Finite basis for analytic strong n-gaps

We identify the finite list of minimal analytic n-gaps which are not weakly countably separated, and we prove that every analytic n-gap which is not countably separated contains a gap from our finite list     

Finite element construction on the basis of analytic solutions of elasticity theory problems

A finite element in the form of a part of a circular ring loaded by a uniformly distributed radial load is constructed on the basis of the exact solution of an elasticity theory problem. This permits a system of resolving equations to be obtained by the finite element method with a three-diagonal matrix. An example is presented that illustrates the accuracy and efficiency of utilization of the elements mentioned.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 85–90, 1988.     

On analytic functions whit gaps. II

Acta Mathematica Hungarica -     

Limit problems for interpolation by analytic radial basis functions

Interpolation problems for analytic radial basis functions like the Gaussian and inverse multiquadrics can degenerate in two ways: the radial basis functions can be scaled to become increasingly flat, or the data points coalesce in the limit while the radial basis functions stay fixed. Both cases call for a careful regularization, which, if carried out explicitly, yields a preconditioning technique for the degenerating linear systems behind these interpolation problems. This paper deals with both cases. For the increasingly flat limit, we recover results by Larsson and Fornberg together with Lee, Yoon, and Yoon concerning convergence of interpolants towards polynomials. With slight modifications, the same technique can also handle scenarios with coalescing data points for fixed radial basis functions. The results show that the degenerating local Lagrange interpolation problems converge towards certain Hermite–Birkhoff problems. This is an important prerequisite for dealing with approximation by radial basis functions adaptively, using freely varying data sites.     

Finite CW complexes with maximal torsion gaps

We investigate some properties of finite CW complexes with maximal homotopy torsion gaps and prove a revision of the Halperin conjecture under an additional condition.

     

Finite basis problem for 2-testable monoids

A monoid S ¹ obtained by adjoining a unit element to a 2-testable semigroup S is said to be 2-testable. It is shown that a 2-testable monoid S ¹ is either inherently non-finitely based or hereditarily finitely based, depending on whether or not the variety generated by the semigroup S contains the Brandt semigroup of order five. Consequently, it is decidable in quadratic time if a finite 2-testable monoid is finitely based.     

Analytical prediction for multiple roll systems with negative gaps

Multiple roll coaters with deformable rolls are widely spread for the coating of thin liquid films with a wet film thickness of only a few microns and below on continuous substrates. The presented analytical solution for multiple roll systems offers for the first time the possibility to predict the performance of multiple roll coaters with a nip feed system and negative gaps. The solution is based on a previously presented solution of the authors for roll pairs and extended to multiple roll systems. The results are validated with experimental data from literature and the main influencing factors of multiple roll systems are investigated. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Orthonormal basis of the octonionic analytic functions

By confirming a conjecture proposed in Li and Peng (2001) [1], we obtain the orthonormal basis for the octonionic analytic functions.     

Finite generation of canonical ring by analytic method

An overview of the analytic proof of the theorem on the finite generation of the canonical ring for the projective algebraic manifold of general type is given.     

The full basis theorem does not imply analytic wellordering

A finite support product of ${\omega }_1$ clones of Jensen's minimal ${\Pi }_2^1$ singleton forcing is used to define a model in which any non-empty analytically definable set of reals contains an analytically definable real (the full basis theorem), but there is no analytically definable wellordering of the reals.     

Finite basis for radical well-mixed difference ideals generated by binomials

In this paper, we prove a finite basis theorem for radical well-mixed difference ideals generated by binomials. As a consequence, every strictly ascending chain of radical well-mixed difference ideals generated by binomials in a difference polynomial ring is finite, which solves an open problem in difference algebra raised by Hrushovski in the binomial case.     

A special polynomial basis of a space of analytic functions

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 40, No. 1, pp. 39–42, January–February, 1988.     

A multiple criteria decision analytic approach for evaluating acid rain policy choices

Multi-Attribute Utility Theoretic Approach is adopted to analyze the problem of acid rain policy choices for multiple impacted groups (agents) under two conditions: exact and imprecise preference information. The analysis involves the setting up of attributes and feasible policy alternatives. Estimates of acid rain impacts are obtained from secondary data. The emphasis is more on framework which allows explorations of compromises and the identification of acceptable impact areas than on exact results. The strongest message of this paper is that even without specifying exact cardinal preferences some dominance relationships can be established between policies in a real-world setting.     

Finite element calculations for systems with multiple Coulomb centers

The presence of multiple Coulomb centers in molecules or solids poses a challenge when solving the effective Schrödinger equation, required as a crucial ingredient in density functional or Hartree–Fock calculations. This is primarily because Kato’s cusp condition needs to be satisfied close to each nucleus and the matrix elements of the Coulomb potential at the nuclei are rather difficult to evaluate when using global basis functions. A novel method for dealing with these challenges is introduced, rewriting the wavefunction as a product of a function satisfying the nuclear cusp conditions and a smooth function, resulting in a transformed variational principle and a regularized potential. Results of three-dimensional finite element calculations based on this ansatz for the ground state of the molecule H₂⁺ in the Born–Oppenheimer approximation are presented, which were obtained using custom written Python/Fortran code.