Tomographic representation of minisuperspace quantum cosmology and noether symmetries

The probability representation, in which cosmological quantum states are described by a standard positive probability distribution, is constructed for minisuperspace models selected by Noether symmetries. In such a case, the tomographic probability distribution provides the classical evolution for the models and can be considered an approach to select “observable” universes. Some specific examples, derived from Extended Theories of Gravity, are worked out. We discuss also how to connect tomograms, symmetries and cosmological parameters.     

A Farkas lemma for difference sublinear systems and quasidifferentiable programming

A new generalized Farkas theorem of the alternative is presented for systems involving functions which can be expressed as the difference of sublinear functions. Various other forms of theorems of the alternative are also given using quasidifferential calculus. Comprehensive optimality conditions are then developed for broad classes of infinite dimensional quasidifferentiable programming problems. Applications to difference convex programming and infinitely constrained concave minimization problems are also discussed.     

Coordination‐Cluster‐Based Molecular Magnetic Refrigerants

Coordination polymers serving as molecular magnetic refrigerants have been attracting great interest. In particular, coordination cluster compounds that demonstrate their apparent advantages on cryogenic magnetic refrigerants have attracted more attention in the last five years. Herein, we mainly focus on depicting aspects of syntheses, structures, and magnetothermal properties of coordination clusters that serve as magnetic refrigerants on account of the magnetocaloric effect. The documented molecular magnetic refrigerants are classified into two primary categories according to the types of metal centers, namely, homo‐ and heterometallic clusters. Every section is further divided into several subgroups based on the metal nuclearity and their dimensionalities, including discrete molecular clusters and those with extended structures constructed from molecular clusters. The objective is to present a rough overview of recent progress in coordination‐cluster‐based molecular magnetic refrigerants and provide a tutorial for researchers who are interested in the field.

     

A new theorem of the alternative

Although the theorems of the alternative have been well known for a long time, their relationship to linear least squares problems and steepest descent directions was revealed only recently. This relationship was used by the author to derive a new theorem of the alternative. The present research extends this theorem to the _p norm,p > 1.     

Absolute Valued Strongly Power-Associative Triple Systems

Absolute valued triple system are the natural ternary extension of absolute valued algebras. In this article we classify strongly power-associative absolute valued triple systems.     

Enveloping Algebras of Solvable Malcev Algebras of Dimension Five

We study the universal enveloping algebras of the one-parameter family of solvable 5-dimensional non-Lie Malcev algebras. We explicitly determine the universal nonassociative enveloping algebras (in the sense of Pérez-Izquierdo and Shestakov) and the centers of the universal enveloping algebras. We also determine the universal alternative enveloping algebras.     

Nonlinear nonhomogeneous Robin problems with gradient dependent reaction

We consider a Robin problem driven by a nonlinear, nonhomogeneous differential operator and a reaction term which depends on the gradient. Using a topological approach based on the Leray–Schauder Alternative Principle, we show the existence of a weak solution.     

新型环保制冷剂氟化醚类物质的热力学分析

本文筛选了可能作为替代制冷剂的氟化醚类（ＨＦＥｓ）纯物质和混合物,然后对这些工质的制冷循环性能进行了热力学分析。分析结果表明：在醚类纯质及混合物中 ｃ－ＨＦＥ２１６、 ＨＦＥ１４３ａ、 ｃ－Ｅ２－２１６、 ｃ－ＨＦＥ２１６／ＨＦＥ１４３ａ和ｃ－ＨＦＥ２１６／ｃ－Ｅ２－２１６适合替代 ＣＦＣ１２和 ＨＦＣ１３４ａ ; ＨＦＥ１２５适合替代 ＣＦＣ１１５; ＨＦＥ１３４、 ＨＦＥ２４５ｃｂ β和 ＨＦＥ１４３／ＨＦＥ３１－１０适合替代 ＣＦＣ１１４ ; ＨＦＥ３３８ｍｆ、 ＨＦＥ２４５ｆａ、 ＨＦＥ１４３、 ＨＰＥ２６３ｆｂ、 ＨＦＥ２３６ｅａ／ＨＰＥ２４５ｆａ和 ＨＦＥ２３６ｅａ／ＨＦＥ１４３有望成为ＣＦＣ１１的替代物。