Spectral Analysis of a Transport Operator Arising in Growing Cell Populations

The present paper is concerned with the spectral analysis of a transport-like operator derived from a model introduced by Rotenberg describing the growth of a cell population. Each cell of this population is distinguished by its degree of maturity μ and its maturation velocity v. The biological boundaries of μ = 0 and μ = a (a > 0) are fixed and tightly coupled through mitosis. At mitosis daughter cells and mother cells are related by a general reproduction rule which covers all known biological ones. We first discuss in detail the spectrum of the streaming operator for smooth and partly smooth boundary conditions. Next, we discuss the existence and nonexistence of eigenvalues of the transport operator in the half plane {λ ∈ ℂ : Reλ > where denotes the spectral bound of the streaming operator. In particular, the strict monotonicity of the leading eigenvalue (when it exists) of the transport operator with respect to different parameters of the equation is also considered. We close the paper by describing in detail the various essential spectra of the transport operator for wide classes of collision and boundary operators.     

Existence of Solutions for Impulsive Parabolic Partial Differential Equations

We discuss the propagation of heat along a homogeneous rod of length A under the influence of a nonlinear heat source and impulsive effects at fixed times. This problem is described by an initial-boundary value problem for a nonlinear parabolic partial differential equation subjected to impulsive effects at fixed times. Using Green's function, we convert the problem into a nonlinear integral equation. Sufficient conditions are provided that enable the application of fixed point theorems to prove existence and uniqueness of solutions.     

Silicene structures on silver surfaces

In this paper we report on several structures of silicene, the analog of graphene for silicon, on the silver surfaces Ag(100), Ag(110) and Ag(111). Deposition of Si produces honeycomb structures on these surfaces. In particular, we present an extensive theoretical study of silicene on Ag(111) for which several recent experimental studies have been published. Different silicene structures were obtained only by varying the silicon coverage and/or its atomic arrangement. All the structures studied show that silicene is buckled, with a Si-Si nearest neighbor distance varying between 2.28 and 2.5 ?. Due to the buckling in the silicene sheet, the apparent (lateral) Si-Si distance can be as low as 1.89 ?. We also found that for a given coverage and symmetry, one may observe different scanning tunneling microscopy images corresponding to structures that differ by only a translation.     

Quelques nouvelles propriétés de régularité de l'opérateur de Gribov

In this work, we establish new regularity properties for Gribov's operator:H=A ^* A ₊ iA ^*(A+A ^*)A;(,)², whereA ^* andA are the creation and annihilation operators. Particularly, we prove that for all >0,H ^–1 is in the class of Carleman's operatorl ₁₊.     

Synthesis and Characterization of the New Lacunar Zincophosphate [C6H10N2][ZnP2O8H2]·0.6H2O

The new zincophosphate of chemical formula [C₆H₁₀N₂][ZnP₂O₈H₂] · 0.6H₂O was hydrothermally synthesized with p‐phenylenediamine as structure‐directing agent. The title compound crystallizes in the trigonal symmetry (proposed space group P3m1), where inorganic zincophosphate chains form layers due to the half occupancy of the unique crystallographic zinc site. The layers are separated from each other by p‐phenylenediammonium dications with hydrogen bonding scheme involving the ammonium protons that reveals a pillar‐like 3D structure aspect. The compound was characterized by powder X‐ray diffraction, multinuclear solid‐state NMR, scanning electron microscopy, chemical analysis, and thermogravimetric analysis.     

Molecular structure investigation of Z-3N(2-ethoxyphenyl)-2-N′(2-ethoxyphenyl)-imino-thiazolidin-4-one by <Emphasis Type="Italic">ab initio</Emphasis>, DFT and X-ray diffraction methods

We report here the synthesis of the Z-3N(2-ethoxyphenyl)-2-N′(2-ethoxyphenyl)-imino-thiazolidin-4-one compound. The crystal structure is determined by X-ray diffraction. The compound crystallizes in the monoclinic system with the space group P2_1/n and cell parameters: a = 9.4094(10) Å, b = 9.3066(10) Å, c = 20.960(2) Å, β = 99.0375(10)°, V = 1812.7(3) ų and Z = 4. The structure is refined to final R = 0.05 for 2083 observed reflections. The molecule in the crystal exhibits the intermolecular hydrogen bonds of C–H…O, C–H…N, and C–H…S types. Ab initio calculations are also performed at Hartree–Fock (HF) and density functional theory (DFT) levels. The full HF and DFT geometry optimization is carried out using the 6-31G(d,p) basis set. The observed molecular structure is compared with that calculated by both HF and DFT methods. The optimized geometry of the titled compound is found to be consistent with the structure determined by X-ray diffraction.     

Electron-rich iron/ruthenium arylalkynyl complexes for third-order nonlinear optics: redox-switching between three states

The new [(η(2)-dppe)(η(5)-C(5)Me(5))Fe(C≡C-1,4-C(6)H(4)C≡C)Ru(η(2) -dppe)(2) C≡C(C(6)H(5))] complex (3-H) and its hexanuclear relative [{(η(2)-dppe)(η(5)-C(5) Me(5))Fe(C≡C-1,4-C(6)H(4)-C≡C)Ru(η(2)-dppe)(2)(C≡C-1,4-C(6)H(4)C≡C)(3)(1,3,5-C(6)H(3))] (4) have been synthesized and characterized. The linear and cubic nonlinear optical properties of these compounds in their various redox states have been studied along with those of the analogous complexes [(η(2)-dppe)(η(5)-C(5)Me(5))Fe(C≡C-1,4-C(6)H(4)C≡C)Ru(η(2)-dppe)(2)R][PF(6)](n) (n=0-2; R=Cl, 2-Cl; R=C≡C(4-C(6)H(4)NO(2)),3-NO(2)). We show that molecules exhibiting large third-order nonlinearities can be obtained by assembling such dinuclear Fe/Ru units around a central 1,3,5-substituted C(6)H(3) core. These data are discussed with a particular emphasis on the large changes in their nonlinear (third-order) optical properties brought about by oxidation. Experimental and computational (DFT) evidence for the electronic structures of these compounds in their various redox states is presented using 3-H(n+) as a prototypical model. Single crystals of this complex in its mono-oxidized state (3-H[PF(6)]) provide the first structural data for such carbon-rich Fe(III) /Ru(II) heteronuclear mixed-valent (MV) systems. Although experimental evidence for the structure of the dioxidized states was more difficult to obtain, the theoretical study reveals that 3-H(2+) can be considered to have a biradical structure with two independent spins. The low-lying absorptions that appear in the near-infrared (NIR) range for all these compounds following oxidation correspond to intervalence charge-transfer (IVCT) bands for the mono-oxidized states and to ligand-to-metal charge-transfer (LMCT) transitions for the dioxidized states. These play a crucial role in the strong optical modulation achieved. The possibility of accessing additional states with distinct linear or nonlinear optical properties is also briefly discussed.