In this paper we point out that the spacetime uncertainty relation proposed for string theory has strong cosmological implications that can solve the flatness problem and the horizon problem without the need of inflation. We make minimal assumptions about the very early universe.

We study contracting and costly renegotiation in settings of complete, but unverifiable information, using the mechanism-design approach. We show how renegotiation activity is best modeled in the fundamentals of the mechanism-design framework, so that noncontractibility of renegotiation amounts to a constraint on the problem. We formalize and clarify the Renegotiation-Proofness Principle (RPP),...

In this paper, we study the relationships between left (right) semi-uninorms and implications on a complete lattice. We firstly discuss the residual operations of left and right semi-uninorms and show that the right (left) residual operator of a conjunctive right (left) ∨-distributive left (right) semi-uninorm is a right ∧-distributive implication that satisfies the neutrality principle. Then, ...

Propagating possibilistic and probabilistic variables through a mapping yields a fuzzy random variable. We propose a method to attach probability intervals to events pertaining to the output variable. We show that this method is consistent with classical approaches to fuzzy random variables and that the obtained probability interval is the mean value of the fuzzy probability defined by viewing ...

We present a procedure for calculating an upper limit on the number of signal events which incorporates the Poisson uncertainty in the background, estimated from control regions of one or two dimensions. For small number of signal events, the upper limit obtained is more stringent than that extracted without including the Poisson uncertainty. This trend continues until the number of background ...

We give a real-variable proof of the Hardy uncertainty principle. The method is based on energy estimates for evolutions with positive viscosity, convexity properties of free waves with Gaussian decay at two different times, elliptic L2-estimates and the invertibility of the Fourier transform on L2(Rn) and S′(Rn).

In this paper, we develop Terence Tao’s harmonic analysis method and apply it to restricted sumsets. The well known Cauchy-Davenport theorem asserts that if ∅ 6= A,B ⊆ Z/pZ with p a prime, then |A+ B| > min{p, |A|+ |B| − 1}, where A + B = {a + b : a ∈ A, b ∈ B}. In 2005, Terence Tao gave a harmonic analysis proof of the Cauchy-Davenport theorem, by applying a new form of the uncertainty princip...

Delayed renewal process and delayed renewal reward process are introduced in the framework of uncertainty theory and their uncertainty distributions are provided. Furthermore, delayed renewal theorem on the limit value of the expected renewal rate of the process and delayed renewal reward theorem on the limit value of the long-run expected reward per unit time are presented. At last, some examp...

We define lacunary Fourier series on a compact connected semisimple Lie group G. If f ∈ L1(G) has lacunary Fourier series and f vanishes on a non empty open subset of G, then we prove that f vanishes identically. This result can be viewed as a qualitative uncertainty principle.