Field-induced particle pairing in an Ising system

We study the thermodynamic behavior of an Ising system on a Bethe lattice in which rearranging particles are decorating with their presence the bonds of the system, causing the local exchange coupling to depend on the decoration status. Such magnetic models have been proposed in efforts to understand the mechanisms responsible for the pairing of electrons in high-T_c superconductivity. In order to study in some detail this aspect, we focus on the question of conditions under which particle pairing occurs, and more specifically, on the role of an external magnetic field. We find a low-temperature region of the phase diagram where significant particle clustering occurs when the field is introduced.     

Classifying spaces and homotopy sets of axes of pairings

We consider the maps between classifying spaces of the form . The main theorem shows that if the restriction map on is a weak epimorphism, then the restriction on should factor through the classifying spaces of the center of the compact Lie group . An application implies that is an H-space (Hopf space) if and only if is abelian.

     

Quadratic forms for the 1-D semilinear Schrödinger equation

This paper is concerned with 1-D quadratic semilinear
Schrödinger equations. We study local well posedness in classical Sobolev space of the associated initial value problem and periodic boundary value problem. Our main interest is to obtain the lowest value of which guarantees the desired local well posedness result. We prove that at least for the quadratic cases these values are negative and depend on the structure of the nonlinearity considered.

     

Complex formation of hydronium ion with several crown ethers in 1,2-dichloroethane,acetonitrile, and nitrobenzene solutions

A conductance study concerning the interaction between hydronium ion and several crown ethers in acetonitrile, nitrobenzene and 1,2-dichloroethane solutions has been carried out at 25°C. The stability constants of the resulting 1:1 complexes in acetonitrile and nitrobenzene solutions were determined from the molar conductance-mole ratio data and found to vary in the order 18C6>DB30C10>DC18C6>DB18C6>DB21C7>DB24C8>B15C5. In 1,2-dichloroethane solution, the complexation process results in the dissociation of ion pairs. There is an inverse relationship between the stabilities of the complexes and the Gutmann donicity of the solvents. In nitrobenzene solution, some evidence for the formation of a 2:1 sandwich adduct between the smaller crowns (i.e., B15C5 and 18-crowns) are observed from the molar conductance-mole ratio data which is supported by the¹H NMR data.     

Remarks on the correlation function implied by the Bjerrum theory of ion pairing

The Friedman theory of correlation functions implied by the Bjerrum theory is generalized by taking into account additional terms and by improving the basic expression for the free energy. By combining the mean spherical approximation (MSA) and the mass action law (MAL) good agreement with HNC and MC data is reached.     

Dissociation constants: NH4OH as a standard

It is proposed that NH₄OH be used as a standard for determining dissociation constants on a standard basis. Ultrasonic absorption and electrical conductance measurements as a function of pressure provide the basis for quantitative evaluation of all parameters except activity coefficients. It is shown how the weak ionization of NH₄OH can be used to minimize uncertainty due to activity coefficients. Density data at atmospheric pressure confirm the values used to provide quantitative explanations of the acoustic and conductance data. Application of the differential sound absorption technique should extend the method dissociation constants of other classes of salts, in particular the 1–2, 2–2, and 3–2 sulfates.     

Solving bilinear tensor least squares problems and application to Hammerstein identification

Bilinear tensor least squares problems occur in applications such as Hammerstein system identification and social network analysis. A linearly constrained problem of medium size is considered, and nonlinear least squares solvers of Gauss–Newton‐type are applied to numerically solve it. The problem is separable, and the variable projection method can be used. Perturbation theory is presented and used to motivate the choice of constraint. Numerical experiments with Hammerstein models and random tensors are performed, comparing the different methods and showing that a variable projection method performs best.     

A transfer principle for inequalities in vector lattices

A transfer principle from inequalities with inner products to inequalities containing positive semidefinite symmetric bilinear operators with values in a vector lattices is proved. Some applications are also given.     

Asymmetric Counteranion‐Directed Catalysis: Concept,Definition, and Applications

Recently, the use of enantiomerically pure counteranions for the induction of asymmetry in reactions proceeding through cationic intermediates has emerged as an exciting new concept, which has been termed asymmetric counteranion‐directed catalysis (ACDC). Despite its success, the concept has not been fully defined and systematically discussed to date. This Review closes this gap by providing a clear definition of ACDC and by examining both clear cases as well as more ambiguous examples to illustrate the differences and overlaps with other catalysis concepts.     

Ground State Structure of Hs Super-heavy Isotopes

The ground state properties of Hs nuclei studied in the framework of the relativistic mean field theory revealed that more stable isotopes are located on the proton abundant side of the chain.The last stable nucleus to the proton drip line is ~(256)Hs.The most stable unknown Hs nucleus may be ~(268)Hs.The density dependent delta interaction pairing is used to improve the BCS pairing correction,which results in more reasonable single-particle energy level distributions and nucleon occupation,and it is shown to be available to describe the properties of nuclei in the superheavy region.