On the variance of the sample correlation between two independent lattice processes

1981 ◽  
Vol 18 (4) ◽  
pp. 943-948 ◽  
Author(s):  
Sylvia Richardson ◽  
Denis Hemon
Keyword(s):  
Wide Class ◽  
Asymptotic Expression ◽  
Asymptotic Variance ◽  
First Order ◽  
Sample Correlation ◽  
Lattice Processes ◽  
Independent Lattice

Consider two stochastically independent, stationary Gaussian lattice processes with zero means, {X(u), u (Z2} and {Y(u), u (Z2}. An asymptotic expression for the variance of the sample correlation between {X(u)} and {Y(u)} over a finite square is derived. This expression also holds for a wide class of domains in Z2. As an illustration, the asymptotic variance of the correlation between two first-order autonormal schemes is evaluated.

On the variance of the sample correlation between two independent lattice processes

1981 ◽  
Vol 18 (04) ◽  
pp. 943-948 ◽  
Author(s):  
Sylvia Richardson ◽  
Denis Hemon
Keyword(s):  
Wide Class ◽  
Asymptotic Expression ◽  
Asymptotic Variance ◽  
First Order ◽  
Sample Correlation ◽  
Lattice Processes ◽  
Independent Lattice

Consider two stochastically independent, stationary Gaussian lattice processes with zero means, {X(u), u (Z 2} and {Y(u), u (Z 2}. An asymptotic expression for the variance of the sample correlation between {X(u)} and {Y(u)} over a finite square is derived. This expression also holds for a wide class of domains in Z 2. As an illustration, the asymptotic variance of the correlation between two first-order autonormal schemes is evaluated.

On the notion of algebraic closedness for noncommutative groups and fields

1971 ◽  
Vol 36 (3) ◽  
pp. 441-444 ◽  
Author(s):  
Abraham Robinson
Keyword(s):  
Wide Class ◽  
First Order ◽  
Division Rings ◽  
Ordered Field ◽  
Ordered Fields ◽  
Skew Fields

The notion of algebraic closedness plays an important part in the theory of commutative fields. The corresponding notion in the theory of ordered fields is (not only intuitively but in a sense which can be made precise in a metamathematical framework, compare [4]) that of a real closed ordered field. Several suggestions have been made (see [2] and [8]) for the formulation of corresponding concepts in the theory of groups and in the theory of skew fields (division rings, noncommutative fields). Here we present a concept of this kind, which preserves the principal metamathematical properties of algebraically closed commutative fields and which applies to a wide class of first order theories K, including the theories of commutative and of skew fields and the theories of commutative and of general groups.

scholarly journals DIFFERENTIATION IN P-MINIMAL STRUCTURES AND A p-ADIC LOCAL MONOTONICITY THEOREM

2014 ◽  
Vol 79 (4) ◽  
pp. 1133-1147 ◽  
Author(s):  
TRISTAN KUIJPERS ◽  
EVA LEENKNEGT
Keyword(s):  
Wide Class ◽  
Local Version ◽  
First Order ◽  
Almost Everywhere ◽  
Local Monotonicity ◽  
Definable Functions

AbstractWe prove a p-adic, local version of the Monotonicity Theorem for P-minimal structures. The existence of such a theorem was originally conjectured by Haskell and Macpherson. We approach the problem by considering the first order strict derivative. In particular, we show that, for a wide class of P-minimal structures, the definable functions f : K → K are almost everywhere strictly differentiable and satisfy the Local Jacobian Property.

Undecidability in diagonalizable algebras

1997 ◽  
Vol 62 (1) ◽  
pp. 79-116 ◽  
Author(s):  
V. Yu. Shavrukov
Keyword(s):  
Wide Class ◽  
Formal Theory ◽  
First Order ◽  
Unary Operator ◽  
Diagonalizable Algebra

AbstractIf a formal theory T is able to reason about its own syntax, then the diagonalizable algebra of T is defined as its Lindenbaum sentence algebra endowed with a unary operator □ which sends a sentence φ to the sentence □φ asserting the provability of φ in T. We prove that the first order theories of diagonalizable algebras of a wide class of theories are undecidable and establish some related results.

Role of Diffusion in the Shaping of the High-Absorption State in a Resonatorless Exciton Bistable System

2005 ◽  
Vol 245-246 ◽  
pp. 9-14
Author(s):  
Yuriy V. Gudyma ◽  
Ivanna V. Kruglenko
Keyword(s):  
Asymptotic Expression ◽  
Distribution Functions ◽  
Bistable System ◽  
Unified Approach ◽  
First Order ◽  
Wave Approximation ◽  
First Order Transition ◽  
Switching Wave ◽  
High Absorption

We present a unified approach to description of all the stages of shaping of a highabsorption state in a resonatorless exciton bistable system, as a nonequilibrium first-order transition. The velocity of switching wave front and thickness of interface between phases are determined within the quick switching wave approximation. The size distribution functions of subcritical and supercritical nuclei and asymptotic expression for nucleus radius were obtained.

Negative-existentially complete structures and definability in free extensions

1976 ◽  
Vol 41 (1) ◽  
pp. 95-108 ◽  
Author(s):  
Volker Weispfenning
Keyword(s):  
Commutative Ring ◽  
Polynomial Ring ◽  
Wide Class ◽  
First Order ◽  
Formal Degree ◽  
Atomic Relation

Let R be a commutative ring with 1 and R[X1, …, Xn] the polynomial ring in n variables over R. Then for any relation f(X) = 0 in R[X] there exists a conjunction of equations φf such that f(X) = 0 holds in R[X] iff φf holds in R; φf is of course the formula saying that all the coefficients of f(X) vanish. Moreover, φf is independent of R and formed uniformly for all polynomials f up to a given formal degree. In this paper we investigate first order theories T for which a similar phenomenon holds. More precisely, we let TAH be the universal Horn part of a theory T and look at free extensions of models of T in the class of models of TAH. We ask whether an atomic relation t1(X, a) = t2(X, a) or R(t1(X, a), …, tn(X, a)) in can be equivalently expressed by a finite or infinitary formula φ(a) in , such that φ(y) depends only on ti{X, y) and not on or a1, …, am ∈ A.We will show that for a wide class of theories T “defining formulas” φ(y) in this sense exist and can be taken as infinite disjunctions of positive existential formulas.

scholarly journals Oscillation results for nonlinear second order difference equations with mixed neutral terms

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Said R. Grace ◽  
Jehad Alzabut
Keyword(s):  
Difference Equations ◽  
Wide Class ◽  
Second Order ◽  
Order Difference ◽  
Oscillation Criteria ◽  
First Order ◽  
Oscillatory Behaviors

AbstractIn this paper, we establish new oscillation criteria for nonlinear second order difference equations with mixed neutral terms. The key idea of our approach is to compare with first order equations whose oscillatory behaviors are already known. The obtained results not only improve and extend existing results reported in the literature but also provide a new platform for the investigation of a wide class of nonlinear second order difference equations. The results are supported by examples to demonstrate the validity of the theoretical findings.

Buckling Reliability Analysis for the Cylindrical Shell with Initial Defects

2012 ◽  
Vol 525-526 ◽  
pp. 101-104
Author(s):  
Hai An ◽  
Wei Guang An ◽  
Yuan Yin Gao ◽  
Xiang Hua Song
Keyword(s):  
Cylindrical Shell ◽  
Axial Symmetry ◽  
Reliability Index ◽  
Asymptotic Expression ◽  
Safety Margin ◽  
Axial Loads ◽  
Thin Cylindrical Shell ◽  
First Order ◽  
First Order Second Moment ◽  
Second Moment Method

in this paper, the asymptotic expression of the buckling critical load coefficient of the thin cylindrical shell with local axial symmetry initial defects under the axial loads is deduced by used the Karman-Donnel Equation. The buckling safety margin equation of the cylindrical shell with initial defects is constructed. Furthermore, the buckling reliability index is solved by used AFOSM (Advanced First-Order Second Moment) method. In the end, a numerical example is given to analyze the influence of the band width and amplitude of local axial symmetry initial defects on the structural buckling reliability index.

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