Positivity and Stability for a Population Equation with Diffusion on 1

Using positivity, abstract extrapolation spaces, and a generalization of the Jörgens–Vidav-Voigt perturbation theorem for the essential spectral radius of strongly continuous semigroups given in [19], we study the asymptotic behavior of a linear age-dependent population problem with spatial diffusion where the birth and the death rates depend on the spatial variable.     

[M(CO)4PPh3] radicals (M = Cr, Mo, W): DFT and single crystal EPR investigations

[M(CO)₄PPh₃]⁻ (M = Mo, W) were trapped at 77 K in X-irradiated single crystals of M(CO)₅PPh₃ and studied by EPR. Structures of [M(CO)₄PPh₃]⁻ (M = Cr, Mo, W) were optimized by DFT; predicted g and ³¹P-hyperfine tensors agree with experiments for M = Mo, W. The anions adopt a slightly distorted pyramidal structure with PPh₃ in basal position and the spin mostly delocalized in a metal-d_z² orbital and carbon-p_z orbitals of carbonyls. The EPR tensors are slightly modified by annealing, they suggest that new constraints in the matrix distort the structure of [M(CO)₄PPh₃]⁻ (M = Cr, Mo, W).     

Radical Reactions in an X-Irradiated Phosphaalkene: A single-crystal ESR study

Single crystals of 1-[2,4,6-tri(tert-butyl)phenyl]-2-phenylphosphaethene ( PPPE ) and of ²D- and ¹³C-enriched PPPE were studied by ESR after X-ray irradiation. Two phosphorus-centered radicals were trapped in the crystals. The first one was characterized by its ³¹P, ¹H-, and ¹³C-hyperfine tensors, the second one exhibited coupling with ³¹P only. Comparison of these parameters with those predicted by ab initio calculations on some phosphinyl species indicates that these two radicals probably result, on the one hand, from an addition of a H-atom to the C-atom of the P?C bond and, on the other, from a cyclization of the parent molecule. The proposed mechanisms are consistent with the mutual orientations of the hyperfine eigenvectors and bond directions in the undamaged molecule. A C-centered radical which results from an addition of a H-atom to the P-atom of the phosphaethylene bond is also detected.     

The role of nonbonded sulfur-oxygen interaction in the dissociative electron transfer to nitro-substituted arenesulfenyl chlorides

The electrochemical reduction of p-nitrophenyl sulfenyl chloride, o-nitrophenyl sulfenyl chloride as well as bis(4-nitrophenyl) disulfide and bis(2-dinitrophenyl) disulfide was investigated in acetonitrile at an inert electrode. Reduction standard potentials as well standard heterogeneous electron-transfer rate constants have been determined using convolution analysis. An unexpected big difference in the thermodynamics and kinetics of the initial electron-transfer process as well as a striking change in the reductive cleavage mechanism of the S-Cl bond as a function of the nitro group position on the aryl ring of the aryl sulfenyl chloride is observed. A computational study at the B3LYP level shows that this difference in behavior is due to the through-space nonbonded S...O interaction in the o-nitrophenyl sulfenyl chloride.     

Decay rates of the solution of the Cauchy thermoelastic Bresse system

We consider two Cauchy problems for the one-dimensional thermoelastic Bresse model. Using the energy method in the Fourier space, we show that for the first model, the \({L^{2}}\)-norm of the solution decays with the rate \({(1+t)^{-1/12}}\). In addition, the same decay rate has been obtained for the second model.     

Fixed Point Theorems for (p,q)-Quasi-Contraction Mappings in Cone Metric Spaces

In this work, the authors introduce the concept of $(p,q)$-quasi-contraction mapping in a cone metric space. We prove the existence and uniqueness of a fixed point for a $(p,q)$-quasi-contraction mapping in a complete cone metric space. The results of this paper generalize and unify further fixed point theorems for quasi-contraction, convex contraction mappings and two-sided convex contraction of order $2$.     

Characteristics of a high frequency ion source used in a low-energy accelerator

This work presents the characteristics of a high frequency ion source operating on a low energy, 150 keV accelerator. The latter is to be used as a neutron generator and its design is based on a theoretical analysis which shows that if the axial potential in an electrostatic electrode system is made to increase with four thirds the power of axial distance, inward electric forces will compensate space charge forces tending to blow up the beam. This results in a simplified acceleration tube much shorter and of higher gradient than the conventional acceleration columns. The ion source itself is an ordinary type using axial extraction of the beam, and its main properties investigated are the beam current and beam quality (or emittance). Dependence of the two on different parameters is investigated in a series of tests.     

NH<Subscript>3</Subscript>(CH<Subscript>2</Subscript>)<Subscript>5</Subscript>NH<Subscript>3</Subscript>BiCl<Subscript>5</Subscript>: an efficient and recyclable catalyst for the synthesis of benzoxazole,benzimidazole and benzothiazole heterocycles

In this work, the condensation of aromatic aldehydes with different two-substituted aniline catalyzed by NH₃(CH₂)₅NH₃BiCl₅ as heterogeneous and recyclable catalyst was reported. It was demonstrated that NH₃(CH₂)₅NH₃BiCl₅ can act as an efficient and active catalyst and is reusable for six runs without a significant loss of their catalytic activity. Simple preparation of the catalyst, high catalytic activity and good reusability are noteworthy advantages of this catalytic system in the synthesis of benzoxazole, benzimidazole and benzothiazole heterocycles at room temperature under solvent-free conditions.     

Crystal structure of mixed rubidium–ammonium hydrogen sulfate Rb0.7(NH4)0.3HSO4 at room temperature

The structure of Rb_0.7(NH₄)_0.3HSO₄ has been determined by X-ray analysis. The mixed compound crystallizes in the monoclinic space group P2₁/n with unit cell parameters a = 14.374(6) Å, b = 4.618(6) Å, c = 14.412(2) Å, = 118.03(2)°, V = 844.4(4) ų, and D _cal = 1.536 g cm^–3 for Z = 8. The mixed compound Rb_0.7(NH₄)_0.3HSO₄ is a chain-based structure. The Rb⁺ and NH₄ ⁺ cations are intercalated between chains, formed of HSO₄ ^- groups linked with OHO hydrogen-bonding. Rb_0.7(NH₄)_0.3HSO₄ presents a new type of structural arrangement different from those of pure RbHSO₄ and NH₄HSO₄.     

Dicalcium phosphate dehydrate DCPD as a highly efficient and reusable catalyst for Knoevenagel condensation

We have described the catalytic activities of dicalcium phosphate dihydrate (DCPD) in the condensation reaction of various substituted benzaldehydes with active methylene compound malononitrile. The influences of reaction conditions on the corresponding catalytic behavior have been investigated. The results showed that the DCPD exhibited high catalytic activity and versatility and that it can be recycled without significant loss of its activity for the condensation reactions, which shows the material is a promising new type of heterogeneous catalyst for the condensation reactions. Meanwhile, the catalytic results of DCPD compared favorably with those of other materials for Knoevenagel reactions reported previously.