Degree of independence of numbers

Jittinart Rattanamoong; Vichian Laohakosol

doi:10.1515/ms-2021-0007

Degree of independence of numbers

Mathematica Slovaca ◽

10.1515/ms-2021-0007 ◽

2021 ◽

Vol 71 (3) ◽

pp. 615-626

Author(s):

Jittinart Rattanamoong ◽

Vichian Laohakosol

Keyword(s):

Sufficient Criterion ◽

Real Numbers ◽

Cantor Series

Abstract A new concept of independence of real numbers, called degree independence, which contains those of linear and algebraic independences, is introduced. A sufficient criterion for such independence is established based on a 1988 result of Bundschuh, which in turn makes use of a generalization of Liouville’s estimate due to Feldman in 1968. Applications to numbers represented by Cantor series and product expansions are derived.

A low hemolysis rate is not a sufficient criterion for the qualification of rotary blood pumps

The Thoracic and Cardiovascular Surgeon ◽

10.1055/s-2008-1037927 ◽

2008 ◽

Vol 56 (S 1) ◽

Author(s):

J Müller ◽

M Brodde ◽

P Nüsser ◽

J Müller ◽

K Graichen ◽

...

Keyword(s):

Sufficient Criterion ◽

Blood Pumps ◽

Rotary Blood Pumps ◽

Hemolysis Rate

On Some I-convergence of Difference Double Sequence Classes of Fuzzy Real Numbers Defined by Modulus Function

Journal of Computer and Mathematical Sciences ◽

10.29055/jcms/715 ◽

2017 ◽

Vol 8 (12) ◽

pp. 758-768

Author(s):

Manmohan Das ◽

Sanjay Kumar Das

Keyword(s):

Double Sequence ◽

Modulus Function ◽

Real Numbers ◽

Fuzzy Real Numbers

On existence result of a class of nonlinear integral equation

Filomat ◽

10.2298/fil1711593b ◽

2017 ◽

Vol 31 (11) ◽

pp. 3593-3597

Author(s):

Ravindra Bisht

Keyword(s):

Integral Equation ◽

Fixed Point ◽

Existence And Uniqueness ◽

Existence Result ◽

Nonlinear Integral Equation ◽

Continuous Functions ◽

Concave Functions ◽

Real Numbers ◽

Fixed Point Techniques ◽

Uniqueness Of A Solution

Combining the approaches of functionals associated with h-concave functions and fixed point techniques, we study the existence and uniqueness of a solution for a class of nonlinear integral equation: x(t) = g1(t)-g2(t) + ? ?t,0 V1(t,s)h1(s,x(s))ds + ? ?T,0 V2(t,s)h2(s,x(s))ds; where C([0,T];R) denotes the space of all continuous functions on [0,T] equipped with the uniform metric and t?[0,T], ?,? are real numbers, g1, g2 ? C([0, T],R) and V1(t,s), V2(t,s), h1(t,s), h2(t,s) are continuous real-valued functions in [0,T]xR.

Dynamics of a family of orbitally continuous mappings

Filomat ◽

10.2298/fil1711507p ◽

2017 ◽

Vol 31 (11) ◽

pp. 3507-3517

Author(s):

Abhijit Pant ◽

R.P. Pant ◽

Kuldeep Prakash

Keyword(s):

Fixed Points ◽

Julia Sets ◽

Real Numbers ◽

Continuous Mappings ◽

Non Linear

The aim of the present paper is to study the dynamics of a class of orbitally continuous non-linear mappings defined on the set of real numbers and to apply the results on dynamics of functions to obtain tests of divisibility. We show that this class of mappings contains chaotic mappings. We also draw Julia sets of certain iterations related to multiple lowering mappings and employ the variations in the complexity of Julia sets to illustrate the results on the quotient and remainder. The notion of orbital continuity was introduced by Lj. B. Ciric and is an important tool in establishing existence of fixed points.

Hermite-Hadamard and simpson-like type inequalities for differentiable p-quasi-convex functions

Filomat ◽

10.2298/fil1719945i ◽

2017 ◽

Vol 31 (19) ◽

pp. 5945-5953 ◽

Cited By ~ 7

Author(s):

İmdat İsçan ◽

Sercan Turhan ◽

Selahattin Maden

Keyword(s):

Convex Functions ◽

Real Numbers ◽

Absolute Value ◽

Special Means ◽

Quasi Convexity

In this paper, we give a new concept which is a generalization of the concepts quasi-convexity and harmonically quasi-convexity and establish a new identity. A consequence of the identity is that we obtain some new general inequalities containing all of the Hermite-Hadamard and Simpson-like type for functions whose derivatives in absolute value at certain power are p-quasi-convex. Some applications to special means of real numbers are also given.

On calculating extinction probabilities for branching processes in random environments

Journal of Applied Probability ◽

10.1017/s0021900200026553 ◽

1969 ◽

Vol 6 (03) ◽

pp. 478-492 ◽

Cited By ~ 5

Author(s):

William E. Wilkinson

Keyword(s):

Generating Functions ◽

Infinite Sequence ◽

Branching Processes ◽

Transition Probability ◽

Transition Probability Matrix ◽

Random Environments ◽

Real Numbers ◽

Discrete Time Markov Chain ◽

Extinction Probabilities ◽

Image Position

Consider a discrete time Markov chain {Zn } whose state space is the non-negative integers and whose transition probability matrix ║Pij ║ possesses the representation where {Pr }, r = 1,2,…, is a finite or denumerably infinite sequence of non-negative real numbers satisfying , and , is a corresponding sequence of probability generating functions. It is assumed that Z 0 = k, a finite positive integer.

Some Properties Involving q-Hermite Polynomials Arising from Differential Equations and Location of Their Zeros

Mathematics ◽

10.3390/math9111168 ◽

2021 ◽

Vol 9 (11) ◽

pp. 1168

Author(s):

Cheon Seoung Ryoo ◽

Jung Yoog Kang

Keyword(s):

Differential Equations ◽

Hermite Polynomials ◽

Real Numbers ◽

Different Types

Hermite polynomials are one of the Apell polynomials and various results were found by the researchers. Using Hermit polynomials combined with q-numbers, we derive different types of differential equations and study these equations. From these equations, we investigate some identities and properties of q-Hermite polynomials. We also find the position of the roots of these polynomials under certain conditions and their stacked structures. Furthermore, we locate the roots of various forms of q-Hermite polynomials according to the conditions of q-numbers, and look for values which have approximate roots that are real numbers.

A variation on Nθ ward continuity

Georgian Mathematical Journal ◽

10.1515/gmj-2018-0037 ◽

2020 ◽

Vol 27 (2) ◽

pp. 191-197 ◽

Cited By ~ 1

Author(s):

Huseyin Cakalli ◽

Mikail Et ◽

Hacer Şengül

Keyword(s):

Real Numbers

AbstractThe main purpose of this paper is to introduce the concept of strongly ideal lacunary quasi-Cauchyness of sequences of real numbers. Strongly ideal lacunary ward continuity is also investigated. Interesting results are obtained.

Powers: The No-Successor Problem

Journal of the American Philosophical Association ◽

10.1017/apa.2020.13 ◽

2021 ◽

pp. 1-18

Author(s):

JOHN PEMBERTON

Keyword(s):

Continuous Time ◽

Real Numbers ◽

Causal Relations

Abstract This essay considers the implications for the powers metaphysic of the no-successor problem: As there are no successors in the set of real numbers, one state cannot occur just after another in continuous time without there being a gap between the two. I show how the no-successor problem sets challenges for various accounts of the manifestation of powers. For powers that give rise to a manifestation that is a new state, the challenge of no-successors is similar to that faced on Bertrand Russell's analysis by causal relations. Powers whose manifestation is a processes and powers that manifest through time (perhaps by giving rise to changing through time) are challenged differently. To avoid powers appearing enigmatic, these challenges should be addressed, and I point to some possible ways this might be achieved. A prerequisite for addressing these challenges is a careful focus on the nature and timing of the manifesting and manifestation of powers.

Real Numbers

Real and Complex Numbers for Physicists ◽

10.1063/9780735421578_012 ◽

2020 ◽

pp. 1-52

Author(s):

Nicolas A. Pereyra

Keyword(s):

Real Numbers