We investigate Ordered Binary Decision Diagrams (OBDDs) — a model for computing Boolean functions. It is known that OBDD’s complexity can extremely depend on the order of reading variables. There are techniques for constructing functions that do not allow choosing the optimal order for reading the input, one of which we use in this paper. A function “Shuffled Inequality” NEQS is presented, for which a lower and an upper bounds for the complexity of nondeterministic OBDD are proved. The upper bound is an improvement of a previously known result. A quantum measure-many non-deterministic OBDD is constructed that is more efficient than the classical one. The hierarchy of complexity classes defined on the basis of OBDD models is clarified.

This paper is devoted to the problem of existence of positive weak solutions for a class of fractional Kirchhoff-type systems with multiple parameters. By using the sub-supersolution method and some analysis techniques, we prove a new existence result. To the best of our knowledge, our results are new in the study of fractional Kirchhoff-type systems.

The existence and uniqueness of the solution of a boundary value problem with conditions on two characteristic planes and on a plane that is not a characteristic for a system of hyperbolic equations with multiple characteristics are proved. An analogue of the Riemann-Hadamard method is developed for this problem, the definition of the Riemann-Hadamard matrix is given. The solution of this problem is constructed in terms of the introduced Riemann-Hadamard matrix.

The article studies the continuation of the solution of the Cauchy problem for the biharmonic equation in the domain G from its known values on the smooth part S of the boundary дG. The considered problem belongs to the problems of mathematical physics, in which there is no continuous dependence of solutions on the initial data. It is assumed that the solution to the problem exists and is continuously differentiable in a closed domain with exactly given Cauchy data. For this case, an explicit formula for the continuation of the solution is established.

Extensions of Cline’s formula for some new generalized inverses such as strong Drazin inverse, generalized strong Drazin inverse, Hirano inverse and generalized Hirano inverse are presented. These extend many known results, e.g., Z. Wu and Q. Zeng, Extensions of Cline’s formula for some new generalized inverses, Filomat 35, 477-483 (2021).

The regularity properties of nonlocal anisotropic elliptic equations with parameters are investigated in abstract weighted L_p spaces. The equations include the variable coefficients and abstract operator function A = A (x) in a Banach space E in leading part. We find the sufficient growth assumptions on A and appropriate symbol polynomial functions that guarantee the uniformly separability of the linear problem. It is proved that the corresponding anisotropic elliptic operator is sectorial and is also the negative generator of an analytic semigroup. Byusing these results, the existence and uniqueness of maximal regular solution of the nonlinear nonlocal anisotropic elliptic equation is obtained in weighted L_p spaces. In application, the maximal regularity properties of the Cauchy problem for degenerate abstract anisotropic parabolic equation in mixed L_p norms, the boundary value problem for anisotropic elliptic convolution equation, the Wentzel-Robin type boundary value problem for degenerate integro-differential equation and infinite systems of degenerate elliptic integro-differential equations are obtained.

Based on the concept of majorization for the probability distribution, a definition of the majorization of a quantum channel by a probability distribution is introduced. It is shown that the proposed approach makes it possible to solve the problem of taking the extremes of convex functions from the output eigenvalues of mixed unitary channels in the case when summation in the definition of the channel is carried out according to the Heisenberg-Weyl group.

Let φ be a trace on von Neumann algebra M, A, B ϵ M and ||B|| < 1, [A, B] = AB—BA. Then φ(|[A,B]|) ≤ 2 φ(|A|). Let τ be a faithful normal semifinite trace on M, S(M, τ) be the *-algebra of all τ-measurable operators. If A ϵ L₂(M, τ) and Re A = λ|A| with λ ϵ {—1,1}, then A = λ|A|. An operator A ϵ L₂(M, τ) is Hermitian if and only if τ(A²) = τ(A*A). Let positive operators A, B ϵ S(M, τ) be invertible in S(M, τ) and Y := (A^-1 — B^-1)(A — B). If Y, A^1/2YA^-1/2 ϵ L₁(M, τ), then τ(Y) ≤ 0. Let an operator A ϵ S(M, τ) be hyponormal and A = B + iC be its Cartesian decomposition. If 1) BC ϵ L₁(M, τ), оr 2) C = C³ ϵ M and [B, C] ϵ L₁(M, τ), then A is normal.