Sharp Lipschitz estimates for operator dbar_M on a q-concave CR manifold

We prove that the integral operators $R_r$ and $H_r$ constructed in \cite{P} and such that $$f = \bar\partial_{\bold M} R_r(f) + R_{r+1}(\bar\partial_{\bold M} f) + H_r(f),$$ for a differential form $f \in C_{(0,r)}^{\infty}({\bold M})$ on a regular q-concave CR manifold ${\bold M}$ admit sharp estimates in the Lipschitz scale

On a perturbation method for stochastic parabolic PDE

In the article we address two issues related to the perturbation method introduced by Zhang and Lu, and applied to solving linear stochastic parabolic PDE. Those issues are: the construction of the perturbation series, and its convergence

Functional Galois connections and a classification of symmetric conservative clones with a finite carrier

We propose a classification of symmetric conservative clones with a finite carrier. For the study, we use the functional Galois connection $(Inv_Q, Pol_Q)$, which is a natural modification of the connection $(Inv, Pol)$ based on the preservation relation between functions $f$ on a set $A$ (of all finite arities) and sets of functions $h\in A^Q$ for an arbitrary set $Q$

Boundary integral formula for harmonic functions on Riemann surfaces

We construct a boundary integral formula for harmonic functions on open, smoothly-bordered subdomains of Riemann surfaces embeddable into \C\P^2. The formula may be considered as an analogue of the Green's formula for domains in \C

Solvability of the generalized Possio equation in 2D subsonic aeroelasticity

We study solvability of the {\it generalized Possio integral equation} - a tool in analysis of a boundary value problem in 2D subsonic aeroelasticity with the Kutta-Joukowski condition - {\it "zero pressure discontinuity"} - $\psi(x,0,t)=0$ on the complement of a finite interval in the whole real line $\R$. The corresponding problem with boundary condition on finite intervals adjacent to the "chord" was considered in \cite{P}.Comment: 16 page

Explicit Hodge-type decomposition on projective complete intersections

We construct an explicit homotopy formula for the d-bar complex on a complete intersection subvariety V in CP^n. This formula can be interpreted as a Hodge-type decomposition for residual currents on V

Residual d-bar-cohomology and the complex Radon transform on subvarieties of CPn

We show that the complex Radon transform realizes an isomorphism between the space of residual $\bar\partial$-cohomologies of a locally complete intersection subvariety in a linearly concave domain of {\C}P^n and the space of holomorphic solutions of the associated homogeneous system of differential equations withconstant coefficients in the dual domain in ({\C}P^n)^*

Inversion formulas for complex Radon transform on projective varieties and boundary value problems for systems of linear PDE

Let G\subset \C P^n be a linearly convex compact with smooth boundary, D={\C}P^n\setminus G, and let D^* \subset (\C P^n)^* be the dual domain. Then for an algebraic, not necessarily reduced, complete intersection subvariety $V$ of dimension $d$ we construct an explicit inversion formula for the complex Radon transform $R_V:\ H^{d,d-1}(V\cap D)\to H^{1,0}(D^*)$, and explicit formulas for solutions of an appropriate boundary value problem for the corresponding system of differential equations with constant coefficients on $D^*$

Explicit Hodge decomposition on Riemann surfaces

We present a construction of the explicit Hodge decomposition for $\bar\partial$-equation on Riemann surfaces

N -> Delta DVCS, exclusive DIS processes and skewed quark distributions in large N_c limit

We evaluate the amplitude of Bethe-Heitler process: \gamma^* p -> \gamma \Delta^+ -electron bremsstrahlung of photon accompanied by the excitation of \Delta$isobar. We show that this background is suppressed at small momentum transfer squared t to a proton relative to that for \gamma^* p -> \gamma p and \gamma^* p\to -> \Delta^+ - DVCS processes. From experimental point of view, this means that N -> N and N -> \Delta skewed quark distributions (SQD's) might be measurable at small momentum transfer. Several implications and applications of the QCD factorization theorem for the processes \gamma_{L}^* + p -> h_f +h_s are discussed where h_f - the particle produced along photon momentum$\vec q$ maybe either a meson or a baryon. We discuss also t dependence of DVCS and exclusive meson production as the practical criteria to distinguish between soft and hard regime. Basing on the large-N_c picture of the nucleon as a soliton of the effective chiral Lagrangian we derive relations between N -> N and N ->\Delta SQD's which can be used to estimate amplitude of N -> \Delta DVCS .Comment: 8 pages, latex. Contribution to the Workshop " Jefferson Lab Physics and Instrumentation with 6-12 GeV Beams", Newport News, VA, June 15-18, 199