The discrete groups which are fundamental groups of manifolds are at the heart of some of the most challenging problems in geometry and topology. These problems have motivated mathematicians to use both geometry and functional analysis (including C*-algebras) to study groups. This geometry and functional analysis approach is culminated in the statement of the Baum-Connes conjecture. K- theory is the language of the Baum-Connes conjecture, as well as the setting for most approaches to its proof. The study of K-nuclearity of C*-algebras and K-amenability of groups have contributed significantly to our understanding of the Baum-Connes conjecture. Similarly, K-exactness of C*-algebras and groups is the K-theoretic version of exactness. Indeed, a group G is called K-exact if the minimal tensor product by Cr*G preserves the K-theoretic cyclic six-term exact sequence, regardless of whether it preserves short exact sequences of C*-algebras. It is known that every coarsely embeddable group satisfies the coarse Baum-Connes. In this work we investigate the relationship between K-exactness and coarse embeddability of groups into a Hilbert space H.
Badminton is primarily a power sport in which athletes must accelerate and shift in multiple directions around the court. Players must smash the shuttlecock with a high velocity and immediately be prepared to return a volley. The role of biomechanics in attaining high performance cannot be overlooked, since it is the only science, which helps identify the faults of performing technique very precisely. High-speed module film for exactness has been used extensively to examine in details of the movements, which occur too fast for the human eye to detect. To investigate the relationship of selected linear and angular kinematic variables with the performance of smash (forehand) in badminton, Digital photography technique was used.The stick figures were preferred on transparency by using joint point method, and the various angular kinematics variables were obtaining it moment contact. Segmentation method was employed in order to assess the center of gravity of the body during time of moment contact with the shuttle. The performance of the selected photo was used as the criterion measure for the study.
Layout-induced parasitics have significant effects on the behavior of circuits in general and the performance of high-frequency analog ones in particular. To achieve parasite-inclusive performance-closure, layout-aware circuit synthesis methodologies are beginning to emerge. In layout-in-the-loop synthesis methodologies, performance analysis is based on the generation of a concrete layout for the explored circuit sizes. A parasite-inclusive circuit is extracted from the layout using a standard extractor and is analyzed using a simulator to determine whether the required constraints are met; this is time consuming. Various approaches of estimating parasitics lack the correctness that would only come from examining the layout itself. The proposed approach tries to include the exactness of the layout to be generated without actually generating it. It relies on using pre-generated structures for the specified unsized circuit; these structures are generated pre-synthesis and contain the information that a layout would have provided to a synthesis process if it was to be generated. This information contains extraction specifics for modules, their location and routing characteristics.
In computer graphics, can we represent an arbitrary distorted object with exactness mathematically and analytically? Why does JPGE 2000 have blurred edges in highly compressed images? How to process the mass data in the fields such as stock market, medical research, or the Internet efficiently in real time? During the past a few decades, Wavelets based on B-Splines have successfully overcome the drawback of Fourier Analysis and become the important industrial standards. However, they can not represent many important industrial shapes precisely, which is crucial, for example, in aircraft design. Although NURBs ( nonuniform rational B-Splines) have solved the problem, the challenge of constructing corresponding wavelets from NURBs remains due to the complicate rational structure of NURBs. There is an uncertainty that whether such a MRA NURBlet structure exists. The dissertation makes a novel move by successfully constructing biorthogonal NURBlets based on cubic NURBs on interval.