We introduce the concept of maximal lineability cardinal number, mL(M), of a subset M of a topological vector space and study its relation to the cardinal numbers known as: additivity A(M), homogeneous lineability HL(M), and lineability L(M) of M . In particular, we will describe, in terms of L, the lineability and spaceability of the families of the following Darboux-like functions on Rn, n ≥ ...

We derive a new zero-curvature formalism for the sine-Gordon (sG) equation which permits the introduction of a local sine-Gordon hierarchy (in contrast to the traditionally accepted nonlocal higher-order sG equations). In complete analogy to other completely integrable hierarchies of soli-ton equations, such as the KdV, AKNS, and Toda hierarchies, our local sG hierarchy is recursively construct...

1 Abstract This paper describes the design and simulation of an 8-bit dedicated processor for calculating the Sine and Cosine of an Angle using CORDIC Algorithm (COordinate Rotation DIgital Computer), a simple and efficient algorithm to calculate hyperbolic and trigonometric functions. We have proposed a dedicated processor system, modeled by writing appropriate programs in VHDL, for calculatin...

This paper presents a novel low complexity, frequency domain algorithm for reconstruction of speech from the melfrequency cepstral coe cients (MFCC), commonly used by speech recognition systems, and the pitch frequency values. The reconstruction technique is based on the sinusoidal speech representation. A set of sine-wave frequencies is derived using the pitch frequency and voicing decisions, ...

In this paper, we study the reconstruction of functions in spline subspaces from local averages. We present an average sampling theorem for shift invariant subspaces generated by cardinal B-splines and give the optimal upper bound for the support length of averaging functions. Our result generalizes an earlier result by Aldroubi and Gröchenig.

In previous papers, the Fourier transform (FT) has been generalized into the fractional Fourier transform (FRFT), the linear canonical transform (LCT), and the simplified fractional Fourier transform (SFRFT). Because the cosine, sine, and Hartley transforms are very similar to the FT, it is reasonable to think they can also be generalized by the similar way. In this paper, we will introduce sev...

We show that for each positive integer k there is a sequence Fn : R → R of continuous functions which represents via point-wise limits arbitrary functions G : X → R defined on domains X ⊆ R of sizes not exceeding a standard cardinal characteristic of the continuum.

For topological spaces X and Y, let Qp(X,Y) be the space of all quasicontinuous functions from to Y with topology pointwise convergence. In this paper, we study cardinal invariants such as cellularity, character, weight, density, pseudocharacter spread Qp(X,Y). We also discuss properties restriction induced maps related