The small octagon with longest perimeter

The convex octagon with unit diameter and maximum perimeter is determined. This answers an open question dating from 1922. The proof uses geometric reasoning and an interval arithmetic based global optimization algorithm to solve a series of non-linear and non-convex programs involving trigonometric functions.     

Two-dimensional electrophoresis of the total polypeptides in ripe red grape berries.

The total polypeptide composition of mature grape berries was analyzed by one-dimensional sodium dodecyl sulfate-polyacrylamide gel electrophoresis and two-dimensional electrophoresis (isoelectric focusing in the first dimension followed by sodium dodecyl sulfate-polyacrylamide gel electrophoresis in the second dimension), followed by Coomassie Blue and nitrate silver staining, respectively. Adapted methods for total protein preparation of grapes and for two-dimensional gel electrophoretic separation of polypeptides are presented. The grape patterns presented up to 52 fractions with Mrs ranging from 15,000 to 110,000. The polypeptides displayed pIs from 4.6 to 7.3. A group of spots from Mr 28,000 to 83,000 and with a pI from 4.6 to 5.4 was strongly silver stained. The Mr 28,000 spot, pI 4.6, was revealed to be a complex of four fractions. Reproducible separations were obtained with the different carrier ampholyte mixtures tested.     

Some aspects of relativistic motion that depends on one spatial variable

Specific relativistic effects associated with the instability of potential motions that depend on one spatial variable, including the instability of isentropic flows with respect to solenoidal perturbations, are considered. A general theorem is proved. Estimates and solutions are obtained in limiting cases of the separate action of the various effects of relativity and in the absence of other nonlinear hydrodynamic effects. It is shown that many already known solutions of the equations of relativistic hydrodynamics are unstable with respect to the development of transverse solenoidal components of the velocity.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 103, No. 1, pp. 82–96, April, 1995.     

AeDEn: An adaptive framework for dynamic distribution over mobile environments

Mobile computing is a domain in great expansion. Wireless networks (gsm, satellite, etc) and Portable Information Appliances pias (laptops, PDAs, cellular phones, etc) are developing very rapidly. More and more mobile users would like to execute their applications with the same quality of service as on their desktop station, whatever their needs in memory and computing power. Using such applications in a mobile environment raises new challenges. Some of these applications are extremely costly in system and network resources, whereas pias resources are poor and wireless networks offer a very variable quality of connection. In this paper we propose an adaptive and dynamic distribution of applications on the local environment to overcome the poorness of available resources on pias, and to reduce and regulate variability effects. Moreover, due to the variety of distribution policies, we propose a framework providing adaptive distribution policies.     

Which new RSA-signatures can be computed from certain given RSA-signatures?

We consider the following problem. A signature authority issues RSA-signatures of certain types to an individual, and the individual tries, by using the signatures he received, to compute an RSA-signature of a type not issued by the authority. Is the individual able to do this? The RSA-signatures are products of rational powers of residue classes modulo the composite number N of the underlying RSA-system, and the residue classes are chosen at random by the signature authority. The rational exponents in the product determine the type of the signature. We prove that computing an RSA-signature of a particular type, from given RSA-signatures of other types, is polynomial time reducible to computing RSA-roots x ^1/d (mod N) for random x and some positive integer d. This extends results of Akl and Taylor [1] and Shamir [11] from one variable to arbitrarily many variables. As an application of this, under the assumption that for the individual it is infeasible to compute RSA-roots, we give necessary and sufficient conditions describing whether it is feasible for that individual to compute RSA-signatures of a prescribed type from signatures of other types that he received before from the authority.