Results 1 to 10 of about 1,141,676 (232)
Bounds of the Mertens Functions [PDF]
Advances in Dynamical Systems and Applications, 2020 In this paper we derive new properties of Mertens function and discuss about a likely upper bound of the absolute value of the Mertens function √log(𝑥!) > |𝑀(𝑥)| when 𝑥 > 1. Using this likely bound we show that we have a sufficient condition to prove the Riemann Hypothesis.
Darrell Cox +2 more
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On functions of bounded variation [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2016 AbstractThe recently introduced concept of ${\mathcal D}$-variation unifies previous concepts of variation of multivariate functions. In this paper, we give an affirmative answer to the open question from [20] whether every function of bounded Hardy–Krause variation is Borel measurable and has bounded ${\mathcal D}$-variation.
Aistleitner, Christoph +3 more
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Expoential bounds on the number of causal triangulations [PDF]
, 2014 We prove that the number of combinatorially distinct causal 3-dimensional triangulations homeomorphic to the 3-dimensional sphere is bounded by an exponential function of the number of tetrahedra.
Durhuus, Bergfinnur, Jonsson, Thordur
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An inequality for bounded functions [PDF]
Mathematical Inequalities & Applications, 2014 In this note we prove optimal inequalities for bounded functions in terms of their deviation from their mean. These results extend and generalize some known inequalities due to Thong (2011) and Perfetti (2011)
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Sharp rate of average decay of the Fourier transform of a bounded set [PDF]
, 2003 We prove that the spherical mean of the Fourier transform of the characteristic function of a bounded convex set (without any additional assumptions) or a bounded set with a C^{3/2} boundary decays at infinity at the same rate as the Fourier transform of
Brandolini, L. +2 more
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On Functions of Bounded Rotation [PDF]
Proceedings of the American Mathematical Society, 1972 For fixed k_ 2, denote by Vk and Rk the classes of functions regular in the unit disc and having boundary and radial rotation, respectively, at most klT. The concept of order of a function is defined for both Vk and Rk. For functions in these classes, the growth of integral and coefficient means is studied in terms of the order of the function.
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Bounding The Smarandache Function [PDF]
Smarandache Notions Journal archive, 2002 The article illustrates the importance of being able to calculate the Smarandache function for prime powers. This paper will be considering that process.
Mark Farris, Patrick Mitchell
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Robust identification from band-limited data [PDF]
, 1997 Consider the problem of identifying a scalar bounded-input/bounded-output stable transfer function from pointwise measurements at frequencies within a bandwidth.
Baratchart, L. +3 more
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Functions with bounded spectrum [PDF]
Transactions of the American Mathematical Society, 1995 Let 0 o , has the same behavior as the sequence sup |£Q|'/I 0. In other words, if we know all "far points" of supp Ff, we can wholly describe this behavior without any concrete calculation of ||Z)a/||p , a > 0 . A Paley-Wiener-Schwartz theorem for a nonconvex case, which is a consequence of the result, is given.
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On bounded functions with bounded 𝑛th differences [PDF]
Proceedings of the American Mathematical Society, 1959 We consider real valued functions f defined in a closed interval I (bounded or unbounded), with nth differences $$ \Delta _{h}^{n}f(x) = \sum\limits_{i} {{{{( - 1)}}^{{n - i}}}} \left( {\begin{array}{*{20}{c}} n \\ i \\ \end{array} } \right)f(x + ih) $$ bounded for some fixed n.
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