Principal Singularities Research Articles

TO SAVE MANKIND: PROPOSED IS AN ALTERNATIVE TO MINING BLOCKCHAINS

The concept of blockchains arouses an admiration due to its reasonableness and ease of implementation within existing infrastructure of Internet. The essential flawisan unacceptably big (from the point of view of ecology and common sence) power waste. The matter concerns the destinies of mankind, because uncontrollably expanding mining blockchains inevitably leads to overheating of Earth and thendeath of all living things. The solution being proposed is based on that follows: mining blockchains is not the goal in itself. The end goal is the reliable safekeeping of some valued constant (invariable) file. We propose not to RESIDE this file in the usual storage medium but to GENERATE it by a proper finite-state automaton. The principal singularity of the automaton circuit is an exeptional testability with respect to all multiple stuck-at faults. It is due to building the circuit according to the Theory of widened long flip-flop. The availis that mining is EXCLUSED as well as consumption of any significant power.

Critical principal singularities of hypersurfaces in Euclidean 4-spaces

Critical principal singularities of hypersurfaces in Euclidean 4-spaces

A mixed integral equation of mechanics and a generalized projection method of its solution

A mixed multidimensional integral equation containing integral operators of various types is studied. The case in which the equation has one compact, self-adjoint, and strongly positive operator (with constant limits of integration) and two non-self-adjoint integral Volterra operators (with a variable upper limit of integration) is considered. To solve the equation, an effective projection method allowing one to obtain the result in a form with explicitly distinguished principal singularities is proposed.

The Limits of True Knowledge (Metaphysical and Topological Aspects)

The present article studies the correlation of true cognition not with the performance of certain cognitive or probative procedures by a subject, but with the processes occurring to the object of cognition. Therefore, the limits of truth coincide with the inexhaustible regularity or with nature in the antique, or Kant's interpretation. Opposite to science, art deals with principal singularity: its objects remain the objects of art as long as they cannot be confused with anything else. The present article considers some illegal cognitive intrusions, both leftwards from the limits of truth where the quantum objects (ensembles) are found, and rightwards, where the definiteness of the subject and the soul itself are determined.

Modern methods of training specialists in nanotechnology

New technologies of nanotechnology specialists continuous education are examined. Its touch diploma and postgraduate education. The principal singularity of technology is the workplace education. Possibilities of forming of sequence of course, choice of his maintenance are underlined with orientation on the individual trajectory of studies. This technology allows realizing the modern process of necessary knowledge transfer that is adjusted to the professional features of engineers

Critical behaviour of the MHD flow in convergent-divergent channels

The effect of external Magnetohydrodynamic (MHD) field on the steady two-dimensional nonlinear flow through Convergent-Divergent Channels of a viscous incompressible electrically conducting fluid is investigated. We compute the critical behaviour of the solution govern by the equation. Our approach uses the power series in order to observe the instability of the problem. The series is then summed by using various generalizations of the approximants. We find the critical values of various parameters and type of the principal singularity for different choice of MHD effect.DOI: 10.3329/jname.v7i2.5635

Effects in a Two-Velocity Dynamical System Associated with the Coincidence of the Velocities in an Interval

The behavior of the principal singularities of the fundamental solution of the problem for a dynamical system in which two components of the wave propagate with different velocities is studied. We show that the principal singularities of the wave can pass from one component to the other whenever in the system there exists an interval in which the velocities of propagation coincide for both components. Bibliography: 3 titles.

Distributional Wiener-Ikehara theorem and twin primes

The Wiener-Ikehara theorem was devised to obtain a simple proof of the prime number theorem. It usesno other information about the zeta function ~(z) than that it is zero-free and analytic for Re z ⩾ 1, apart from a simple pole at z = 1 with residue 1. In the Wiener-Ikehara theorem, the boundary behavior of a Laplace transform in the complex plane plays a crucial role. Subtracting the principal singularity, a first order pole, the classical theorem requires uniform convergence to a boundary function on every finite interval. Here it is shown that local pseudofunction boundary behavior, which allows mild singularities, is necessary and sufficient for the desired asymptotic relation. It follows that the twin-prime conjecture is equivalent to pseudofunction boundary behavior of a certain analytic function.

A case study of methods of series summation: Kelvin–Helmholtz instability of finite amplitude

We compute the singularities of the solution of the Birkhoff–Rott equation that governs the evolution of a planar periodic vortex sheet. Our approach uses the Taylor series obtained by Meiron et al. [J. Fluid Mech. 114 (1982) 283] for a flat sheet subject initially to a sinusoidal disturbance of amplitude a. The series is then summed by using various generalisations of the Padé method. We find approximate values for the location and type of the principal singularity as a ranges from zero to infinity. Finally, the results are used as a basis to guide the choice of methods of summing series arising from problems in fluid mechanics.

Airfoil vibration in the wake of an obstacle: Effects of inflow nonuniformity and vortex sheet

Obstacles in flow produce wakes that can cause significant vibration of devices located within the wakes. Such vibration appears in many situations, from landing an aircraft on a ship deck to operations of rotating machinery. There are two principal singularities of these wakes that define incoming flow for the downstream devices. First, the time-average velocity profiles are highly nonuniform. Second, flow separation from obstacles is accompanied by generation of large vortices. An initial mathematical study of this flow-induced vibration of the devices includes quasipotential approach in determination of time-averaged flow parameters and determination of amplitude response of elastic airfoils (device cross sections) on perturbation. Perturbation frequencies depend on the obstacle drag, size and free-stream speed. Vortex sizes depend also on Reynolds number. Numerical modeling shows a certain difference between the foil response on gust flow and its response on excitations caused by the obstacle wakes.

Étude symbolique de la perte de régularité C ∞ par morceaux dans l'interaction d'ondes semi-linéaires

We consider the interaction of two piecewise smooth waves for a first order semilinear system. We know that under geometric hypotheses the piecewise smooth regularity can be not conserved after the interaction. A symbolic study allows us to prove that this loss does not appear on principal singularities. We then show the microlocal mechanism of the creation and the propagation of a logarithmic singularity.

Improving the convergence of the modal decomposition of internal waves generated by a moving dipole

Existing results on the singularities in the neighbourhood of the plane of symmetry of the wave track of the fundamental solution of the linear equation of internal waves in Boussinesq form, obtained for exponential stratification are extended to cover arbitrary stratification. Use is made of well-known asymptotic expansions in powers of the mode number of the eigenvalues and eigenfunctions of the Sturm-Liouville problem. Apart from the principal singularity, available when using the method of “frozen coefficients”, the next singularity is singled out and it is demonstrated that this is an essential part of the approximate calculation of the wave pattern near the plane of symmetry of the track. 1999 Elsevier Science Ltd. All rights reserved.

Principal singularities of the S matrix for a system of one-dimensional particles

Explicit expressions are obtained for the principal singularities of the S matrix in a system of one-dimensional particles described by the Hamiltonian -1/2 ..delta.. + ..sigma..v(x/sub i/ - x/sub j/). The conditions under which the principal singularities are free of diffraction effects are established.

Percolation with restricted valence

The authors have enumerated exactly the square lattice site animals with vertex degree less than or equal to three and with up to fourteen sites in the cluster. Using series analysis techniques estimates have been made of the location, exponent and amplitude of the principal singularity in the animal generating function for maximum vertex degree v=2, 3 and 4. It is shown rigorously that the dominant singularity in the generating function must have a different exponent for v=2 than for v=3 and the numerical results suggest that the generating function diverges with an exponent of 4/3 for v=2 but logarithmically for both v=3 and v=4.

Singularities in solutions of the Einstein equations for a static spherically symmetric field

The nature of the singularities in the solutions of Einstein's equations for a static spherically symmetric field is investigated as a function of the choice of additional conditions. It is shown that the principal singularity — the Schwarzschild sphere — can be produced or established by certain conditions without changing the physical assumptions or the gravitational equations themselves. Different solutions are obtained which are equivalent from the point of view of observations since the theoretical variations of the astronomical effects are far beyond the limits of experimental possibilities.

Use of Numerical Integration in the Computation of the Expectation Value of H2 with Applications to H2

The use of numerical integration for evaluating the expectation values of the Hamiltonian and the square of the Hamiltonian is difficult due to the presence of singularities in the integrand. A basis set is discussed which removes one of the principal singularities from Hψ in the case of the hydrogen molecule. This basis set is used and all integrals are evaluated numerically to obtain variational upper bounds and Weinstein and Temple lower bounds for the ground state of H2. First-excited-state upper bounds are obtained by a method involving the expectation value of the square of the Hamiltonian and the possibility of computing excited-state wavefunctions by minimization of the width, W=〈H2〉—〈H〉2, is discussed.

Secular Fluctuation of the October Precipitation in the Carpathian Region of the Danube Basin

There appears an ever increasing need of studying not only the changes of values of climatic elements but also the changes of their annual variation. A convenient method of satisfying this need is the study of the principal singularities of the weather and of the singularities of individual climatic elements. Apart from purely synoptic analyses and the formal study of secular series of climatic elements, studies concerning the values of climatic elements and their dependence on the changes of factors of the atmospheric circulation as well as research into the geographical laws governing these changes are also most necessary. An analysis of the annual variation of precipitation in Brno has shown that this annual variation is very different in the successive distinct periods (1851/1875, 1876/1900, 1901/1925, 1926/1950) of the past one hundred years. An analysis of the annual variation in other European stations has confirmed the reality of these changes throughout Europe. We have analysed more fully the changes in the variation of autumn precipitation, and particular attention has been paid to the October precipitation in the Carpathian part of the Danube basin for the period 1901/50, from which the necessary synoptic and meteorological material is already available. In the annual variation of precipitation in this region there occurs a secondary October, or November, maximum. The principal cause of increased precipitation in October is the intensive precipitation of certain synoptic situations, which can be characterized (according to the catalogue of P. Hess and H. Brezowsky) as (GT) types TM, NW, E, SE+S, or (according to Fr. Rein an M. Konček's catalogue) as types Bc, Cc, Ec, SWc2 and NWc. Increased frequency of these situations occurs at the beginning and towards the end of the month of October. Diurnal totals of precipitation in these situations are so great that October registers a high monthly total, although most days in October have otherwise low diurnal amount of precipitation. In the diurnal variation of the October precipitation amounts a significant change has also taken place during the past fifty years. Thus, in the period 1901/1925, the maximum of precipitation occurs at the beginning of the month (about October 5th) and towards the end of the month there is little rainfall; in the period 1926/1950 the amount of precipitation is small at the beginning of the month and the maximum occurs towards the end (about October 25th). In both cases the minimum of precipitation occurs in the middle of the month (about October 15th). A change in the period referred to has also taken place in the variation of synoptic situations. The variation of precipitation is not much affected by the most frequent synoptic types W(GT) and HM(GT), but it agrees strikingly with the variation of otherwise infrequent situations, such as TM and NW. The last two situations should be regarded as the cause of the October precipitation singularities referred to. The variation of precipitation in Hungary and in the greater part of the Rumanian territory has similar characteristics as in Czechoslovakia. But there appears also a secondary maximum at the end of the month in the period 1926/1950. Southern and eastern Rumania has a different regime of precipitation. The above mentioned three distinct (in regard to precipitation) sections of October, which roughly coincide with three October decades, have been analysed according to the degree of similarity in precipitation. The synoptic basis of this method has been justified by M. Bouët, and in our study we have only modified the conditions for its climatological application. The maps of the degrees of similarity demonstrate that the region of moderate to considerable degree of similarity covers roughly the basin of the rivers Morava and Vah with Nitra and also north-~ astern and central Hungary. The remaining regions show a low degree of similarity or have an indifferent or even opposite regime of precipitation. In the above mentioned region there occurs roughly the same climatological fluctuation of the precipitation regime. Research of this type is important for a dynamic conception of the term of physiographical milieu in which a change of the precipitation regime affects changes in the hydrological regime with all consequences for biogeographical conditions. Besides its contribution to the theory of climate and to the rising science of climate forecast it is of great value for studies concerned with methods of climatological classification.

A Tauberian Theorem for Partitions

based on the transformation theory of the elliptic modular functions. Later researches have tended in the direction of a still deeper study of particular problems, culminating in the exact formulae of Rademacher [6] and his followers, or in the direction of a broader and more elementary treatment giving less precise results than (1). But a specification of properties of the generating functions sufficient for the deduction of (1), but not highly extravagant, seems to be lacking. In this paper we show how to deduce (1) from an elementary knowledge of the asymptotic behaviour of the generating functions when z(= x + iy) approaches the principal singularity z = 1 in an arbitrarily wide 'Stolz angle' I y I < A (1 x), (O < A < oo). A general result to which the method naturally leads is set out as Theorem 2 in ?3, with indications of some of the more immediate applications. Theorem 2 is deduced from Theorem 1, a Tauberian theorem for the integral