scholarly journals Crystallographic model of an atom and the dimension of real Euclidean space in Mendeleev's Table

2008 ◽  
Vol 64 (a1) ◽  
pp. C617-C617
Author(s):  
T.F. Veremeichik
Keyword(s):  
Euclidean Space ◽  
Real Euclidean Space

On Certain Functional Identities in EN

1971 ◽  
Vol 23 (2) ◽  
pp. 315-324 ◽  
Author(s):  
A. McD. Mercer
Keyword(s):  
Euclidean Space ◽  
Taylor Series ◽  
Dimensional Space ◽  
The Real ◽  
Higher Dimensional ◽  
Isolated Points ◽  
Functional Identities ◽  
Image Position ◽  
Special Case ◽  
Real Euclidean Space

1. If f is a real-valued function possessing a Taylor series convergent in (a — R, a + R), then it satisfies the following operational identity1.1in which D2 = d2/du2. Furthermore, when g is a solution of y″ + λ2y = 0 in (a – R, a + R), then g is such a function and (1.1) specializes to1.2In this note we generalize these results to the real Euclidean space EN, our conclusions being Theorems 1 and 2 below. Clearly, (1.2) is a special case of (1.1) but in higher-dimensional space it is of interest to allow g, now a solution of1.3to possess singularities at isolated points away from the origin. It is then necessary to consider not only a neighbourhood of the origin but annular regions also.

Inequalities and separation for Schrödinger type operators in L2(Rn)

1978 ◽  
Vol 79 (3-4) ◽  
pp. 257-265 ◽  
Author(s):  
W. N. Everitt ◽  
M. Giertz
Keyword(s):  
Euclidean Space ◽  
Differential Expression ◽  
Integral Inequalities ◽  
Laplacian Operator ◽  
Generalized Derivatives ◽  
Maximal Domain ◽  
Definition Of ◽  
Schrödinger Type Operators ◽  
Real Euclidean Space

SynopsisThe symmetric differential expression M determined by Mf = − Δf;+qf on G, where Δ is the Laplacian operator and G a region of n-dimensional real euclidean space Rn, is said to be separated if qfϵL2(G) for all f ϵ Dt,; here D1 ⊂ L2(G) is the maximal domain of definition of M determined in the sense of generalized derivatives. Conditions are given on the coefficient q to obtain separation and certain associated integral inequalities.

The convergence of a sum of independent random variables

1963 ◽  
Vol 59 (2) ◽  
pp. 411-416
Author(s):  
G. De Barra ◽  
N. B. Slater
Keyword(s):  
Distribution Function ◽  
Euclidean Space ◽  
Rate Of Convergence ◽  
Radial Distribution Function ◽  
Random Variables ◽  
Covariance Matrices ◽  
Independent Random Variables ◽  
Second Moments ◽  
Image Position ◽  
Real Euclidean Space

Let Xν, ν= l, 2, …, n be n independent random variables in k-dimensional (real) Euclidean space Rk, which have, for each ν, finite fourth moments β4ii = l,…, k. In the case when the Xν are identically distributed, have zero means, and unit covariance matrices, Esseen(1) has discussed the rate of convergence of the distribution of the sumsIf denotes the projection of on the ith coordinate axis, Esseen proves that ifand ψ(a) denotes the corresponding normal (radial) distribution function of the same first and second moments as μn(a), thenwhere and C is a constant depending only on k. (C, without a subscript, will denote everywhere a constant depending only on k.)

An upper bound for the cardinality of ans-distance subset in real euclidean space

COMBINATORICA ◽  
1981 ◽  
Vol 1 (2) ◽  
pp. 99-102 ◽  
Author(s):  
Eiichi Bannai ◽  
Etsuko Bannai
Keyword(s):  
Euclidean Space ◽  
Upper Bound ◽  
Real Euclidean Space

Pointing in Real Euclidean Space

1997 ◽  
Vol 20 (5) ◽  
pp. 916-922 ◽  
Author(s):  
Itzhack Y. Bar-Itzhack ◽  
Daniel Hershkowitz ◽  
Leiba Rodman
Keyword(s):  
Euclidean Space ◽  
Real Euclidean Space

An upper bound for the cardinality of ans-distance subset in real euclidean space, II

COMBINATORICA ◽  
1983 ◽  
Vol 3 (2) ◽  
pp. 147-152 ◽  
Author(s):  
Eiichi Bannai ◽  
Etsuko Bannai ◽  
Dennis Stanton
Keyword(s):  
Euclidean Space ◽  
Upper Bound ◽  
Real Euclidean Space

REAL EUCLIDEAN SPACE

1962 ◽  
pp. 1-15
Author(s):  
A.R. AMIR-MOÉZ ◽  
A.L. FASS
Keyword(s):  
Euclidean Space ◽  
Real Euclidean Space

scholarly journals MULTIDIMENSIONAL HYBRID BOUNDARY VALUE PROBLEM

2018 ◽  
Vol 58 (6) ◽  
pp. 402-413
Author(s):  
Marzena Szajewska ◽  
Agnieszka Maria Tereszkiewicz
Keyword(s):  
Euclidean Space ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Special Functions ◽  
Boundary Value ◽  
Fundamental Region ◽  
The Real ◽  
Real Euclidean Space

The purpose of this paper is to discuss three types of boundary conditions for few families of special functions orthogonal on the fundamental region. Boundary value problems are considered on a simplex F in the real Euclidean space Rn of dimension n > 2.

Sorting vectors

1970 ◽  
Vol 68 (1) ◽  
pp. 153-157 ◽  
Author(s):  
Rollo Davidson
Keyword(s):  
Euclidean Space ◽  
Linear Space ◽  
Inner Product ◽  
Real Euclidean Space

1. Introduction: In what follows, X will be a real inner-product linear space (inner product (x, y), norm |x| = (x, x)½); En will be n-dimensional real Euclidean space. We shall be dealing with sets {as: 1 ≤ s ≤ rk; r ≥ 1, k ≥ 2} of elements of X; we write a for the vector (a1; …, ark), and put . We suppose that |as| ≤ ∈ (< 0) for every s.

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