Introduction to random division multiple access (RDMA) applicable for mobile satellite communications

This paper describes in particular Random Division Multiple Access (RDMA) applicable in Mobile Satellite Communications (MSC). In satellite communication systems, as a rule, especially in Mobile Satellite Communications (MSC) many users are active at the same time. The problem of simultaneous communications between many single or multipoint mobile satellite users, however, can be solved by using Multiple Access (MA) technique. Since the resources of the systems such as the transmitting power and the bandwidth are limited, it is advisable to use the channels with complete charge and to create a different MA to the channel. This generates a problem of summation and separation of signals in the transmission and reception parts, respectively. Deciding this problem consists in the development of orthogonal channels of transmission in order to divide signals from various users unambiguously on the reception part.

Multifractal spectra for random self-similar measures via branching processes

Start with a compact setK⊂Rd. This has a random number of daughter sets, each of which is a (rotated and scaled) copy ofKand all of which are insideK. The random mechanism for producing daughter sets is used independently on each of the daughter sets to produce the second generation of sets, and so on, repeatedly. The random fractal setFis the limit, asngoes to ∞, of the union of thenth generation sets. In addition,Khas a (suitable, random) mass which is divided randomly between the daughter sets, and this random division of mass is also repeated independently, indefinitely. This division of mass will correspond to a random self-similar measure onF. The multifractal spectrum of this measure is studied here. Our main contributions are dealing with the geometry of realisations inRdand drawing systematically on known results for general branching processes. In this way we generalise considerably the results of Arbeiter and Patzschke (1996) and Patzschke (1997).

Multifractal spectra for random self-similar measures via branching processes

Start with a compact set K ⊂ Rd. This has a random number of daughter sets, each of which is a (rotated and scaled) copy of K and all of which are inside K. The random mechanism for producing daughter sets is used independently on each of the daughter sets to produce the second generation of sets, and so on, repeatedly. The random fractal set F is the limit, as n goes to ∞, of the union of the nth generation sets. In addition, K has a (suitable, random) mass which is divided randomly between the daughter sets, and this random division of mass is also repeated independently, indefinitely. This division of mass will correspond to a random self-similar measure on F. The multifractal spectrum of this measure is studied here. Our main contributions are dealing with the geometry of realisations in Rd and drawing systematically on known results for general branching processes. In this way we generalise considerably the results of Arbeiter and Patzschke (1996) and Patzschke (1997).

A NEW MODEL FOR COMPETITION BETWEEN MANY LANGUAGES

Time evolution of number of cities, population of cities, world population, and size distribution of present languages are studied in terms of a new model, where population of each city increases by a random rate and decreases by a random division. World population and size distribution of languages come out in good agreement with the available empirical data.

Cohesins Determine the Attachment Manner of Kinetochores to Spindle Microtubules at Meiosis I in Fission Yeast

ABSTRACT During mitosis, sister kinetochores attach to microtubules that extend to opposite spindle poles (bipolar attachment) and pull the chromatids apart at anaphase (equational segregation). A multisubunit complex called cohesin, including Rad21/Scc1, plays a crucial role in sister chromatid cohesion and equational segregation at mitosis. Meiosis I differs from mitosis in having a reductional pattern of chromosome segregation, in which sister kinetochores are attached to the same spindle (monopolar attachment). During meiosis, Rad21/Scc1 is largely replaced by its meiotic counterpart, Rec8. If Rec8 is inactivated in fission yeast, meiosis I is shifted from reductional to equational division. However, the reason rec8Δ cells undergo equational rather than random division has not been clarified; therefore, it has been unclear whether equational segregation is due to a loss of cohesin in general or to a loss of a specific requirement for Rec8. We report here that the equational segregation at meiosis I depends on substitutive Rad21, which relocates to the centromeres if Rec8 is absent. Moreover, we demonstrate that even if sufficient amounts of Rad21 are transferred to the centromeres at meiosis I, thereby establishing cohesion at the centromeres, rec8Δ cells never recover monopolar attachment but instead secure bipolar attachment. Thus, Rec8 and Rad21 define monopolar and bipolar attachment, respectively, at meiosis I. We conclude that cohesin is a crucial determinant of the attachment manner of kinetochores to the spindle microtubules at meiosis I in fission yeast.

Shapes of Rectangular Prisms After Repeated Random Division

The shape of a rectangular prism in (d + 1)-dimensions is defined as Y = (Y 1, Y 2, · ··, Yd ), Yn = Ln/Ln +1 where the Ln are the prism's edge lengths, in ascending order. We investigate shape distributions that are invariant when the prism is cut into two, also rectangular, prisms, with one prism retained for measurement and the other discarded. Interesting new distributions on [0, 1] d arise.