Algebraic polynomial
Local maxima of a random algebraic polynomial
... Abstract. We present a useful formula for the expected number of maxima of a normal process ξ(t) that occur belowa level u. In the derivation we assume chiefly that ξ(t), ξ (t), and ξ (t) have, with probability one, ...
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Zeros of an algebraic polynomial with nonequal means random coefficients
... random algebraic polynomial a 0 + a 1 x + a 2 x 2 + ··· + a n− 1 x n− 1 ...random polynomial is dictated by the mean of the first group of the coefficients in the interval (−1, 1) and the mean of the ...
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On the Existence of Non-Linear Invariants and Algebraic Polynomial Constructive Approach to Backdoors in Block Ciphers
... One of the major open problems in block cipher cryptanalysis is to discover new specific types of invariant properties which can hold for a larger number of rounds. In this paper we study non-linear Boolean ...
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ASYMPTOTIC ESTIMATES OF LEVEL CROSSINGS OF A RANDOM ALGEBRAIC POLYNOMIAL
... and Kostlan, H , The average number of maxima of a random algebraic curve, Proc.. Level crossings of random trigonometric polynomial, Proc.[r] ...
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ANALYTICAL EXPECTATION OF NUMBER OF LEVEL CROSSINGS OF A RANDOM TRIGONOMETRIC POLYNOMIAL
... variance of N ( 0 , 2 ) . The only attempt so far is ….where an (fairly large) upper bound is obtained. Indeed this could be justified since the problem with finding the variance consists of different levels of ...
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Dynamic Analysis of Rectangular Isotropic Plates Using Weak-Form Variational Principle
... develop algebraic polynomial shape functions based on static deflection configurations of orthogonal beam network that simulate the deflection of rectangular plate with various boundary conditions as ...
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Expected number of zeros of a random trigonometric polynomial
... 2 However, less . The only attempt so far is ….where an (fairly large) upper bound is obtained. Indeed this could be justified since the problem with finding the variance consists of different levels of ...
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On some constants in simultaneous approximation
... Pointwise estimates for the error which is feasible in simultaneous approximation of a function and its derivatives by an algebraic polynomial were originally pursued from theoretical.. [r] ...
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STRONG RESULT & ASYMPTOTIC ESTIMATES OF REAL ZEROS OF RANDOM POLYNOMIALS
... random algebraic polynomial for the expected number of real zeros of a random algebraic polynomial of the form The strong result for the lower bound was obtained in the general case by Their ...
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AVERAGE NUMBER OF REAL ZEROS OF RA NDOM TRIGONOMETRIC POLYNOMIAL
... KEYWORDS AND PHRASES: Independent, identically distributed random variables, random algebraic polynomial, random algebraic equation, real roots, domain of attraction of.. the nor[r] ...
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STRONG RESULT & ASYMPTOTIC ESTIMATES OF REAL ZEROS OF RANDOM POLYNOMIALS
... Keywords and phrases: Independent, identically distributed random variables, random algebraic polynomial, random algebraic equation, real roots, domain of attraction of the n[r] ...
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Measures of Maxima & Minima of a Cauchy Random Polynomial
... 1.4. Corresponding to each root of f(x) =0 in (0, 1). There exists a root of f (-x) =0 in (-1, 0) and conversely. Again f(x) =0 has a root in (1, ∞) implies x n f (G) =0 has root in (0, 1) where G=1/x. Sambadham [5] ...
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ANALYTICAL EXPECTATION OF NUMBER OF LEVEL CROSSINGS OF A RANDOM TRIGONOMETRIC POLYNOMIAL
... expectation of N 0 ( 0 , 2 ) N ( 0 , 2 ) is asymptotic to 2n / 3 . In [3] and [5] we show that this asymptotic number of crossings remains invariant for any K K n such that K 2 /n 0 as n . However, less ...
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Pick matrix conditions for sign definite solutions of the algebraic Riccati equation
... In this paper, we have restricted ourselves to the case in which (A, B) is a con- trollable pair, mainly in order to be able to use image representations. As a possible direction for future research, we mention the ...
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Toward A More Efficient Gröbner-based Algebraic Cryptanalysis
... The idea in this paper is to use such relations to improve algebraic attacks that are based on computation of Gröbner basis. In integral cryptanalysis, these relations are computed by a specific algebra that is ...
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Relationships between Darboux Integrability and Limit Cycles for a Class of Able Equations
... planar polynomial vector fields can be constructed possessing sufficient invariant algebraic ...a polynomial system of degree has at least invariant algebraic curves, then it has either a ...
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Algorithms for the computation of approximations by algebraic functions
... The main results established were that a clear formulation of the approximation problem leads to the existence of a unique approximating algebraic form which determines the polynomial co[r] ...
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New Strategies for Computing Gröbner Bases
... Algebraic methods can be classified into numerical and symbolic methods. Nu- meric methods can be sub-categorized into homotopy and iterative methods. Iterative methods, essentially, compute a sequence of ...
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Rewriting Environment for Arithmetic Circuit Verification
... a polynomial, referred to as as signature, over the variables representing the internal signals of the ...signature polynomial (starting with Sig out ) represents an output ...
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Matrix Computational Assumptions in Multilinear Groups
... (purely algebraic) generic model for the graded encodings in order to obtain meaningful results about the hardness and separations of computational ...completely algebraic formulation that follows the ideas ...
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