Pitfalls on evaluating pair exchange interactions for modelling molecule-based magnetism

Human know-how is crucial to cross-examine and challenge computations before trusting any result for modelling magnetic properties in molecule-based materials.

Exact upper bound for sorting Rn with LE

A permutation over alphabet [Formula: see text] is a sequence over [Formula: see text], where every element occurs exactly once. [Formula: see text] denotes symmetric group defined over [Formula: see text]. [Formula: see text] denotes the Identity permutation. [Formula: see text] is the reverse permutation i.e., [Formula: see text]. An operation, that we call as an LE operation, has been defined which consists of exactly two generators: set-rotate that we call Rotate and pair-exchange that we call Exchange (OEIS). At least two generators are the required to generate [Formula: see text]. Rotate rotates all elements to the left (moves leftmost element to the right end) and Exchange is the pair-wise exchange of the two leftmost elements. The optimum number of moves for transforming [Formula: see text] into [Formula: see text] with LE operation are known for [Formula: see text]; as listed in OEIS with identity A048200. However, no general upper bound is known. The contributions of this article are: (a) a novel upper bound for the number of moves required to sort [Formula: see text] with LE has been derived; (b) the optimum number of moves to sort the next larger [Formula: see text] i.e., [Formula: see text] has been computed; (c) an algorithm conjectured to compute the optimum number of moves to sort a given [Formula: see text] has been designed.

2,4-STUD 2,4-STUDY OF THE STRUC Y OF THE STRUCTURE OF THE P TURE OF THE PAIR EXCHANGE DERIVATIVES E TIVES ETHYL ESTER DIO YL ESTER DIOXOPENTANOATE ACID BY THE METHOD OF PMR AND SAR

Analysis of the scientific literature shows that data on nitrogenous derivatives of ketoaldehyde and ketoesters, their synthesis, tautomerization and Complexing ability are incomplete, in some cases their coordination compounds remain abstract, which requires special attention. As a result of the study of the electronic and spatial structures of the complex molecules, it became possible to determine the causes of the "composition-structure-properties" relationship of chemical compounds in a much more complex structure. The structure and tautomerization of para-exchange acylgases of ethyl ether of 2,4-dioxopentanoic acid in various solvents are studied in the article. role of Stephen Krashen's ideas in the theory of second language learning

BCS-BEC Crossover and Pairing Fluctuations in a Two Band Superfluid/Superconductor: A T Matrix Approach

We investigate pairing fluctuation effects in a two band fermionic system, where a shallow band in the Bardeen–Cooper–Schrieffer–Bose–Einstein condensation (BCS-BEC) crossover regime is coupled with a weakly interacting deep band. Within a diagrammatic T matrix approach, we report how thermodynamic quantities such as the critical temperature, chemical potential, and momentum distributions undergo the crossover from the BCS to BEC regime by tuning the intraband coupling in the shallow band. We also generalize the definition of Tan’s contact to a two band system and report the two contacts for different pair-exchange couplings. The present results are compared with those obtained by the simpler Nozières–Schmitt–Rink approximation. We confirm a pronounced enhancement of the critical temperature due to the multiband configuration, as well as to the pair-exchange coupling.

SUPERFLUID TO BOSE METAL TRANSITION IN SYSTEMS WITH RESONANT PAIRING

Experiments in thin films whose thickness can be modified and by this way induce a superconductor to insulator transition, seem to suggest that in the quantum critical regime of this phase transition there might be a Bose metal, i.e., uncondensed bosonic carriers with a finite dissipation. This poses a fundamental problem as to our understanding of how such a state could be justified. On the basis of a simple Boson-Fermion model, where bosonic and fermionic degrees of freedom are strongly inter-related via a Boson-Fermion pair exchange coupling g, we illustrate how such a bosonic metal phase could possibly come about. We show that, as we approach the quantum critical point at some critical gc from the superfluid side, the superfluid phase locking is sustained only for longer and longer spatial scales. On a finite spatial scale, the boson have a quasi-free itinerant behavior with metallic features. At the quantum critical point the systems exhibits a phase separation which shows a ressemblance to that of a He 3– He 4 mixture. This could be the clue to the apparent dilemma of a Bose metal at zero temperature.