Search results for "Mathematica"

A semiempirical method based on geminal functions

1968

An attempt has been made to develop a semiempirical method which considers only the n- and π-electrons, with the eigenfunctions expressed as an antisymmetrized product of two-electron functions or geminals. These geminals are expressed as a linear combination of products of Huckel-type MO's and the matrix elements are evaluated assuming the strong orthogonality condition to hold among the geminals, with an average effective Hamiltonian where the interaction between paired electrons is explicitly included.

Lessons learned with the SAGE spectrometer

2012

The SAGE spectrometer combines a high-efficiency γ-ray detection system with an electron spectrometer. Some of the design features have been known to be problematic and surprises have come up during the early implementation of the spectrometer. Tests related to bismuth germanate Compton-suppression shields, electron detection efficiency and an improved cooling system are discussed in the paper.

A new mathematical function for describing electrophoretic peaks.

2005

A new model is proposed for characterizing skewed electrophoretic peaks, which is a combination of leading and trailing edge functions, empirically modified to get a rapid recovery of the baseline. The peak model is a sum of square roots and is called thereby "combined square roots (CSR) model". The flexibility of the model was checked on theoretical and experimental peaks with asymmetries in the range of 0-10 (expressed as the ratio of the distance between the center and the trailing edge, and the center and the leading edge of the chromatographic peak, measured at 10% of peak height). Excellent fits were found in all cases. The new model was compared with other three models that have show…

Unconventional Finite Automata and Algorithms

2016

Elektroniskā versija nesatur pielikumus

The periods of the generalized Jacobian of a complex elliptic curve

2015

Abstract We show that the toroidal Lie group G = ℂ2/Λ, where Λ is the lattice generated by (1, 0), (0, 1) and (τ̂, τ͂), with τ̂ ∉ ℝ, is isomorphic to the generalized Jacobian JL of the complex elliptic curve C with modulus τ̂, defined by any divisor class L ≡ (M) + (N) of C fulfilling M − N = [℘ (τ͂) : ℘´(τ͂) : 1] ∈ C. This follows from an apparently new relation between the Weierstrass sigma and elliptic functions.

Optimization of the domain in elliptic variational inequalities

1988

This paper is concerned with a nonsmooth shape optimization problem for the Signorini unilateral boundary-value problem. The necessary optimality conditions are derived. The results of computations are presented.

The Wiener test and potential estimates for quasilinear elliptic equations

1994

On ( p ( x ),  q ( x ))‐Laplace equations in ℝN without Ambrosetti‐Rabinowitz condition

2021

In the present work, we consider a (p(x), q(x))-elliptic equation describing the behavior of a double-phase anisotropic problem which has relevance in electrorheological fluid applications. The analysis leads to the existence of weak (nonnegative) solutions in the special case of potential terms with critical frequency and a superlinear reaction term. In order to prove the existence result, we combine critical point theory of mountain pass type with related topological and variational methods. Basically, the approach is variational, but we do not impose any Ambrosetti-Rabinowitz type condition for the superlinearity of the reaction. More specifically, we apply the Euler-Lagrange functional …

Abstract Estimates of the Rate of Convergence for Optimal Control Problems

1997

A method for solving optimal control problems with general elliptic operators is presented and analyzed. Especially, estimates of the rate of convergence for the control problems with the proposed approach are derived independently of the underlying approximation method. Some numerical experiments with the proposed method are included.

Boundary accessibility and elliptic harmonic measures

1988

Suppose G is a bounded domain in R n such that the complement of G satisfies a capacity dcnsity condition. It is shown that all elliptic measures in G have a support set with Moreover, the capacity density condition cannot be removed. A nonlinear version of the result is also given.