This Rapid Communication presents an analytical study of the bouncing of a completely inelastic ball on a vertically vibrated plate. The interplay of saddle-node and period-doubling bifurcations leads to an intricate structure of the bifurcation diagram with uncommon properties, such as an infinity of bifurcation cascades in a finite range of the control parameter Gamma. A pseudochaotic behavio...

Computer algebra systems (CAS) are sometimes expected to compute with infinities symbolically. Since operations on such objects do not always conform to a sufficient and consistent set of rules for ordinary arithmetic, some compromises are necessary. We discuss a few options and implementations.

We prove a preservation theorem for positive Horn definability inא0-categorical structures.In particular, we define and study a construction which we call the periodic power of a structure, anddefine a periomorphism of a structure to be a homomorphism from the periodic power of the structureto the structure itself. Our preservation theorem states that, over anא0-categorical ...

Of course, before an unending number of objections start pouring in to my bottomless email box, I need to clarify this brazen claim. After all, humans have been grappling with the concept of infinity for many millennia and mathematicians seem to have (at least in the last 150 years or so) finally tamed it. First, building on the work of Euler, Cauchy and Weierstrass, we now have the ability to ...

We are so used to think by ourselves that we almost forget how rare and strange this psychological feat actually is. The ability to retract ‘within’ oneself is a recent and culturally determined phaenomenon which was hardly available throughout the major part of human history.[9] To think is to think aloud. Even in our own Antiquity to think and to speak did largely coincide [7]. If we look at ...

In the late 1950’s F. A. E. Pirani, A. Trautman, R. K. Sachs, H. Bondi, E. T. Newman, R. Penrose and others began exploring possibilities to establish in Einstein’s nonlinear theory a notion of gravitational radiation which is covariant and not based on approximations. The proposal they finally came up with relies, however, on an idealization. The solutions to Einstein’s field equations were as...

Hauser (et al.) [1] claim that a core property of the human language faculty is recursion and that this property “yields discrete infinity” of natural languages. On the other hand, recursion is often motivated by the observation that there are infinitely many sentences that should be generated by a finite number of rules. It should be obvious that one cannot pursue both arguments simultaneously...

—This paper proposes a direct, and simple approach to the H∞ norm calculation in more general settings. In contrast to the method based on the Kalman–Yakubovich–Popov lemma, our approach does not require a controllability assumption, and returns a sinusoidal input that achieves the H∞ norm of the system including its frequency. In addition, using a semidefinite programming duality, we present a...

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We analyze the radiative aspects of nonsymmetric gravity theory to show that, in contrast to General Relativity, its nonstationary solutions cannot simultaneously exhibit acceptable asymptotic behavior at both future and past null infinity: good behavior at future null infinity is only possible through the use of advanced potentials with concomitant unphysical behavior at past null infinity.