scholarly journals On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
J. M. Sepulcre
Keyword(s):  
Important Class ◽  
Exponential Polynomial ◽  
Critical Interval ◽  
Real Numbers ◽  
Positive Real ◽  
Exponential Polynomials ◽  
The Real ◽  
Linearly Independent ◽  
Pointwise Characterization

We provide the proof of a practical pointwise characterization of the setRPdefined by the closure set of the real projections of the zeros of an exponential polynomialP(z)=∑j=1ncjewjzwith real frequencieswjlinearly independent over the rationals. As a consequence, we give a complete description of the setRPand prove its invariance with respect to the moduli of thecj′s, which allows us to determine exactly the gaps ofRPand the extremes of the critical interval ofP(z)by solving inequations with positive real numbers. Finally, we analyse the converse of this result of invariance.

scholarly journals Three proofs of Minkowski's second inequality in the geometry of numbers

1965 ◽  
Vol 5 (4) ◽  
pp. 453-462 ◽  
Author(s):  
R. P. Bambah ◽  
Alan Woods ◽  
Hans Zassenhaus
Keyword(s):  
Convex Set ◽  
Geometry Of Numbers ◽  
Real Numbers ◽  
Open Convex ◽  
Positive Real ◽  
Original Proof ◽  
Linearly Independent ◽  
Image Position

Let K be a bounded, open convex set in euclidean n-space Rn, symmetric in the origin 0. Further let L be a lattice in Rn containing 0 and put extended over all positive real numbers ui for which uiK contains i linearly independent points of L. Denote the Jordan content of K by V(K) and the determinant of L by d(L). Minkowski's second inequality in the geometry of numbers states that Minkowski's original proof has been simplified by Weyl [6] and Cassels [7] and a different proof hasbeen given by Davenport [1].

FRACTAL IMAGES OF GENERALIZED JULIA SETS

Fractals ◽  
1996 ◽  
Vol 04 (04) ◽  
pp. 533-541 ◽  
Author(s):  
KIM-KHOON ONG ◽  
AICHYUN SHIAH ◽  
ZDZISLAW E. MUSIELAK
Keyword(s):  
Real Axis ◽  
Complex Plane ◽  
Julia Sets ◽  
Real Numbers ◽  
Positive Real ◽  
The Real ◽  
Fractal Images ◽  
Zero Values ◽  
Principal Value ◽  
Iteration Function

The iteration function [Formula: see text], where both α and β are positive real numbers, is used to generate families of the generalized Julia sets, [Formula: see text]. The calculations are restricted to the principal value of zα + iβ and the obtained results demonstrate that classical Julia sets, [Formula: see text] are significantly deformed when non-zero values of β are considered. As a result of this deformation, the area of stable regions in the complex plane changes and a process of splitting and shifting takes place along the real axis. It is shown that this process is responsible for the formation of new fractal images of generalized Julia sets.

scholarly journals Universality probability of a prefix-free machine

2012 ◽  
Vol 370 (1971) ◽  
pp. 3488-3511 ◽  
Author(s):  
George Barmpalias ◽  
David L. Dowe
Keyword(s):  
Turing Degree ◽  
Real Numbers ◽  
Arithmetical Hierarchy ◽  
Halting Problem ◽  
The Real ◽  
The Third ◽  
Free Machine

We study the notion of universality probability of a universal prefix-free machine, as introduced by C. S. Wallace. We show that it is random relative to the third iterate of the halting problem and determine its Turing degree and its place in the arithmetical hierarchy of complexity. Furthermore, we give a computational characterization of the real numbers that are universality probabilities of universal prefix-free machines.

scholarly journals A generalisation of Minkowski's second inequality in the geometry of numbers

1966 ◽  
Vol 6 (2) ◽  
pp. 148-152 ◽  
Author(s):  
A. C. Woods
Keyword(s):  
Convex Set ◽  
Discrete Point ◽  
Geometry Of Numbers ◽  
Real Numbers ◽  
Open Convex ◽  
Positive Real ◽  
Linearly Independent ◽  
Point Set

Let K be a bounded open convex set in euclidean n-space Rn symmetric in the origin 0. Further let L be a discrete point set in Rn containing 0 and at least n linearly independent points of Rn. Put mi = inf ui extended over all positive real numbers ui for which uiK contains i linearly independent points of L, i = 1, 2, …, n.

scholarly journals On the characterization of Jensen m-convex polynomials

2017 ◽  
Vol 3 (2) ◽  
pp. 140-148
Author(s):  
Teodoro Lara ◽  
Nelson Merentes ◽  
Roy Quintero ◽  
Edgar Rosales
Keyword(s):  
Convex Functions ◽  
Polynomial Functions ◽  
Real Polynomial ◽  
Real Numbers ◽  
The Real ◽  
Class Of Functions

AbstractThe main objective of this research is to characterize all the real polynomial functions of degree less than the fourth which are Jensen m-convex on the set of non-negative real numbers. In the first section, it is established for that class of functions what conditions must satisfy a particular polynomial in order to be starshaped on the same set. Finally, both kinds of results are combined in order to find examples of either Jensen m-convex functions which are not starshaped or viceversa.

Characterization of distributive semigroup operations on the positive real numbers

2019 ◽  
Vol 100 (2) ◽  
pp. 585-604 ◽  
Author(s):  
Sin-Ei Takahasi ◽  
Takeshi Miura ◽  
Hirokazu Oka
Keyword(s):  
Real Numbers ◽  
Positive Real
Sign in / Sign up

Export Citation Format

Share Document