We point out that results obtained by M. Ribarič and L. Šušteršič, hep-th/0403084, and byM. Blasone, P. Jizba and H. Kleinert, quant-ph/0409021, suggest that the path-integral formalism is the key to a derivation of quantum physics from classical, deterministic physics in the four-dimensional space-time. These results and the ’t Hooft conjecture, hep-th/0104219, suggest to consider a relativist...

We extend Zeilberger's fast algorithm for deenite hypergeometric sum-mation to non-hypergeometric holonomic sequences. The algorithm generalizes to diierential and q-cases as well. Its theoretical justiication is based on a description by linear operators and on the theory of holonomy. R esum e. Nous etendons l'algorithme rapide de Zeilberger pour la sommation hy-perg eom etrique d eenie aux su...

A partition of a non-negative integer n is a non-increasing sequence of positive integers whose sum is n. For example, The 5 partitions of 4 are 4, 3 + 1, 2 + 2, 2 + 1 + 1, and 1 + 1 + 1 + 1. To explain Ramanujan’s famous three partition congruences, the partition statistics, the rank (resp. the crank) were introduced by Dyson [8] (resp. Andrews and Garvan [3]). Atkin and Garvan [5] initiated t...

The radio continuum spectra of 74 galaxies were used to separate thermal and non-thermal radio emission. The thermal fraction f1GHz th at 1 GHz and the non-thermal spectral index αnth of the radio continuum emission were determined. The mean values are 〈f1GHz th 〉 = 0.08± 0.01 and 〈αnth〉 = 0.83± 0.02. Even at 10 GHz the radio continuum emission ofmost of the galaxies is dominated by the synchro...

A detailed an alysis was mad e of th e response characteristic s of single cells in th e lat eral geniculate nucleus of the macaqu e monkey. Th e goa l was to understand how the se cells cont rib ute to th e proc essing of visual information. Dat a were an alyzed from a representative sa mple of 147 cells, whose respons es to eq ua l-energy spectra (prese nte d as diffuse flash es of monocbroma...

We propose a new theory to characterize equilibrium topological phase with non-equilibrium quantum dynamics by introducing the concept of high-order charges, novel phenomena being predicted. Through dimension reduction approach, we can $d$-dimensional ($d$D) integer-invariant lower-dimensional number quantified which $s$th-order charges denote monopoles confined on $(s-1)$th-order band inversio...

Previous studies in rat and mouse documented that a subpopulation of dorsal root ganglion (DRG) neurons innervating non-visceral tissues express tyrosine hydroxylase (TH). Here we studied whether or not mouse DRG neurons retrogradely traced with Fast Blue (FB) from colorectum or urinary bladder also express immunohistochemically detectable TH. The lumbar sympathetic chain (LSC) and major pelvic...