Non‐self‐adjoint singular second‐order dynamic operators on time scale

In this study, maximal dissipative second‐order dynamic operators on semi‐infinite time scale are studied in the Hilbert space , that the extensions of a minimal symmetric operator in limit‐point case. We construct a self‐adjoint dilation of the dissipative operator together with its incoming and outgoing spectral representations so that we can determine the scattering function of the dilation as stated in the scheme of Lax‐Phillips. Moreover, we construct a functional model of the dissipative operator and identify its characteristic function in terms of the Weyl‐Titchmarsh function of a self‐adjoint second‐order dynamic operator. Finally, we prove the theorems on completeness of the system of root functions of the dissipative and accumulative dynamic operators.     

Nonexistence of nontrivial global solutions for nonlocal in time differential inequalities

In this paper, some nonlocal in time differential inequalities of Sobolev type are considered. Using the nonlinear capacity method, sufficient conditions for the nonexistence of nontrivial global classical solutions are provided.     

Optimal time delays in a class of reaction-diffusion equations

ABSTRACT

A class of semilinear parabolic reaction diffusion equations with multiple time delays is considered. These time delays and corresponding weights are to be optimized such that the associated solution of the delay equation is the best approximation of a desired state function. The differentiability of the mapping is proved that associates the solution of the delay equation to the vector of weights and delays. Based on an adjoint calculus, first-order necessary optimality conditions are derived. Numerical test examples show the applicability of the concept of optimizing time delays.     

Effects of substituents on bridging ligands on the single‐molecule magnet properties of Zn2Dy2 cluster complexes

Two new Zn₂Dy₂ complexes were constructed from Zn (II) salen‐type Schiff base complex fragment and 2,6‐pyridinedimethanol (H₂pdm) or its Br‐substituted analogue (4‐bromopyridine‐2,6‐diyl)dimethanol (H₂Brpdm); their molecular formulas are [Zn₂Dy₂(L)₂(pdm)₂(MeOH)₂](ClO₄)₂ [ 1 , H₂L = N, N′‐ bis(3‐methoxysalicylidene)‐1,3‐diaminopropane] and [Zn₂Dy₂(L)₂(Brpdm)₂(MeOH)₂](ClO₄)₂ [ 2 ], the Dy (III) ions of which have a NO₇ triangular dodecahedral coordination sphere. The two complexes show not only ferromagnetic interaction but also field‐induced single‐molecule magnet (SMM) behavior, which are rare Dy (III)‐containing cluster complexes with the NO₇ triangular dodecahedral coordination sphere that can show good magnetic relaxation. The energy barrier value of complex 2 is higher than those of complex 1 and the Dy (III) complexes with the DyNO₇ triangular dodecahedral coordination configuration reported in the literature.     

Portable single-sided NMR measurements at variable temperatures: Implementation of a thermo-controlled device and application to the heating of bread dough

A temperature control unit was implemented to vary the temperature of samples studied on a commercial Mobile Universal Surface Explorer nuclear magnetic resonance (MOUSE-NMR) apparatus. The device was miniaturized to fit the maximum MOUSE sampling depth (25 mm). It was constituted by a sample holder sandwiched between two heat exchangers placed below and above the sample. Air was chosen as the fluid to control the temperature at the bottom of the sample, at the interface between the NMR probe and the sample holder, in order to gain space. The upper surface of the sample was regulated by the circulation of water inside a second heat exchanger placed above the sample holder. The feasibility of using such a device was demonstrated first on pure water and then on several samples of bread dough with different water contents. For this, T1 relaxation times were measured at various temperatures and depths and were then compared with those acquired with a conventional compact closed-magnet spectrometer. Discussion of results was based on biochemical transformations in bread dough (starch gelatinization and gluten heat denaturation). It was demonstrated that, within a certain water level range, and because of the low magnetic field strength of the MOUSE, a linear relationship could be established between T1 relaxation times and the local temperature in the dough sample.