Synthesis of α,α′-bisdialkylphosphonoisopropylnitroxyls

Conclusions Some,-bisdialkylphosphonoisopropylnitroxyl radicals were obtained by the thermolysis of dialkyl -nitrosoisopropylphosphonates and isolated in the pure state.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 8, pp. 1867–1868, August, 1979.     

Statistical Approximation by Double Poisson–Cauchy Singular Integral Operators

In this paper we show that it is possible to approximate a continuous and 2π-periodic function on the disk centered at origin with radius π by means of double Poisson–Cauchy singular integral operators which do not need to be positive in general. Our results cover not only the classical approximation but also the statistical approximation process.     

Chiral resonant solitons in Chern–Simons theory and Broer–Kaup type new hydrodynamic systems

New Broer–Kaup type systems of hydrodynamic equations are derived from the derivative reaction–diffusion systems arising in SL(2, R) Kaup–Newell hierarchy, represented in the non-Madelung hydrodynamic form. A relation with the problem of chiral solitons in quantum potential as a dimensional reduction of 2 + 1 dimensional Chern–Simons theory for anyons is shown. By the Hirota bilinear method, soliton solutions are constructed and the resonant character of soliton interaction is found.     

Improved parallel preconditioners for multidisciplinary topology optimisations

Two commonly used preconditioners were evaluated for parallel solution of linear systems of equations with high condition numbers. The test cases were derived from topology optimisation applications in multiple disciplines, where the material distribution finite element methods were used. Because in this optimisation method, the equations rapidly become ill-conditioned due to disappearance of large number of elements from the design space as the optimisations progresses, it is shown that the choice for a suitable preconditioner becomes very crucial. In an earlier work the conjugate gradient (CG) method with a Block-Jacobi preconditioner was used, in which the number of CG iterations increased rapidly with the increasing number processors. Consequently, the parallel scalability of the method deteriorated fast due to the increasing loss of interprocessor information among the increased number of processors. By replacing the Block-Jacobi preconditioner with a sparse approximate inverse preconditioner, it is shown that the number of iterations to converge became independent of the number of processors. Therefore, the parallel scalability is improved.     

Energy in the Schwarzschild-de Sitter Spacetime

The energy (due to matter and fields including gravitation) of the Schwarzschild-de Sitter spacetime is investigated by using the Møller energy-momentum definition in both general relativity and teleparallel gravity. We found the same energy distribution for a given metric in both of these different gravitation theories. It is also independent of the teleparallel dimensionless coupling constant, which means that it is valid in any teleparallel model. Our results sustain that (a) the importance of the energy-momentum definitions in the evaluation of the energy distribution of a given spacetime and (b) the viewpoint of Lessner that the Møller energy-momentum complex is a powerfifi concept of energy and momentum.     

Role of the 30° Telescope in Evaluation of Laryngeal Masses During Direct Laryngoscopy

SUMMARY: Visualization of enlarged laryngeal lesions is the most important factor in choosing a surgical technique, especially for partial surgery. For this reason standard microlaryngoscopy, a computed tomography (CT) scan of the larynx, and 30 degrees telescopic microlaryngoscopy were compared during evaluation of the laryngeal ventricul and sub-glottic area. The histopatholgoical findings of the specimens collected under each modality were simultaneously compared. Comparison of the histopathological findings, which corresponded to inspection with the 30 degrees telescopic method, was more significant than with the use of standard microlaryngoscopy or the CT scan. The aim of the current study therefore was to determine the importance of the 30 degrees telescopic microlaryngoscopic method for the evaluation of the laryngeal ventricle and subglottic area.     

Statistical convergence of double-complex Picard integral operators

In this work, we study the statistical approximation properties of the double-complex Picard integral operators. We also show that our statistical approach is more applicable than the classical one.     

Statistical approximation by positive linear operators on modular spaces

In this paper, we investigate the problem of statistical approximation to a function by means of positive linear operators defined on a modular space. Especially, in order to get more powerful results than the classical aspects we mainly use the concept of statistical convergence. A non-trivial application is also presented.     

Lattice-free sets,multi-branch split disjunctions,and mixed-integer programming

In this paper we study the relationship between valid inequalities for mixed-integer sets, lattice-free sets associated with these inequalities and the multi-branch split cuts introduced by Li and Richard (Discret Optim 5:724–734, 2008). By analyzing $n$ -dimensional lattice-free sets, we prove that for every integer $n$ there exists a positive integer $t$ such that every facet-defining inequality of the convex hull of a mixed-integer polyhedral set with $n$ integer variables is a $t$ -branch split cut. We use this result to give a finite cutting-plane algorithm to solve mixed-integer programs. We also show that the minimum value $t$ , for which all facets of polyhedral mixed-integer sets with $n$ integer variables can be generated as $t$ -branch split cuts, grows exponentially with $n$ . In particular, when $n=3$ , we observe that not all facet-defining inequalities are 6-branch split cuts.