All Articles

Summary: In this article the questions of existence and uniqueness of (ω, c)−periodic solution of boundary value problem for an impulsive system of ordinary differential equations with product of two nonlinear functions and mixed maxima are studied. This problem is reduced to the investigation of solvability of the system of nonlinear functionalintegral equations. The method of contracted mapping is used in the proof of unique solvability of nonlinear functional-integral equations in the space BD([0, ω],Rn). Obtained an estimate for the (ω, c)−periodic solution of the studying problem.

Summary: This paper investigates an age-structured optimal harvest control model from both theoretical and numerical perspectives. First, we apply classical optimal control techniques to establish the existence of an optimal control, derive the necessary conditions, conduct a steady-state analysis, and characterize the bang-bang regime. Subsequently, we numerically solve of the problem using an appropriate discretization method to support the theoretical results.

Summary: This work presents a novel and comprehensive approach to the study of Bertrand curves in 4-dimensional Minkowski space (R41 ). We introduce a new Frenet frame specifically tailored for analyzing Bertrand curves in the (1, 3)-normal plane, which allows us to derive significant relationships between the curvature functions κ1, κ2, and κ3. Our analysis provides new formulas and explicit conditions for these curvatures, offering a deeper understanding of their geometric properties in R41 . We investigate four distinct cases of Bertrand curves, each characterized by specific conditions on the curvature functions. For each case, we derive explicit solutions and relationships, demonstrating the versatility of our approach. Furthermore, we establish the existence of a Bertrand mate curve ζ∗ for a given Bertrand curve ζ and derive the parameter λ that defines the mate curve. This parameter is expressed in terms of the curvature functions, providing a clear connection between the original curve and its mate. To illustrate the practical application of our theoretical results, we provide detailed examples of Bertrand curve pairs in R41 . These examples include the explicit construction of the Frenet frames and the computation of the associated curvature functions, showcasing the effectiveness of our methodology.

Summary: This article explores minimum of an extremal in the variational problem with delay under the degeneracy of the Weierstrass condition. Here for study the minimality of extremal, variations of the Weierstrass type are used in two forms: in the form of variations on the right with respect to the given point, and in the form of variations on the left with respect to the same point. Further, using these variations, formulas for the increments of the functional are obtained. The exploring of the minimality of the extremal with the help of these formulas is conducted under the assumption that the Weierstrass condition degenerates. As a result, considering different forms of degenerations (degeneracy of the Weieristrass condition at a single point and at points of a certain interval), we obtain the necessary conditions of the inequality type and the equality type for a strong and weak local minimum. A specific example is given to demonstrate the effectiveness of the results obtained in this article.

Summary: We explicitly determine the algebraic point families of a given degree over Q of the curve C1,2(7) with affine equation: y7 = x(x − 1)2 This curve is a special case of the family of quotients of Fermat curves Cr,s(p) described in [11] of affine equation: yp = xr(x − 1)s with 1 ≤ r, s, r + s ≤ p; for r = 1, s = 2 and p = 7 such a curve was considered in [10]. This curve has been studied by O. Sall in [14], where the author gives a parametrisation of the cubic points. It should be noted, however, that the method used by O. Sall does not allow us to determine the set of points of degree greater than 3. We have therefore used a geometric method to extend this work and determine the quartic points [4]. In this note, we describe all the families of algebraic points of given degree, geometrically specifying the contact lines and the curve containing them, by applying the fundamental Abel-Jacobi theorem [1, 9], before using these results with a Q-basis of the linear systems L(m∞) and combining the contact order of the curve and specific points to obtain analytical expressions for these families of points.

Summary: In the present work, we consider the metric questions of diffeomorphic mappings of the manifolds. We find such bases on tangential spaces of manifolds corresponding to given mappings, which allow investigate their metric properties, independent of connection coefficients, by using of strictly analysis’ methods. For simplicity of our considerations, we suffice with consideration of manifolds defined by finite number of maps. When our consideration is restricted with neighborhoods of some points, we shall suffice with one map defining the manifold.

Summary: It is considered the vector-valued grand Lebesgue space Lp) (X) ≡ Lp) (J;X), 1 < p < ∞, and the concept of a t-basis, generated by some bilinear map (where J = [−π, π)), is introduced. It is proved that the exponential system E ≡ eint n∈Z forms a t-basis for Np) (X), when X is a UMD space, where Np) (X) is the closure of Xvalued infinitely differentiable functions in Lp) (X). The concept of the t-Riesz property of the system E in Np) (X) is defined. It is established that this system has the t-Riesz property, when X is a UMD space. Using these facts, the X-valued grand Hardy classes mH± p) (X) of X-valued analytic functions are introduced, and some of their properties are proved. The obtained results are applied to establish the t-basicity of the perturbed exponential system in Np) (X).

Summary: In this work a nonlocal problem for the Laplace equation in an unbounded domain is considered. The notion of a strong solution of this problem is defined. Using the Fourier method, we prove the correct solvability of the considered problem in Sobolev spaces generated by a weighted mixed-norm. This problem in the classical formulation was previously considered by E. I. Moiseev [1]. The same type of problem was considered in the work of M. E. Lerner and O. A. Repin [2].

Summary: In this study, we examine cubic stochastic operators, which we will refer to as quasi-strictly non-Volterra cubic operators. Firstly, the definition of a quasi-strictly non-Volterra operator is provided, and the structure of an arbitrary quasi-strictly non- Volterra cubic operator on a two-dimensional simplex S2 is described. Secondly, the fixed and limit points of the quasi-strictly non-Volterra operator on S2 are investigated. It is proven that there exists a repelling unique fixed point.

Summary: This study investigates the impact of climatic factors on agricultural output between 1970 and 2022 in Türkiye. The Bayesian Model Averaging (BMA) method was utilized to select the independent variables for the model. The augmented ARDL (A-ARDL) approach was employed to analyze the cointegration relationship between the variables. Then, the CCR, DOLS, and FMOLS techniques were applied to assess the long-term dynamics. The key findings of the study are as follows: (i) The BMA analysis identified the carbon dioxide emissions, cultivated agricultural area, minimum average temperature, and 10 cm ground temperature as the significant independent variables. (ii) The A-ARDL results indicate a long-term association between the selected variables. (iii) The minimum average temperature is positively associated with the agricultural sector’s share in GDP. (iv) Increases in carbon dioxide emissions, 10 cm ground temperature, and cultivated agricultural area were found to decrease the agricultural sector’s share in GDP. In summary, the findings of study confirms the multi-dimensioned and non-linear character of climate-agriculture relations, challenging overly simplistic interpretations. From a policy perspective, the evidence puts emphasis on the need for climat-smart agricultural policies that bind together temperature regulation, emissions reduction, and efficient land use. Such insights are particularly significant for nations such as Türkiye that experience both extreme climatic volatility as well as structural challenges within their agricultural systems.