Global Classical Solutions to the 3D Nordström-Vlasov System

The Nordström-Vlasov system describes the kinetic evolution of self-gravitating collisionless matter in the framework of a relativistic scalar theory of gravitation. We prove global existence and uniqueness of classical solutions for the corresponding initial value problem in three dimensions when the initial data for the scalar field are smooth and the initial particle density is smooth with compact support.     

Kinetic control in the formation of meso-dithia[3.3]-paracyclophane S,S′-dioxide

meso-(R,S)-Dithia[3.3]-paracyclophane S,S′-dioxide is formed with complete stereoselection by the thermolysis of 3,3′-[1,4-phenylene-bis(methylenesulfinyl)]-dipropanoate—that generates in situ two transient sulfenic acid functions—in the presence of p-diethynylbenzene. By employing an improved procedure that we have recently optimized, the title compound has been prepared in a 70% yield as a single diastereoisomer. A density functional B3LYP/6-311+G(d,p) study demonstrates that the final syn-addition cyclization step takes place under kinetic control, through a five-membered transition state that defines the stereochemistry of the resulting cyclophane.     

Long‐Lived Radical Cation Salts Obtained by Interaction of Monocyclic Arenes with Niobium and Tantalum Pentahalides at Room Temperature: EPR and DFT Studies

The 1:3 reactions of the alkoxy arenes 1,4‐(MeO)₂C₆H₄ and 1,4‐F₂‐2,5‐(MeO)₂C₆H₂ with TaF₅ in chloroform at 40–50 °C resulted in formation in about 35 % yield of the long‐lived radical cation salts [1,4‐(MeO)₂C₆H₄][Ta₂F₁₁] ( 2 a ) and [1,4‐F₂‐2,5‐(MeO)₂C₆H₂][Ta₂F₁₁] ( 2 b ), respectively. The non‐alkoxy‐substituted [arene][M₂X₁₁] [M=Ta, X=F: arene=C₆H₅Me ( 2 c ), 1,4‐C₆H₄Me₂ ( 2 d ), C₆H₅F ( 2 e ), C₆H₅NO₂ ( 2 f ); M=Nb, X=F: arene=C₆H₅Me ( 4 a ), 1,4‐C₆H₄Me₂ ( 4 b ), C₆H₅F ( 4 c ), C₆H₅NO₂ ( 4 d ); M=Ta, X=Cl: arene=1,4‐C₆H₄Me₂ ( 5 )] were obtained from the 3:1 reactions of MX₅ with the appropriate arene in chloroform at temperatures in the range 40–90 °C. Compounds 2 – 5 were detected by EPR spectroscopy (in CHCl₃) at room temperature, and their gas‐phase structures were optimized by DFT calculations. Formation of the M^IV species [MX₄(NCMe)₂] [M=Ta, X=F ( 3 a ); M=Nb, X=F ( 3 b ); M=Ta, X=Cl ( 3 c )] was ascertained by EPR spectroscopy on solutions obtained by treatment of the reaction mixtures with acetonitrile. Non‐selective reactions occurred upon combination of 1,4‐F₂‐2,5‐(MeO)₂C₆H₂ with AgNbF₆ (in CH₂Cl₂) and 1,4‐(MeO)₂C₆H₄ with SbF₅.     

A modified Schwarzian Korteweg-de Vries equation in 2 + 1 dimensions with lots of isochronous solutions

Physics of Atomic Nuclei - A modified version of the integrable Schwarzian Korteweg de Vries equation in 2 + 1 dimensions is introduced, and it is pointed out that it possesses lots of isochronous...     

Absolute continuity for Banach space valued mappings

We consider the notion ofp, λ, δ-absolute continuity for Banach space valued mappings introduced in [2] for real valued functions and for λ=1. We investigate the validity of some basic properties that are shared byn, λ-absolutely continuous functions in the sense of Maly and hencl. We introduce the class δ-BV _λ,loc^p and we give a characterization of the functions belonging to this class.     

Novel rate equations describing isochronous chemical reactions

A simple mathematical model involving two first-order Ordinary Differential Equations (ODEs) with fourth-degree polynomial nonlinearities is introduced. The initial-value problem for this system of two ODEs is solved in terms of elementary functions: for an open set of initial data, this solution is isochronous, i.e., completely periodic with a fixed period (independent of the initial data); in the complementary set of initial data, it blows up at a finite time. This system is likely to be of applicative interest: for instance it models the time evolution of two chemical substances in a spatially homogeneous situation, provided this evolution is characterized by six appropriate chemical reactions whose rates are simply expressed in terms of three a priori arbitrary parameters, or alternatively by five appropriate reactions whose rates are simply expressed in terms of two a priori arbitrary parameters.     

A new goldfish model

A new integrable (indeed, solvable) model of goldfish type is identified, and some of its properties are discussed. A version of its Newtonian equations of motion reads as follows:

Properties of the Zeros of the Sum of two Polynomials

Some properties—including relations having a Diophantine character—of the zeros of the sum of two polynomials are reported.