Results 11 to 20 of about 53,856 (206)

On certain arithmetical products involving the divisors of an integer [PDF]

Notes on Number Theory and Discrete Mathematics
We study the arithmetical products Π d^d, Πd^{1/d} and Πd^{log d}, where d runs through the divisors of an integer n>1.
József Sándor
doaj   +1 more source

On HT-convexity and Hadamard-type inequalities

Journal of Inequalities and Applications, 2020
In the paper, the authors define a new notion of “HT-convex function”, present some Hadamard-type inequalities for the new class of HT-convex functions and for the product of any two HT-convex functions, and derive some inequalities for the arithmetic ...
Shu-Ping Bai, Shu-Hong Wang, Feng Qi
doaj   +1 more source

Some new arithmetic functions [PDF]

Notes on Number Theory and Discrete Mathematics
We introduce and study some new arithmetic functions, connected with the classical functions φ (Euler's totient), ψ (Dedekind's function) and σ (sum of divisors function).
József Sándor, Krassimir Atanassov
doaj   +1 more source

On Fejér’s inequality: generalizations and applications

Journal of Inequalities and Applications, 2023
This paper deals with generalizations and refinements of Fejér’s inequality with some new applications. We introduce a real mapping M f ω ( t ) $\mathcal{M}_{f}^{\omega}(t)$ and obtain some its functional properties.
Mohsen Rostamian Delavar
doaj   +1 more source

Formal Proofs for Nonlinear Optimization [PDF]

, 2015
We present a formally verified global optimization framework. Given a semialgebraic or transcendental function $f$ and a compact semialgebraic domain $K$, we use the nonlinear maxplus template approximation algorithm to provide a certified lower bound of
Allamigeon, Xavier, Gaubert, Stéphane, Magron, Victor, Werner, Benjamin   +3 more
core   +4 more sources

On certain bounds for the divisor function [PDF]

Notes on Number Theory and Discrete Mathematics
We offer various bounds for the divisor function d(n), in terms of n, or other arithmetical functions.
József Sándor
doaj   +1 more source

Non-Symbolic Magnitude Processing Is a Strong Correlate of Symbolic Math Skills in Children From Ghana and Côte d'Ivoire. [PDF]

Dev Sci
ABSTRACT The ability to understand and compare non‐symbolic (e.g., dot arrays) and symbolic (e.g., Arabic numerals) magnitudes is a critical foundation for learning math. A meta‐analysis has revealed that symbolic magnitude processing is a stronger predictor of math performance than non‐symbolic, but the evidence base is restricted almost entirely to ...
Bugden S, Ansari D, Lichand G, Avornyo EA, Wolf S.   +4 more
europepmc   +2 more sources

A note on the approximation of divisor functions [PDF]

Notes on Number Theory and Discrete Mathematics
We offer an arithmetic proof of a result from the recent paper [1]. A more general result is provided, too.
József Sándor
doaj   +1 more source

Corrected Dual-Simpson-Type Inequalities for Differentiable Generalized Convex Functions on Fractal Set

Fractal and Fractional, 2022
The present paper provides several corrected dual-Simpson-type inequalities for functions whose local fractional derivatives are generalized convex. To that end, we derive a new local fractional integral identity as an auxiliary result.
Abdelghani Lakhdari, Wedad Saleh, Badreddine Meftah, Akhlad Iqbal   +3 more
doaj   +1 more source

A note on newly introduced arithmetic functions φ+ and σ+ [PDF]

Notes on Number Theory and Discrete Mathematics
In a recent paper [7], the authors introduced new arithmetic functions φ⁺, σ⁺ related to the classical functions φ, and σ, respectively. In this note, we study the behavior of Σ_{n≤x, ω(n)=2}(φ⁺-φ)(n), and Σ_{n≤x, ω(n)=2}(σ⁺-σ)(n), for any real number x ...
Sagar Mandal
doaj   +1 more source