Results 31 to 40 of about 10,597,961 (334)
Mean values of multiplicative functions over function fields [PDF]
Research in Number Theory, 2015 We discuss the mean values of multiplicative functions over function fields. In particular, we adapt the authors’ new proof of Halász’s theorem on mean values to this simpler setting.
A. Granville +2 more
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IEEE Transactions on Automatic Control, 2021 This article is concerned with the exponential mean-square stabilization problem for a class of discrete-time strict-feedback nonlinear systems subject to multiplicative noises.
Min Wang +3 more
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Some characterizations of specially multiplicative functions
International Journal of Mathematics and Mathematical Sciences, 2003 A multiplicative function f is said to be specially multiplicative if there is a completely multiplicative function fA such that f(m)f(n)=∑d|(m,n)f(mn/d2)fA(d) for all m and n.
Pentti Haukkanen
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Learning Optimal Controllers for Linear Systems With Multiplicative Noise via Policy Gradient
IEEE Transactions on Automatic Control, 2021 The linear quadratic regulator (LQR) problem has reemerged as an important theoretical benchmark for reinforcement learning-based control of complex dynamical systems with continuous state and action spaces.
Benjamin J. Gravell +2 more
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Multiplicative functionals and entire functions [PDF]
Studia Mathematica, 1996 [Part I, cf. Stud. Math. 119, No. 3, 289-297 (1996; Zbl 0868.46037).] The following result is proved in this very interesting paper: Let \(A\) be a complex Banach algebra with a unit \(e\), let \(F\) be a nonconstant entire function, and let \(T\) be a linear functional with \(T(e) = 1\) and such that \(T\circ F\) defined from \(A\) to the complex ...
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Some characterizations of totients
International Journal of Mathematics and Mathematical Sciences, 1996 An arithmetical function is said to be a totient if it is the Dirichlet convolution between a completely multiplicative function and the inverse of a completely multiplicative function. Euler's phi-function is a famous example of a totient.
Pentti Haukkanen
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On the Multiple Gamma-Functions
Tokyo Journal of Mathematics, 1998 The authors obtain generalizations of the Shintani type infinite product representations for the \(r\)-ple gamma functions \(\Gamma_r(w;\widetilde\omega)\) and \(r\)-ple Stirling's modular forms \(\rho_r(\widetilde\omega)\) in the sense of Barnes. As an application, ``a simple proof'' of the inversion formulas of theta-function and Dedekind \(\eta ...
KATAYAMA, Koji, OHTSUKI, Makoto
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Hermite–Hadamard type inequalities for multiplicatively harmonic convex functions
Journal of Inequalities and Applications, 2023 In this work, the notion of a multiplicative harmonic convex function is examined, and Hermite–Hadamard inequalities for this class of functions are established.
Serap Özcan, Saad Ihsan Butt
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Water Poverty Index Calculation: Additive or Multiplicative Function?
, 2013 As South Africa is a water-stressed country, determining how to most efficiently use its already scarce water resource is of utmost importance. This research aims to quantify the difference in the water poverty index when calculated with the additive ...
C. V. D. Vyver
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Solutions and Stability of Generalized Kannappan’s and Van Vleck’s Functional Equations
Annales Mathematicae Silesianae, 2018 We study the solutions of the integral Kannappan’s and Van Vleck’s functional equations ∫Sf(xyt)dµ(t)+∫Sf(xσ(y)t)dµ(t)= 2f(x)f(y), x,y ∈ S; ∫Sf(xσ(y)t)dµ(t)-∫Sf(xyt)dµ(t)= 2f(x)f(y), x,y ∈ S; where S is a semigroup, σ is an involutive automorphism of S ...
Elqorachi Elhoucien, Redouani Ahmed
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