Approximate analytic expression for the eigenenergies of the anharmonic oscillator V(x)=Ax6+Bx2

An approximate analytic expression for the eigenenergies of the anharmonic oscillator V(x)=Ax6+Bx2 is introduced, starting from particular analytic solutions which are valid when certain relations between the parameters A and B are held. © 1995 The American Physical Society.

Analytic perturbation theory for bound states in the transfer matrix spectrum of weakly correlated lattice ferromagnetic spin systems

We consider general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high temperature region ('beta' << 1). Each model is characterized by a single site apriori spin distribution taken to be even. We also take the parameter 'alfa' = ('S POT.4') - 3 '(S POT.2') POT.2' > 0, i.e. in the region which we call Gaussian subjugation, where ('S POT.K') denotes the kth moment of the apriori distribution. Associated with the model is a lattice quantum field theory known to contain a particle of asymptotic mass -ln 'beta' and a bound state below the two-particle threshold. We develop a 'beta' analytic perturbation theory for the binding energy of this bound state. As a key ingredient in obtaining our result we show that the Fourier transform of the two-point function is a meromorphic function, with a simple pole, in a suitable complex spectral parameter and the coefficients of its Laurent expansion are analytic in 'beta'.

The analytic torsion of a disc

In this article, we study the Reidemeister torsion and the analytic torsion of the m dimensional disc, with the Ray and Singer homology basis (Adv Math 7:145-210, 1971). We prove that the Reidemeister torsion coincides with a power of the volume of the disc. We study the additional terms arising in the analytic torsion due to the boundary, using generalizations of the Cheeger-Muller theorem. We use a formula proved by Bruning and Ma (GAFA 16:767-873, 2006) that predicts a new anomaly boundary term beside the known term proportional to the Euler characteristic of the boundary (Luck, J Diff Geom 37:263-322, 1993). Some of our results extend to the case of the cone over a sphere, in particular we evaluate directly the analytic torsion for a cone over the circle and over the two sphere. We compare the results obtained in the low dimensional cases. We also consider a different formula for the boundary term given by Dai and Fang (Asian J Math 4:695-714, 2000), and we compare the results. The results of these work were announced in the study of Hartmann et al. (BUMI 2:529-533, 2009).

An analytic method to compute the stress dependence on the dimensions and its influence in the characteristics of triple gate devices

Triple-gate devices are considered a promising solution for sub-20 nm era. Strain engineering has also been recognized as an alternative due to the increase in the carriers mobility it propitiates. The simulation of strained devices has the major drawback of the stress non-uniformity, which cannot be easily considered in a device TCAD simulation without the coupled process simulation that is time consuming and cumbersome task. However, it is mandatory to have accurate device simulation, with good correlation with experimental results of strained devices, allowing for in-depth physical insight as well as prediction on the stress impact on the device electrical characteristics. This work proposes the use of an analytic function, based on the literature, to describe accurately the strain dependence on both channel length and fin width in order to simulate adequately strained triple-gate devices. The maximum transconductance and the threshold voltage are used as the key parameters to compare simulated and experimental data. The results show the agreement of the proposed analytic function with the experimental results. Also, an analysis on the threshold voltage variation is carried out, showing that the stress affects the dependence of the threshold voltage on the temperature. (C) 2011 Elsevier Ltd. All rights reserved.

Short communication: Principal components and factor analytic models for test-day milk yield in Brazilian Holstein cattle

A total of 46,089 individual monthly test-day (TD) milk yields (10 test-days), from 7,331 complete first lactations of Holstein cattle were analyzed. A standard multivariate analysis (MV), reduced rank analyses fitting the first 2, 3, and 4 genetic principal components (PC2, PC3, PC4), and analyses that fitted a factor analytic structure considering 2, 3, and 4 factors (FAS2, FAS3, FAS4), were carried out. The models included the random animal genetic effect and fixed effects of the contemporary groups (herd-year-month of test-day), age of cow (linear and quadratic effects), and days in milk (linear effect). The residual covariance matrix was assumed to have full rank. Moreover, 2 random regression models were applied. Variance components were estimated by restricted maximum likelihood method. The heritability estimates ranged from 0.11 to 0.24. The genetic correlation estimates between TD obtained with the PC2 model were higher than those obtained with the MV model, especially on adjacent test-days at the end of lactation close to unity. The results indicate that for the data considered in this study, only 2 principal components are required to summarize the bulk of genetic variation among the 10 traits.

A factor-analytic reinterpretation of the Clark-Trow "educational philosophies"

Each of four principal components analyses (n = 3,944) incorporated student self-ratings (Most accurate to Least accurate) on one of the four Clark-Trow educational philosophies: Vocational, Academic, Collegiate, Nonconformist. The analyses of these 25-variable correlation matrices yielded 2 factors differentially associated with educational philosophy: Sociability versus Independence (replacing Clark-Trow's "Identification with the College") and Liberalism versus Conservatism (replacing Clark-Trow's "Involvement with Ideas"). The Vocational philosophy was associated primarily with Conservatism, the Collegiate with Sociability, and the Nonconformist with Liberalism; the Academic was moderately associated with both Independence and Liberalism.