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.

The central limit theorem ensures that a sum of random variables tends to a Gaussian distribution as their total number tends to infinity. However, for a class of positive random variables, we find that the sum tends faster to a log-normal distribution. Although the sum tends eventually to a Gaussian distribution, the distribution of the sum is always close to a log-normal distribution rather t...

Let N be an imaginary abelian number field. We know that hN , the relative class number of N , goes to infinity as fN , the conductor of N , approaches infinity, so that there are only finitely many imaginary abelian number fields with given relative class number. First of all, we have found all imaginary abelian number fields with relative class number one: there are exactly 302 such fields. I...