Given a quasi-definite linear functional u in the space of polynomials with complex coefficients, let us consider corresponding sequence monic orthogonal (SMOP short) (Pn)n≥0. For canonical Christoffel transformation u˜=(x−c)u SMOP (P˜n)n≥0, we are interested to study relation between u˜ and u(1)˜, where u(1) is for associated first kind (Pn(1))n≥0, u(1)˜=(x−c)u(1) its transformation. This prob...

This paper proposes a new method to find the equations of transformation matrix for the rotation angles of the two rotational axes and the coordinates of the three linear axes of an orthogonal multi-axis milling machine. This approach provides intuitive physical meanings for rotation angles of multi-axis machines, which can be used to evaluate the accuracy of the conversion from CL data to NC d...

One of the major drawbacks of the symmetric QR algorithm is that it is not parallelizable. Each orthogonal similarity transformation that is needed to reduce the original matrix A to diagonal form is dependent upon the previous one. In view of the evolution of parallel architectures, it is therefore worthwhile to consider whether there are alternative approaches to reducing an n × n symmetric m...

We demonstrate that the structure of a 3D point set with a single bilateral symmetry can be reconstructed from an uncalibrated affine image, modulo a Euclidean transformation, up to a four parameter family of symmetric objects that could have given rise to the image. If the object has two orthogonal bilateral symmetries, the shape can be reconstructed modulo similarity. Both results are demonst...

The present contribution proposes a new remarkably eecient image compression algorithm for graylevel images based on dyadic wavelet transformation. In order to achieve perfect reconstruction, orthogonal decomposition is applied. Scalar quantization of wavelet coeecients is combined with run-length coding. Code word assignment is performed by semi-adaptive Huuman coding (determined by validity t...

The paper presents a fully differential log-domain low-pass second order filter. The topology was derived, using a LINELIN transformation, from a standard state-variable biquad. The filter allow for orthogonal parameter tuning. Its low-frequency gain (H0), natural pulsation (ω0) and quality factor (Q) can be tuned continuously by varying only DC bias currents. The filter was implemented in a ge...

We construct a family of BCn-symmetric biorthogonal abelian functions generalizing Koornwinder’s orthogonal polynomials, and prove a number of their properties, most notably analogues of Macdonald’s conjectures. The construction is based on a direct construction for a special case generalizing Okounkov’s interpolation polynomials. We show that these interpolation functions satisfy a collection ...

The concept of k-coherence of two positive measures μ1 and μ2 is useful in the study of the Sobolev orthogonal polynomials. If μ1 or μ2 are compactly supported onRthen any 0-coherentpair or symmetrically 1-coherent pair (μ1, μ2) must contain a Jacobi measure (up to affine transformation). Here examples of k-coherent pairs (k ≥ 1) when neither μ1 nor μ2 are Jacobi are constructed.

Integration of periodic functions on the real line with an even rational weight function is considered. A transformation method of such integrals to the integrals on (−1, 1) with respect to the Szegő-Bernstein weights and a construction of the corresponding Gaussian quadrature formulas are given. The recursion coefficients in the three-term recurrence relation for the corresponding orthogonal p...