scholarly journals Preliminary Discussion on Several Problems Related to the Divisor Function

2020 ◽  
Vol 3 (1) ◽  
Author(s):  
Yongmin Wang
Keyword(s):  
High Power ◽  
Prime Numbers ◽  
Divisor Function ◽  
Additive Theory ◽  
Integer Coefficients ◽  
Power Sum ◽  
Preliminary Discussion

This paper is divided into three parts to discuss the divisor function. It mainly combines the high power sum of the divisor function to study the solution number of the polynomial with integer coefficients "g(x)=0(modq)", and to improve some of the conclusions in the second chapter of Additive Theory of Prime Numbers and prove the improved conclusions.

scholarly journals On the Matchings-Jack Conjecture for Jack Connection Coefficients Indexed by Two Single Part Partitions

10.37236/5085 ◽  
2016 ◽  
Vol 23 (1) ◽  
Author(s):  
Andrei L. Kanunnikov ◽  
Ekaterina A. Vassilieva
Keyword(s):  
Arbitrary Number ◽  
Symmetric Functions ◽  
Recurrence Formula ◽  
Integer Partitions ◽  
Integer Coefficients ◽  
Power Sum ◽  
Connection Coefficients ◽  
Algebraic Framework ◽  
Commutative Subalgebras ◽  
Single Part

This article is devoted to the study of Jack connection coefficients, a generalization of the connection coefficients of the classical commutative subalgebras of the group algebra of the symmetric group closely related to the theory of Jack symmetric functions. First introduced by Goulden and Jackson (1996) these numbers indexed by three partitions of a given integer $n$ and the Jack parameter $\alpha$ are defined as the coefficients in the power sum expansion of some Cauchy sum for Jack symmetric functions. Goulden and Jackson conjectured that they are polynomials in $\beta = \alpha-1$ with non negative integer coefficients of combinatorial significance, the Matchings-Jack conjecture.In this paper we look at the case when two of the integer partitions are equal to the single part $(n)$. We use an algebraic framework of Lasalle (2008) for Jack symmetric functions and a bijective construction in order to show that the coefficients satisfy a simple recurrence formula and prove the Matchings-Jack conjecture in this case. Furthermore we exhibit the polynomial properties of more general coefficients where the two single part partitions are replaced by an arbitrary number of integer partitions either equal to $(n)$ or $[1^{n-2}2]$.

scholarly journals Conjecture in Additive Twin Primes Numbers Theory

2013 ◽  
Vol 5 ◽  
pp. 27-30
Author(s):  
Ibrahima Gueye
Keyword(s):  
Prime Numbers ◽  
Additive Theory ◽  
Twin Primes ◽  
Theory Of Numbers

For two millennia, the prime numbers have continued to fascinate mathematicians. Indeed, a conjecture which dates back to this period states that the number of twin primes is infinite. In 1949 Clement showed a theorem on twin primes. For the record, the theorem of Clement has quickly been known to be ineffective in the development of twin primes because of the factorial. This is why I thought ofusing the additive theory of numbers to find pairs of twin primes from the first two pairs of twin primes. What I have formulated as a conjecture. In same time i presentmy idea about the solution of the Goldbach’s weak conjecture.

Intervals without primes near elements of linear recurrence sequences

2018 ◽  
Vol 14 (02) ◽  
pp. 567-579
Author(s):  
Artūras Dubickas
Keyword(s):  
Recurrence Relation ◽  
Arithmetic Progression ◽  
Prime Numbers ◽  
Linear Recurrence ◽  
Integer Coefficients ◽  
Salem Numbers ◽  
Consecutive Integers ◽  
Linear Recurrence Relation ◽  
Recurrence Sequences ◽  
Positive Integers

Let [Formula: see text] be an unbounded sequence of integers satisfying a linear recurrence relation with integer coefficients. We show that for any [Formula: see text] there exist infinitely many [Formula: see text] for which [Formula: see text] consecutive integers [Formula: see text] are all divisible by certain primes. Moreover, if the sequence of integers [Formula: see text] satisfying a linear recurrence relation is unbounded and non-degenerate then for some constant [Formula: see text] the intervals [Formula: see text] do not contain prime numbers for infinitely many [Formula: see text]. Applying this argument to sequences of integer parts of powers of Pisot and Salem numbers [Formula: see text] we derive a similar result for those sequences as well which implies, for instance, that the shifted integer parts [Formula: see text], where [Formula: see text] and [Formula: see text] runs through some infinite arithmetic progression of positive integers, are all composite.

scholarly journals HIGH POWER SUM FREQUENCY GENERATION OF 230.8—223.2nm IN BBO CRYSTAL

1990 ◽  
Vol 39 (2) ◽  
pp. 190
Author(s):  
LU SHI-PING ◽  
YUAN YI-QIAN ◽  
YANG LI-SHU ◽  
WU CUN-KAI
Keyword(s):  
High Power ◽  
Sum Frequency Generation ◽  
Sum Frequency ◽  
Power Sum ◽  
Frequency Generation

Dynamic Modeling and Wear-Based Remaining Useful Life Prediction of High Power Clutch Systems

2005 ◽  
Vol 48 (2) ◽  
pp. 208-217 ◽  
Author(s):  
Matthew Watson ◽  
Carl Byington ◽  
Douglas Edwards ◽  
Sanket Amin
Keyword(s):  
Dynamic Modeling ◽  
High Power ◽  
Life Prediction ◽  
Remaining Useful Life ◽  
Useful Life

Less Power, Greater Conflict

2018 ◽  
Vol 49 (1) ◽  
pp. 47-62 ◽  
Author(s):  
Petra C. Schmid
Keyword(s):  
Low Power ◽  
High Power ◽  
Goal Pursuit ◽  
Goal Conflict ◽  
Personal Goals ◽  
Multiple Goals ◽  
Objective Performance ◽  
The Future ◽  
The Way

Abstract. Power facilitates goal pursuit, but how does power affect the way people respond to conflict between their multiple goals? Our results showed that higher trait power was associated with reduced experience of conflict in scenarios describing multiple goals (Study 1) and between personal goals (Study 2). Moreover, manipulated low power increased individuals’ experience of goal conflict relative to high power and a control condition (Studies 3 and 4), with the consequence that they planned to invest less into the pursuit of their goals in the future. With its focus on multiple goals and individuals’ experiences during goal pursuit rather than objective performance, the present research uses new angles to examine power effects on goal pursuit.

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