A real analytic surface inside complex 3-space with an isolated, nondegenerate complex tangent is shown to be biholomorphically equivalent to a fixed real algebraic variety. The analyticity of the normalizing transformation is proved using a rapid convergence argument. Real surfaces in higher dimensions are also shown to have an algebraic normal form. 1 2

In this paper, three new methods for two-dimensional (2-D) adaptive notch filter (ANF) are proposed. They not only contain similar and simpler structures but also can be derived by simpler adaptive algorithms compared with the previous ones. They are helpful for 2-D signal processing. Simulation results show that they can eliminate 2-D sinusoidal signals successfully.

In this paper a new method of frequency tracking based on modified adaptive notch filter is proposed to solve the problem of dynamic frequency tracking of low capacity power system, the ANF equations is discretizated, the influence of the ANF parameters on frequency tracking is analyzed, the band-pass pre-filter and the low-pass post-filter are applied. With applying iterative updates synchrono...

A caterpillar unicyclic graph is a unicyclic graph in which the removal of all pendant vertices makes it a cycle. In this paper, the unique caterpillar unicyclic graph with minimum algebraic connectivity among all caterpillar unicyclic graphs is determined.

We consider the Fourier Entropy-Influence (FEI) conjecture in the context of cryptographic Boolean functions. We show that the FEI conjecture is true for the functions satisfying the strict avalanche criterion, which forms a subset of asymptotic log–density 1 in the set of all Boolean functions. Further, we prove that the FEI conjecture is satisfied for plateaued Boolean functions, monomial alg...

In this paper, we discuss some methods of constructing frequency/time hopping (FH/TH) sequences over GF (p) by taking successive k-tuples of given sequences over GF (p). We are able to characterize those p-ary sequences whose k-tuple versions now over GF (p) have the maximum possible linear complexities (LCs). Next, we consider the FH/TH sequence generators composed of a combinatorial function ...

following the categorical approach to universal algebra through algebraic theories, proposed by f.~w.~lawvere in his phd thesis, this paper aims at introducing a similar setting for general topology. the cornerstone of the new framework is the notion of emph{categorically-algebraic} (emph{catalg}) emph{topological theory}, whose models induce a category of topological structures. we introduce t...

We present an algorithm that computes the weight of a Boolean function from its Algebraic Normal Form (ANF). For functions acting on high number of variables (n > 30) and having low number of monomials in its ANF, the algorithm is advantageous over the standard method of computing weight which requires the transformation of function’s ANF to its truth table with a complexity of O(n2) operations...

A new IIR adaptive notch filter (ANF) with fast convergence rate, accurate estimation of notch frequencies, and modest realization complexity is presented in this paper. The problem of obtaining a notch filter from a given signal containing multiple sine waves in noise is first formulated as the conventional problem of system identification. Then the new ANF is developed via the algorithm of St...

We construct the algebra of integro-differential operators over an ordinary integro-differential algebra directly in terms of normal forms. In the case of polynomial coefficients, we use skew polynomials for defining the integro-differential Weyl algebra as a natural extension of the classical Weyl algebra in one variable. Its normal forms, algebraic properties and its relation to the localizat...