Boundary characteristics of meromorphic functions with summable spherical derivation and annular functions. Consideration

In this paper we formulate classical theorems Plesner and Meyer on the boundary behavior of meromorphic functions and their refinement and strengthening - Gavrilov's and Kanatnikov's theorems. An application of these theorems to classes of meromorphic functions with integrable spherical derivative and annular holomorphic functions is presented. Collingwood's theorem on boundary singularities of the Tsuji function as well as Kanatnikov's theorems are formulated. Kanatnikov's theorems strengthen and generalize Collingwood's theorem to broader classes of meromorphic functions with summable spherical derivatives. Special attention is paid to the boundary properties of annular holomorphic functions. The behavior of annular holomorphic functions on the boundary of the unit circle is considered. It is shown that Gavrilov's P-sequences play an important role in the study of the boundary properties of holomorphic and meromorphic functions.

Prosodic prominence in a stressless language: An acoustic investigation of Indonesian

Although it has been proposed that all languages may have some lexical stress property, recent studies of (Standard) Indonesian have concluded, based primarily on perception, that lexical stress is not present in this language. While it is philosophically problematic to prove the non-existence of a phenomenon, we examine data from a large-scale production study for both direct and indirect evidence of stress, contributing to the growing body of literature in this field. In the first case, evidence is sought that indicates that a particular syllable in a word exhibits acoustic properties typically associated with prominence (i.e. fundamental frequency (f0), duration, intensity, vowel quality). In the second case, evidence of enhancement of these properties on a particular syllable under focus is sought, for a more abstract stress property that is not overtly manifested at the word level. Although we find no evidence of lexical prominence, we observe acoustic patterns consistent with a higher level prominence corresponding to focus, manifested by strong (Intonational Phrase) boundary properties. Overall, our findings reveal that there is strong support for a class of languages lacking lexical stress, and in the absence of a stressed syllable to enhance, focus may be manifested prosodically as boundary properties.

Temporal interfaces and metamaterial response enabled by boundaries

In the last years, temporal metamaterials have been exploited as a novel platform for conceiving several electromagnetic and optical devices based on the anomalous scattering response achieved at a single or multiple sudden change of their medium properties, which however is difficult to carry out in a realistic scenario In this letter we investigate on the possibility to emulate the scattering response of a temporal metamaterial without acting on the medium properties, but on the effective refractive index and wave impedance perceived by the wave during the propagation within a guiding structure rather than the actual material, by acting on its boundaries. The work presents in closed form the scattering coefficients achieved when the boundary properties are suddenly modified for inducing an effective temporal interface. In this framework, temporally controlled metasurfaces can be used to implement the proposed concept, giving an easier path also to the design and realization of novel devices at microwave and optical frequencies.

Temporal interfaces and metamaterial response enabled by boundaries

In the last years, temporal metamaterials have been exploited as a novel platform for conceiving several electromagnetic and optical devices based on the anomalous scattering response achieved at a single or multiple sudden change of their medium properties, which however is difficult to carry out in a realistic scenario In this letter we investigate on the possibility to emulate the scattering response of a temporal metamaterial without acting on the medium properties, but on the effective refractive index and wave impedance perceived by the wave during the propagation within a guiding structure rather than the actual material, by acting on its boundaries. The work presents in closed form the scattering coefficients achieved when the boundary properties are suddenly modified for inducing an effective temporal interface. In this framework, temporally controlled metasurfaces can be used to implement the proposed concept, giving an easier path also to the design and realization of novel devices at microwave and optical frequencies.

APPROXIMATION OF FUNCTIONS BY GAUSS-WEIERSTRASS INTEGRALS

When considering various schemes and algorithms for game problems of dynamics, researchers often have to deal with solutions of partial differential equations. A special place among the latter is occupied by the so-called equations of elliptic type (according to the corresponding classification), with the help of which natural and social processes can be described most fully and qualitatively. Moreover, the mathematical apparatus of partial differential equations of elliptic type makes it possible to get into the environment of deterministic phenomena and thus makes it possible to foresee their future. This fact undoubtedly increases the significance of the above type of equations among others in the sense of their application to mathematical modeling. At the same time, one of the most important concepts in applied mathematics is the concept of the modulus of continuity. The term "modulus of continuity" and its definition were introduced by Henri Lebesgue at the beginning of the last century in order to study various properties of continuous functions. Using the concept of the modulus of continuity and its properties, it is possible to investigate the belonging of the object under study to a certain class of functions: Hölder, Lipschitz, Zygmund, etc. This undoubtedly makes it possible to approximate functions of various kinds of operators most effectively. In this paper, using the example of the Gauss-Weierstrass integral as a solution to the corresponding differential equation of elliptic type, we study its rate of convergence in terms of the modulus of continuity of the second order to the function by which it was actually constructed. Namely, the boundary properties of the Gauss-Weierstrass integral were studied as a linear positive operator that realizes its best approximation on functions from the Zygmund class. The results obtained in this article can further be used to solve many problems in applied mathematics.

On the property of homothetic mean value on periodically perforated domains

We study boundary properties of one class of periodic functions as $\varepsilon \rightarrow 0$, where $\varepsilon$ is a period of periodically perforated domain. We show that their weak limit is the homothetic mean value of such functions.

Investigation of selected parameters effect on 3D printed sand mold properties through Taguchi method

Purpose The major concern technologies during the processing through three-dimensional printing (3DP) are the mechanical and boundary properties of sand models. The parameters such as activator content, resolution X, layer thickness and re-coater speed play a vital role in 3DP sand components. The purpose of this paper is to recommend the optimal process parameters for the best sand mold properties. Design/methodology/approach In this paper, taking the parameters of the activator content, resolution X, layer thickness and re-coater speed as the influence factors, an orthogonal test of L16(44) was designed to discuss the influences of those parameters on the mechanical and boundary properties. Three-point bending (3PB) test was used to characterize the actual bending strength, and the boundary accuracy was assessed by the deviation of the three-point bending samples compared with its design scale. Findings The experimental results showed that the resolution X and layer thickness are the main parameters affecting sand mold properties. The strength will attain its maximum when the resolution X and layer thickness are the minimum. The optimal parameters were screened and verified by the confirmation test. The optimal process parameters for best strength and less gas evolution are the activator of 0.19%, resolution X of 0.1 mm, layer thickness of 0.28 mm and re-coater speed of 210 mm/s. Originality/value The novelty of this paper is the select of significant parameters on 3D-printed sand model properties. A mathematical model was built to analyze the effect of these parameters. The optimal process parameters for the best properties were got.