On the behaviour of solutions of the differential equations
N. Parhi, S. Parhi (1986)
Annales Polonici Mathematici
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N. Parhi, S. Parhi (1986)
Annales Polonici Mathematici
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Jan Andres, Jan Vorácek (1984)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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Si dimostra un teorema di esistenza di soluzioni periodiche dell'equazione differenziale ordinaria del terzo ordine con le funzioni , , periodiche in di periodo .
A. J. Irving (2015)
Acta Arithmetica
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Improving on a theorem of Heath-Brown, we show that if X is sufficiently large then a positive proportion of the values n³ + 2: n ∈ (X,2X] have a prime factor larger than .
Jan Andres, Jan Vorácek (1984)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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Si dimostra un teorema di esistenza di soluzioni periodiche dell'equazione differenziale ordinaria del terzo ordine con le funzioni , , periodiche in di periodo .
S. Sędziwy (1969)
Annales Polonici Mathematici
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Ján Andres (1986)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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Per l'equazione differenziale ordinaria non lineare del 3° ordine indicata nel titolo, studiata da numerosi autori sotto l'ipotesi , si dimostra l'esistenza di almeno una soluzione limitata sopprimendo l'ipotesi suddetta.
Mariusz Ska/lba (2005)
Colloquium Mathematicae
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A classical theorem of M. Fried [2] asserts that if non-zero integers have the property that for each prime number p there exists a quadratic residue mod p then a certain product of an odd number of them is a square. We provide generalizations for power residues of degree n in two cases: 1) n is a prime, 2) n is a power of an odd prime. The proofs involve some combinatorial properties of finite Abelian groups and arithmetic results of [3].
Ján Andres (1986)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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Per l'equazione differenziale ordinaria non lineare del 3° ordine indicata nel titolo, studiata da numerosi autori sotto l'ipotesi , si dimostra l'esistenza di almeno una soluzione limitata sopprimendo l'ipotesi suddetta.
M. Kisielewicz (1977)
Colloquium Mathematicae
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Jean-Marie De Koninck, Imre Kátai (2016)
Colloquium Mathematicae
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We obtain estimates for the average value of the largest prime factor P(n) in short intervals [x,x+y] and of h(P(n)+1), where h is a complex-valued additive function or multiplicative function satisfying certain conditions. Letting stand for the sum of the digits of n in base q ≥ 2, we show that if α is an irrational number, then the sequence is uniformly distributed modulo 1.
Houyu Zhao, Jianguo Si (2009)
Annales Polonici Mathematici
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We study existence of analytic solutions of a second-order iterative functional differential equation in the complex field ℂ. By constructing an invertible analytic solution y(z) of an auxiliary equation of the form invertible analytic solutions of the form for the original equation are obtained. Besides the hyperbolic case 0 < |α| < 1, we focus on α on the unit circle S¹, i.e., |α|=1. We discuss not only those α at resonance, i.e. at a root of unity, but also near resonance...
Florian Luca, Pantelimon Stănică (2003)
Colloquium Mathematicae
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We show that if p ≠ 5 is a prime, then the numbers cover all the nonzero residue classes modulo p.
Eva Tesaříková (1987)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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Michał Kisielewicz (1979)
Annales Polonici Mathematici
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Artūras Dubickas (2006)
Acta Mathematica Universitatis Ostraviensis
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We are interested whether there is a nonnegative integer and an infinite sequence of digits in base such that the numbers where are all prime or at least do not have prime divisors in a finite set of prime numbers If any such sequence contains infinitely many elements divisible by at least one prime number then we call the set unavoidable with respect to . It was proved earlier that unavoidable sets in base exist if and that no unavoidable set exists in base Now,...
Tai-Wei Chen, Chung-I Ho, Jyh-Haur Teh (2016)
Commentationes Mathematicae Universitatis Carolinae
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For a double complex , we show that if it satisfies the -lemma and the spectral sequence induced by does not degenerate at , then it degenerates at . We apply this result to prove the degeneration at of a Hodge-de Rham spectral sequence on compact bi-generalized Hermitian manifolds that satisfy a version of -lemma.
Yuqiang Feng, Xincheng Ding (2012)
Annales Polonici Mathematici
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We are concerned with the solvability of the fourth-order four-point boundary value problem ⎧ , t ∈ [0,1], ⎨ u(0) = u(1) = 0, ⎩ au”(ζ₁) - bu”’(ζ₁) = 0, cu”(ζ₂) + du”’(ζ₂) = 0, where 0 ≤ ζ₁ < ζ₂ ≤ 1, f ∈ C([0,1] × [0,∞) × (-∞,0],[0,∞)). By using Guo-Krasnosel’skiĭ’s fixed point theorem on cones, some criteria are established to ensure the existence, nonexistence and multiplicity of positive solutions for this problem.
S. Ponnusamy, A. Vasudevarao, M. Vuorinen (2009)
Colloquium Mathematicae
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For μ ∈ ℂ such that Re μ > 0 let denote the class of all non-vanishing analytic functions f in the unit disk with f(0) = 1 and in . For any fixed z₀ in the unit disk, a ∈ ℂ with |a| ≤ 1 and λ ∈ ̅, we shall determine the region of variability V(z₀,λ) for log f(z₀) when f ranges over the class . In the final section we graphically illustrate the region of variability for several sets of parameters.
Yingpu Deng, Dandan Huang (2015)
Acta Arithmetica
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We describe a primality test for with an odd prime p and a positive integer n, which are a particular type of generalized Fermat numbers. We also present special primality criteria for all odd prime numbers p not exceeding 19. All these primality tests run in deterministic polynomial time in the input size log₂M. A special 2pth power reciprocity law is used to deduce our result.