waves. Special attention is given to the relationship between the wave-amplification and critical-level behaviour. It is shown that there exists a critical level within the shear layer and the wave incident upon the shear layer is over-reflected, that is, more energy is reflected back towards the source than was originally emitted. The mechanism of the over-reflection (or wave amplification) is due to the fact that the excess reflected energy is extracted by the wave from the external magnetic field. It is also found that the absence of critical level within the shear layer leads to non-amplification of waves. For the case of very large vertical wavelength of waves, the coefficients of incident, reflected and transmitted energy are calculated. In this limiting situation, the wave is neither amplified nor absorbed by the shear layer. Finally, it is shown that resonance occurs at a particular value of the phase velocity of the wave.     

Stochastically larger component of a random vector

Summary Definitions of different strengths are given to the notion of ‘a stochastically larger component of a two-dimensional random vector.’ Some of them reduce to the known definitions of stochastic order relationship when the components are stochastically independent. The definitions and the approach are related to nonparametric problems.