http://hdl.handle.net/11716/12374 2026-04-17T07:48:12Z 2026-04-17T07:48:12Z Szpond, Justyna http://hdl.handle.net/11716/12385 2023-09-05T07:48:51Z 2010-01-01T00:00:00Z

Some properties of analytic sets with proper projections Szpond, Justyna We give an affective criterion when an analytic set with proper projection is algebraic. We take an ideal of polynomials vanishing on the set then we construct a polydisc convenient for reduction. If this polydisc is "large enough" we can apply the division theorem in the ring of formal power series convergent in this polydisc to prove that the set is algebraic.

2010-01-01T00:00:00Z Bahyrycz, Anna http://hdl.handle.net/11716/12384 2023-09-06T12:59:44Z 2010-01-01T00:00:00Z

On systems of equations with unknown multifunctions related to the plurality function Bahyrycz, Anna Let $T$ be a nonempty set. Inspired by a problem posed by Z. Moszner in [10] we investigate for which additional assumptions put on multifunctions $Z(t):T → 2^{ℝ(m)}$, which fulfil condition \[ ⋃_{t ∈ T} Z(t)=ℝ(m)\], and the system of conditions \[Z(t1)^{k1} ∩ Z(t2)^{k2} + Z(t1)^{l1} ∩ Z(t2)^{l2} ⊂ Z(t1)^{k1l1} ∩ Z(t2)^{k2l2}\] for all $t1,t2 ∈ T$ and for all $k1,k2,l1,l2 ∈ \{0,1\}$ such that $k1l1 + k2l2 ≠ 0$, where $ℝ(m) := [0,+∞)^m ∖ \{0_m\}, Z(t)^1 := Z(t), Z(t)^0 := ℝ(m) ∖ Z(t)$, the multifunctions are also satisfying system of equations obtained by replacing the inclusion in the above conditions by the equality. Next we study if this system of equations are equivalent to some system of conditional equations.

2010-01-01T00:00:00Z Akhalaia, George Manjavidze, Nino http://hdl.handle.net/11716/12383 2023-09-05T07:15:24Z 2010-01-01T00:00:00Z

Boundary value problems with shift for generalized analytic vectors Akhalaia, George; Manjavidze, Nino This paper is a survey of the most important work of the well-known Georgian mathematician Professor Giorgi Manjavidze “Boundary value problems for analytic and generalized analytic functions”. Here we present his original approach to the subject. The main attention is paid to the construction of the canonical matrices which are used in the construction of the general solutions of the considered problems. Explicit conditions of normal solvability and index formulas are obtained.

2010-01-01T00:00:00Z Wiśniewski, Damian http://hdl.handle.net/11716/12382 2023-09-05T07:07:26Z 2010-01-01T00:00:00Z

Boundary value problems for a second-order elliptic equation in unbounded domains Wiśniewski, Damian We investigate the behaviour of weak solutions to the boundary value problems for the second order elliptic linear equation in a neighborhood of innity. The exponent of the decreasing rate of solutions at innity has been exactly calculated.

2010-01-01T00:00:00Z