For simplicity, we adopt the following rules: X, Y denote sets, n, m, k, i denote natural numbers, r denotes a real number, R denotes an element of RF, K denotes a field, f , f1, f2, g1, g2 denote finite sequences, r1, r2, r3 denote real-valued finite sequences, c1, c2 denote complex-valued finite sequences, and F denotes a function. Let us consider X, Y and let F be a positive yielding partial...

We use the following convention: x, t, t1, t2, r, a, b are real numbers and F , G are partial functions from R to R. Let F be a partial function from R to R and let t be a real number. We say that t is a period of F if and only if: (Def. 1) t 6= 0 and for every x holds x ∈ domF iff x+t ∈ domF and if x ∈ domF, then F (x) = F (x+ t). Let F be a partial function from R to R. We say that F is perio...

We introduce a diversified top-k partial MaxSAT problem, a combination of partial MaxSAT problem and enumeration problem. Given a partial MaxSAT formula F and a positive integer k, the diversified top-k partial MaxSAT is to find k maximal solutions for F such that the k maximal solutions satisfy the maximum number of soft clauses of F . This problem can be widely used in many applications inclu...

The study of the Dirichlet problem with arbitrary measurable data for harmonic functions in unit disk ???? is due to dissertation Luzin. Later on, known monograph Vekua was devoted boundary-value problems only Hölder continuous generalized analytic functions, i.e., complex-valued f(z) complex variable z = x + iy first partial derivatives by Sobolev satisfying equations form $$ {\partial}_{\over...

A partial group as defined in [3] is a semigroup S which satisfies the following axioms. (i) For every x ∈ S, there exists a (necessarily unique) element ex ∈ S, called the partial identity of x such that exx =xex =x and if yx =xy =x then ex y = yex = ex. (ii) For every x ∈ S, there exists a (necessarily unique) element x−1 ∈ S, called the partial inverse of x such that xx−1 = x−1x = ex and exx...