Results 241 to 250 of about 2,856 (267)

Algorithm 32 automatic computation of integrals with singular integrand, over a finite or an infinite range

Computing, 1976
A numerical quadrature algorithm is developed, for integrands which may exhibit some kind of singular behaviour within the finite of infinite integration range. Using the automatical FORTRAN IV integration program, one should provide the abscissae the function is not “smooth” at. The quadrature formula has been obtained by applying the trapezoidal rule
Elise de Doncker, Robert Piessens
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Generalized Scaling Theory for Critical Phenomena Including Essential Singularities and Infinite Dimensionality [PDF]

Physical Review Letters, 2012
We propose a generic scaling theory for critical phenomena that includes power-law and essential singularities in finite and infinite dimensional systems. In addition, we clarify its validity by analyzing the Potts model in a simple hierarchical network,
Tomoaki Nogawa, Takehisa Hasegawa, Koji Nemoto   +2 more
exaly   +2 more sources

Finite Versus Infinite in Singularity Dynamics

2000
We study the dynamics of particle systems near solution singularities for different types of potentials. Solution singularities appear in finite time, but they can be blown up and removed to infinity with the help of certain transformations, thus creating the framework of a dynamical system.
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On the design of output feedback for finite and infinite pole assignment in singular systems with application to the control problem of constrained robots

Circuits, Systems, and Signal Processing, 1994
For a given square solvable singular systemEx=Ax+Bu with outputy=Cx we present a useful chain of transformations, acting on the quadruplet {E, A, B C}. The application of this chain enables the design of an output feedback for obtaining (provided the problem is solvable) finite and infinite pole assignment with regularity.
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Singular Finite-Horizon $$H_{\infty }$$ Problem

2022
Valery Y. Glizer, Oleg Kelis
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The Arithmetic Singularity: Why Prime Patterns Suggest Finite Recursion, Not Infinite Depth

The Ulam spiral reveals striking diagonal patterns in the distribution of prime numbers when integers are mapped to polar coordinates using θ = √n. Conventional interpretation holds that these patterns reflect hidden structure in the primes themselves, awaiting discovery within an infinite mathematical realm. We challenge this view.
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Singular Finite-Horizon Zero-Sum Differential Game

2022
Valery Y. Glizer, Oleg Kelis
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Finite-time cosmological singularities and the possible fate of the Universe

Physics Reports, 2023
Supriya Pan, Shin'ichi Nojiri, Jaime Haro Cases   +2 more
exaly  

INFINITE WHOLE — FINITE FRACTION Infinity as extent, not as division: rewriting the fundamental equations of physics without singularities

Modern physics rests on an implicit postulate: space, time, and physical quantities are infinitely divisible. This postulate, although mathematically convenient, produces aberrations: singularities, divergences, infinities. We propose a fundamental distinction between infinity as extent (possible, as totality) and infinity as division (absurd, as ...
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UNDER THE HYPOTHESES OF THE INITIAL CONDITIONS OF THE MILLENNIUM PROBLEM ABOUT THE NAVIER-STOKES EQUATIONS, THERE  CANNOT BE SHAPED IN FINITE TIME,  ANY VELOCITIES BLOW-UPS TO INFINITE (SINGULARITIES) ​

In this article, we give a very short proof (Theorem 3.4) that, under the hypotheses of the initial conditions of the millennium problem about the Navier-Stokes equations, there cannot be shaped in finite time,  velocities blow-ups to infinite (singularities).
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