# The Reception of the Theory of Distributions

## Related Articles

- Malliavin calculus for difference approximations of multidimensional diffusions: Truncated local limit theorem. Kulik, A. M. // Ukrainian Mathematical Journal;Mar2008, Vol. 60 Issue 3, p395
The truncated local limit theorem is proved for difference approximations of multidimensional diffusions. Under very mild conditions on the distributions of difference terms, this theorem states that the transition probabilities of these approximations, after truncation of some asymptotically...

- On some fractal differential equations of mathematical models of catastrophic situations. Nakhusheva, V. // Differential Equations;Apr2013, Vol. 49 Issue 4, p487
On the basis of the Pearson and Kolmogorov equations, we suggest and study nonlocal differential equations that permit one to obtain evolution laws for the distribution density of random variables, determine the transition function of densities of non-Markov processes and Brownian motion via the...

- LIE THEOREM VIA RANK 2 DISTRIBUTIONS (INTEGRATION OF PDE OF CLASS ? = 1). KRUGLIKOV, BORIS // Journal of Nonlinear Mathematical Physics (Atlantis Press);Jun2012, Vol. 19 Issue 2, p-1
In this paper we investigate compatible overdetermined systems of PDEs on the plane with one common characteristic. Lie's theorem states that its integration is equivalent to a system of ODEs, and we give a new proof by relating it to the geometry of rank 2 distributions. We find a criterion for...

- On the mean value of log Ï±(n). Lixia Li; Heng Liu // Scientia Magna;2009, Vol. 5 Issue 4, p26
Let n > 1 be an integer, Ï±(n) denote the number of regular integers m(mod n) such that 1 â‰¤ m â‰¤ n. In this paper we shall investigate the mean value of the function log Ï±(n) by the convolution method.

- Weyl Asymptotic Formula for the Laplacian on Domains with Rough Boundaries. Netrusov, Yu.; Safarov, Yu. // Communications in Mathematical Physics;Jan2005, Vol. 253 Issue 2, p481
We study asymptotic distribution of eigenvalues of the Laplacian on a bounded domain in R n. Our main results include an explicit remainder estimate in the Weyl formula for the Dirichlet Laplacian on an arbitrary bounded domain, sufficient conditions for the validity of the Weyl formula for the...

- Exact small ball asymptotics in weighted L2-norm for some Gaussian processes. Nazarov, A.; Pusev, R. // Journal of Mathematical Sciences;Dec2009, Vol. 163 Issue 4, p409
We find the exact small ball asymptotics under weighted L2-norm for a wide class of Gaussian processes which generate boundary-value problems for ordinary differential equations. Sharp constants in the asymptotics are derived for a number of processes connected with special functions....

- On the Efficient Evaluation of Coalescence Integrals in Population Balance Models. Hackbusch, W. // Computing;Oct2006, Vol. 78 Issue 2, p145
The solution of population balance equations is a function f( t, r, x) describing a population density of particles of the property x at time t and space r. For instance, the additional independent variable x may denote the particle size. The describing partial differential equation contains...

- Perturbation theory based on the Einsteinâ€“Boltzmann system. II. Illustration of the theory for an almost-Robertsonâ€“Walker geometry. Banach, Zbigniew; Piekarski, Sl\awomir // Journal of Mathematical Physics;Nov94, Vol. 35 Issue 11, p5885
This is the second in a pair of articles, the overall objective of which is to describe within the framework of the Einsteinâ€“Boltzmann system a self-consistent perturbation method which leads to a tractable set of integrodifferential equations for the rate of change of the metric and the...

- Oscillation properties of some functional fourth order hyperbolic differential equations. Petrova, Z. // AIP Conference Proceedings;Nov2012, Vol. 1497 Issue 1, p265
In this paper, we apply our recent results for fourth order functional ordinary differential equations and inequalities and obtain sufficient conditions for oscillation of all sufficiently smooth solutions of the following equation

i+j =...