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.     

Performance improvement of plasmonic sensors using a combination of AC electrokinetic effects for (bio)target capture

Analytes concentration techniques are being developed with the appealing expectation to boost the performance of biosensors. One promising method lies in the use of electrokinetic forces. We present hereafter a new design for a microstructured plasmonic sensor which is obtained by conventional microfabrication techniques, and which can easily be adapted on a classical surface plasmon resonance imaging (SPRI) system without further significant modification. Dielectrophoretic trapping and electro‐osmotic displacement of the targets in the scanned fluid are performed through interdigitated 200 μm wide gold electrodes that also act as the SPR‐sensing substrate. We demonstrate the efficiency of our device's collection capabilities for objects of different sizes (200 nm and 1 μm PS beads, as well as 5–10 μm yeast cells). SPRI is relevant for the spatial analysis of the mass accumulation at the electrode surface. We demonstrate that our device overcomes the diffusion limit encountered in classical SPR sensors thanks to rapid collection capabilities (<1 min) and we show a consequent improvement of the detection limit, by a factor >300. This study of an original device combining SPRI and electrokinetic forces paves the way to the development of fully integrated active plasmonic sensors with direct applications in life sciences, electrochemistry, environmental monitoring and agri‐food industry.     

New regiospecific synthesis of 2-trifluoromethyl-1,5 diazapentadiene compounds and of 2-trifluoromethylquinolines, their cyclization products

2-trifluoromethylquinolines 5 are synthesized in high yields using a perfluoroalkylated gem-iodoacetoxy derivative 3 and arylamines 4. The intermediate of this reaction, 2-trifluoromethyl-1,5-diazapentadiene compound 6, was isolated. The procedures are easy, and yields are in general high. This sequence represents a valuable new synthesis of substituted 2-trifluoromethylquinolines and of 2-trifluoromethyl-diazapentadienes (vinamidine compounds).     

A nonlinear problem having a continuous locus of singular points and no multiple solutions

The boundary-value problem ?z″ = (z² ? t²)z′, ? > 0, z(? 1) = α, z(0) = β, t? [?1, 0], has been shown to have a solution, and moreover, depending on the choice of α and β, multiple solutions to it exist. We consider the more general equation f(z, t)z″ = (z^r ? t^s)z′ for a particular non-negative function f(z, t), and integrate the equation exactly. Depending on α and β, we find that either there are no solutions, or that only unique solutions exist. The conclusion is that the presence of a continuous locus of singular points, given by z^r = t^s, does not necessarily produce multiple solutions.     

6-alkoxy-3,4-dihydro-2h-pyrans from substituted α,β-unsaturated esters

Cycloaddition reactions of substituted α,β-unsaturated esters with various electronich olefins lead to 6-alkoxy-3,4-dihydro-2H-pyrans.     

On the Chaoticity of Some Tensor Product Weighted Backward Shift Operators Acting on Some Tensor Product Fock–Bargmann Spaces

In Advances in Mathematical Physics (2011) we showed that the weighted shift \(z^{p}\frac{d^{p+1}}{dz^{p+1}} (p=0, 1, 2,\ldots )\) acting on classical Bargmann space \(\mathbb {B}_{p}\) is chaotic operator. In Journal of Mathematical physics (2014), we constructed an chaotic weighted shift \(\mathbb {M}^{*^{p}}\mathbb {M}^{p+1} (p=0, 1, 2,\ldots )\) on some lattice Fock–Bargmann \(\mathbb {E}_{p}^{\alpha }\) generated by the orthonormal basis \( {e_{m}^{(\alpha ,p)}(z) = e_{m}^{\alpha } ; m=p, p+1,\ldots }\) where \( {e_{m}^{\alpha }(z) = (\frac{2\nu }{\pi })^{1/4}e^{\frac{\nu }{2}z^{2}}e^{-\frac{\pi ^{2}}{\nu }(m +\alpha )^{2} +2i\pi (m +\alpha )z}; m \in \mathbb {N}}\) with \(\nu , \alpha \) are real numbers; \(\nu > 0\), \(\mathbb {M}\) is an weighted shift and \(\mathbb {M^{*}}\) is the adjoint of the \(\mathbb {M}\). In this paper we study the chaoticity of tensor product \(\mathbb {M}^{*^{p}}\mathbb {M}^{p+1}\otimes z^{p}\frac{d^{p}}{dz^{p+1}} (p=0, 1, 2, \ldots )\) acting on \(\mathbb {E}_{p}^{\alpha }\otimes \mathbb {B}_{p}\).     

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.     

Energy harvesting using hybridization of dielectric nanocomposites and electrets

Electrostrictive polymers have been investigated as electroactive materials for electromechanical energy harvesting. This kind of material is isotope, i.e. there is no permanent polarization compared with piezoelectric material, so in order to ensure its polarization and scavenging energy, the electrostrictive polymers need necessarily an application of a static field. To avoid this problem, we used the hybridization of electrostrictive polymer with electret. The present work aims an analytical modeling for predicting the power convert when the material was mechanically excited. The study was carried out on polyurethane and terpolymer [P(VDF–TrFE–CFE)] films, either without filler or filled with carbon nanopowder. Experimental measurements of the harvested power showed a good agreement with the theoretical behavior predicted by the proposed model. It was also shown that the incorporation of nanofillers increased the power harvested from 5.22 · 10^?2 to 1.498 · 10^?1 μW cm^?3 and from 6.87 · 10^?1 to 1.76 μW cm^?3 in polyurethane and in the terpolymer, respectively. Copyright © 2015 John Wiley & Sons, Ltd.