501 research outputs found
On the variance of the number of occupied boxes
We consider the occupancy problem where balls are thrown independently at
infinitely many boxes with fixed positive frequencies. It is well known that
the random number of boxes occupied by the first n balls is asymptotically
normal if its variance V_n tends to infinity. In this work, we mainly focus on
the opposite case where V_n is bounded, and derive a simple necessary and
sufficient condition for convergence of V_n to a finite limit, thus settling a
long-standing question raised by Karlin in the seminal paper of 1967. One
striking consequence of our result is that the possible limit may only be a
positive integer number. Some new conditions for other types of behavior of the
variance, like boundedness or convergence to infinity, are also obtained. The
proofs are based on the poissonization techniques.Comment: 34 page
An estimate for the average spectral measure of random band matrices
For a class of random band matrices of band width , we prove regularity of
the average spectral measure at scales , and find its
asymptotics at these scales.Comment: 19 pp., revised versio
Nanoparticles as agents for targeted delivery in the treatment of vascular pathologies
The strategy of treatment of cardiovascular diseases with preparations based on nanoparticles. For the visualization of atherosclerotic plaques, nanoparticles conjugated with indium (111In) based on antibodies bound to LOX-1 receptors of low density were used in mic
Kernel estimates for nonautonomous Kolmogorov equations with potential term
Using time dependent Lyapunov functions, we prove pointwise upper bounds for
the heat kernels of some nonautonomous Kolmogorov operators with possibly
unbounded drift and diffusion coefficients and a possibly unbounded potential
term
Poisson cluster measures: Quasi-invariance, integration by parts and equilibrium stochastic dynamics
Abstract The distribution µ cl of a Poisson cluster process in X = R d (with i.i.d. clusters) is studied via an auxiliary Poisson measure on the space of configurations in X = n X n , with intensity measure defined as a convolution of the background intensity of cluster centres and the probability distribution of a generic cluster. We show that the measure µ cl is quasiinvariant with respect to the group of compactly supported diffeomorphisms of X and prove an integration-by-parts formula for µ cl . The corresponding equilibrium stochastic dynamics is then constructed using the method of Dirichlet forms
OPERATION MODES AND CHARACTERISTICS OF PLASMA DIPOLE ANTENNA
Existence modes of surface electromagnetic wave on a plasma cylinder, operating modes and characteristics of the plasma antenna were studied in this paper. Solutions of the dispersion equation of surface wave were obtained for a plasma cylinder with finite radius for different plasma density values. Operation modes of the plasma asymmetric dipole antenna with finite length and radius were researched by numerical simulation. The electric field distributions of the plasma antenna in near antenna field and the radiation pattern were obtained. These characteristics were compared to characteristics of the similar metal antenna. Numerical models verification was carried out by comparing of the counted and measured metal antenna radiation patterns
Computer Simulation of a Plasma Vibrator Antenna
The use of new plasma technologies in antenna technology is widely discussed nowadays. The plasma antenna must receive and transmit signals in the frequency range of a transceiver. Many experiments have been carried out with plasma antennas to transmit and receive signals. Due to lack of experimental data and because experiments are difficult to carry out, there is a need for computer (numerical) modeling to calculate the parameters and characteristics of antennas, and to verify the parameters for future studies. Our study has modeled plasma vibrator (dipole) antennas (PDA) and metal vibrator (dipole) antennas (MDA), and has calculated the characteristics of PDAs and MDAs in the full KARAT electro-code. The correctness of the modeling has been tested by calculating a metal antenna using the MMANA program
Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
This paper is devoted to a deeper understanding of the heat flow and to the
refinement of calculus tools on metric measure spaces (X,d,m). Our main results
are:
- A general study of the relations between the Hopf-Lax semigroup and
Hamilton-Jacobi equation in metric spaces (X,d).
- The equivalence of the heat flow in L^2(X,m) generated by a suitable
Dirichlet energy and the Wasserstein gradient flow of the relative entropy
functional in the space of probability measures P(X).
- The proof of density in energy of Lipschitz functions in the Sobolev space
W^{1,2}(X,d,m).
- A fine and very general analysis of the differentiability properties of a
large class of Kantorovich potentials, in connection with the optimal transport
problem.
Our results apply in particular to spaces satisfying Ricci curvature bounds
in the sense of Lott & Villani [30] and Sturm [39,40], and require neither the
doubling property nor the validity of the local Poincar\'e inequality.Comment: Minor typos corrected and many small improvements added. Lemma 2.4,
Lemma 2.10, Prop. 5.7, Rem. 5.8, Thm. 6.3 added. Rem. 4.7, Prop. 4.8, Prop.
4.15 and Thm 4.16 augmented/reenforced. Proof of Thm. 4.16 and Lemma 9.6
simplified. Thm. 8.6 corrected. A simpler axiomatization of weak gradients,
still equivalent to all other ones, has been propose
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