Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Institution
- Publication
- Publication Type
Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Polynomials, Primes And The Pte Problem, Joseph C. Foster
Polynomials, Primes And The Pte Problem, Joseph C. Foster
Theses and Dissertations
This dissertation considers three different topics. In the first part of the dissertation, we use Newton Polygons to show that for the arithmetic functions g(n) = n t , where t ≥ 1 is an integer, the polynomials defined with initial condition P g 0 (X) = 1 and recursion P g n (X) = X n Xn k=1 g(k)P g n−k (X) are X/ (n!) times an irreducible polynomial. In the second part of the dissertation, we show that, for 3 ≤ n ≤ 8, there are infinitely many 2-adic integer solutions to the Prouhet-Tarry-Escott (PTE) problem, that are …
The Siebeck-Marden-Northshield Theorem And The Real Roots Of The Symbolic Cubic Equation, Emil Prodanov
The Siebeck-Marden-Northshield Theorem And The Real Roots Of The Symbolic Cubic Equation, Emil Prodanov
Articles
The isolation intervals of the real roots of the symbolic monic cubic polynomial x 3 ` ax2 ` bx ` c are determined, in terms of the coefficients of the polynomial, by solving the Siebeck–Marden–Northshield triangle — the equilateral triangle that projects onto the three real roots of the cubic polynomial and whose inscribed circle projects onto an interval with endpoints equal to stationary points of the polynomial.
A Method For Locating The Real Roots Of The Symbolic Quintic Equation Using Quadratic Equations, Emil Prodanov
A Method For Locating The Real Roots Of The Symbolic Quintic Equation Using Quadratic Equations, Emil Prodanov
Articles
A method is proposed with which the locations of the roots of the monic symbolic quintic polynomial $x^5 + a_4 x^4 + a_3 x^3 + a_2 x^2 + a_1 x + a_0$ can be determined using the roots of two {\it resolvent} quadratic polynomials: $q_1(x) = x^2 + a_4 x + a_3$ and $q_2(x) = a_2 x^2 + a_1 x + a_0$, whose coefficients are exactly those of the quintic polynomial. The different cases depend on the coefficients of $q_1(x)$ and $q_2(x)$ and on some specific relationships between them. The method is illustrated with the full analysis of one of …
Combinatorial Models For Representations Of Simple And Affine Lie Algebras, Adam Lee Schultze
Combinatorial Models For Representations Of Simple And Affine Lie Algebras, Adam Lee Schultze
Legacy Theses & Dissertations (2009 - 2024)
Part I: Koskta-Foulkes polynomials are Lusztig's q-analogues of weight multiplicities for irreducible representations of semisimple Lie algebras. It has long been known that these polynomials can be written with all non-negative coefficients. A statistic on semistandard Young tableaux with partition content, called \textit{charge}, was used to give a combinatorial formula exhibiting this fact in type $A$. Defining a charge statistic beyond type $A$ has been a long-standing problem. In the first part of this thesis, we take a completely new approach based on the definition of Kostka-Foulkes polynomials as an alternating sum over Kostant partitions, which can be thought of …
On The Growth Of Maximum Modulus Of Rational Functions With Prescribed Poles, Lubna Wali Shah
On The Growth Of Maximum Modulus Of Rational Functions With Prescribed Poles, Lubna Wali Shah
Turkish Journal of Mathematics
In this paper we prove a sharp growth estimate for rational functions with prescribed poles and restricted zeros in the Chebyshev norm on the unit disk in the complex domain. In particular we extend a polynomial inequality due to Dubinin (2007) to rational functions which also improves a result of Govil and Mohapatra (1998).