Non-standard Case Research Articles

MATHEMATICAL ANALYSIS OF SUCCESSIVE LINEAR APPROXIMATION FOR MOONEY-RIVLIN MATERIAL MODEL IN FINITE ELASTICITY

For calculating large deformations of solid bodies, we have proposed a method of successive linear approximation, by considering the relative Lagrangian formulation. In this article we briefly describe this method, which is applied for nearly incompressible Mooney-Rivlin materials. We prove the existence and uniqueness of weak solutions for associated boundary value problems that arise in each step of the method. In our analysis we consider also a non-standard case, where the coefficients present in the constitutive function of Mooney-Rivlin materials do not satisfy the usual E-inequalities.

Phase structure of the linear sigma model with the non-standard symmetry breaking term

The phase structure of the linear sigma model at finite isospin chemical potential μ and temperature T is systematically studied in the non-standard case of symmetry breaking by means of the Cornwall–Jackiw–Tomboulis effective potential. The latter quantity is calculated in the improved Hartree–Fock approximation which preserves the Goldstone theorem and the thermodynamic consistency. It results that the charged pions are condensed for μ equal to the pion mass in vacuum and the pion condensation corresponds to a first-order phase transition for 0 ⩽ T ⩽ 175.813 MeV, whereas at higher temperature it becomes a second-order phase transition. Moreover, the chiral-symmetry restoration, which is a first-order phase transition, occurs for 138.464 MeV ⩽ T ⩽ 147.168 MeV. The phase diagrams for both pion and chiral condensates are obtained.

Bootstrapping the NPMLE for doubly truncated data

Doubly truncated data appear in a number of applications, including astronomy and survival analysis. In this paper we review the existing methods to compute the nonparametric maximum likelihood estimator (NPMLE) under double truncation, which has no explicit form and must be approximated numerically. We introduce the bootstrap as a suitable method to estimate the finite sample distribution of the NPMLE under double truncation. The performance of the bootstrap is investigated in a simulation study. The nonstandard case in which the right- and left-truncation times determine each other is covered. As an illustration, nonparametric estimation and inference on the birth process and the age at diagnosis for childhood cancer in North Portugal is considered.

Deep trench, landslide and effects on the foundations of a residential building: A case study

The case study discussed in this paper deals with the excavation of an excessively deep and long trench in a clay slope made at one edge of an urban connecting road. The subsequent failure of the top portion of the slope did not cause any human casualty, but did severe damage to a neighbouring retaining wall and to an adjacent building. The works aimed at the stabilization of the slope are suspected to have increased the damage to the foundation system of the building. The aim of this paper is to show that all these events could be foreseen just by relying on the basic concepts of mechanics and on proper engineering practice. The causes for the landslide, and subsequent problems, are to be found in an excessive confidence in soil cohesion and in the application of standard engineering procedures in a non-standard case.

Matter-wave solitons in the presence of collisional inhomogeneities: Perturbation theory and the impact of derivative terms

We study the dynamics of bright and dark matter-wave solitons in the presence of a spatially varying nonlinearity. When the spatial variation does not involve zero crossings, a transformation is used to bring the problem to a standard nonlinear Schrödinger form, but with two additional terms: an effective potential one and a non-potential term. We illustrate how to apply perturbation theory of dark and bright solitons to the transformed equations. We develop the general case, but primarily focus on the non-standard special case whereby the potential term vanishes, for an inverse square spatial dependence of the nonlinearity. In both cases of repulsive and attractive interactions, appropriate versions of the soliton perturbation theory are shown to accurately describe the soliton dynamics.

Analytical reconsideration of the von Neumann paradox in the reflection of a shock wave over a wedge

The reflection of weak shock waves has been reconsidered analytically using shock polars. Based on the boundary condition across the slipstream, the solutions of the three-shock theory (3ST) were classified as “standard-3ST solutions” and “nonstandard-3ST solutions.” It was shown that there are two situations in the nonstandard case: A situation whereby the 3ST provides solutions of which at least one is physical and a situation when the 3ST provides a solution which is not physical, and hence a reflection having a three-shock confluence is not possible. In addition, it is shown that there are initial conditions for which the 3ST does not provide any solution. In these situations, a four-wave theory, which is also presented in this study, replaces the 3ST. It is shown that four different wave configurations can exist in the weak shock wave reflection domain, a Mach reflection, a von Neumann reflection, a ?R (this reflection is not named yet!), and a modified Guderley reflection (GR). Recall that the wave configuration that was hypothesized by Guderley [“Considerations of the structure of mixed subsonic-supersonic flow patterns,” Air Materiel Command Technical Report No. F-TR-2168-ND, ATI No. 22780, GS-AAF-Wright Field No. 39, U.S. Wright–Patterson Air Force Base, Dayton, OH (October 1947); Theorie Schallnaher Strömungen (Springer-Verlag, Berlin, 1957)] and later termed Guderley reflection did not include a slipstream (see Fig. 7). Our numerical study revealed that the wave structure proposed by Guderley must be complemented by a slipstream (see Fig. 4) in order to be relevant for explaining the von Neumann paradox. Hereafter, for simplicity, this modified GR wave configuration will be also termed Guderley reflection. The domains and transition boundaries between these four types of reflection are elucidated.

Record linkage for database integration using fuzzy integrals

Given two-data databases, record linkage algorithms try to establish which records of these files contain information on the same individual. Standard record linkage algorithms assume that both files are described using the same attributes. In this article, we study the nonstandard case when the attributes are not the same. We apply aggregation operators for extracting relevant information for this purpose. We restrict to the case of numerical databases. © 2008 Wiley Periodicals, Inc.

The classification of surfaces of general type with nonbirational bicanonical map

We classify surfaces of general type whose bicanonical map factors through a rational map of degree 2 to a rational or ruled surface. We prove that if such a surface has no pencil of genus 2 curves, then it is the smooth minimal model of a double plane branched along a reduced curve with certain singularities, a configuration already suggested by Du Val in the 1950s. This result allows us to complete the classification of surfaces of general type presenting the nonstandard case, with the possible exception of those with p g = q ≤ 1 p_g=q\le 1 .

ASYMPTOTIC RUIN PROBABILITIES IN FINITE HORIZON WITH SUBEXPONENTIAL LOSSES AND ASSOCIATED DISCOUNT FACTORS

Consider a discrete-time insurance risk model with risky investments. Under the assumption that the loss distribution belongs to a certain subclass of the subexponential class, Tang and Tsitsiashvili (Stochastic Processes and Their Applications 108(2): 299–325 (2003)) established a precise estimate for the finite time ruin probability. This article extends the result both to the whole subexponential class and to a nonstandard case with associated discount factors.

ASSESSMENTS ON THE MULTIJUNCTION SOLAR CELLS PHOTOELECTRIC EFFICIENCY RELATED TO THE SEMICONDUCTOR BAND GAP AND OUTDOOR CONDITIONS

The solar cell photoelectric efficiency is a concept introduced to assess the energy conversion process of photons into electron-hole pairs. A study on the correlation between photoelectric efficiency and semiconductor materials band gap of multijunction solar cells is presented. This is based on an integrated computer model used to perform the simulations over solar standard spectrum AM1.5G as well as a non-standard case, which includes the cells operating in outdoor conditions. We find that over a diffuse solar flux, the solar cell photoelectric efficiency increases whenever the cells are made from a semiconductor material with band gap higher than that optimized over the AM1.5G spectrum. Consequently, this opens a new possibility to increase the photovoltaic modules efficiency.

A backprojection-filtration algorithm for nonstandard spiral cone-beam CT with an n-PI-window

For applications in bolus-chasing computed tomography (CT) angiography and electron-beam micro-CT, the backprojection-filtration (BPF) formula developed by Zou and Pan was recently generalized by Ye et al to reconstruct images from cone-beam data collected along a rather flexible scanning locus, including a nonstandard spiral. A major implication of the generalized BPF formula is that it can be applied for n-PI-window-based reconstruction in the nonstandard spiral scanning case. In this paper, we design an n-PI-window-based BPF algorithm, and report the numerical simulation results with the 3D Shepp–Logan phantom and Defrise disk phantom. The proposed BPF algorithm consists of three steps: cone-beam data differentiation, weighted backprojection and inverse Hilbert filtration. Our simulated results demonstrate the feasibility and merits of the proposed algorithm.

Bare forms and lexical insertions in code-switching: A processing-based account

Bare forms (or O forms), uninflected lexical L2 insertions in contexts where the matrix language expects morphological marking, have been recognized as an anomaly in different approaches to code-switching. Myers-Scotton (1997, 2002) has explained their existence in terms of structural incongruity between the matrix and embedded languages, while Poplack (Budzhak-Jones and Poplack, 1997) looks to distributional symmetries or asymmetries with other anomalous phenomena such as non-standard case marking. In corpus-based studies, bare forms often emerge as clinal in nature, with full matrix language marking appearing alongside bare forms. This suggests that discrete structural constraints are not the only factors, nor necessarily always the dominant ones in play. In this paper it is proposed that on-line processing constraints governed in particular by lexical frequency effects and inherent latencies associated with inflectional attachment may lead to bare forms. The argument is based on a multilingual corpus of native Arabic speakers from the city of Maiduguri in northeastern Nigeria.

Stochastic model for non-standard case-cohort design.

Application of case-cohort design to multi-state disease progression in epidemiological studies has been barely addressed. To estimate multi-state disease natural history, we proposed non-homogeneous exponential regression stochastic model to accommodate the data requiring a non-standard case-cohort design. We allowed transition rates to vary with time by modelling the time of transitions between two states with Weibull distribution. The exponential regression model was used to assess the effect of patient-specific covariates on multi-state disease progressions. This method was successfully applied to two epidemiological applications. The first application was to elucidate the effect of betel quids, smoking and alcohol on three-state disease progression, from normal, through leukoplakia and finally to oral cancer. The second application was to extend the three-state to a five-state model to estimate transition rates from normal to diminutive adenoma to small adenoma to large adenoma and finally to invasive carcinoma of the colon and rectum. Finally, an index for assessing the treatment efficacy for pre-cancerous lesion was developed by comparing transition probabilities derived from the proposed model with the probabilities of malignant transformation after a medical regime.

Time-dependent Stokes and Navier–Stokes problems with boundary conditions involving pressure, existence and regularity

This paper is concerned with the time-dependent Stokes and Navier–Stokes problems with nonstandard boundary conditions: the pressure is given on some part of the boundary. The stationary case was first studied by Bégue, Conca, Murat and Pironneau and, next, their study were completed by Bernard, mainly about regularity. In this paper, the Stokes problem is studied by a method analogous to that of Temam for the standard problem, combined with regularity results of Bernard for the nonstandard stationary case. We obtain existence, uniqueness and regularity H 2. In addition, in two dimensions, a regularity W 2, r , r⩾2, is proved. Next, for the nonstandard Navier–Stokes problem, we present some existence, uniqueness and regularity H 2 results. The proof of existence is based on a fixed point method.

HIGHER-ORDER ITERATIVE LEARNING CONTROL BY POLE PLACEMENT AND NOISE FILTERING

This paper makes a comprehensive examination of likely sources that may give rise to higher-order iterative learning control (ILC) laws. Possibilities considered are higher-order model structure, improved learning speed, minimization of various quadratic cost functions, ILC designs based on predictive control, pole placement, direct and indirect adaptive control, and noise filtering. It is shown that among these possibilities, only a non-standard case of pole placement and noise filtering will naturally result in iterative learning controllers with orders higher than one.

On the Standard H2 Problem

This note presents frequency domain solutions of the standard MIMO H2 problem and some non-standard H2 problems. In the standard case the results are equivalent to the well known state space formulae. The non-standard case is a fairly straightforward generalization of the standard case and relies on factorizations over polynomial matrices and stable matrices. Also, a frequency domain formulation of LQR is explored.

Problem solving strategies and mathematical resources: A longitudinal view on problem solving in a function based approach to algebra

This study is an attempt to analyze students' construction of function based problem solving methods in introductory algebra. It claims that for functions to be a main concept for learning school algebra, a complex process that has to be developed during a long period of learning must take place. The article describes a longitudinal observation of a pair of students that studied algebra for 3 years using a function approach, including intensive use of graphing technology. Such a long observation is difficult to carry out and even more difficult to report. We watched for three years classrooms using the ‘Visual-Math’ sequence, and sampled students that exhibited various levels of mathematics achievement. The analysis method presented here is a non-standard case study of a pair of lower achievers students and their work is often juxtaposed to the work of other pairs participating in the study. The students' attempts to solve a linear break-even problem is analyzed along three interviews which present the development of the use of mathematical resources and the patterns of problem solving at different learning phases. Beyond describing solving attempts, the article offers terms for describing and explaining what and how do learners appreciate and make out of solving introductory school algebra problems over a three years course.

Two-parameter nonstandard deformation of 2×2 matrices

We introduce a two-parameter deformation of 2×2 matrices without imposing any condition on the matrices and give the universal R-matrix of the nonstandard quantum group which satisfies the quantum Yang–Baxter relation. Although in the standard two-parameter deformation the quantum determinant is not central, in the nonstandard case it is central. We note that the quantum group thus obtained is related to the quantum supergroup GLp,q(1|1) by a transformation.

New method for composite optimal control of singularly perturbed systems

In this paper, a new method, based on a generalized algebraic Riccati equation arising in descriptor systems, is presented to solve the composite optimal control problem of singularly perturbed systems. Contrary to the existing method, the slow subsystem is viewed as a special kind of descriptor system. A new composite optimal controller is obtained which is valid for both standard and non-standard singularly perturbed systems. It is shown that the composite optimal control can be obtained simply by revising the solution of the slow regulator problem. It is proven that the composite optimal control can achieve a performance which is O(εe2) close to the optimal performance. Although this result is well-known for the standard singularly perturbed systems, it is new in the non-standard case. The equivalence between the new composite optimal controller and the existing one is also established for the standard singularly perturbed systems.

Presenting and publishing case reports.

The educational value of case reports and the four main categories of information they include are described. Checklists and directions for effective spoken presentations are detailed, so the presenter knows not only the information the audience is likely to expect, but the techniques that will help convey the information. A typical case as it might be presented during rounds is shown with questions for discussion. Guidelines for writing case reports for publication also are included, such as journal selection, descriptions of the standard and nonstandard case formats, the content of the three main sections of the typical case report, and the directions that journal editors typically ask reviewers to follow.