The Finnish-Polish-Ukrainian Summer School in Complex Analysis. Opening address
The generalized -algebra structure on BGG sequences and generalized associative operad
The global solvability to the equations of motion of viscous gas with an artificial viscosity
The graded representations of an affine Lie algebra
The Helmholtz decomposition and the weak Neumann problem in
The iterated version of a translative integral formula for sets of positive reach
By taking into account the work of J. Rataj and M. Zähle [Geom. Dedicata 57, 259-283 (1995; Zbl 0844.53050)], R. Schneider and W. Weil [Math. Nachr. 129, 67-80 (1986; Zbl 0602.52003)], W. Weil [Math. Z. 205, 531-549 (1990; Zbl 0705.52006)], an integral formula is obtained here by using the technique of rectifiable currents.This is an iterated version of the principal kinematic formula for sets of positive reach and generalized curvature measures.
The Lefschetz type theorem for a class of noncompact mappings
The Legendre transformation in differential spaces
The Legendre transformations on differential spaces (in the sense of Sikorski) is studied, and some properties for spaces with singularities are investigated. A mechanical interpretation of the Legendre transformation is also given.
The maximal function of a complex measure
The method of discretization in time and partial differential equations
The numerical solution of compressible flows in time dependent domains
This work is concerned with the numerical solution of inviscid compressible fluid flow in moving domains. Specifically, we assume that the boundary part of the domain (impermeable walls) are time dependent. We consider the Euler equations, which describe the movement of inviscid compressible fluids. We present two formulations of the Euler equations in the ALE (Arbitrary Lagrangian-Eulerian) form. These two formulations are discretized in space by the discontinuous Galerkin method. We apply a semi-implicit linearization...
The optimal control problem in coefficients for the pseudoparabolic variational inequality
The parabolic equations as a limiting case of hyperbolic and elliptic equations
The Penrose transform and Clifford analysis
[For the entire collection see Zbl 0742.00067.]The Penrose transform is always based on a diagram of homogeneous spaces. Here the case corresponding to the orthogonal group is studied by means of Clifford analysis [see F. Brackx, R. Delanghe and F. Sommen: Clifford analysis (1982; Zbl 0529.30001)], and is presented a simple approach using the Dolbeault realization of the corresponding cohomology groups and a simple calculus with differential forms (the Cauchy integral formula for solutions of...
The Penrose transform for Dirac equation
The Penrose transform is discussed for the Dirac equation corresponding to an orthogonal group in even dimensions. The authors outline a simple approach to the calculation which involves using the Dolbeault realization of cohomology groups rather than hypercohomology and spectral sequence. The details will be given elsewhere.
The periodic boundary value problem for some second order ordinary differential equations
The Poisson transform for higher order differential operators
The principal prolongation of first order -structures
The author uses the concept of the first principal prolongation of an arbitrary principal filter bundle to develop an alternative procedure for constructing the prolongations of a class of the first-order -structures. The motivation comes from the almost Hermitian structures, which can be defined either as standard first-order structures, or higher-order structures, but if they do not admit a torsion-free connection, the classical constructions fail in general.
The rank of vector fields of Grassmannian manifolds
The regularity condition for some natural functors