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The agricultural sector has always been in the centre of attention of the state policy and the government initiates a number of measures to increase effectiveness and productivity of this sector of the economy. However, these measures are not always effective, and a question often arises about the results obtained against public resources spent in this sphere. The given research aimed revealing the effectiveness of the state assistance programs implemented in the RA agricultural sector, for the purpose of which a survey of the main beneficiaries of the sector was developed. In particular, separate surveys were conducted among farmers (both for households and commercial organizations) and experts in the field of agriculture. The results of the surveys made it possible to identify the main shortcomings and advantages of state support programs, as well as opportunities for their improvement.

В работе исследуется периодическая краевая задача для класса полулинейных дифференциальных включений дробного порядка из интервала (3,4) в банаховом пространстве, для которых многозначная нелинейность удовлетворяет условию регулярности, выраженному в терминах мер некомпактности. Для доказательства существования решения задачи конструируется соответствующая функция Грина. Затем вводится в рассмотрение многозначный разрешающий оператор в пространстве непрерывных функций. После чего поставленная задача сводится к задаче существования неподвижных точек разрешающего мультиоператора. Для доказательства существования неподвижных точек используется обобщенная теорема типа Б.Н. Садовского.

We consider a non-local boundary value problem for a feedback control system described by a semilinear functional-differential inclusion of fractional order with infinite delay in a separable Banach space. The general principle of existence of solutions to the problem in terms of the difference from zero of the topological degree of the corresponding vector field is given. We prove a concrete example (Theorem 6) of the implementation of this general principle. The existence of an optimal solution to the posed problem is proved, which minimizes the given lower semicontinuous quality functional.

In this paper, we study a periodic boundary value problem for a class of semilinear differential inclusions of fractional order in a Banach space for which the multivalued nonlinearity satisfies the regularity condition expressed in terms of measures of noncompactness. To prove the existence of solutions to the problem, we first construct the corresponding Green function. Then we introduce into consideration a multivalued resolving operator in the space of continuous functions and reduce the posed problem to the existence of fixed points of the resolving multioperator. To prove the existence of a fixed point, a generalized theorem of B.N. Sadovskii type for a condensing multivalued map is used.

In this paper, we present the results on Frege proof complexities of some DNFtautologies. At first we introduce the notion of complete DNFs and prove that complete DNFs are tautologies, we also show that if the proof complexities for the set of complete DNFs are polynomially bounded, then the set of DNF-tautologies D, for which the number of non-negated variables in every conjunct is O(log(D)), also has polynomially bounded proof complexities. Later we show that the set of all balanced DNF-tautologies has polynomial proof complexities..

On a linear manifold of the space of square summable functions on a finite segment vanishing at its ends, we consider the operator of left-sided Caputo fractional differentiation. We prove that the adjoint for it is the operator of right-sided Caputo fractional differentiation. Similar results are established for the Riemann–Liouville fractional differentiation operators. We also demonstrate that the operator, which is represented as the sum of the left-sided and the right-sided fractional differentiation operators is self adjoint. The known properties of the Caputo and Riemann–Liouville fractional derivatives are used to substantiate the results.

We study a semilinear fractional order differential inclusion in a separable Banach space E of the form $$ {}^{C}D^{q}x(t)\in Ax(t)+ F\bigl(t,x(t)\bigr),\quad t\in [0,T], $$ where ${}^{C}D^{q}$ is the Caputo fractional derivative of order $0 < q < 1$ , $A \colon D(A) \subset E \rightarrow E$ is a generator of a $C_{0}$ -semigroup, and $F \colon [0,T] \times E \multimap E$ is a nonlinear multivalued map. By using the method of the generalized translation multivalued operator and a fixed point theorem for condensing multivalued maps, we prove the existence of a mild solution to this inclusion satisfying the nonlocal boundary value condition: $$ x(0)\in \Delta (x), $$ where $\Delta : C([0,T];E) \multimap E$ is a given multivalued map. The semidiscretization scheme is developed and applied to the approximation of solutions to the considered nonlocal boundary value problem.

The paper presents a formal representation of solutions of non-scalar semilinear differential equations in Banach spaces by means of the Mattag-Leffler function.

In the present paper, we show that the solution set of a fractional order semilinear differential inclusion in a Banach space has the topological structure of an -set. This result allows to apply a fixed point result for condensing multimaps to the translation multioperator along the trajectories of such inclusion and to prove the existence of solutions satisfying periodic and anti-periodic boundary value conditions. An example concerning with a fractional order feedback control system is presented.

Here we generalize the notions of determinative conjunct and strongly equal tautologies formany-valued logic (MVL) and compare the proof complexity measures of strongly equal many-valued tautologies in some proof systems of MVL. It is proved that in some “weak” proof system the strongly equal many-valued tautologies have the same proof complexities, while in the “strong” proof systems the measures of proof complexities for strongly equal tautologies can essentially differ from each other.

We obtained results on the existence and uniqueness of a mild solution for a fractional-order semi-linear differential inclusion in a Hilbert space whose right-hand side contains an unbounded linear monotone operator and a Carath&eacute, odory-type multivalued nonlinearity satisfying some monotonicity condition in the phase variables. We used the Yosida approximations of the linear part of the inclusion, the method of a priori estimates of solutions, and the topological degree method for condensing vector fields. As an example, we considered the existence and uniqueness of a solution to the Cauchy problem for a system governed by a perturbed subdifferential inclusion of a fractional diffusion type.

We apply the topological degree theory for condensing maps to study approximation of solutions to a fractional-order semilinear differential equation in a Banach space. We assume that the linear part of the equation is a closed unbounded generator of a C 0 $C_{0}$ -semigroup. We also suppose that the nonlinearity satisfies a regularity condition expressed in terms of the Hausdorff measure of noncompactness. We justify the scheme of semidiscretization of the Cauchy problem for a differential equation of a given type and evaluate the topological index of the solution set. This makes it possible to obtain a result on the approximation of solutions to the problem.

We consider the periodic boundary value problem (PBVP) for a semilinear fractional-order delayed functional differential inclusion in a Banach space. We introduce and study a multivalued integral operator whose fixed points coincide with mild solutions of our problem. On that base, we prove the main existence result (Theorem ). We present an example dealing with existence of a trajectory for a time-fractional diffusion type feedback control system with a delay satisfying periodic boundary value condition.