共查询到20条相似文献,搜索用时 15 毫秒
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Mehmet Özer Yasar Polatoglu Gürsel Hacibekiroglou Antonios Valaristos Amalia N. Miliou Antonios N. Anagnostopoulos Antanas Čenys 《Nonlinear Analysis: Theory, Methods & Applications》2008
The dynamic behaviour of the one-dimensional family of maps f(x)=c2[(a−1)x+c1]−λ/(α−1) is examined, for representative values of the control parameters a,c1, c2 and λ. The maps under consideration are of special interest, since they are solutions of the relaxed Newton method derivative being equal to a constant a. The maps f(x) are also proved to be solutions of a non-linear differential equation with outstanding applications in the field of power electronics. The recurrent form of these maps, after excessive iterations, shows, in an xn versus λ plot, an initial exponential decay followed by a bifurcation. The value of λ at which this bifurcation takes place depends on the values of the parameters a,c1 and c2. This corresponds to a switch to an oscillatory behaviour with amplitudes of f(x) undergoing a period doubling. For values of a higher than 1 and at higher values of λ a reverse bifurcation occurs. The corresponding branches converge and a bleb is formed for values of the parameter c1 between 1 and 1.20. This behaviour is confirmed by calculating the corresponding Lyapunov exponents. 相似文献
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Paul-Emile Maing 《Nonlinear Analysis: Theory, Methods & Applications》2008,68(12):3913-3922
This paper is concerned with the Cauchy problem for the fast diffusion equation ut−Δum=αup1 in RN (N≥1), where m∈(0,1), p1>1 and α>0. The initial condition u0 is assumed to be continuous, nonnegative and bounded. Using a technique of subsolutions, we set up sufficient conditions on the initial value u0 so that u(t,x) blows up in finite time, and we show how to get estimates on the profile of u(t,x) for small enough values of t>0. 相似文献
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We consider a multidimensional diffusion X with drift coefficient b(α,Xt) and diffusion coefficient ?σ(β,Xt). The diffusion sample path is discretely observed at times tk=kΔ for k=1…n on a fixed interval [0,T]. We study minimum contrast estimators derived from the Gaussian process approximating X for small ?. We obtain consistent and asymptotically normal estimators of α for fixed Δ and ?→0 and of (α,β) for Δ→0 and ?→0 without any condition linking ? and Δ. We compare the estimators obtained with various methods and for various magnitudes of Δ and ? based on simulation studies. Finally, we investigate the interest of using such methods in an epidemiological framework. 相似文献
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For a fixed prime p, the maximum coefficient (in absolute value) M(p) of the cyclotomic polynomial Φpqr(x), where r and q are free primes satisfying r>q>p exists. Sister Beiter conjectured in 1968 that M(p)≤(p+1)/2. In 2009 Gallot and Moree showed that M(p)≥2p(1−?)/3 for every p sufficiently large. In this article Kloosterman sums (‘cloister man sums’) and other tools from the distribution of modular inverses are applied to quantify the abundancy of counter-examples to Sister Beiter’s conjecture and sharpen the above lower bound for M(p). 相似文献
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We show that the equality m1(f(x))=m2(g(x)) for x in a neighborhood of a point a remains valid for all x provided that f and g are open holomorphic maps, f(a)=g(a)=0 and m1,m2 are Minkowski functionals of bounded balanced domains. Moreover, a polynomial relation between f and g is obtained. 相似文献
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By a perturbation method and constructing comparison functions, we reveal how the inhomogeneous term h affects the exact asymptotic behaviour of solutions near the boundary to the problem △u=b(x)g(u)+λh(x), u>0 in Ω, u|∂Ω=∞, where Ω is a bounded domain with smooth boundary in RN, λ>0, g∈C1[0,∞) is increasing on [0,∞), g(0)=0, g′ is regularly varying at infinity with positive index ρ, the weight b, which is non-trivial and non-negative in Ω, may be vanishing on the boundary, and the inhomogeneous term h is non-negative in Ω and may be singular on the boundary. 相似文献
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Let k be any field, G be a finite group acting on the rational function field k(xg:g∈G) by h⋅xg=xhg for any h,g∈G. Define k(G)=k(xg:g∈G)G. Noether’s problem asks whether k(G) is rational (= purely transcendental) over k. A weaker notion, retract rationality introduced by Saltman, is also very useful for the study of Noether’s problem. We prove that, if G is a Frobenius group with abelian Frobenius kernel, then k(G) is retract k-rational for any field k satisfying some mild conditions. As an application, we show that, for any algebraic number field k, for any Frobenius group G with Frobenius complement isomorphic to SL2(F5), there is a Galois extension field K over k whose Galois group is isomorphic to G, i.e. the inverse Galois problem is valid for the pair (G,k). The same result is true for any non-solvable Frobenius group if k(ζ8) is a cyclic extension of k. 相似文献
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Let K(n,1) denote the minimal cardinality of a binary code of length n and covering radius one. Fundamental for the theory of lower bounds for K(n,1) is the covering excess method introduced by Johnson and van Wee. Let δi denote the covering excess on a sphere of radius i, 0≤i≤n. Generalizing an earlier result of van Wee, Habsieger and Honkala showed δp−1≥p−1 whenever n≡−1 (mod p) for an odd prime p and δ0=δ1=?=δp−2=0 holds. In the present paper we give the new estimation δp−1≥(p−2)p−1 instead. This answers a question of Habsieger and yields a “general improvement of the general excess bound” for binary codes with covering radius one. The proof uses a classification theorem for certain subset systems as well as new congruence properties for the δ-function, which were conjectured by Habsieger. 相似文献
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M. Gürdal 《Expositiones Mathematicae》2009,27(2):153-160
In the present paper we consider the Volterra integration operator V on the Wiener algebra W(D) of analytic functions on the unit disc D of the complex plane C. A complex number λ is called an extended eigenvalue of V if there exists a nonzero operator A satisfying the equation AV=λVA. We prove that the set of all extended eigenvalues of V is precisely the set C?{0}, and describe in terms of Duhamel operators and composition operators the set of corresponding extended eigenvectors of V. The similar result for some weighted shift operator on ?p spaces is also obtained. 相似文献
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We reinvestigate the 2D problem of the inhomogeneous incipient infinite cluster where, in an independent percolation model, the density decays to pc with an inverse power, λ, of the distance to the origin. Assuming the existence of critical exponents (as is known in the case of the triangular site lattice) if the power is less than 1/ν, with ν the correlation length exponent, we demonstrate an infinite cluster with scale dimension given by DH=2−βλ. Further, we investigate the critical case λc=1/ν and show that iterated logarithmic corrections will tip the balance between the possibility and impossibility of an infinite cluster. 相似文献
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Let x(s), s∈Rd be a Gaussian self-similar random process of index H. We consider the problem of log-asymptotics for the probability pT that x(s), x(0)=0 does not exceed a fixed level in a star-shaped expanding domain T⋅Δ as T→∞. We solve the problem of the existence of the limit, θ?lim(−logpT)/(logT)D, T→∞, for the fractional Brownian sheet x(s), s∈[0,T]2 when D=2, and we estimate θ for the integrated fractional Brownian motion when D=1. 相似文献
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Let K be a closed convex subset of a q-uniformly smooth separable Banach space, T:K→K a strictly pseudocontractive mapping, and f:K→K an L-Lispschitzian strongly pseudocontractive mapping. For any t∈(0,1), let xt be the unique fixed point of tf+(1-t)T. We prove that if T has a fixed point, then {xt} converges to a fixed point of T as t approaches to 0. 相似文献
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In a rapidly growing population one expects that two individuals chosen at random from the nth generation are unlikely to be closely related if n is large. In this paper it is shown that for a broad class of rapidly growing populations this is not the case. For a Galton–Watson branching process with an offspring distribution {pj} such that p0=0 and ψ(x)=∑jpjI{j≥x} is asymptotic to x−αL(x) as x→∞ where L(⋅) is slowly varying at ∞ and 0<α<1 (and hence the mean m=∑jpj=∞) it is shown that if Xn is the generation number of the coalescence of the lines of descent backwards in time of two randomly chosen individuals from the nth generation then n−Xn converges in distribution to a proper distribution supported by N={1,2,3,…}. That is, in such a rapidly growing population coalescence occurs in the recent past rather than the remote past. We do show that if the offspring mean m satisfies 1<m≡∑jpj<∞ and p0=0 then coalescence time Xn does converge to a proper distribution as n→∞, i.e., coalescence does take place in the remote past. 相似文献
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Let k be a field of characteristic zero and R a factorial affine k-domain. Let B be an affineR-domain. In terms of locally nilpotent derivations, we give criteria for B to be R-isomorphic to the residue ring of a polynomial ring R[X1,X2,Y] over R by the ideal (X1X2−φ(Y)) for φ(Y)∈R[Y]?R. 相似文献