Do some chemotaxis-growth models possess Lyapunov functionals?

In spirit of a result by W. Alt from 1980 we give some sufficient criteria that guarantee the existence of Lyapunov functionals for parabolic cross-diffusion models including chemotaxis-growth models with non-diffusive chemotactic signals (resp. with non-diffusive memory).     

Projective Reed–Muller type codes on rational normal scrolls

In this paper we study an instance of projective Reed–Muller type codes, i.e., codes obtained by the evaluation of homogeneous polynomials of a fixed degree in the points of a projective variety. In our case the variety is an important example of a determinantal variety, namely the projective surface known as rational normal scroll, defined over a finite field, which is the basic underlining algebraic structure of this work. We determine the dimension and a lower bound for the minimum distance of the codes, and in many cases we also find the exact value of the minimum distance. To obtain the results we use some methods from Gröbner bases theory.     

Characterization of an Algerian diatomite by inverse gas chromatography: Specific and non-specific contribution and Lewis acid–base parameters

The fundamental understanding of the behavior of a solid is intimately related to the understanding of the interactions on the surface of the latter, a major challenge in particular if the material is natural and ecological. The infinite dilution-inverse gas chromatography was used to evaluate the surface thermodynamic properties of several phases (grafted and/or coated) diatomite. A series of non- or polar-solute probes were injected at temperatures of 45?°C and 90?°C. The dispersive surface free energies values of the supports decrease with increasing temperature and their active surface is amphoteric with predominantly acidic character.     

Aharonov–Bohm effects in magnetohydrodynamics

It is shown that an Aharonov–Bohm (AB) effect exists in magnetohydrodynamics (MHD). This effect is best described in terms of the MHD variational variables (Kats, 2004; Yahalom and Lynden-Bell, 2008; Yahalom, 2010) [1], [10], [12]. If a MHD flow has a non-trivial topology some of the functions appearing in the MHD Lagrangian are non-single-valued. These functions have properties similar to the phases in the AB celebrated effect (Aharonov and Bohm, 1959; van Oudenaarden et al., 1998) [2], [3]. While the manifestation of the quantum AB effect is in interference fringe patterns (Tonomura et al., 1982) [4], the manifestation of the MHD Aharonov–Bohm effects are through new dynamical conservation laws.     

Evidence for Atropisomerism in Polycyclic γ-Butenolides: Synthesis,Scope, and Spectroscopic Studies

Design and development of a domino cyclative approach for the synthesis of new polycyclic γ-butenolides from β-aryl-Z-enoate propargylic alcohols, through the interception of an intermediate of the Z-enoate-assisted Meyer–Schuster rearrangement, has been reported. A systematic NMR analysis of various derivatives of this class revealed and supported the potential atropisomerism associated with them. These molecules represent first examples of butenolide ring-based atropisomeric compounds in organic chemistry. The synthetic process involves a synchronous construction of both rings with concurrent creation of the potential stereogenic rotational axis.     

Comment on ‘Ab initio study: the potential energy curves and rovibrational spectrum of low-lying excited states of HCl+ cation’ (Molecular Physics, 114:19, 2817–2823)

In a recent article, Y. Liu, X. Cheng, H. Cheng, J. Cheng and X. Song [Mol. Phys., 114:19, 2817–2823] report on the calculation of potential energy curves and the derivation of spectroscopic constants and line intensities for the lowest energy electronic states of HCl⁺. There are several shortcomings in the article; the most notable being the incorrect ordering of the ²П_3/2 and ²П_1/2 state energies, erroneous selection rules, which lead to the absence of a Q-branch in their predicted spectra, incorrect Höln–London factors, and a missing appendix.     

Engineering a Small HOMO–LUMO Gap and Intramolecular C−H Borylation by Diborene/Anthracene Orbital Intercalation

The diborene 1 was synthesized by reduction of a mixture of 1,2-di-9-anthryl-1,2-dibromodiborane(4) ( 6 ) and trimethylphosphine with potassium graphite. The X-ray structure of 1 shows the two anthryl rings to be parallel and their π(C₁₄) systems perpendicular to the diborene π(B=B) system. This twisted conformation allows for intercalation of the relatively high-lying π(B=B) orbital and the low-lying π* orbital of the anthryl moiety with no significant conjugation, resulting in a small HOMO–LUMO gap (HLG) and ultimately a C−H borylation of the anthryl unit. The HLG of 1 was estimated to be 1.57 eV from the onset of the long wavelength band in its UV/Vis absorption spectrum (THF, λ_onset=788 nm). The oxidation of 1 with elemental selenium afforded diboraselenirane 8 in quantitative yield. By oxidative abstraction of one phosphine ligand by another equivalent of elemental selenium, the B−B and C¹−H bonds of 8 were cleaved to give the cyclic 1,9-diborylanthracene 9 .     

Hedging mortality/longevity risks of insurance portfolios for life insurer/annuity provider and financial intermediary

In this paper, we propose two risk hedge schemes in which a life insurer (an annuity provider) can transfer mortality (longevity) risk of a portfolio of life (annuity) exposures to a financial intermediary by paying the hedging premium of a mortality-linked security. The optimal units of the mortality-linked security which maximize hedge effectiveness for a life insurer (an annuity provider) can be derived as closed-form formulas under the risk hedge schemes. Numerical illustrations show that the risk hedge schemes can significantly hedge the downside risk of loss due to mortality (longevity) risk for the life insurer (annuity provider) under some stochastic mortality models. Besides, finding an optimal weight of a portfolio of life and annuity business, the financial intermediary can reduce the sensitivity to mortality rates but the model risk; a security loading may be imposed on the hedge premium for a higher probability of gain to compensate the financial intermediary for the inevitable model risk.