scholarly journals Asymptotic analysis of powers of matrices

2006 ◽  
Vol 2006 ◽  
pp. 1-12
Author(s):  
Diego Dominici
Keyword(s):  
Asymptotic Analysis ◽  
Linear Combination ◽  
Asymptotic Approximation ◽  
First Order

We analyze the representation ofAnas a linear combination ofAj,0≤j≤k−1, whereAis ak×kmatrix. We obtain a first-order asymptotic approximation ofAnasn→∞, without imposing any special conditions onA. We give some examples showing the application of our results.

The Disturbance Due to a Slender Ship Oscillating in Waves in a Fluid of Finite Depth

1966 ◽  
Vol 10 (04) ◽  
pp. 242-252 ◽  
Author(s):  
V. J. Monacella
Keyword(s):  
Ideal Fluid ◽  
Asymptotic Approximation ◽  
Velocity Potential ◽  
Wave Length ◽  
Hydrodynamic Pressure ◽  
Finite Depth ◽  
First Order ◽  
Incident Plane ◽  
Progressive Waves ◽  
Body Potential

The disturbance due to a ship, free to oscillate on the surface of an ideal fluid of finite depth, is studied. The ship is in the presence of oblique, incident, plane progressive waves. Green's theorem is used to represent the velocity potential, and an asymptotic approximation for the first-order slender-body potential valid for all points in the fluid to within a wave length of the ship is found. This is used to determine the hydrodynamic pressure on the bottom of the fluid. Numerical results are presented for the case of a spheroid.

Boundary layers of an anchored magnetic field in a highly conductive flow

2010 ◽  
Vol 466 (2123) ◽  
pp. 3153-3166 ◽  
Author(s):  
Manuel Núñez ◽  
Alberto Lastra
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Asymptotic Analysis ◽  
Small Parameter ◽  
Order Approximation ◽  
First Order ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
First Order Approximation ◽  
Distance To The Boundary

The effects of the flow of an electrically conducting fluid upon a magnetic field anchored at the boundary of a domain are studied. By taking the resistivity as a small parameter, the first-order approximation of an asymptotic analysis yields a boundary layer for the magnetic potential. This layer is analysed both in general and in three particular cases, showing that while in general its effects decrease exponentially with the distance to the boundary, several additional effects are highly relevant.

The effect of normal blowing on the flow near a rotating disk of infinite extent

1971 ◽  
Vol 47 (4) ◽  
pp. 789-798 ◽  
Author(s):  
H. K. Kuiken
Keyword(s):  
Asymptotic Analysis ◽  
Thin Layer ◽  
Rotating Disk ◽  
Complete Agreement ◽  
Viscous Effects ◽  
First Order ◽  
Numerical Integrations ◽  
Infinite Extent

The effect of blowing through a porous rotating disk on the flow induced by this disk is studied. For strong blowing the flow is almost wholly inviscid. First-order viscous effects are encountered only in a thin layer at some distance from the disk. The results of an asymptotic analysis are compared with numerical integrations of the full equations and complete agreement is found.

TOWARDS THE SIEGEL RING IN GENUS FOUR

2008 ◽  
Vol 04 (04) ◽  
pp. 563-586 ◽  
Author(s):  
MANABU OURA ◽  
CRIS POOR ◽  
DAVID S. YUEN
Keyword(s):  
Linear Combination ◽  
Irreducible Component ◽  
Modular Forms ◽  
Quotient Ring ◽  
Siegel Modular Forms ◽  
Weight Enumerators ◽  
New Techniques ◽  
First Order ◽  
The Difference ◽  
Infinite Set

Runge gave the ring of genus three Siegel modular forms as a quotient ring, R3/〈J(3)〉 where R3 is the genus three ring of code polynomials and J(3) is the difference of the weight enumerators for the e8 ⊕ e8 and [Formula: see text] codes. Freitag and Oura gave a degree 24 relation, [Formula: see text], of the corresponding ideal in genus four; where [Formula: see text] is also a linear combination of weight enumerators. We take another step towards the ring of Siegel modular forms in genus four. We explain new techniques for computing with Siegel modular forms and actually compute six new relations, classifying all relations through degree 32. We show that the local codimension of any irreducible component defined by these known relations is at least 3 and that the true ideal of relations in genus four is not a complete intersection. Also, we explain how to generate an infinite set of relations by symmetrizing first order theta identities and give one example in degree 32. We give the generating function of R5 and use it to reprove results of Nebe [25] and Salvati Manni [37].

Asymptotic analysis of positive solutions of first-order cyclic functional differential systems

2017 ◽  
Vol 24 (1) ◽  
pp. 63-80
Author(s):  
Jaroslav Jaroš ◽  
Kusano Takaŝi
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Analysis ◽  
Positive Solutions ◽  
Continuous Functions ◽  
Regularly Varying Functions ◽  
Differential Systems ◽  
First Order ◽  
Functional Differential Systems ◽  
Functional Differential ◽  
Scalar Equations

AbstractThe structure and the asymptotic behavior of positive increasing solutions of functional differential systems of the form$x^{\prime}(t)=p(t)\varphi_{\alpha}\bigl{(}y(k(t))\bigr{)},\quad y^{\prime}(t)=% q(t)\varphi_{\beta}\bigl{(}x(l(t))\bigr{)}$are investigated in detail, where α and β are positive constants,${p(t)}$and${q(t)}$are positive continuous functions on${[0,\infty)}$,${k(t)}$and${l(t)}$are positive continuous functions on${[0,\infty)}$tending to${\infty}$witht, and${\varphi_{\gamma}(u)=\lvert u\rvert^{\gamma}\operatorname{sgn}u}$,${\gamma>0}$,${u\in\mathbb{R}}$. An extreme class of positive increasing solutions, calledrapidly increasing solutions, of the system above is analyzed by means of regularly varying functions. The results obtained find applications to systems of the form$x^{\prime}(g(t))=p(t)\varphi_{\alpha}\bigl{(}y(k(t))\bigr{)},\quad y^{\prime}(% h(t))=q(t)\varphi_{\beta}\bigl{(}x(l(t))\bigr{)},$and to scalar equations of the type$\Bigl{(}p(t)\varphi_{\alpha}\bigl{(}x^{\prime}(g(t))\bigr{)}\Bigr{)}^{\prime}=% p(t)\varphi_{\beta}\bigl{(}x(l(t))\bigr{)}.$

scholarly journals Examples of linear multi-box splines

2012 ◽  
Vol 15 ◽  
pp. 444-462
Author(s):  
Abdellatif Bettayeb
Keyword(s):  
Linear Combination ◽  
Piecewise Linear ◽  
Linear Functions ◽  
Order Derivative ◽  
Box Splines ◽  
Piecewise Linear Functions ◽  
Finite Linear Combination ◽  
First Order ◽  
Box Spline ◽  
Finite Linear

AbstractLet S1=S1(v0,…,vr+1) be the space of compactly supported C0 piecewise linear functions on a mesh M of lines through ℤ2 in directions v0,…,vr+1, possibly satisfying some restrictions on the jumps of the first order derivative. A sequence ϕ=(ϕ1,…,ϕr) of elements of S1 is called a multi-box spline if every element of S1 is a finite linear combination of shifts of (the components of) ϕ. We give some examples for multi-box splines and show that they are stable. It is further shown that any multi-box spline is not always symmetric

A New Simulating Model of Wireless Channel - Rayleigh-Normal Model

2010 ◽  
Vol 34-35 ◽  
pp. 1497-1500
Author(s):  
Ao Feng Zhang ◽  
Zhi Liao ◽  
Xi Long Qu
Keyword(s):  
Stochastic Process ◽  
Wireless Communications ◽  
Linear Combination ◽  
Wireless Channel ◽  
Statistical Characteristics ◽  
Normal Model ◽  
Lognormal Model ◽  
First Order ◽  
Communications System

Simulating and researching for characteristics of channel is essential when designing a wireless communications system. Based on the research of existed simulating methods, this paper proposed the Rayleigh-Normal simulating model which looks received signal as the linear combination of Rayleigh stochastic process and Normal stochastic process. This method was used to simulate the first-order statistical characteristics of Rayleigh model, Ricean model, Nakagami model, Lognormal model and so on, the simulating results prove that Rayleigh-Normal simulating model is a correct and valid simulating model for wireless channel.

scholarly journals An application of graphical enumeration to PA

2003 ◽  
Vol 68 (1) ◽  
pp. 5-16
Author(s):  
Andreas Weiermann
Keyword(s):  
Normal Form ◽  
Asymptotic Analysis ◽  
Natural Number ◽  
Proof Theory ◽  
Peano Arithmetic ◽  
First Order ◽  
Primitive Recursive Arithmetic ◽  
Independence Result ◽  
Primitive Recursive

AbstractFor α less than ε0 let Nα be the number of occurrences of ω in the Cantor normal form of α. Further let ∣n∣ denote the binary length of a natural number n, let ∣n∣h denote the h-times iterated binary length of n and let inv(n) be the least h such that ∣n∣h ≤ 2. We show that for any natural number h first order Peano arithmetic, PA, does not prove the following sentence: For all K there exists an M which bounds the lengths n of all strictly descending sequences 〈α0, …, αn〉 of ordinals less than ε0 which satisfy the condition that the Norm Nαi of the i-th term αi is bounded by K + ∣i∣ · ∣i∣i.As a supplement to this (refined Friedman style) independence result we further show that e.g., primitive recursive arithmetic, PRA, proves that for all K there is an M which bounds the length n of any strictly descending sequence 〈α0, …, αn〉 of ordinals less than ε0 which satisfies the condition that the Norm Nαi of the i-th term αi is bounded by K + ∣i∣ · inv(i). The proofs are based on results from proof theory and techniques from asymptotic analysis of Polya-style enumerations.Using results from Otter and from Matoušek and Loebl we obtain similar characterizations for finite bad sequences of finite trees in terms of Otter's tree constant 2.9557652856.…

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