Leçons de calcul différentiel et de calcul intégral, rédigées d'après les méthodes et les ouvrages publiés ou inédits de A. L. Cauchy. Tome IV., Ier fasc.: Calcul des variations.

Available on demand as hard copy or computer file from Cornell University Library.

Notes on a calculus of Turán operators.

Cover title.

Leçons sur le calcul des variations

Available on demand as hard copy or computer file from Cornell University Library.

A quantitative study of rhythm; the effect of variations in intensity, rate and duration,

Mode of access: Internet.

Partial regularity of weak solutions of the liquid crystal equilibrium system

For a parameter, we consider the modified relaxed energy of the liquid crystal system. Each minimizer of the modified relaxed energy is a weak solution to the liquid crystal equilibrium system. We prove the partial regularity of minimizers of the modified relaxed energy. We also prove the existence of infinitely many weak solutions for the special boundary value x.

Regularity and relaxed problems of minimizing biharmonic maps into spheres

For n >= 5 and k >= 4, we show that any minimizing biharmonic map from Omega subset of R-n to S-k is smooth off a closed set whose Hausdorff dimension is at most n - 5. When n = 5 and k = 4, for a parameter lambda is an element of [0, 1] we introduce lambda-relaxed energy H-lambda of the Hessian energy for maps in W-2,W-2 (Omega; S-4) so that each minimizer u(lambda) of H-lambda is also a biharmonic map. We also establish the existence and partial regularity of a minimizer of H-lambda for lambda is an element of [0, 1).

Positive solutions of a Neumann problem with competing critical nonlinearities

We present existence results for a Neumann problem involving critical Sobolev nonlinearities both on the right hand side of the equation and at the boundary condition.. Positive solutions are obtained through constrained minimization on the Nehari manifold. Our approach is based on the concentration 'compactness principle of P. L. Lions and M. Struwe.

Using empirical evidence of variations in worker performance to extend the capabilities of discrete event simulations in manufacturing

Discrete event simulation of manufacturing systems has become widely accepted as an important tool to aid the design of such systems. Often, however, it is applied by practitioners in a manner which largely ignores an important element of industry; namely, the workforce. Workers are usually represented as simple resources, often with deterministic performance values. This approach ignores the potentially large effect that human performance variation can have on a system. A long-term data collection exercise is described with the aim of quantifying the performance variation of workers in a typical automotive assembly plant. The data are presented in a histogram form which is immediately usable in simulations to improve the accuracy of design assessment. The results show levels of skewness and range which are far larger than anticipated by current researchers and practitioners in the field.

Subdifferentials of Performance Functions and Calculus of Coderivatives of Set-Valued Mappings

The paper contains calculus rules for coderivatives of compositions, sums and intersections of set-valued mappings. The types of coderivatives considered correspond to Dini-Hadamard and limiting Dini-Hadamard subdifferentials in Gˆateaux differentiable spaces, Fréchet and limiting Fréchet subdifferentials in Asplund spaces and approximate subdifferentials in arbitrary Banach spaces. The key element of the unified approach to obtaining various calculus rules for various types of derivatives presented in the paper are simple formulas for subdifferentials of marginal, or performance functions.

Fractional Calculus of the Generalized Wright Function

Mathematics Subject Classification: 26A33, 33C20.

Fractional Calculus of P-transforms

MSC 2010: 44A20, 33C60, 44A10, 26A33, 33C20, 85A99

Principles of Extremum and Application to some Problems of Analysis

AMS subject classification: 41A17, 41A50, 49Kxx, 90C25.

The influence of variations in eating disorder-related symptoms on processing of emotional faces in a non-clinical female sample:an eye-tracking study

This study aimed to: i) determine if the attention bias towards angry faces reported in eating disorders generalises to a non-clinical sample varying in eating disorder-related symptoms; ii) examine if the bias occurs during initial orientation or later strategic processing; and iii) confirm previous findings of impaired facial emotion recognition in non-clinical disordered eating. Fifty-two females viewed a series of face-pairs (happy or angry paired with neutral) whilst their attentional deployment was continuously monitored using an eye-tracker. They subsequently identified the emotion portrayed in a separate series of faces. The highest (n=18) and lowest scorers (n=17) on the Eating Disorders Inventory (EDI) were compared on the attention and facial emotion recognition tasks. Those with relatively high scores exhibited impaired facial emotion recognition, confirming previous findings in similar non-clinical samples. They also displayed biased attention away from emotional faces during later strategic processing, which is consistent with previously observed impairments in clinical samples. These differences were related to drive-for-thinness. Although we found no evidence of a bias towards angry faces, it is plausible that the observed impairments in emotion recognition and avoidance of emotional faces could disrupt social functioning and act as a risk factor for the development of eating disorders.

Membrane protein extraction and purification using styrene-maleic acid (SMA) co-polymer:effect of variations in polymer structure

The use of styrene maleic acid (SMA) co-polymers to extract and purify transmembrane proteins, whilst retaining their native bilayer environment, overcomes many of the disadvantages associated with conventional detergent based procedures. This approach has huge potential for the future of membrane protein structural and functional studies. In this investigation we have systematically tested a range of commercially available SMA polymers, varying in both the ratio of styrene to maleic acid and in total size, for the ability to extract, purify and stabilise transmembrane proteins. Three different membrane proteins (BmrA, LeuT and ZipA) which vary in size and shape were used. Our results show that several polymers can be used to extract membrane proteins comparably to conventional detergents. A styrene:maleic acid ratio of either 2:1 or 3:1, combined with a relatively small average molecular weight (7.5-10 kDa) is optimal for membrane extraction, and this appears to be independent of the protein size, shape or expression system. A subset of polymers were taken forward for purification, functional and stability tests. Following a one-step affinity purification SMA 2000 was found to be the best choice for yield, purity and function. However the other polymers offer subtle differences in size and sensitivity to divalent cations that may be useful for a variety of downstream applications.