Results 61 to 70 of about 11,114,666 (310)

Adult‐Onset Subacute Sclerosing Panencephalitis Presenting With Subacute Cognitive Deficits

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT We describe the case of a 41‐year‐old man diagnosed with adult‐onset subacute sclerosing panencephalitis (SSPE). The patient presented with subacute progressive cognitive deficits and a neuropsychological profile indicating predominant frontoparietal dysfunction. MRI showed only mild parietal‐predominant cerebral atrophy.
Dennis Yeow, Nicola McKern, Vincent Oxenham, Kate Ahmad, Omar Ahmad   +4 more
wiley   +1 more source

Inequalities with Some Arithmetic Functions

Mathematics
In the paper, some new inequalities are formulated and proved with the classical arithmetic functions φ (of Euler) and ψ (of Dedekind).
József Sándor, Krassimir Atanassov
doaj   +1 more source

A new class of infinite products, and Euler's totient

International Journal of Mathematics and Mathematical Sciences, 1994
We introduce some new infinite products, the simplest being(1−y)∏k=2∞∏j∈ϕk(1−ykqj)1/k=(1−y1−qy)1/(1−q),where ϕk is the set of positive integers less than and relatively prime to k, valid for |y|∧|qy| both less than unity, with q≠1.
Geoffrey B. Campbell
doaj   +1 more source

A note on $(a,b)$-Fibonacci sequences and specially multiplicative arithmetic functions [PDF]

Mathematica Bohemica
A specially multiplicative arithmetic function is the Dirichlet convolution of two completely multiplicative arithmetic functions. The aim of this paper is to prove explicitly that two mathematical objects, namely $(a,b)$-Fibonacci sequences and ...
Emil Daniel Schwab, Gabriela Schwab
doaj   +1 more source

Some Properties of Extended Euler’s Function and Extended Dedekind’s Function

Mathematics, 2020
In this paper, we find some properties of Euler’s function and Dedekind’s function. We also generalize these results, from an algebraic point of view, for extended Euler’s function and extended Dedekind’s function, in algebraic number fields ...
Nicuşor Minculete, Diana Savin
doaj   +1 more source

Arithmetic exponent pairs for algebraic trace functions and applications [PDF]

Algebra & Number Theory, 2016
We study short sums of algebraic trace functions via the $q$-analogue of van der Corput method, and develop methods of arithmetic exponent pairs that coincide with the classical case while the moduli has sufficiently good factorizations.
Jie Wu, Ping Xi
semanticscholar   +1 more source

Hopfield Neural Networks for Online Constrained Parameter Estimation With Time‐Varying Dynamics and Disturbances

International Journal of Adaptive Control and Signal Processing, EarlyView.
This paper proposes two projector‐based Hopfield neural network (HNN) estimators for online, constrained parameter estimation under time‐varying data, additive disturbances, and slowly drifting physical parameters. The first is a constraint‐aware HNN that enforces linear equalities and inequalities (via slack neurons) and continuously tracks the ...
Miguel Pedro Silva
wiley   +1 more source

Matrices induced by arithmetic functions acting on certain Krein spaces

Special Matrices, 2017
In this paper, we study matrices induced by arithmetic functions under certain Krein-space representations induced by (multi-)primes less than or equal to fixed positive real numbers.
Cho Ilwoo
doaj   +1 more source

Arithmetic Means for a Class of Functions and the Modified Bessel Functions of the First Kind

Mathematics, 2019
In the paper, by virtue of the residue theorem in the theory of complex functions, the authors establish several identities between arithmetic means for a class of functions and the modified Bessel functions of the first kind, present several identities ...
Feng Qi, Shao-Wen Yao, Bai-Ni Guo
doaj   +1 more source

Abel Summation of Ramanujan-Fourier Series [PDF]

, 2015
Using Abel summation the paper proves a weak form of the Wiener-Khinchin formula for arithmetic functions with point-wise convergent Ramanujan-Fourier expansions.
Washburn, John
core