THE DIMENSION FOR RANDOM SUB-SELF-SIMILAR SET

In this article,the Hausdorff dimension and exact Hausdorff measure function of any random sub-self-similar set are obtained under some reasonable conditions.Several examples are given at the end.     

Lower bounds for transition probabilities on graphs

The paper presents two results. The first one provides separate conditions for the upper and lower estimates of the distribution of the time of exit from balls of a random walk on a weighted graph. The main result of the paper is that the lower estimate follows from the elliptic Harnack inequality. The second result is an off-diagonal lower bound for the transition probability of the random walk.     

Pure adaptive search in monte carlo optimization

Pure adaptive search constructs a sequence of points uniformly distributed within a corresponding sequence of nested regions of the feasible space. At any stage, the next point in the sequence is chosen uniformly distributed over the region of feasible space containing all points that are equal or superior in value to the previous points in the sequence. We show that for convex programs the number of iterations required to achieve a given accuracy of solution increases at most linearly in the dimension of the problem. This compares to exponential growth in iterations required for pure random search.     

Pure adaptive search in global optimization

Pure adaptive seach iteratively constructs a sequence of interior points uniformly distributed within the corresponding sequence of nested improving regions of the feasible space. That is, at any iteration, the next point in the sequence is uniformly distributed over the region of feasible space containing all points that are strictly superior in value to the previous points in the sequence. The complexity of this algorithm is measured by the expected number of iterations required to achieve a given accuracy of solution. We show that for global mathematical programs satisfying the Lipschitz condition, its complexity increases at mostlinearly in the dimension of the problem.This work was supported in part by NATO grant 0119/89.     

Synthesis, morphology and random laser action of ZnO nanostructures

Three-dimensional (3-D) ZnO random-wall nanostructures and one-dimensional (1-D) ZnO nanorods were prepared on silicon substrates by a simple solid-vapour phase thermal sublimation technique. Optical pumped random lasing has been observed in the ZnO random-wall arrays with a threshold intensity of 0.38 MW/cm² in the emission wavelength from 380 to 395 nm. The optical gain was attributed to the closed-loop scattering and light amplification of the ZnO random-wall. The experimental result suggests that the morphology of nanostructure is the key factor to effect random lasing.     

Propagator matrices as matrices of power''s series. II. It''s relationship with HF''s stability problem and alternative solutions

Some non-singlet quasi-instabilities (QIs) cases that arise in the calculation of NMR-J parameters are analyzed within response theory. The relationship between ‘very close to zero’ eigenvalues of the principal propagator and the rate of convergency for specific coupling pathways is shown by a power series implemented to calculate the principal propagator matrix. A natural criterion for the analysis of the stability problem emerges from that series. This is more general and accurate compared with previous proposals. Its relationship with π-type molecular orbitals is given. We present an alternative scheme to minimize the effects of non-singlet QIs in such a way that the NMR-J parameters become close to the best theoretical calculations for H₂CX (X=CH₂, NH and O).     

A strong law of large numbers for generalized random sets from the viewpoint of empirical processes

In this article we prove a strong law of large numbers for Borel measurable nonseparably valued random elements in the case of generalized random sets.

     

Self-organized critical pinball machine

The nature of self-organized criticality (SOC) is pin-pointed with a simple mechanical model: a pinball machine. Its phase space is fully parameterized by two integer variables, one describing the state of an on-going game, the other describing the state of the machine. This is the simplest possible SOC system, having only two degrees of freedom and no spatial correlations, yet is not solvable by analytical means.     

Discrete and Continuous Time Modulated Random Walks with Heavy-Tailed Increments

We consider a modulated process S which, conditional on a background process X, has independent increments. Assuming that S drifts to −∞ and that its increments (jumps) are heavy-tailed (in a sense made precise in the paper), we exhibit natural conditions under which the asymptotics of the tail distribution of the overall maximum of S can be computed. We present results in discrete and in continuous time. In particular, in the absence of modulation, the process S in continuous time reduces to a Lévy process with heavy-tailed Lévy measure. A central point of the paper is that we make full use of the so-called “principle of a single big jump” in order to obtain both upper and lower bounds. Thus, the proofs are entirely probabilistic. The paper is motivated by queueing and Lévy stochastic networks.     

BERNOULLI CONVOLUTIONS ASSOCIATED WITH CERTAIN NON-PISOT NUMBERS

1　IntroductionForany 0 <λ <1 ,letνλ　denotethedistributionof ∞n=0 εnλn wherethecoefficientsεnareeither0or1 ,chosenindependentlywithprobability12 foreach .Itistheinfiniteconvo lutionproductofthedistributions 12 (δ0 +δλn) ,givingrisetotheterm“infiniteBernoulliconvolution”orsimply“Bernoulliconvolution” .TheBernoulliconvolutioncanbeexpressedasaself similarmeasureνλsatisfyingtheequationνλ =12 νλ φ- 10 + 12 νλ φ- 11,( 1 .1 )whereφ0 (x) =λxand φ1(x) =λx + 1 .Thisme…