A sharper uncertainty principle

The work strengthens the result established by L. Cohen on uncertainty principle involving phase derivative. We propose stronger uncertainty principles not only in the classical setting for Fourier transform, but also for self-adjoint operators. We also deduce the conditions that give rise to the equal relation of the uncertainty principle. Examples are provided to show that the new uncertainty principle is truly sharper than the existing ones in literature.     

Why Matter Occupies so Large a Volume？

The paper represents a rigorous treatment of the underlying quantum theory, not just in words but providing the underlying technical details, as to why matter occupies so large a volume and its intimate connection with the Pauli exclusion principle, as more and more matter is put together, as well as of the contraction or shrinkage of ＂bosonic matter＂, upon collapse, for which the Panli exclusion is abolished. From the derived explicit bounds of integrals of powers of the particle number densities, explicit bounds on probabilities of the occurrences of the events just described are extracted. These probabilities lead one to infer the change of the ＂size＂ or extension of such matter, upon expansion or contraction, respectively, as their content is increased.     

Large sample prediction intervals for future geometric mean a comparative study

This paper provides simulation comparisons among the performance of 11 possible prediction intervals for the geometric.mean of a Pareto distribution with parameters (αB, ). Six different procedures were used to obtain these intervals , namely; true inter -val , pivotal interval , maximum likelihood estimation interval, centrallimit teorem interval, variance stabilizing interval and a mixture of the above intervals . Some of these intervals are valid if the observed sample size m,are large , others are valid if both, n and the future sample size m, are large. Some of these intervals require a knowledge of α or B, while others do not. The simulation validation and efficiency study shows that intervals depending on the MLE's are the best. The second best intervalsare those obtained through pivotal methods or variance stabilization transformation. The third group of intervals is that which depends on the central limit theorem when λ is known. There are two intervals which proved to be unacceptable under any criterion.     

On a hidden symmetry of quantum harmonic oscillators

We consider a six-parameter family of the square integrable wave functions for the simple harmonic oscillator, which cannot be obtained by the standard separation of variables. They are given by the action of the corresponding maximal kinematical invariance group on the standard solutions. In addition, the phase space oscillations of the electron position and linear momentum probability distributions are computer animated and some possible applications are briefly discussed. A visualization of the Heisenberg uncertainty principle is presented.     

Was Pauling Mistaken about Metals?

Pauling described metallic bonds using resonance. The maximum probability domains in the Kronig–Penney model can show a picture of it. When the walls are opaque (and the band gap is large) the maximum probability domain for an electron pair essentially corresponds to the region between the walls: the electron pairs are localized within two consecutive walls. However, when the walls become transparent (and the band gaps closes), the maximum probability domain can be moved through the system without a significant loss in probability.     

Uncertainty and Certainty Relations for Pauli Observables in Terms of Renyi Entropies of Order α∈ （0; 1]

We obtain uncertainty and certainty relations of state-independent form for the three Paufi observables with use of the Renyi entropies of order α∈ （0; 1]. It is shown that these entropic bounds are tight in the sense that they are always reached with certain pure states. A new result is the condition for equality in Renyi-entropy uncertainty relations for the Pauli observables. Upper entropic bounds in the pure-state case are also novel. Combining the presented bounds leads to a band, in which the rescaled average Renyi a-entropy ranges for a pure measured state. A width of this band is compared with the Tsallis formulation derived previously.     

Persistence of sums of correlated increments and clustering in cellular automata

Let $T$ be the first return time to $(?\infty ,0]$ of sums of increments given by a functional of a stationary Markov chain. We determine the asymptotic behavior of the survival probability, $\mathbb{P}(T\ge t)～C{t}^{?1∕2}$ for an explicit constant $C$. Our analysis is based on a connection between the survival probability and the running maximum of the time-reversed process, and relies on a functional central limit theorem for Markov chains. As applications, we recover known clustering results for the 3-color cyclic cellular automaton and the Greenberg–Hastings model, and we prove a new clustering result for the 3-color firefly cellular automaton.     

Anti‐Pasch optimal packings with triples

It is shown that for , there exists an optimal packing with triples on points that contains no Pasch configurations. Furthermore, for all (mod 6), there exists a pairwise balanced design of order , whose blocks are all triples apart from a single quintuple, and that has no Pasch configurations amongst its triples.