Oscillation theorems for fourth order functional differential equations

The authors investigate the oscillatory behavior of all solutions of the fourth order functional differential equations $\frac{d^{3}}{dt^{3}}(a(t)(\frac{dx(t)}{dt})^{\alpha})+q(t)f(x[g(t)])=0$ and $\frac{d^{3}}{dt^{3}}(a(t)(\frac{dx(t)}{dt})^{\alpha})=q(t)f(x[g(t)])+p(t)h(x[\sigma(t)])$ in the case where ∫ ^∞ a ^?1/α (s)ds<∞. The results are illustrated with examples.     

Streptidinium sulfate monohydrate

In streptidinium sulfate monohydrate {systematic name: 1,1′‐[(1S,3R,4S,6R)‐2,4,5,6‐tetrahydroxycyclohexane‐1,3‐diyl]diguanidinium sulfate monohydrate}, C₈H₂₀N₆O₄²⁺·SO₄²⁻·H₂O, at 100 (2) K, the components are arranged in double helices based on hydrogen bonds. One helix contains streptidinium cations and the other contains disordered sulfate anions and solvent water molecules. The helices are linked into a three‐dimensional hydrogen‐bonded network by O—H...O and N—H...O hydrogen bonds.     

The Finite Horizon Optimal Multi-Modes Switching Problem: The Viscosity Solution Approach

In this paper we show existence and uniqueness of a solution for a system of m variational partial differential inequalities with inter-connected obstacles. This system is the deterministic version of the Verification Theorem of the Markovian optimal m-states switching problem. The switching cost functions are arbitrary. This problem is in relation with the valuation of firms in a financial market.     

Influence of annealing temperature on structural and optical properties of ZnO: In thin films prepared by ultrasonic spray technique

Transparent conducting indium doped zinc oxide was deposited on glass substrate by ultrasonic spray method. The In doped ZnO samples with indium concentration of 3 wt.% were deposited at 300, 350 and 400 °C with 2 min of deposition time. The effects of substrate temperature and annealing temperature on the structural, electrical and optical properties were examined. The DRX analyses indicated that In doped ZnO films have polycrystalline nature and hexagonal wurtzite structure with (0 0 2) preferential orientation and the maximum average crystallite size of ZnO: In before and annealed at 500 °C were 45.78 and 55.47 nm at a substrate temperature of 350 °C. The crystallinity of the thin films increased by increasing the substrate temperature up 350 °C, the crystallinity improved after annealing temperature at 500 °C. The film annealed at 500 °C and deposited at 350 °C show lower absorption within the visible wavelength region. The band gap energy increased from E_g = 3.25 to 3.36 eV for without annealing and annealed films at 500 °C, respectively, indicating that the increase in the transition tail width. This is due to the increase in the electrical conductivity of the films after annealing temperature.     

The theoretical treatment of cooling processes in porous rocket thrustchambers

One of the most promising approaches for future high pressure rocket combustion chambers is the application of porous carbon fiber reinforced ceramics in conjunction with the effusion cooling in fluid‐cooled rocket engines. In order to determine the coolant mass flow through the porous material, the influences of the temperature have to be taken into account additionally. Thus, one has to deal with interacting continua governed by non‐isothermal processes, when designing a porous rocket combustion chamber for realistic operating conditions such as extremely high temperatures. Describing coupled solid‐fluid problems efficiently, it is generally convenient to utilize macroscopic strategies like the Theory of Porous Media (TPM). While in the past, most of the multiphase problems based on the TPM have been treated isothermally, the present contribution extends the theoretical treatment to non‐isothermal problems. This is achieved by proceeding from a thermoelastic solid skeleton saturated by a compressible viscous pore‐fluid, whereas a separate temperature field has to be established for each constituent. Finally, the efficiency of the developed model will be briefly discussed by computing some simple non‐isothermal physical effects, which are solved by the FE tool PANDAS. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Oscillation of 2nd-order Nonlinear Noncanonical Difference Equations with Deviating Argument

The purpose of this paper is to establish some new criteria for the oscillation of the second-order nonlinear noncanonical difference equations of the form \[ \Delta \left( a\left( n\right) \Delta x\left( n\right) \right) +q(n)x^{\beta }\left( g(n)\right) =0,\text{ \ \ }n\geq n_{0} \] under the assumption \[ \sum_{s=n}^{\infty }\frac{1}{a\left( s\right) }<\infty \text{.} \] Corresponding difference equations of both retarded and advanced type are studied. A particular example of Euler type equation is provided in order to illustrate the significance of our main results.     

A new one‐step synthesis of pyrimido‐[1,2‐b][1,2,4,5]tetrazines

Hydrazonoyl halides 4 react readily with either 3‐amino‐2,3‐dihydro‐6‐methyl‐2‐thioxo‐4(1H)‐pyrimidinone 5 or 3‐amino‐6‐methyl‐2‐methylthio‐4(3H)‐pyrimidinone 6 to form 6H‐pyrimido[1,2‐b][1,2,4,5]tetrazin‐6‐ones 9. The mechanism of the studied reactions is discussed. © 2000 John Wiley & Sons, Inc. Heteroatom Chem 11:87–90, 2000