Applications of OHAM and MOHAM for Fractional Seventh-Order SKI Equations

In this article, a comparative study between optimal homotopy asymptotic method and multistage optimal homotopy asymptotic method is presented. These methods will be applied to obtain an approximate solution to the seventh-order Sawada-Kotera Ito equation. The results of optimal homotopy asymptotic method are compared with those of multistage optimal homotopy asymptotic method as well as with the exact solutions. The multistage optimal homotopy asymptotic method relies on optimal homotopy asymptotic method to obtain an analytic approximate solution. It actually applies optimal homotopy asymptotic method in each subinterval, and we show that it achieves better results than optimal homotopy asymptotic method over a large interval; this is one of the advantages of this method that can be used for long intervals and leads to more accurate results. As far as the authors are aware that multistage optimal homotopy asymptotic method has not been yet used to solve fractional partial differential equations of high order, we have shown that this method can be used to solve these problems. The convergence of the method is also addressed. The fractional derivatives are described in the Caputo sense.

Breeding biology of the Woodcock (Scolopax rusticola L.) in the Carpathian Basin

Based on 356 observations of Woodcock nestings published in the Hungarian hunting and ornithological literature between 1846 and 2019, which also includes published and unpublished personal observations, it can be stated that the nesting dates of Woodcock in Hungary are scattered over a large interval. 47.3% of all nestings registered with exact dates (n=93) happen in April. The second peak of breeding in June does not stand out significantly. Based on the data of the clutches (n=65) reported with known number of eggs, as well as the clutches (n=14) – probably with full number of eggs – found in the Hungarian egg collections, the average number of eggs per clutch was 3.8. Based on the observational data of the Woodcock families (n=36) observed during the study period, the number of chicks per hen was 3.6, of which the hens were able to raise an average of 2.8 chicks up to a flying age.

Eco-localization of a prey in a spider orb web

Orb web spiders locate the position of a perturbation in the web because of a prey impact through highly sensitive slit sensilla at the tip of their legs. Thus, the web serves as a self-made extension of its sensory space which transmits vibrations from the perturbation point to the spider location. These vibrations may contain the information required by the spider to rapidly identify the position where the prey has impacted and approach to it before it flies away. For axially symmetric orb webs supported at the boundary and for a spider which stays at the center of the web, it was shown that the knowledge of the transverse deflection time history at the eight spider legs, for a sufficiently large interval of time, contains enough information to localize the position of the prey. In this article, we address the same inverse problem of localization of the prey, but we suppose that the spider knows only a small number of selected information of the transverse displacement, such as, for example, the maxima of the response of the time history at the eight control points. We show how this reduced information still allows the spider to obtain a fairly accurate angular localization of the prey, for different prey and orb web characteristics.

A MODEL OF EXPRESSIONIST STRATEGY DEVELOPMENT IN THE WORK OF THE WRITER (ON THE EXAMPLE OF THE WORKS OF LEO PERUTS)

The purpose of this study is to present a model for the development of the expressionist method in the genre of the novel using the example of the evolution of the novelistic work of the Austrian writer of the early twentieth century L. Perutz. The results obtained: the creative method of the Austrian writer is moving from scientific knowledge to mysticism; in the center of all novels created with a large interval, there is always a confused hero, broken by what is happening (in other words, the absurdity of the world), whose state is often conveyed through gestures; the author finally moves away from linear narration to dividing the plot into almost autonomous stories, thematically gravitating more and more to the distant historical past. Scientific novelty: the novels of L. Perutz are for the first time examined in relative detail through the prism of the aesthetics of expressionism.

A Modified Iterative Method for Solving Nonlinear Functional Equation

An iterative method (AIM) is one of the numerical method, which is easy to apply and very time convenient for solving nonlinear differential equations. However, if we want to work in a large interval, sometimes it may be difficult to apply AIM. Therefore, a multistage AIM named Multistage Modified Iterative Method (MMIM) is introduced in this article to work in a large computational interval. The applicability of MMIM for increasing the solution domain of the given problems is construed in this article. Some problems are solved numerically using MMIM, which provides a better result in the extended interval as compared to AIM. Comparison tables and some graphs are included to demonstrate the results.

Hybrid Compound Function/Subinterval Perturbation Method for Kinematic Analysis of a Dual-Crane System With Large Bounded Uncertainty

By introducing the subinterval perturbation method (SIPM), a hybrid compound function/subinterval perturbation method (HCFSPM) is presented for a dual-crane system (DCS) with large interval variables. The HCFSPM employs the SIPM to decompose a large interval variable into several subinterval variables with small uncertain levels. The interval kinematic compound function vectors and their inverses are approximated by the first-order Taylor and Neumann series, respectively. Based on the monotonic technique, the bounds of original luffing angle vectors are derived. Compared with the first-order compound function/interval perturbation method and the Monte Carlo method, numerical examples verify the effectiveness of the HCFSPM at conducting uncertain kinematic analysis of the DCS, especially when it comes to large uncertain levels.

New method for the numerical solution of the Fredholm linear integral equation on a large interval

The traditional numerical process to tackle a linear Fredholm integral equation on a large interval is divided into two parts, the first is discretization, and the second is the use of the iterative scheme to approach the solutions of the huge algebraic system. In this paper we propose a new method based on constructing a generalization of the iterative scheme, which is adapted to the system of linear bounded operators. Then we don’t discretize the whole system, but only the diagonal part of the system. This system is built by transforming our integral equation. As discretization we consider the product integration method and the Gauss–Seidel iterative method as iterative scheme. We also prove the convergence of this new method. The numerical tests developed show its effectiveness.