scholarly journals Consecutive Quadratic Residues and Primitive Roots in the Sequences Formed by Twice-differentiable Functions

2021 ◽  
Vol -1 (-1) ◽  
Author(s):  
Mengyao Jing ◽  
Huaning Liu
Keyword(s):  
Differentiable Functions ◽  
Quadratic Residues ◽  
Primitive Roots

scholarly journals A LINEAR COMPLEXITY ANALYSIS OF QUADRATIC RESIDUES AND PRIMITIVE ROOTS SPACINGS

2019 ◽  
Vol 19 (1) ◽  
pp. 27-37
Author(s):  
Mihai Caragiu ◽  
Shannon Tefft ◽  
Aaron Kemats ◽  
Travis Maenle
Keyword(s):  
Linear Complexity ◽  
Complexity Analysis ◽  
Quadratic Residues ◽  
Primitive Roots

scholarly journals Polynomials that represent quadratic residues at primitive roots

1982 ◽  
Vol 98 (1) ◽  
pp. 123-137 ◽  
Author(s):  
Daniel Madden ◽  
William Vélez
Keyword(s):  
Quadratic Residues ◽  
Primitive Roots

APPLICATIONS OF LERCH’S THEOREM TO PERMUTATIONS OF QUADRATIC RESIDUES

2019 ◽  
Vol 100 (3) ◽  
pp. 362-371
Author(s):  
LI-YUAN WANG ◽  
HAI-LIANG WU
Keyword(s):  
Positive Integer ◽  
Quadratic Residues ◽  
Primitive Roots ◽  
Permutation Problems

Let $n$ be a positive integer and $a$ an integer prime to $n$. Multiplication by $a$ induces a permutation over $\mathbb{Z}/n\mathbb{Z}=\{\overline{0},\overline{1},\ldots ,\overline{n-1}\}$. Lerch’s theorem gives the sign of this permutation. We explore some applications of Lerch’s result to permutation problems involving quadratic residues modulo $p$ and confirm some conjectures posed by Sun [‘Quadratic residues and related permutations and identities’, Preprint, 2018, arXiv:1809.07766]. We also study permutations involving arbitrary $k$th power residues modulo $p$ and primitive roots modulo a power of $p$.

Differentiable Functions Have Sparse Graphs

1978 ◽  
Vol 4 (1) ◽  
pp. 91
Author(s):  
Laczkovich ◽  
Petruska
Keyword(s):  
Sparse Graphs ◽  
Differentiable Functions

scholarly journals Some generalizations of the Hermite–Hadamard integral inequality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Slavko Simić ◽  
Bandar Bin-Mohsin
Keyword(s):  
Integral Inequality ◽  
Target Function ◽  
Convexity Property ◽  
Concave Functions ◽  
Differentiable Functions

AbstractIn this article we give two possible generalizations of the Hermite–Hadamard integral inequality for the class of twice differentiable functions, where the convexity property of the target function is not assumed in advance. They represent a refinement of this inequality in the case of convex/concave functions with numerous applications.

scholarly journals Explicit, Determinantal, and Recurrent Formulas of Generalized Eulerian Polynomials

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 37
Author(s):  
Yan Wang ◽  
Muhammet Cihat Dağli ◽  
Xi-Min Liu ◽  
Feng Qi
Keyword(s):  
General Formula ◽  
Bell Polynomials ◽  
Eulerian Polynomials ◽  
Differentiable Functions ◽  
Faà Di Bruno Formula ◽  
Derivatives Of

In the paper, by virtue of the Faà di Bruno formula, with the aid of some properties of the Bell polynomials of the second kind, and by means of a general formula for derivatives of the ratio between two differentiable functions, the authors establish explicit, determinantal, and recurrent formulas for generalized Eulerian polynomials.

scholarly journals A new bound for the Jensen gap pertaining twice differentiable functions with applications

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shahid Khan ◽  
Muhammad Adil Khan ◽  
Saad Ihsan Butt ◽  
Yu-Ming Chu
Keyword(s):  
Differentiable Functions
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