Solution Of Many Other Problems Research Articles

A Review Study of Wireless Sensor Networks and Its Security

The confluence of cheap wireless communication, sensing and computation has produced a new group of smart devices and by using thousands of these kind of devices in self-organizing networks has formed a new technology that is called wireless sensor networks (WSNs). WSNs use sensor nodes that placed in open areas or in public places and with a huge number that creates many problems for the researchers and network designer, for giving an appropriate design for the wireless network. The problems are security, routing of data and processing of large amount of data etc. This paper describes the types of WSNs and the possible solutions for tackling the listed problems and solution of many other problems. This paper will deliver the knowledge about the WSN and types with literature review so that a person can get more knowledge about this emerging field.

Navier –Stokes Second Exact Transformation

In this article second Navier - Stokes (NSE) exact transformation to the simpler equations is covered. This transformation is executed by classical methods of Mathematical Analysis. It is shown that 3-D NSE can be conversed to a traditional vector form which looks like 2-D Vorticity Transport Equations. Second result, as well as first one, is very important for the solution of Navier-Stokes existence and smoothness one of seven Millennium Prize Problems that were stated by the Clay Mathematics Institute. The proof of solution' existence of such equations is simpler than traditional NSE. New equations will simplify the solutions of many other problems of Applied Mathematics in engineering, aeronautics, etc.

Lighthill and the triple-deck, separation and transition

In 1953 James Lighthill, conducting an investigation into the potential mechanisms for upstream influence within boundary layers in supersonic flow, published a theoretical approach which explicitly took into account the influence of viscosity on a disturbance to an incident boundary-layer profile. In doing so he was able to predict a length-scale for upstream influence which scales with the global Reynolds number R, assumed large, as R−3/8. The physical process he identified is now referred to as a pressure–displacement (or viscous–inviscid) interaction. This article discusses Lighthill’s original paper and then proceeds to show how an appreciation of this interaction mechanism can help in the solution of many other problems in fluid mechanics and especially those of flow separation and late-stage laminar–turbulent transition. Finally, the article gives a brief description of the similarities between these two processes as seen from the unifying viewpoint of Lighthill’s pressure–displacement interaction.

NAIVE SINGULAR PERTURBATION THEORY

The paper demonstrates, via extremely simple examples, the shocks, spikes, and initial layers that arise in solving certain singularly perturbed initial value problems for first-order ordinary differential equations. As examples from stability theory, they are basic to many asymptotic techniques. First, we note that limiting solutions of linear homogeneous equations [Formula: see text] on t≥0 are specified by the zeros of [Formula: see text], rather than by the turning points where a(t) becomes zero. Furthermore, solutions to the solvable equations [Formula: see text] for k=1, 2 or 3 can feature canards, where the trivial limit continues to apply after it becomes repulsive. Limiting solutions of the separable equation [Formula: see text] may likewise involve switchings between the zeros of c(x) located immediately above and below x(0), if they exist, at zeros of A(t). Finally, limiting solutions of many other problems follow by using asymptotic expansions for appropriate special functions. For example, solutions of [Formula: see text] can be given in terms of the Bessel functions Kj(t4/4ε) and Ij(t4/4ε) for j=3/8 and -5/8.

A new method for quantitative modelling of quasibrittle fracture

A slow-crack method for precise measurement of the stress intensity factor K I for cracks in bodies of complex shapes is proposed. It is based on registration of slow-crack growth under static loads in the model prepared of a polymer glass for which the fundamental dependence of K I on the crack rate is known. It is shown that PMMA glasses meet all the main requirements for model material. The comparison of experimental and theoretical values of K I for a central crack loaded by two wedge forces in rectangular and circular plates was carried out. It shows that the precision of K I measurements is no less than 2–3%. The proposed method may be effectively applied for solution of many other problems of the fracture mechanics.

Social Policy and the Social Infrastructure

The broad social program of development of Soviet society, which was thoroughly reflected in the Constitution of the USSR, is evidence of the vast changes that have taken place in the life of the Soviet poeple following the triumph of the Great October Socialist Revolution. At the same time, the present social policy of the CPSU actively influences the development of social production, the rise in living standards, the effectiveness of the economy, and the solution of many other problems relating to the economic development of the nation.

Royal Society Medal Awards

THE King has approved the recommendations made by the Council of the Royal Society for the award of the two Royal Medals for the current year as follows: Prof. J. D. Bernal, professor of physics at Birkbeck College, University of London, for his work on the structure of proteins and other substances by X-ray methods, and for the solution of many other problems requiring a physical approach; Dr. E. J. Salisbury, director of the Royal Botanic Gardens, Kew, for his notable contributions to plant ecology and to the study of the British flora generally.