All Articles

Summary: The article considers the effect of the properties of wood chip materials on the sharpening of circular saw blades with the aim to develop new technologies of sharpening cutting tools. The characteristic wear of saw blade teeth is investigated, and features of teeth sharpening are considered. The influence of imbalance on wear and sharpening of circular saw blades is analyzed.

Summary: This study proposes a new queue-dependent (s, S)-type replenishment policy in the queueing-inventory systems. If the inventory level is greater than s, no restocking order is sent; otherwise, the replenishment is performed to reach the maximum value S, regardless of the stock level at the moment. Orders are replenished in two ways: the regular order and the urgent order. Lead times of the two-type orders are exponentially distributed with different parameters. The urgent orders require a shorter delivery time than the regular orders. The queue-dependent replenishment policy is defined as follows: when the inventory level drops to s, if the number of the customers is less than predefined threshold value r, the regular order is made; if the number is more or equal r, the urgent order is sent. When the inventory level drops to zero, one customer becomes impatient, regardless of the customer’s number in the queue. Arrival of customers is according to a Markovian arrival process and the service times are adapted by a phase-type distribution. The mathematical model of the system is developed using a continuous-time Markov chain with an infinite state space. Stability condition and then the steady-state distribution are derived by using the matrix-geometric method. The influences of the parameters on the performance measures are discussed with numerical examples. An optimization problem is solved, where the criterion is the expected total cost, and the controlled parameters are the reorder point s and the threshold parameter r.

Summary: The study investigates the nexus between innovation, labor migrations, energy consumption and CO2 emissions in Germany for the period 1990–2020. This study applied a dynamic simulated ARDL (DS-ARDL) model for estimation, which can observe the negative and positive variations in variables both in long run and short run. The dependent variable in DS-ARD provides a more intuitive picture of dynamic effects than coefficients alone. In Addition, DS-ARDL may provide reliable estimations even if sample size is smaller. The results of this study suggest a long-term relationship among innovation, migration, energy consumption, and CO2 emissions. The results also confirm that migration has a positive relationship with CO2 emissions, while innovation has an adverse effect on CO2 emissions in long run. Policymakers can take action on both ends of the supply and demand spectrum to lessen the impact of migration on Germany's CO2 emissions. Human capital accumulation provided by international migration; therefore, receiving countries should encourage rapid technological advancement and improve their citizens' spending habits.

Summary: In this paper we consider the Dirichlet problem for the Laplace equation in Hardy classes generated by an additive-invariant Banach function space on the unit circle. It is shown that the classical Dirichlet problem for the Laplace equation has a unique solution for every boundary function from the considered space. It is considered a boundary problem for the Laplace equation with oblique derivatives in the Hardy classes generated by separable subspaces of rearrangement-invariant spaces in which the infinitely differentiable functions are dense. Noetherness of this problem is established and the index of this problem is calculated.

Summary: We determine the set of algebraic points of degree degree l ≥ 2 over Q on the curve X given by the affine equation n2 = 3(m5 −1) and this result extends a result of Siksek who described in [5] the set of algebraic points of degree 1 on this curve.

Summary: Let G be a locally compact hypergroup and let K be a compact subhypergroup such that (G,K) is a Gelfand pair. Let μ be a bounded complex-valued Borel measure on G , and let T♮μ be the corresponding convolution operator of L1♮(G), the subset of L1(G) consisting of K-bi-invariant functions. Suppose that S is a bounded linear operator on a Banach space X. We prove that every linear operator Ψ : X −→ L1♮(G) such that ΨS = T♮ μΨ is continuous if and only if (S, T ♮ μ) has no critical eigenvalues.

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.