Lectures on applied mathematics.

Includes bibliography.

A course in mathematical analysis.

An unabridged and unaltered republication of the Hedrick-Dunkel translation (v. 1-2); v. 3. newly translated by Howard G. Bergmann.

Geschichte der Variationsrechnung ...

No more published.

Die Variationsrechnung.

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

Untersuchungen zur Variationsrechnung.

Diss.--Berlin.

Leçons sur les fonctions de lignes,

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

Cours de calcul différentiel et intégral.

Mode of access: Internet.

Cours d'analyse de l'École polytechnique /

1. t. Calcul différentiel: Variables réelles. Variables complexes. Séries. Applications géométriques de la série de Taylor. Courbes planes algébriques.--2. t. Calcul intégral: Intégrales indéfinies. Intégrales définies. Des fonctions représentées par des intégrales définies. Potentiels newtoniens. Séries de Fourier. Intégrales complexes. Fonctions elliptiques. Intégrales abéliennes.--3. t. Équations différentielles ordinaires. Équations linéaires. Équations aux dérivées partielles. Calcul des variations. Potentiels newtoniens.

The Herglotz variational problem on spheres and its optimal control approach

The main goal of this paper is to extend the generalized variational problem of Herglotz type to the more general context of the Euclidean sphere S^n. Motivated by classical results on Euclidean spaces, we derive the generalized Euler-Lagrange equation for the corresponding variational problem defined on the Riemannian manifold S^n. Moreover, the problem is formulated from an optimal control point of view and it is proved that the Euler-Lagrange equation can be obtained from the Hamiltonian equations. It is also highlighted the geodesic problem on spheres as a particular case of the generalized Herglotz problem.

Fractional variational problems depending on indefinite integrals and with delay

The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on presence of time delay. We exemplify with one example, where we nd analytically the minimizer.

The Perception of Smile Attractiveness Variations from Esthetic Norms, Photographic Framing and Order of Presentation

Objectives: To evaluate the attractiveness of a smile according to variations from esthetic norms, photographic framing, and the order of the presentation of photographs.Materials and Methods: A photograph of an individual was selected and digitally manipulated to create the following smiles: an ideal control smile (I), a smile with diastema (D1), a smile with midline deviation (LM3), a smile with deviation from the long axes of the lateral incisors (10D), and a smile with an inverted smile arc (LSRV). The manipulated photographs were developed in framings of the face and of the mouth and evaluated by 20 laypeople. For half the evaluators, the presentation started with facial photographs and, for the other half, the presentation began with the mouth shots. Evaluators were asked to rank the photographs from the least to the most attractive; then, each photograph was awarded a mark (scale of 0.0 to 10.0).Results: In both presentations, the smiles I, LM3, 10D, and LSRV received favorable ratings, whereas the D1 smile got poor ratings. The photographic framings used (face vs mouth) and the order of presentation of the photographs did not influence the rankings.Conclusion: The absence of variations from beauty norms of a smile has a positive impact on its esthetic perception, but variations from the norms do not necessarily result in reduced attractiveness. (Angle Orthod. 2009;79:634-639.)

Rapid screening of 4000 individuals for germ-line variations in the BRAF gene

Background: The BRAF gene is frequently somatically altered in malignant melanoma. A majority of variations are at the valine 600 residue leading to a V600E substitution that constitutively activates the kinase. We screened 4000 patient and control DNAs for germ-line variations at the valine 600 residue. Methods: We developed a novel assay by adapting single-base variation assays and software for MALDI-TOF (matrix-assisted laser desorption/ionization time-of-flight) mass spectrometry to screen for all 5 reported variants at codon 600 of the BRAF gene. We screened a case-control collection comprising samples from 1082 melanoma patients and 154 of their unaffected relatives from 1278 families and from 2744 individuals from 659 unselected twin families with no history of melanoma. A panel of 66 melanoma cell lines was used for variation-positive controls. Results: All melanoma cell lines that we had found previously to carry a codon 600 variation were verified in this study. Three of the 4 possible variants (V600E n = 47, V600K n = 2, V600R n = 1) were detected, but no case of V600D was available. No germ-line variants were found in the samples from the 3980 melanoma patients or from the control individuals. Conclusions: This new assay is a high-throughput, automated alternative to standard sequencing and can be used as a rapid initial screen for somatic variants associated with melanoma. Germ-line variants at valine 600 are unlikely to exist and do not contribute to the reported role of the BRAF gene in melanoma predisposition. (c) 2006 American Association for Clinical Chemistry.

The effects of material variations in high value manufacturing industries

It has never been easy for manufacturing companies to understand their confidence level in terms of how accurate and to what degree of flexibility parts can be made. This brings uncertainty in finding the most suitable manufacturing method as well as in controlling their product and process verification systems. The aim of this research is to develop a system for capturing the company’s knowledge and expertise and then reflect it into an MRP (Manufacturing Resource Planning) system. A key activity here is measuring manufacturing and machining capabilities to a reasonable confidence level. For this purpose an in-line control measurement system is introduced to the company. Using SPC (Statistical Process Control) not only helps to predict the trend in manufacturing of parts but also minimises the human error in measurement. Gauge R&R (Repeatability and Reproducibility) study identifies problems in measurement systems. Measurement is like any other process in terms of variability. Reducing this variation via an automated machine probing system helps to avoid defects in future products.Developments in aerospace, nuclear, oil and gas industries demand materials with high performance and high temperature resistance under corrosive and oxidising environments. Superalloys were developed in the latter half of the 20th century as high strength materials for such purposes. For the same characteristics superalloys are considered as difficult-to-cut alloys when it comes to formation and machining. Furthermore due to the sensitivity of superalloy applications, in many cases they should be manufactured with tight tolerances. In addition superalloys, specifically Nickel based, have unique features such as low thermal conductivity due to having a high amount of Nickel in their material composition. This causes a high surface temperature on the work-piece at the machining stage which leads to deformation in the final product.Like every process, the material variations have a significant impact on machining quality. The main cause of variations can originate from chemical composition and mechanical hardness. The non-uniform distribution of metal elements is a major source of variation in metallurgical structures. Different heat treatment standards are designed for processing the material to the desired hardness levels based on application. In order to take corrective actions, a study on the material aspects of superalloys has been conducted. In this study samples from different batches of material have been analysed. This involved material preparation for microscopy analysis, and the effect of chemical compositions on hardness (before and after heat treatment). Some of the results are discussed and presented in this paper.

The work of nurse practitioners : a national work sampling study

Aim: This paper is a report of a study of variations in the pattern of nurse practitioner work in a range of service fields and geographical locations, across direct patient care, indirect patient care and service-related activities. Background. The nurse practitioner role has been implemented internationally as a service reform model to improve the access and timeliness of health care. There is a substantial body of research into the nurse practitioner role and service outcomes, but scant information on the pattern of nurse practitioner work and how this is influenced by different service models. --------- Methods: We used work sampling methods. Data were collected between July 2008 and January 2009. Observations were recorded from a random sample of 30 nurse practitioners at 10-minute intervals in 2-hour blocks randomly generated to cover two weeks of work time from a sampling frame of six weeks. --------- Results: A total of 12,189 individual observations were conducted with nurse practitioners across Australia. Thirty individual activities were identified as describing nurse practitioner work, and these were distributed across three categories. Direct care accounted for 36.1% of how nurse practitioners spend their time, indirect care accounted for 32.2% and service-related activities made up 31.9%. --------- Conclusion. These findings provide useful baseline data for evaluation of nurse practitioner positions and the service effect of these positions. However, the study also raises questions about the best use of nurse practitioner time and the influences of barriers to and facilitators of this model of service innovation.