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1.
The asymptotic optimal scaling of random walk Metropolis (RWM) algorithms with Gaussian proposal distributions is well understood
for certain specific classes of target distributions. These asymptotic results easily extend to any light tailed proposal
distribution with finite fourth moment. However, heavy tailed proposal distributions such as the Cauchy distribution are known
to have a number of desirable properties, and in many situations are preferable to light tailed proposal distributions. Therefore
we consider the question of scaling for Cauchy distributed proposals for a wide range of independent and identically distributed
(iid) product densities. The results are somewhat surprising as to when and when not Cauchy distributed proposals are preferable
to Gaussian proposal distributions. This provides motivation for finding proposal distributions which improve on both Gaussian
and Cauchy proposals, both for finite dimensional target distributions and asymptotically as the dimension of the target density,
d → ∞. Throughout we seek the scaling of the proposal distribution which maximizes the expected squared jumping distance (ESJD). 相似文献
2.
A. G. Basuev 《Theoretical and Mathematical Physics》2007,153(2):1539-1574
For the Ising model in half-space at low temperatures and for the “unstable boundary condition,” we prove that for each value
of the external magnetic field μ, there exists a spin layer of thickness q(μ) adjacent to the substrate such that the mean
spin is close to −1 inside this layer and close to +1 outside it. As μ decreases, the thickness of the (−1)-spin layer changes
jumpwise by unity at the points μq, and q(μ) → ∞ as μ → +0. At the discontinuity points μq of q(μ), two surface phases coexist. The surface free energy is piecewise analytic in the domain Re μ > 0 and at low temperatures.
We consider the Ising model in half-space with an arbitrary external field in the zeroth layer and investigate the corresponding
phase diagram. We prove Antonov’s rule and construct the equation of state in lower orders with the precision of x7, x = e−7ɛ. In particular, with this precision, we find the points of coexistence of the phases 0, 1, 2 and the phases 0, 2, 3, where
the phase numbers correspond to the height of the layer of unstable spins over the substrate.
Dedicated to Roland L’vovich Dobrushin
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 2, pp. 220–261, November, 2007. 相似文献
3.
C. Baxa 《Acta Mathematica Hungarica》2003,100(4):303-308
Let α be an irrational number and let D
N*(α) and DN(α) denote the star-discrepancy and the discrepancy of the sequence (nα)n
≥1 mod 1, resp. We study properties of the maps α→ v *(α) = limsupN
→∞
N D
N*(α)/log N and α→v(α) = limsupN
→∞
N D
N(α)/log N where α is transcendental but not a U-number.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
4.
LetW be a real algebraic set. We show that the following families of integer-valued functions onW coincide: (i) the functions of the formω →λ(X
ω
), where X
ω
are the fibres of a regular morphismf :X →W of real algebraic sets, (ii) the functions of the formω →χ(X
ω
), where X
ω
are the fibres of a proper regular morphismf :X →W of real algebraic sets, (iii) the finite sums of signs of polynomials onW. Such functions are called algebraically constructible onW. Using their characterization in terms of signs of polynomials we present new proofs of their basic functorial properties
with respect to the link operator and specialization.
Research partially supported by an Australian Research Council Small Grant. Second author also partially supported by KBN
610/P3/94. 相似文献
5.
Gap and InP nanocrystals were synthesized from Na3P and GaCI3 at low temperature (80–100°C) and atmospheric pressure. The samples were characterized by XRD and TEM measurements. The surface
reactivity of Gap nanocrystals was studied by heating in N2. The weight of the nanocrystals increased at the temperature between 370°C and 480°C. It can be concluded that N, molecule
was absorbed and reactivated on the surface of Gap nanocrystals. Keywords: gallium phosphide, indium phosphide, nanocrystal,
surface reactivity. 相似文献
6.
E. A. Zhizhina 《Theoretical and Mathematical Physics》1997,112(1):844-856
We consider the stochastic model of planar rotators x(t)={xk(t), k∈Zd}, t≥0, xk(t)∈T1, at high temperature. For the decay of correlations <fA(x(0)), gA+k(t) (x(t))>, the asymptotic formula is obtained at t→∞, k(t)→∞, k(t)∈Zd. The basic methods we used are the spectral analysis of the Markov semigroup generator and the saddle-point method.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 112, No. 1, pp. 67–80. 相似文献
7.
α-Sn thin films have been grown on GaAs (001) single crystal substrates by molecular beam epitaxy (MBE). The α-Sn growth process
has been characterizedin situ by reflection high energy electron diffraction (RHEED), and the transmission electron microscope (TEM) was used to analyze
the interface structures. The measurement results indicate that our metastable a-Sn films have both higher temperature stability
which increases by 30°C (from 70 to 100°C) and thickness stability which increases by 200 nm (from 500 to 700 nm) in comparison
with previous reports. Other improvements in electrical properties have also been observed. In addition, a new model of multiquantum
well structure has been suggested.
Project supported by the National Natural Science Foundation of China (Grant No. 69586001). 相似文献
8.
We define a partial order on the set No,c of pairs (O,C), where O is a nilpotent orbit and C is a conjugacy class in A(O), Lusztig’s canonical quotient of A(O). We
then show that there is a unique order-reversing duality map No,c → LNo,c that has certain properties analogous to those of the original Lusztig–Spaltenstein duality map. This generalizes work of
E. Sommers. 相似文献
9.
We investigate the limiting fluctuations of the order parameter in the Hopfield model of spin glasses and neural networks
with finitely many patterns at the critical temperature 1/β
c
= 1. At the critical temperature, the measure-valued random variables given by the distribution of the appropriately scaled
order parameter under the Gibbs measure converge weakly towards a random measure which is non-Gaussian in the sense that it
is not given by a Dirac measure concentrated in a Gaussian distribution. This remains true in the case of β = β
N
→β
c
= 1 as N→∞ provided β
N
converges to β
c
= 1 fast enough, i.e., at speed ?(1/). The limiting distribution is explicitly given by its (random) density.
Received: 12 May 1998 / Revised version: 14 October 1998 相似文献
10.
We consider the collision dynamics produced by three beads with masses (m
1, m
2, m
3) sliding without friction on a ring, where the masses are scaled so that m
1 = 1/ɛ, m
2 = 1, m
3 = 1 − ɛ, for 0 ⩽ ɛ ⩾ 1. The singular limits ɛ = 0 and ɛ = 1 correspond to two equal mass beads colliding on the ring with a wall, and without a wall respectively. In both these
cases, all solutions are periodic and the eigenvalue distributions (around the unit circle) associated with the products of
collision matrices are discrete. We then numerically examine the regime which parametrically connects these two states, i.e.
0 < ɛ < 1, and show that the eigenvalue distribution is generically uniform around the unit circle, which implies that the dynamics
are no longer periodic. By a sequence of careful numerical experiments, we characterize how the uniform spectrum collapses
from continuous to discrete in the two singular limits ɛ → 0 and ɛ → 1 for an ensemble of initial velocities sampled uniformly on a fixed energy surface. For the limit ɛ → 0, the distribution forms Gaussian peaks around the discrete limiting values ± 1, ± i, with variances that scale in power law form as σ
2 ∼ αɛ
β. By contrast, the convergence in the limit ɛ → 1 to the discrete values ±1 is shown to follow a logarithmic power-law σ
2 ∼ log(ɛ
β). 相似文献
11.
Franc Forstnerič 《Journal of Geometric Analysis》2003,13(1):77-94
Let S be a closed connected real surface and π: S→X a smooth embedding or immersion of S into a complex surface X. We denote
by I(π) (resp. by I±(π) if S is oriented) the number of complex points of π (S)∪X counted with algebraic multiplicities. Assuming that I(π)≤0
(resp. I±(π)≤0 if S is oriented) we prove that π can be C0 approximated by an isotopic immersion π1: S→X whose image has a basis of open Stein neighborhood in X which are homotopy equivalents to π1 (S). We obtain precise results for surfaces in
and find an immersed symplectic sphere in
with a Stein neighborhood. 相似文献
12.
E. A. Rovba 《Mathematical Notes》1997,61(2):221-226
Summation rational positive operatorsD
4n−n(x; f) of the Jackson type are constructed on the real axis. The corresponding approximations of continuous functionsf onℝwith coinciding finite limits limx→−∞
f(x) and limx→+∞
f(x) are estimated.
Translated fromMatematischeskie Zametki, Vol. 61, No. 2, pp. 270–277, February, 1997.
Translated by N. K. Kulman 相似文献
13.
负相依随机变量的自正则化中心极限定理与部分和的方差估计 总被引:1,自引:0,他引:1
§ 1 IntroductionWe firstintroduce some concepts.Random variables X and Y are called negative dependent ( ND) if for any pair ofmonotonically non-decresing functions f and g,Cov{ f( X) ,g( Y) }≤ 0 .Clearly itis equivalenttoP( X≤ x,Y≤ y)≤ P( X≤ x) P( Y≤ y)for all x,y∈R.A random sequence{ Xi,i≥ 1 } is said to be negative quadrant dependent( NQD) if any pairof variables Xi,Xj( i≠j) are ND.A sequence of random variables{ Xi,i≥ 1 } is said to be linear negative quadrand depend… 相似文献
14.
G. A. Noskov 《Algebra and Logic》1997,36(2):117-132
A group Γ has type F Pn if a trivial ℤΓ-module ℤ has a projective resolution P:…Pn → … → P1 → P0 → ℤ in which ℤΓ-module Pn,…P1, P0 are finitely generated. Let the finitely generated group Γ be a split extension of the Abelian group M by an Abelian group
Q, suppose M is torsion free, and assume Γ∈F Pm, m≥2. Then the invariant ∑
c
M
is m-tame.
Translated fromAlgebra i Logika, Vol. 36, No. 2, pp. 194–218, March–April, 1997. 相似文献
15.
Xueyan Xiang Qian He Wenshan Yang 《分析论及其应用》2007,23(3):243-254
Recently, q-Bernstein polynomials have been intensively investigated by a number of authors. Their results show that for q ≠ 1, q-Bernstein polynomials possess of many interesting properties. In this paper, the convergence rate for iterates of both q-Bernstein polynomials and their Boolean sum are estimated. Moreover, the saturation of {Bn(., qn)} when n → ∞ and convergence rate of Bn(f,q;x) when f ∈ C^n-1 [0, 1], q → ∞ are also presented. 相似文献
16.
Walter Bergweiler 《Journal d'Analyse Mathématique》1994,63(1):121-129
Let (zj) be a sequence of complex numbers satisfying |zj|→ ∞ asj → ∞ and denote by n(r) the number of zj satisfying |zj|≤ r. Suppose that lim infr → ⇈ log n(r)/ logr > 0. Let ϕ be a positive, non-decreasing function satisfying ∫∞ (ϕ(t)t logt)−1
dt < ∞. It is proved that there exists an entire functionf whose zeros are the zj such that log log M(r,f) = o((log n(r))2ϕ(log n(r))) asr → ∞ outside some exceptional set of finite logarithmic measure, and that the integral condition on ϕ is best possible here.
These results answer a question by A. A. Gol’dberg. 相似文献
17.
Evgueni Doubtsov 《Journal of Fourier Analysis and Applications》2006,12(3):225-231
Let μ be a measure on the complex sphere. Denote by μpq the projection of μ on H(p, q), the space of complex spherical harmonics. Assume that μpq = 0 if (p − 1)q ≠ 0, and ∥μ1q∥∞ → 0 as q → ∞. Then μ is absolutely continuous with respect to Lebesgue measure on the sphere. 相似文献
18.
We relate Artin's braid groupB
℞=lim→Bn to a certain groupF′ ofpl-homeomorphisms of the interval. Namely, there exists a short exact sequence 1→B
∞→A→F′→1 whereH
kA=0,k≥1. 相似文献
19.
Bengt Josefson 《Israel Journal of Mathematics》1990,71(3):321-327
An example of a Banach spaceE is given with the following properties: Every bounding setA⊂E (i.e.f(A) is bounded for each holomorphic functionf:E →C) is relatively compact but there are relatively non-compact limited setsA (i.e.T(A) is relatively compact for each bounded linear mapT:E →c
0). 相似文献
20.
D. V. Gugnin 《Proceedings of the Steklov Institute of Mathematics》2009,266(1):59-90
We introduce and study polynomially dependent homomorphisms, which are special linear maps between associative algebras with
identity. The multiplicative structure is much involved in the definition of such homomorphisms (we consider only the case
of maps f: A → B with commutative B). The most important particular case of these maps are the Frobenius n-homomorphisms, which were introduced by V.M. Buchstaber and E.G. Rees in 1996–1997. A 1-homomorphism f: A → B is just an algebra homomorphism (the algebra B is commutative). A typical example of an n-homomorphism is given by the sum of n algebra homomorphisms, f = f
1 + ... + f
n
, f
i
: A → B, 1 ≤ i ≤ n. Another example is the trace of n × n matrices over a field R of characteristic zero, tr: M
n
(R) → R, and, more generally, the character of any n-dimensional representation, tr ρ: A → R, ρ: A → M
n
(R). The properties of n-homomorphisms (some of which were proved by Buchstaber and Rees under additional conditions) are derived, and a general theory
of polynomially dependent homomorphisms is developed. One of the main results of the paper is a uniqueness theorem, which
distinguishes the classes of n-homomorphisms among all polynomially dependent homomorphisms by a single natural completeness condition. As a topological
application of n-homomorphisms, we consider the theory of n-homomorphisms between commutative C*-algebras with identity. We prove that the norm of any such n-homomorphism is equal to n and describe the structure of all such n-homomorphisms, which generalizes the classical Gelfand transform (the case of n = 1). An interesting fact discovered is that the Gelfand transform, which is a functorial bijection between appropriate spaces
of maps, becomes a homeomorphism after considering natural topologies on these spaces. 相似文献