The capacitance of the circular parallel plate capacitor is calculated by expanding the solution to the Love integral equation into a Fourier cosine series. Previously, this kind of expansion has been carried out numerically, resulting in accuracy problems at small plate separations. We show that this bottleneck can be alleviated, by calculating all expansion integrals analytically in terms of ...

We consider two integral transforms which are frequently used in integral geometry and related fields, namely the cosine and the spherical Radon transform. Fast algorithms are developed which invert the respective transforms in a numerically stable way. So far, only theoretical inversion formulas or algorithms for atomic measures have been derived, which are not so important for applications. W...

A discrete-cosine-transformation (DCT) based decomposition method is proposed for modeling part form error, which decomposes the error field into a series of independent error modes. Compression, which ensures a compact model, is achieved by correlation reduction or mode truncation based on good energy compaction property of DCT. The part error related to assembly process (rigid body modes) and...

S. A. Telyakovskiı̆ (1964, Izv. Akad. Nauk. SSR. Ser. Mat. 28, 1209–1236) proved an integrability condition for cosine series. No condition superior to that has been given so far. In this paper we identify the atomic structure of the Hardy type space that can be associated with this condition. As a consequence, we conclude that Telyakovskiı̆’s condition is equivalent to certain Sidon type inequal...

Similarity measures are an important tool in pattern recognition and medical diagnosis. To overcome some disadvantages of existing cosine similarity measures for simplified neutrosophic sets (SNSs) in vector space, this paper proposes improved cosine similarity measures for SNSs based on the cosine function, including single valued neutrosophic cosine similarity measures and interval neutrosoph...

The acceleration of an option pricing technique based on Fourier cosine expansions on the graphics processing unit (GPU) is reported. European options, in particular with multiple strikes, and Bermudan options will be discussed. The influence of the number of terms in the Fourier cosine series expansion, the number of strikes, as well as the number of exercise dates for Bermudan options is expl...