Asymptotic Behavior of Solutions of Integral Equations with Homogeneous Kernels

The multidimensional integral equation of second kind with a homogeneous of degree (−n) kernel is considered. The special class of continuous functions with a given asymptotic behavior in the neighborhood of zero is defined. It is proved that, if the free term of the integral equation belongs to this class and the equation itself is solvable, then its solution also belongs to this class. To solve this problem, a special research technique is used. The above-mentioned technique is based on the decomposition of both the solution and the free term in spherical harmonics.

Ephemeral islands, plunging quantum extremal surfaces and BCFT channels

We consider entanglement entropies of finite spatial intervals in Minkowski radiation baths coupled to the eternal black hole in JT gravity, and the related problem involving free fermion BCFT in the thermofield double state. We show that the non-monotonic entropy evolution in the black hole problem precisely matches that of the free fermion theory in a high temperature limit, and the results have the form expected for CFTs with quasiparticle description. Both exhibit rich behaviour that involves at intermediate times, an entropy saddle with an island in the former case, and in the latter a special class of disconnected OPE channels. The quantum extremal surfaces start inside the horizon, but can emerge from and plunge back inside as time evolves, accompanied by a characteristic dip in the entropy also seen in the free fermion BCFT. Finally an entropy equilibrium is reached with a no-island saddle.

Prototype Implementation of Innovative Braille Translator for the Visually Impaired With Hearing Deficiency

Text-to-Braille conversion as well as speech-to-Braille conversion are not available in combined form so far for the visually impaired, and there is tremendous need of a device that can look after this special class of people. The present chapter deals with a novel model that is designed to help both types of impaired people, be it visual problem or related with hearing. The proposal is itself unique and is also supported by experimental results available within the laboratory condition. This device will help people to read from text with their Braille language and will also help to convert the same form to audio signal. Since text and audio are the two main interfaces for any person to communicate with the external world apart from functionalities of sensory organs, the work has relevance. With the help of DANET, the same data, in text or speech form, can be accessed in more than one digital device simultaneously.

On a special class of modified integral operators preserving some exponential functions

<p style='text-indent:20px;'>In the present paper, we consider a general class of operators enriched with some properties in order to act on <inline-formula><tex-math id="M1">\begin{document}$ C^{\ast }( \mathbb{R} _{0}^{+}) $\end{document}</tex-math></inline-formula>. We establish uniform convergence of the operators for every function in <inline-formula><tex-math id="M2">\begin{document}$ C^{\ast }( \mathbb{R} _{0}^{+}) $\end{document}</tex-math></inline-formula> on <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{R} _{0}^{+} $\end{document}</tex-math></inline-formula>. Then, a quantitative result is proved. A quantitative Voronovskaya-type estimate is obtained. Finally, some applications are provided concerning particular kernel functions.</p>

Symbolic Macroconcept Strength/Power in the Aspect of Primary Signs

The purpose of this article was to describe the symbolic component among the primary (motivating) signs of the STRENGTH/POWER macroconcept. Objectives of the article: 1) to identify a complete list of motivating signs of the STRENGTH/POWER macroconcept; 2) to single out symbolic signs among them; 3) to describe the ways of objectification of symbolic primary signs and provide examples from the Russian language. This research is relevant due to the importance of describing the special class of symbolic macroconcepts. The scientific novelty of the paper lies in the fact that for the first time the STRENGTH/POWER macroconcept is presented in the aspect of its primary signs. The key research methods used here are descriptive, interpretive, and conceptual, as well as component analysis of dictionary definitions. The author revealed 59 motivating signs of the STRENGTH/POWER macroconcept on the basis of 10 etymological and historical-etymological dictionaries. None of the dictionaries used contain a complete set of primary signs of this macroconcept. The large number of motivating signs indicates that STRENGTH/POWER is an important macroconcept, whose primary signs have syncretic nature. Eight out of 59 motivating signs are symbolic, which is 1/7 of the total number. This ratio is a sufficient basis for classifying the STRENGTH/POWER macroconcept as symbolic. The language material from the National Corpus of the Russian Language shows the relevance of all the identified symbolic signs. Symbolic primary signs of the STRENGTH/POWER macroconcept in Russian linguoculture can be presented in the form of three blocks: 1) the transcendental (‘god’, ‘general name of the second angelic rank’, ‘miracles’); 2) the vital component of a person (‘spirit’, ‘soul’, ‘life’); 3) unusual human abilities (‘divine gift of producing miracles’, ‘ability to make changes in other things’).

The teaching of reading in New Zealand special classes : a thesis submitted for the degree of Master of Arts in education

All too frequently the standard work on reading disability dismisses the problem of the slow-learning child in a few lines. Few authorities on reading have attempted to trace, systematically, the implications of their reading research for the child of low intelligence. As a teacher of special class children I feel that one is only free to experiment with the practical and social aspects of special education when a systematic programme, adapted to the needs of low intelligence children, has minimised the difficulties of academic instruction.

The teaching of reading in New Zealand special classes

All too frequently the standard work on reading disability dismisses the problem of the slow-learning child in a few lines. Few authorities on reading have attempted to trace, systematically, the implications of their reading research for the child of low intelligence. As a teacher of special class children I feel that one is only free to experiment with the practical and social aspects of special education when a systematic programme, adapted to the needs of low intelligence children, has minimised the difficulties of academic instruction.

The teaching of reading in New Zealand special classes

All too frequently the standard work on reading disability dismisses the problem of the slow-learning child in a few lines. Few authorities on reading have attempted to trace, systematically, the implications of their reading research for the child of low intelligence. As a teacher of special class children I feel that one is only free to experiment with the practical and social aspects of special education when a systematic programme, adapted to the needs of low intelligence children, has minimised the difficulties of academic instruction.

Tackling Noise Pollution With Slow Sound

Noise pollution can reduce the quality and even the length of our lives, causing around 12,000 early deaths in Europe each year. Devices called resonators can be used to reduce unwanted noise from engines and fans, by cancelling out sound waves. However, the sound waves of low-pitched noises are difficult to cancel because they are very big: sometimes as long as 17 m! To cancel such large sound waves would require an impractically large resonator. One solution to this problem is to make the resonator from a special class of material called a metamaterial. Metamaterials have specially designed structures that give them properties that are not found in ordinary materials. This article explains how we used mathematics to design a metamaterial that slows down sound waves. Slowing the sound allows us to use smaller resonators, so we can cancel lower-pitched noises than we can with ordinary materials.

Holographic M5 branes in AdS7 × S4

We study classical M5 brane solutions in the probe limit in the AdS7× S4 background geometry that preserve the minimal amount of supersymmetry. These solutions describe the holography of codimension-2 defects in the 6d boundary dual $$ \mathcal{N} $$ N = (0, 2) supersymmetric gauge theories. The general solution is described in terms of holomorphic functions that satisfy a scaling condition. We show the behavior of the world-volume of a special class of BPS solutions near the AdS boundary region can be characterized by general equations, which describe it as intersections of the zeros of holomorphic functions in three complex variables with a 5-sphere.