We study a semiclassical random walk with respect to a probability measure with a finite number n0 of wells. We show that the associated operator has exactly n0 exponentially close to 1 eigenvalues (in the semiclassical sense), and that the other are O(h) away from 1. We also give an asymptotic of these small eigenvalues. The key ingredient in our approach is a general factorization result of p...

We study the blow-up of H-perimeter minimizing sets in the Heisenberg group H, n ≥ 2. We show that the Lipschitz approximations rescaled by the square root of excess converge to a limit function. Assuming a stronger notion of local minimality, we prove that this limit function is harmonic for the Kohn Laplacian in a lower dimensional Heisenberg group.

In the present paper, we study rotational surfaces in the three dimensional pseudo-Galilean space G3. Also, we characterize rotational surfaces in G3 in terms of the position vector field, Gauss map and Laplacian operator of the second fundamental form on the surface.

Several systems of differential operators are constructed and their study is commenced. These systems are generalizations, in a reasonable sense, of the Heisenberg Laplacian operators introduced by Folland and Stein. In particular, they admit large groups of conformal symmetries; various real form of the special linear groups, even special orthogonal groups, and the exceptional group of type E6...

The Laplacian Distribution has been widely used to characterize the distribution of DCT coefficients in a great deal of research on statistical attributes of DCT for the reason that Laplacian distribution can achieve a good balance between the simplification of the model and fidelity to the real empirical data. But in our research, we found that there is a large discrepancy between the real dat...

This is the third part of our work with a common title. The first [11] and the second part [12] will be also referred in the sequel as Part I and Part II, respectively. This third part was not planned at the beginning, but a lot of recently published papers on the signless Laplacian eigenvalues of graphs and some observations of ours justify its preparation. By a spectral graph theory we unders...

Recent works on the relationship between the electro-encephalogram (EEG) data and psychological stimuli show that EEG recordings can be used to recognize an auditory stimulus presented to a subject. The recognition rate is, however, strongly affected by technical and physiological artifacts. In this work, subjects were presented seven auditory simuli in the form of English words (first, second,...

In this paper we consider the problem of efficiently computing ǫ-sketches for the Laplacian and its pseudoinverse. Given a Laplacian and an error tolerance ǫ, we seek to construct a function f such that for any vector x (chosen obliviously from f), with high probability (1 − ǫ)xAx ≤ f(x) ≤ (1+ǫ)xAx where A is either the Laplacian or its pseudoinverse. Our goal is to construct such a sketch f ef...