The characterization of a class of subspace pseudoframes with arbitrary real number translations

2009 ◽  
Vol 42 (5) ◽  
pp. 2696-2706 ◽  
Author(s):  
Qingjiang Chen ◽  
Zhi Shi ◽  
Huaixin Cao
Keyword(s):  
Real Number ◽  
Arbitrary Real Number

A Characterization of the Quadratic Irrationals

1991 ◽  
Vol 34 (1) ◽  
pp. 36-41 ◽  
Author(s):  
Tom C. Brown
Keyword(s):  
Real Number ◽  
Quadratic Equation ◽  
Substitution Property

AbstractLet α be a positive irrational real number, and let fα (n) = [(n + l)α] — [nα] — [α],n > 1, where [x] denotes the greatest integer not exceeding x. It is shown that the sequence fα has a certain 'substitution property' if and only if α is the root of a quadratic equation over the rationals.

scholarly journals FUZZY INSTANTONS

2002 ◽  
Vol 17 (15) ◽  
pp. 2095-2111 ◽  
Author(s):  
HARALD GROSSE ◽  
MARCO MACEDA ◽  
JOHN MADORE ◽  
HAROLD STEINACKER
Keyword(s):  
Real Number ◽  
Matrix Model ◽  
Matrix Algebra ◽  
Quantization Condition ◽  
Constant Factor ◽  
Arbitrary Real Number ◽  
Self Duality ◽  
Duality Condition ◽  
The Matrix ◽  
Fixed Constant

We present a series of instanton-like solutions to a matrix model which satisfy a self-duality condition and possess an action whose value is, to within a fixed constant factor, an integer l2. For small values of the dimension n2 of the matrix algebra the integer resembles the result of a quantization condition but as n → ∞ the ratio l/n can tend to an arbitrary real number between zero and one.

scholarly journals A problem of coefficient determination in parabolic equations solved as moment problem

2017 ◽  
Vol 6 (4) ◽  
pp. 109
Author(s):  
Maria Beatriz Pintarelli
Keyword(s):  
Boundary Conditions ◽  
Real Number ◽  
Moment Problem ◽  
Parabolic Equations ◽  
Arbitrary Real Number ◽  
Initial Condition ◽  
Moments Problem ◽  
Inverse Moment

The problem is to find a(t) y w(x; t) such that wt = a(t) (wx)x+r(x; t) under the initial condition w(x; 0) =fi(x) and the boundary conditions w(0; t) = 0 ; wx(0; t) = wx(1; t)+alfa w(1; t) about a region D ={(x; t); 0 <x < 1; t >0}. In addition it must be fulfilled the integral of w (x, t) with respect to x is equal to E(t) where fi(x) , r(x; t) and E(t) are known functions and alfa is an arbitrary real number other than zero.The objective is to solve the problem as an application of the inverse moment problem. We will find an approximated solution and bounds for the error of the estimated solution using the techniques on moments problem. In addition, the method is illustrated with several examples.

A characterization of the Poisson process

1986 ◽  
Vol 23 (01) ◽  
pp. 233-235 ◽  
Author(s):  
Pushpa Lata Gupta ◽  
Ramesh C. Gupta
Keyword(s):  
Poisson Process ◽  
Real Number ◽  
Renewal Process ◽  
Residual Life ◽  
Mild Conditions

Denoting by v(t) the residual life of a component in a renewal process, Çinlar and Jagers (1973) and Holmes (1974) have shown that if E(v(t)) is independent of t for all t, then the process is Poisson. In this note we prove, under mild conditions, that if E(G(v(t))) is constant, then the process is Poisson. In particular if E((v(t))r) for some specific real number r ≧ 1 is independent of t, then the process is Poisson.

Vertex Connectivity of Fuzzy Graphs with Applications to Human Trafficking

2018 ◽  
Vol 14 (03) ◽  
pp. 457-485 ◽  
Author(s):  
Shanookha Ali ◽  
Sunil Mathew ◽  
John N. Mordeson ◽  
Hossein Rashmanlou
Keyword(s):  
Real Number ◽  
Human Trafficking ◽  
Dynamic Network ◽  
Arbitrary Real Number ◽  
Fuzzy Graph ◽  
Vertex Connectivity ◽  
The Past ◽  
Fuzzy Graphs ◽  
Number Formula ◽  
Fuzzy Vertex

Connectivity is the most important aspect of a dynamic network. It has been widely studied and applied in different perspectives in the past. In this paper, constructions of [Formula: see text]-connected fuzzy graphs for an arbitrary real number [Formula: see text] and average fuzzy vertex connectivity of fuzzy graphs are discussed. Average fuzzy vertex connectivity of fuzzy trees, fuzzy cycles and complete fuzzy graphs are studied. The concept of a uniformly [Formula: see text]-connected fuzzy graph is introduced and characterized towards the end. An application related to human trafficking is also discussed.

scholarly journals On some mathematical properties of the general zeroth-order Randić coindex of graphs

2020 ◽  
Vol 12 (2) ◽  
pp. 75-82
Author(s):  
I. Milovanović ◽  
M. Matejić ◽  
E. Milovanović ◽  
A. Ali
Keyword(s):  
Real Number ◽  
Lower Bounds ◽  
Connected Graph ◽  
Degree Sequence ◽  
Tree Structure ◽  
Vertex Degree ◽  
Arbitrary Real Number ◽  
Zeroth Order ◽  
Mathematical Properties ◽  
Simple Connected Graph

Let G = (V,E), V = {v1, v2,..., vn}, be a simple connected graph of order n, size m with vertex degree sequence ∆ = d1 ≥ d2 ≥ ··· ≥ dn = d > 0, di = d(vi). Denote by G a complement of G. If vertices vi and v j are adjacent in G, we write i ~ j, otherwise we write i j. The general zeroth-order Randic coindex of ' G is defined as 0Ra(G) = ∑i j (d a-1 i + d a-1 j ) = ∑ n i=1 (n-1-di)d a-1 i , where a is an arbitrary real number. Similarly, general zerothorder Randic coindex of ' G is defined as 0Ra(G) = ∑ n i=1 di(n-1-di) a-1 . New lower bounds for 0Ra(G) and 0Ra(G) are obtained. A case when G has a tree structure is also covered.

Solvability by Real Radicals and Fermat Primes

2004 ◽  
Vol 47 (2) ◽  
pp. 229-236
Author(s):  
C. U. Jensen
Keyword(s):  
Real Number ◽  
Number Field ◽  
The Real ◽  
Real Roots ◽  
Fermat Primes ◽  
Real Number Field

AbstractWe give a survey of old and new results concerning the expressibility of the real roots of a solvable polynomial over a real number field by real radicals. A characterization of Fermat primes is obtained in terms of solvability by real radicals for certain ploynomials.

Sturmian words and Cantor sets arising from unique expansions over ternary alphabets

2018 ◽  
Vol 39 (10) ◽  
pp. 2827-2854
Author(s):  
DOYONG KWON
Keyword(s):  
Real Number ◽  
Critical Point ◽  
Golden Ratio ◽  
Complete Characterization ◽  
Cantor Sets ◽  
Finite Alphabet ◽  
Real Numbers ◽  
Sturmian Words

Over a finite alphabet $A$ of real numbers, unique expansions in base $\unicode[STIX]{x1D6FD}$ are considered. A real number $G_{A}$ called the generalized golden ratio is a critical point of a situation of unique expansions. If $\unicode[STIX]{x1D6FD}<G_{A}$, then there are only trivial unique expansions in base $\unicode[STIX]{x1D6FD}$, while there are non-trivial unique expansions in base $\unicode[STIX]{x1D6FD}$ whenever $\unicode[STIX]{x1D6FD}>G_{A}$. Komornik, Lai and Pedicini [Generalized golden ratios of ternary alphabets. J. Eur. Math. Soc.13(4) (2011), 1113–1146] investigated the case where $A$ consists of three real numbers, and demonstrated that Sturmian words curiously emerge out of the generalized golden ratio. The present paper focuses on Sturmian words under this context. For a given alphabet $A=\{a_{1},a_{2},a_{3}\}$ with $a_{1}<a_{2}<a_{3}$, we give a complete characterization of the corresponding Sturmian words effectively and algorithmically, which reveals interesting structures behind the generalized golden ratios.

COMPUTER ALGEBRA REEXAMINATION OF THE SCALED PARTICLE THEORY FOR HARD-SPHERE AND LENNARD-JONES FLUIDS

2008 ◽  
Vol 22 (26) ◽  
pp. 2601-2615 ◽  
Author(s):  
S. B. KHASARE
Keyword(s):  
Real Number ◽  
Computer Algebra ◽  
Hard Sphere ◽  
Physical Property ◽  
Arbitrary Real Number ◽  
Scaled Particle Theory ◽  
Particle Theory ◽  
Hard Sphere Fluid ◽  
Lennard Jones ◽  
Good Agreement

In the present work, an extension of the scaled particle theory (ESPT) for fluid using computer algebra is developed to obtain an equation of state (EOS), for Lennard-Jones fluid. A suitable functional form for surface tension S(r,d,∊) is assumed with intermolecular separation r as a variable, given below: [Formula: see text] where m is arbitrary real number, and d and ∊ are related to physical property such as average or suitable molecular diameter and the binding energy of the molecule respectively. It is found that, for hard sphere fluid ∊ = 0, the above assumption when introduced in scaled particle theory (SPT) frame and choosing arbitrary real number, m = 1/3, the corresponding EOS is in good agreement with the computer simulation of molecular dynamics (MD) result. Furthermore, for the value of m = -1 it gives a Percus–Yevick (pressure), and for the value of m = 1, it corresponds Percus–Yevick (compressibility) EOS.

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