Comment on "Reappraisal of experimental values of third-order elastic constants of some cubic semiconductors and metals"

In a recent paper A. S. Johal and D. J. Dunstan [Phys. Rev. B 73, 024106 (2006)] have applied multivariate linear regression analysis to the published data of the change in ultrasonic velocity with applied stress. The aim is to obtain the best estimates for the third-order elastic constants in cubic materials. From such an analysis they conclude that uniaxial stress data on metals turns out to be nearly useless by itself. The purpose of this comment is to point out that by a proper analysis of uniaxial stress data it is possible to obtain reliable values of third-order elastic constants in cubic metals and alloys. Cu-based shape memory alloys are used as an illustrative example.

Third order elastic constants of bcc Cu-Al-Ni

We have measured the changes in the ultrasonic wave velocity, induced by the application of uniaxial stresses in a Cu-Al-Ni single crystal. From these measurements, the complete set of third-order elastic constants has been obtained. The comparison of results for Cu-Al-Ni with available data for other Cu-based alloys has shown that all these alloys exhibit similar anharmonic behavior. By using the measured elastic constants in a Landau expansion for elastic phase transitions, we have been able to give an estimation of the value of a fourth-order elastic constants combination. The experiments have also shown that the application of a stress in the [001] direction, reduces the material resistance to a (110)[110] shear and thus favors the martensitic transition.

The third order Melnikov function of a quadratic center under quadratic perturbation

We study quadratic perturbations of the integrable system (1+x)dH; where H =(x²+y²)=2: We prove that the first three Melnikov functions associated to the perturbed system give rise at most to three limit cycles.

Dynamics of the third order Lyness' difference equation

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New approximation to the third-order density : application to the calculation of correlated multicenter indices

In this work we present the formulas for the calculation of exact three-center electron sharing indices (3c-ESI) and introduce two new approximate expressions for correlated wave functions. The 3c-ESI uses the third-order density, the diagonal of the third-order reduced density matrix, but the approximations suggested in this work only involve natural orbitals and occupancies. In addition, the first calculations of 3c-ESI using Valdemoro's, Nakatsuji's and Mazziotti's approximation for the third-order reduced density matrix are also presented for comparison. Our results on a test set of molecules, including 32 3c-ESI values, prove that the new approximation based on the cubic root of natural occupancies performs the best, yielding absolute errors below 0.07 and an average absolute error of 0.015. Furthemore, this approximation seems to be rather insensitive to the amount of electron correlation present in the system. This newly developed methodology provides a computational inexpensive method to calculate 3c-ESI from correlated wave functions and opens new avenues to approximate high-order reduced density matrices in other contexts, such as the contracted Schrödinger equation and the anti-Hermitian contracted Schrödinger equation

Weak systems of Gandy, Jensen and Devlin

In Part I, we formulate and examine some systems that have arisen in the study of the constructible hierarchy; we find numerous transitive models for them, among which are supertransitive models containing all ordinals that show that Devlin's system BS lies strictly between Gandy's systems PZ and BST'; and we use our models to show that BS fails to handle even the simplest rudimentary functions, and is thus inadequate for the use intended for it in Devlin's treatise. In Part II we propose and study an enhancement of the underlying logic of these systems, build further models to show where the previous hierarchy of systems is preserved by our enhancement; and consider three systems that might serve for Devlin's purposes: one the enhancement of a version of BS, one a formulation of Gandy-Jensen set theory, and the third a subsystem common to those two. In Part III we give new proofs of results of Boffa by constructing three models in which, respectively, TCo, AxPair and AxSing fail; we give some sufficient conditions for a set not to belong to the rudimentary closure of another set, and thus answer a question of McAloon; and we comment on Gandy's numerals and correct and sharpen other of his observations.

A public key encryption based on third order linear sequences

Based on third order linear sequences, an improvement version of the Diffie-Hellman distribution key scheme and the ElGamal public key cryptosystem scheme are proposed, together with an implementation and computational cost. The security relies on the difficulty of factoring an RSA integer and on the difficulty of computing the discrete logarithm.

Evaluation of the indication for surgical extraction of third molars according to the oral surgeon and the primary care dentist. Experience in the Master of Oral Surgery and Implantology at Barcelona University Dental School

Introduction: Third molar extraction is the most frequent procedure in oral surgery. The present study evaluates the indication of third molar extraction as established by the primary care dentist (PCD) and the oral surgeon, and compares the justification for extraction with the principal reason for patient consultation. Patients and method: A descriptive study was made of 319 patients subjected to surgical removal of a third molar in the context of the Master of Oral Surgery and Implantology (Barcelona University Dental School, Barcelona, Spain) between July 2004 and March 2005. The following parameters were evaluated: sex, age, molar, type of impaction, position according to the classifications of Pell and Gregory and of Winter, and the reasons justifying extraction. Results: The lower third molars were the most commonly extracted molars (73.7%). A total of 69.6% of the teeth were covered by soft tissues only. Fifty-six percent of the lower molars corresponded to Pell and Gregory Class IIB, while 42.1% were in the vertical position. The most common reason for patient reference to our Service of Oral Surgery on the part of the PCD was prophylactic removal (51.0% versus 46.1% in the case of the oral surgeon). Discussion and conclusions. Our results show prophylaxis to be the principal indication of third molar extraction, followed by orthodontic reasons. Regarding third molars with associated clinical symptoms or signs, infectious disease-including pericoronitis- was the pathology most often observed by the oral surgeon, followed by caries. This order of frequency was seen to invert in the case of third molars referred for extraction by the PCD. A vertical position predominated among the third molars with associated pathology

Generalization transitions in Hidden-Layer neural networks for third-order feature discrimination

Stochastic learning processes for a specific feature detector are studied. This technique is applied to nonsmooth multilayer neural networks requested to perform a discrimination task of order 3 based on the ssT-block¿ssC-block problem. Our system proves to be capable of achieving perfect generalization, after presenting finite numbers of examples, by undergoing a phase transition. The corresponding annealed theory, which involves the Ising model under external field, shows good agreement with Monte Carlo simulations.

The institutional vs. the academic definition of the quality of work life. What is the focus of the European Commission?

In recent years, we have seen how the quality of work life has been focused and defined by the European Commission (EC). In our study we compare the EC definition with the academic one and try to see how close they are. We also analyse the possibility of applying the institutional definition to the Spanish case through the development of specific indicators. Our main conclusions are that QWL is increasingly important for policy makers. In addition, it is essential to have objective indicators and to conduct surveys in order to reliably measure QWL.

Periodic solutions of second-order differential inclusions systems with p-Laplacian

Some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with p-Laplacian

On moduli of smoothness of fractional order

In this paper we consider the properties of moduli of smoothness of fractional order. The main result of the paper describes the equivalence of the modulus of smoothness and a function from some class.

On the number of higher order Delaunay triangulations

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An LMI approach to H∞ synchronization of second-order neutral master-slave systems

The H∞ synchronization problem of the master and slave structure of a second-order neutral master-slave systems with time-varying delays is presented in this paper. Delay-dependent sufficient conditions for the design of a delayed output-feedback control are given by Lyapunov-Krasovskii method in terms of a linear matrix inequality (LMI). A controller, which guarantees H∞ synchronization of the master and slave structure using some free weighting matrices, is then developed. A numerical example has been given to show the effectiveness of the method

A Variant of Higher-Order Anti-Unification

We present a rule-based Huet’s style anti-unification algorithm for simply-typed lambda-terms in ɳ long β normal form, which computes a least general higher-order pattern generalization. For a pair of arbitrary terms of the same type, such a generalization always exists and is unique modulo α equivalence and variable renaming. The algorithm computes it in cubic time within linear space. It has been implemented and the code is freely available