In order to the second order Cauchy problem (CP2): x"(t) Ax(t), z(O) z E D(A"), z"(O) y D(A") on a Banach space, Arendt and Kellermann recently introduced the integrated cosine function. This paper is concerned with its basic theory, which contain some properties, perturbation and approximation theorems, the relationship to analytic integrated semigroups, interpolation and extrapolation theorems.

An extension of the simplex algorithm is presented. For a given linear programming problem, a sequence of relaxed linear programming problems is solved until a solution to the original problem is reached. Each successive relaxed problem is obtained from the previous one by adding a single constraint chosen from the constraints violated by the solution to the previous relaxed problem. This added...

Suppose that G is a discrete abelian group and A ⊂ G is a finite symmetric set. We show two main results. (i) Either there is a set H of O(log |A|) subgroups of G with |A△ S H| = o(|A|), or there is a character γ ∈ b G such that −c 1A(γ) = Ω(log c |A|) where c > 0 is the same absolute constant. (ii) If G is finite and |A| = Ω(|G|) then either there is a subgroup H 6 G such that |A△H| = o(|A|), ...

curvature. The boundary of an object is first represented into curvature measured by K-cosine. Then, by modifying the corner detection error, this study proposes a suitable K value and curvature threshold for robust corner detection. Furthermore, the proposed K-cosine corner detection (KCD) was verified with several commonly employed digital objects. The experimental results reveal that the pro...

A BRDF approximation is developed that is suitable for interactive color appearance design in direct lighting provided by environment maps. The BRDFs are approximated as a linear combination of cosine lobes with a fixed set of specular exponents. A nonlinear optimization routine is used to fit the cosine lobes to BRDFs appropriate for a specific color appearance design application: automotive p...

This paper is associated with implementation of Sine & Cosine using Volder’s CORDIC Algorithm. CORDIC algorithm based Systems are used for fast and silicon area efficient computation of the sine and cosine functions. The algorithmic approach for the CORDIC algorithm implementation is presented here. Summary of CORDIC synthesis results based on Actel and XILINX FPGAs is given. Finally applicatio...

We present a preliminary investigation of compression of segmented 3D seismic volumes for the rendering purposes. Promising results are obtained on the base of 3D discrete cosine transforms followed by the SPIHT coding scheme. An accelerated version of the algorithm combines 1D discrete cosine transform in vertical direction with the 2D wavelet transform of horizontal slices. In this case the S...

Cosine similarity is a term-vector-based measure of similarity that has been used widely in information retrieval research. In this study, we collect user judgments of web document similarity in order to investigate the correlation between cosine similarity and users’ perception of similarity on web documents. Experimental results demonstrate that it is hard to deduce that cosine similarity cor...

Selectivity estimation is an important task for query optimization. We propose a technique to perform range query estimation over multiple data streams using micro-clustering. The technique maintains cluster statistics in terms of micro-clusters and cosine series for all streams. These microclusters maintain data distribution information about the stream values using cosine coefficients. These ...

Base band transmission of digital data requires the use of a low pass channel with a bandwidth large enough to accommodate the essential frequency content of the data stream. However the channel is dispersive in that its frequency response deviates from that of an ideal low pass filter. The result of data transmission over such channel is that each received pulse is affected somewhat by adjacen...