The classical result of L. Szekelyhidi states that (under some assumptions) every solution of a general linear equation must be a polynomial function. It is known that Szekelyhidi's result may be generalized to eq...
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The classical result of L. Szekelyhidi states that (under some assumptions) every solution of a general linear equation must be a polynomial function. It is known that Szekelyhidi's result may be generalized to equations where some occurrences of the unknown functions are multiplied by a linear combination of the variables. In this paper we study the equations where two such combinations appear. The simplest nontrivial example of such a case is given by the equation F(x + y) - F(x) - F(y) = yf(x) + xf(y) considered by Fechner and Gselmann (Publ Math Debrecen 80(1-2):143-154, 2012). In the present paper we prove several results concerning the systematic approach to the generalizations of this equation.
A continuous selection of polynomial functions is a continuous function whose domain can be partitioned into finitely many pieces on which the function coincides with a polynomial. Given a set of finitely many polynom...
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A continuous selection of polynomial functions is a continuous function whose domain can be partitioned into finitely many pieces on which the function coincides with a polynomial. Given a set of finitely many polynomials, we show that there are only finitely many continuous selections of it and each one is semi-algebraic. Then, we establish some generic properties regarding the critical points, defined by the Clarke subdifferential, of these continuous selections. In particular, given a set of finitely many polynomials with generic coefficients, we show that the critical points of all continuous selections of it are finite and the critical values are all different, and we also derive the coercivity of those continuous selections which are bounded from below. We point out that some existing results about Lojasiewicz's inequality and error bounds for the maximum function of some finitely many polynomials can be extended to all the continuous selections of them.
Given a finite zero-symmetric near-ring with identity N, we ask whether there is a group G such that N is isomorphic to the inner automorphism near-ring , or whether N is a compatible near-ring. We will show that ther...
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Given a finite zero-symmetric near-ring with identity N, we ask whether there is a group G such that N is isomorphic to the inner automorphism near-ring < I(G);+, o >, or whether N is a compatible near-ring. We will show that there are algorithms that decide these questions. To this end, we study polynomial functions on subdirectly irreducible expanded groups. We prove that the size of a finite subdirectly irreducible expanded group is bounded from above by a function of the number of its zero-preserving unary polynomial functions.
If R is a finite commutative ring, it is well known that there exists a nonzero polynomial in R[T] which is satisfied by every element of R. In this paper, we classify all commutative rings R such that every element o...
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If R is a finite commutative ring, it is well known that there exists a nonzero polynomial in R[T] which is satisfied by every element of R. In this paper, we classify all commutative rings R such that every element of R satisfies a particular monic polynomial. If the polynomial, satisfied by the elements of R, is not required to be monic, then we can give a classification only for Noetherian rings, giving examples to show that the characterization does not extend to arbitrary commutative rings.
In the present paper we solve the generalized form of the functional equation considered in Fechner and Gselmann (Publ Math Debr 80(1-2):143-154, 2012), that is we find general solutions of the following functional eq...
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In the present paper we solve the generalized form of the functional equation considered in Fechner and Gselmann (Publ Math Debr 80(1-2):143-154, 2012), that is we find general solutions of the following functional equation. F(x + y) - F(x) - F(y) = Sigma(m)(i=1) (a(ix) +b(iy))f(alpha(i)x + beta(i)y) for all x, y, a(i),b(i) is an element of R and at alpha(i),beta(i) is an element of Q. Thus we continue investigations presented in Nadhomi et al. (Aequationes Math, 95:1095-1117, 2021) where we generalized the left hand side of Fechner-Gselmann equation. It turns out that under some mild assumption, the pair (F, f) solving (0.1) happens to be a pair of polynomial functions, and in some important cases just the usual polynomials (despite the fact that we assume no regularity of solutions a priori). In the second part of the present paper we formulate an algorithm written in the computer algebra system Maple which determines the polynomial solutions of the functional equations belonging to the class (0.1) (cf. also Borus and Gilanyi in 2013 IEEE 4th International Conference on Cognitive Infocommunications (CogInfoCom), pp 559-562, 2013;Aequationes Math 94(4):723-736, 2020;Gilanyi in Math Pannon 9(1):55-70, 1998).
Whenever a numerical method produces accurate results, it creates an interesting functional equation, and because regularities is not assumed, unexpected solutions can emerge. Thus, this paper is mainly devoted to fin...
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Whenever a numerical method produces accurate results, it creates an interesting functional equation, and because regularities is not assumed, unexpected solutions can emerge. Thus, this paper is mainly devoted to finding solutions to a generalized functional equation constructed in this spirit;namely, we solve the generalized form of the functional equation considered in Fechner and Gselmann (Publ Math Debrecen 80(1-2):143-154, 2012), then considered in Nadhomi et al. (Aequationes Math 95:1095-1117, 2021) and continued in Okeke and Sablik (Results Math 77:125, https://***/10.1007/s00025-022- 01664-x, 2022), that is we find the polynomial functions satisfying the following functional equation [GRAPHICS] special forms. Thus we continue investigations presented in Nadhomi et al. (Aequationes Math 95:1095-1117, 2021) where we generalized the left hand side of Fechner-Gselmann equation and those from Okeke and Sablik (Results Math 77:125, https://***/10.1007/s00025-022- 01664-x, 2022) where the right hand side of the Fechner-Gselmann equation was studied. It turns out that under some assumptions on the parameters involved, the pair (F, f) solving Eq. (0.1) happens to be a pair of polynomial functions.
In this paper, we consider the problem of identifying the type (local minimizer, maximizer or saddle point) of a given isolated real critical point c, which is degenerate, of a multivariate polynomial function f. To t...
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In this paper, we consider the problem of identifying the type (local minimizer, maximizer or saddle point) of a given isolated real critical point c, which is degenerate, of a multivariate polynomial function f. To this end, we introduce the definition of faithful radius of c by means of the curve of tangency of f. We show that the type of c can be determined by the global extrema of f over the Euclidean ball centered at c with a faithful radius. We propose algorithms to compute faithful radius of c and determine its type. (C) 2019 Elsevier Ltd. All rights reserved.
1. When physiological condition is curvilinearly related to environmental conditions, the “optimum” environmental condition is frequently determined by intersecting two straight lines. 2. Errors in this method are d...
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1. When physiological condition is curvilinearly related to environmental conditions, the “optimum” environmental condition is frequently determined by intersecting two straight lines. 2. Errors in this method are discussed, and a more precise method is suggested. 3. The curvilinear function is described by polynomial regression. 4. Optimum values of the independent variable (i.e. those resulting in maximum or minimum physiological responses) are found where the slope is zero, and can be calculated easily from the first derivative of the regression line. 5. Two examples are given: heart rate-temperature and oxygen consumption-pH.
In this paper we prove that if a generalized polynomial function f satisfies the condition f(x) f(y) = 0 for all solutions of the equation x(2) + y(2) = 1, then f is identically equal to 0.
In this paper we prove that if a generalized polynomial function f satisfies the condition f(x) f(y) = 0 for all solutions of the equation x(2) + y(2) = 1, then f is identically equal to 0.
This paper discusses a new method for designing a family of ISI-free pulses that equal or outperform several recently proposed pulses in terms of ISI performance in the presence of sampling errors. We propose a new fa...
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ISBN:
(纸本)9781457702013
This paper discusses a new method for designing a family of ISI-free pulses that equal or outperform several recently proposed pulses in terms of ISI performance in the presence of sampling errors. We propose a new family of improved Nyquist filters derived from an ideal staircase frequency characteristic using interpolation with polynomial functions. The performance of new ISI-free pulses is studied with respect to the ISI error probability, in the presence of timing error. The objective of this paper is to analyze the performance of this family of Nyquist pulses which provides flexibility in designing an appropriate ISI-free pulse shape.
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