Unsteady and chaotic characteristics of natural convection field in vertical slots at large Prandtl number

In this study we examined the unsteady and chaotic characteristics of the natural convection field in vertical slots at large Prandtl number. In the computation, temperature dependence of viscosity was partially taken into consideration. As a result we discovered that the spatial region where a significant temperature fluctuation is detected corresponds to the spatial region where the secondary cells exist. The largest Lyapunov exponents calculated from the temperature on the center line have a local maximum at the lower region of the enclosure when the viscosity change was considered. These characteristics agree well with the experimental ones that have been observed by authors (Ishida, Kure and Kimoto 2001).     

Some inequalities for the polar derivative of a polynomial

LetP(z) be a polynomial of degreen which does not vanish in |z|<1. In this paper, we estimate the maximum and minimum moduli of thekth polar derivative ofP(z) on |z|=1 and thereby obtain compact generalizations of some known results, which among other results, yields interesting refinements of Erdos-Lax theorem and a theorem of Ankeny and Rivlin.     

Numerical calculations of temperature distribution of double layer metallic surface treated by laser beams

A mathematical model of laser beam treatment of double layer alloys (Ni/Fe, Al/Fe and Cr/Fe systems) describing the effect of laser beam on different physical and geometrical parameters of coated layer system has been adapted. The numerical solutions of the non-homogeneous heat-transport differential equation could estimate the temperature of the treated region.The suggested model allows investigation of the temperature distribution as a function of treated surface and laser parameters. The physical parameters of the treated materials were taken as functions of temperature due to the change in the temperature of the treated double layer materials.     

On the Use of the Restitution Condition in Flexible Body Dynamics

The difference between the classical treatment offlexible body impact and the treatment of impact in flexiblemultibody dynamics is due to several fundamental reasons. Inthe classical impact theory, simple structures such as beamsand plates are used. Infinite dimensional models can bedeveloped for these simple structural elements to study theimpact dynamics and the wave propagation problem. Flexiblemultibody impact problems, on the other hand, involve bodieswith complex geometry that cannot be modeled using infinitenumber of degrees of freedom. Furthermore, the classicalimpact theory has been mainly concerned with the impactbetween a rigid mass that moves without constraints beforeit impacts a simple flexible structure. This is not amultibody simulation scenario in which the impact occursbetween kinematically constrained bodies that are subjectedto impulsive constraint forces in addition to the impactforces. These constraint forces can influence the motion ofthe two bodies immediately after impact, and as aconsequence, the simple classical theory scenario of impactdoes not apply. It is the objective of this paper to discussthe use of the restitution condition in flexible multibodyimpact problems and demonstrate that the use of thisapproach does not exclude the classical formulation.Nonetheless, the impulse momentum balance approach can serveas an effective and efficient procedure for solving theimpact problem in finite dimensional models that do not obeythe classical wave theory. Energy results of simplestructural elements are presented in order to demonstratethe consistency of using the impulse momentum balanceapproach in solving impact problems in finite dimensionalflexible body applications.     

A Complete Classification of Curvature Collineations of Cylindrically Symmetric Static Metrics

Curvature collineations are symmetry directions for the Riemann tensor, as isometries are for the metric tensor and Ricci collineations are for the Ricci tensor. Complete listings of many metrics possessing some minimal symmetry have been given for a number of symmetry groups for the latter two symmetries. It is shown that a claimed complete listing of cylindrically symmetric static metrics by their curvature collineations [1] was actually incomplete and is completed here. It turns out that in this complete list, unlike the previous claim, there are curvature collineations that are distinct from the set of isometries and of Ricci collineations. The physical interpretation of some of the metrics obtained is given.     

Fluctuation study of pionisation in ultrarelativistic nucleus-nucleus interaction

The scaled factorial moments and the multifractal moments have been investigated in differentη-intervals to study the dynamical fluctuation of pions produced in 200 AGeV³²S-Ag/Br interaction. In order to investigate the detail characteristics of intermittency behaviour, theF-moments are extracted up to the eighth order of moments in differentM-intervals. The analysis indicates a non-thermal phase transition and different regime of particle production during the hadronisation process.     

1‐Acetyl‐3′‐(4‐bromophenyl)‐3′‐chlorospiro[3H‐indole‐3,2′‐oxetan]‐2(1H)‐one

In the title compound, C₁₈H₁₃BrClNO₃, the heterocyclic ring of the indole is distorted from planarity towards an envelope conformation. The orientations of the indole, oxetane, chloro and bromo­phenyl substituents are conditioned by the sp³ states of the spiro‐junction and the Cl‐attached C atoms.     

Di‐2‐pyridyl ketone N4,N4‐(butane‐1,4‐diyl)thiosemicarbazone

The title compound, C₁₆H₁₇N₅S, is in the thione form and crystallizes with two independent mol­ecules in the asymmetric unit. In both mol­ecules, the penta­methyl­ene­imine five‐membered ring adopts an envelope conformation, and in one of the molecules this ring shows positional disorder. The thione S and hydrazine N atoms are in the Z configuration with respect to the C—N bond.     

Cobalt(II), nickel(II), copper(II) and zinc(II) complexes of conjugated 3-(benzylidene/salicylidene)-β-diketones (having no enolisable γ-carbon proton) and their reactions

Transition Metal Chemistry - The synthesis and structural characterization of new metal(II) chelates (M = CoII, NiII, CuII and ZnII) of neutral conjugated bidentate β-diketone ligands, having...