On Some Infinite Convex Invariants

The present study on some infinite convex invariants. The origin of convexity can be traced back to the period of Archimedes and Euclid. At the turn of the nineteenth centaury , convexicity became an independent branch of mathematics with its own problems, methods and theories. The convexity can be sorted out into two kinds, the first type deals with generalization of particular problems such as separation of convex sets[EL], extremality[FA], [DAV] or continuous selection Michael[M1] and the second type involved with a multi- purpose system of axioms. The theory of convex invariants has grown out of the classical results of Helly, Radon and Caratheodory in Euclidean spaces. Levi gave the first general definition of the invariants Helly number and Radon number. The notation of a convex structure was introduced by Jamison[JA4] and that of generating degree was introduced by Van de Vel[VAD8]. We also prove that for a non-coarse convex structure, rank is less than or equal to the generating degree, and also generalize Tverberg’s theorem using infinite partition numbers. Compare the transfinite topological and transfinite convex dimensions

A Novel Accelerator Combination for the Low Temperature Curing of Silica-Filled NBR Compounds

Zinc salts of ethyl, isopropyl, and butyl xanthates were prepared in the laboratory. The effect of these xanthates in combination with zinc diethyldithiocarbamate (ZDC) on the vulcanization of silica-filled NBR compounds has been studied at different temperatures. The cure times of these compounds were compared with that of NBR compounds containing tetramethylthiuram disulphide/dibenzthiazyl disulphide. The rubber compounds with the xanthates and ZDC were cured at various temperatures from 60 to 150°C. The sheets were molded and properties such as tensile strength, tear strength, crosslink density, elongation at break, compression set, abrasion resistance, flex resistance, heat buildup, etc. were evaluated. The properties showed that zinc salt of xanthate/ZDC combination has a positive synergistic effect on the cure rate and mechanical properties of NBR compounds.

Studies on Xanthate/Dithiocarbamate Accelerator Combination in NR/BR Blends

Zinc butyl xanthate [Zn(bxt)2] was prepared in the laboratory . The effect of this xanthate with zinc diethyl dithiocarbamate (ZDC) on the vulcanization of natural rubber ( NR), polybutadiene rubber (BR), and NR/BR blend has been studied at different temperatures. The amounts of Zn (bxt)2 and ZDC in the compounds were optimized by varying the amount of ZDC from 0 . 75 to 1.5 phr and Zn (bxt)2 from 0 . 75 to 1 .5 phr. The cure characteristics were also studied . HAF filled NR, BR, and NR / BR blend compounds were cured at different temperatures from 60 to 150 C. The sheets were molded and properties such as tensile strength, tear strength, crosslink density and elongation at break, compression set, abrasion resistance, etc. were evaluated. The results show that the mechanical properties of 80NR/20BR blends are closer to that of NR vulcanizates, properties of 60NR/40BR blends are closer to BR vulcanizates, while the 70NR/30BR blends show an intermediate property.

Investigations on the Dynamics of Combination Maps and the Analysis of Bifurcation in a Discontinuous Logistic Map

This thesis is a study of discrete nonlinear systems represented by one dimensional mappings.As one dimensional interative maps represent Poincarre sections of higher dimensional flows,they offer a convenient means to understand the dynamical evolution of many physical systems.It highlighting the basic ideas of deterministic chaos.Qualitative and quantitative measures for the detection and characterization of chaos in nonlinear systems are discussed.Some simple mathematical models exhibiting chaos are presented.The bifurcation scenario and the possible routes to chaos are explained.It present the results of the numerical computational of the Lyapunov exponents (λ) of one dimensional maps.This thesis focuses on the results obtained by our investigations on combinations maps,scaling behaviour of the Lyapunov characteristic exponents of one dimensional maps and the nature of bifurcations in a discontinous logistic map.It gives a review of the major routes to chaos in dissipative systems,namely, Period-doubling ,Intermittency and Crises.This study gives a theoretical understanding of the route to chaos in discontinous systems.A detailed analysis of the dynamics of a discontinous logistic map is carried out, both analytically and numerically ,to understand the route it follows to chaos.The present analysis deals only with the case of the discontinuity parameter applied to the right half of the interval of mapping.A detailed analysis for the n –furcations of various periodicities can be made and a more general theory for the map with discontinuities applied at different positions can be on a similar footing

Convex extendable trees

The concept of convex extendability is introduced to answer the problem of finding the smallest distance convex simple graph containing a given tree. A problem of similar type with respect to minimal path convexity is also discussed.

Influence of Interface Surface Geometries In The Tensile Characteristics Of Friction Welded Joints From Aluminium Alloys

Friction welding is a solid state joining process that produces coalescence in materials, using the heat developed between surfaces through a combination of mechanical induced rubbing motion and applied load. In rotary friction welding technique heat is generated by the conversion of mechanical energy into thermal energy at the interface of the work pieces during rotation under pressure. Traditionally friction welding is carried out on a dedicated machine because of its adaptability to mass production. In the present work, steps were made to modify a conventional lathe to rotary friction welding set up to obtain friction welding with different interface surface geometries at two different speeds and to carry out tensile characteristic studies. The surface geometries welded include flat-flat, flat-tapered, tapered-tapered, concave-convex and convex-convex. A comparison of maximum load, breaking load and percentage elongation of different welded geometries has been realized through this project. The maximum load and breaking load were found to be highest for weld formed between rotating flat and stationary tapered at 500RPM and the values were 19.219kN and 14.28 kN respectively. The percentage elongation was found to be highest for weld formed between rotating flat and stationary flat at 500RPM and the value was 21.4%. Hence from the studies it is cleared that process parameter like “interfacing surface geometries” of weld specimens have strong influence on tensile characteristics of friction welded joints