Multilayer structures of second-order linear differential equations of Euler type and their application to nonlinear oscillations

The purpose of this paper is to present new oscillation theorems and nonoscillation theorems for the nonlinear Euler differential equation t ² x″ + g(x) = 0. Here we assume that xg(x) > 0 if x ≠ 0, but we do not necessarily require that g(x) be monotone increasing. The obtained results are best possible in a certain sense. To establish our results, we use Sturm’s comparison theorem for linear Euler differential equations and phase plane analysis for a nonlinear system of Liénard type. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 12, pp. 1704–1714, December, 2006.     

Optical Devices for Optical Access Networks Recent Progress in Semiconductor Optical Devices and Optical Modules

Cost-effectiveness is essential in developing optical access network systems. To reduce system costs, both improved system and component technologies are required. Reducing the costs of optical devices and modules in an optical network unit is especially necessary. In this paper, the requirements for optical devices in optical access networks and modules are clarified. Moreover, we also review the recent progress in technologies for semiconductor optical devices and hybrid integration for low-cost optical modules in access networks.     

Nonlinear oscillations of second order differential equations of Euler type

We consider the nonlinear equation , where satisfies for , but is not assumed to be sublinear or superlinear. We discuss whether all nontrivial solutions of the equation are oscillatory or nonoscillatory. Our results can be applied even to the case , which is most difficult.

     

Oscillating solutions of scalar delay-differential equations with state dependence

This paper is concerned with the oscillatory behavior of the delay-differential equation X'(t)=F(t,x_t) including the equations x'(t)=-a(t)x(t-r(t,x(t))), [display math001] as special cases.We give conditions for the existence of a nonoscillatory solution of (1) and criteria for the oscillation of all solutions of (1), aiming at extending or generalizing to (1) some of the recent oscillation and nonoscillation results for delay equations of the form x'(t)=-a(t)x(t-p)).     

Novel drug delivery device using silicone: controlled release of insoluble drugs or two kinds of water-soluble drugs

Drug release mechanism from silicone carrier differs depending on physicochemical properties of the drug. So far, there have been few reports on controlled release of insoluble drug and on simultaneous release of two kinds of water-soluble drugs. The purposes of this study are to establish methods for (1). continuous release of insoluble drug, and (2). release of two kinds of water-soluble drugs from silicone carrier. Polystyrene beads (PSTB) and proteins such as interferon (IFN) and human serum albumin (HSA) were used as model drugs. PSTB was released from silicone only when citric acid (CA) and sodium bicarbonate (SB) existed as additives. The release patterns of IFN and HSA were almost same in the case of matrix and covered-rod formulations, but double-layered formulation released them in different patterns. As far as we are aware, this is the first report on the release of insoluble drug from silicone and the controlled release of two kinds of water-soluble drugs.     

Pd(0)‐catalyzed polycondensation of methyl propargyl carbonate and bisphenols under stoichiometrically imbalanced conditions

We found that a novel Pd(0)‐catalyzed polycondensation of methyl propargyl carbonate ( 1 ) and bisphenol analogs 4 such as 4,4′‐dihydroxydiphenyl ether (4b ) proceeded successfully and gave polyethers 5 having exomethylene groups. The polycondensation was affected by the kind of bisphenol analogs used. The molar ratio of 1 and 4 also affected the polymerization behavior. Polyethers 5 with higher molecular weights were obtained by polymerization with 0.5 equiv of 4 toward 1 . The use of 1 equiv of 4 gave poor results. When 4,4′‐dihydroxybenzophenone ( 4d ) was employed as a nucleophile, benzenesulfonamide ( 13 ) was needed as an additive for obtaining the corresponding polyether with higher molecular weight. The Pd(0)‐catalyzed condensation of 1 and p‐hydroxyacetophenone was conducted as a model reaction. The desired compound and three by‐products were produced. Two of the by‐products were formed by reaction of 1 and methanol liberated from 1 . The other one appeared to be formed via hydrogenolysis. The formation of the by‐products suggested that some terminal reactions took place in the polycondensation of 1 and 4 . © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2250–2261, 2008     

Growth conditions for oscillation of nonlinear differential equations with p-Laplacian

In this paper, oscillation criteria are established for all solutions of second-order nonlinear differential equations of the form

     

Effects of temperature on nitration of sulfamates

Ammonium dinitramide (ADN) has attracted great interest as a potential oxidizer for next generation rocket propellants. It is a halogen-free alternative to ammonium perchlorate, which is currently in wide used as a solid propellant oxidizer. However, in ADN synthesis, N-nitration is necessary to form the N-(NO₂)₂ group. Using a reaction calorimeter, the thermal behavior of nitration of sulfamates (K, Na, and NH₄) using a mixture of acids (HNO₃/H₂SO₄ and HNO₃/AcOH) as the nitration agent was examined. The heat of decomposition of potassium sulfamate at ?10 °C was greater than that at 20 °C. The heat of decomposition decreased in the following order: K salt>Na salt>NH₄ salt in HNO₃/H₂SO₄. The dipole moments of the sulfamates were calculated, and the results revealed that the electronic states of nitrogen were different. Thus, the dipole moments of sulfamates affect the decomposition heat of sulfamates. The heat of decomposition in HNO₃/AcOH was larger than that in HNO₃/H₂SO₄.     

Existence of limit cycles for Liénard-type systems with p-Laplacian

The purpose of this paper is to give sufficient conditions under which an equivalent system to the equation has at least one stable limit cycle, where is the one-dimensional p-Laplacian. The main results are proved by means of phase plane analysis with the Poincaré-Bendixson theorem. Sufficient conditions are also given for the origin to be unstable and for all solutions to be bounded in the future. Jitsuro Sugie: Supported in part by Grant-in-Aid for Scientific Research 16540152     

Structures and Dynamic Solution Behavior of Cationic,Two‐Coordinate Gold(I)–π‐Allene Complexes

A family of seven cationic gold complexes that contain both an alkyl substituted π‐allene ligand and an electron‐rich, sterically hindered supporting ligand was isolated in >90 % yield and characterized by spectroscopy and, in three cases, by X‐ray crystallography. Solution‐phase and solid‐state analysis of these complexes established preferential binding of gold to the less substituted C?C bond of the allene and to the allene π face trans to the substituent on the uncomplexed allenyl C?C bond. Kinetic analysis of intermolecular allene exchange established two‐term rate laws of the form rate=k₁[complex]+k₂[complex][allene] consistent with allene‐independent and allene‐dependent exchange pathways with energy barriers of ΔG^≠₁=17.4–18.8 and ΔG^≠₂=15.2–17.6 kcal mol^?1, respectively. Variable temperature (VT) NMR analysis revealed fluxional behavior consistent with facile (ΔG^≠=8.9–11.4 kcal mol^?1) intramolecular exchange of the allene π faces through η¹‐allene transition states and/or intermediates that retain a staggered arrangement of the allene substituents. VT NMR/spin saturation transfer analysis of [{P(tBu)₂o‐binaphthyl}Au(η²‐4,5‐nonadiene) ]⁺SbF₆^? ( 5 ), which contains elements of chirality in both the phosphine and allene ligands, revealed no epimerization of the allene ligand below the threshold for intermolecular allene exchange (ΔG^≠_298K=17.4 kcal mol^?1), which ruled out the participation of a η¹‐allylic cation species in the low‐energy π‐face exchange process for this complex.