A remark on the mild solutions of non-local evolution equations

We provide a counterexample to some recent publications concerning the existence of the mild solutions of the non-local evolution equations, and indicate that in the study of the non-local evolution equations, the operators from which the mild solutions may be derived are in general not compact, thus those fixed point theorems requiring the compactness of the operators are not applicable.     

On fundamental groups of compact Hausdorff spaces

We discuss which groups can be realized as the fundamental groups of compact Hausdorff spaces. In particular, we prove that the claim ``every group can be realized as the fundamental group of a compact Hausdorff space' is consistent with the Zermelo-Fraenkel-Choice set theory.

     

Recent trends and open issues in reverse engineering

This paper discusses recent trends in the field of reverse engineering, particularly those highlighted at the Second Working Conference on Reverse Engineering, held in July 1995. The trends observed include increased orientation toward tasks, grounding in complex real-world applications, guidance from empirical study, analysis of non-code sources, and increased formalization. The paper also summarizes open research issues and provides pointers to future events and sources of information in this area.     

The optical-mechanical analogy in general relativity: Exact Newtonian forms for the equations of motion of particles and photons

In many metrics of physical interest, the gravitational field can be represented as an optical medium with an effective index of refraction. We show that, in such a metric, the orbits of both massive and massless particles are governed by a variational principle which involves the index of refraction and which assumes the form of Fermat's principle or of Maupertuis's principle. From this variational principle we derive exact equations of motion of Newtonian form which govern both massless and massive particles. These equations of motion are applied to some problems of physical interest.     

Fluorescence correlation spectroscopic studies of diffusion within the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate

Fluorescence correlation spectroscopy (FCS) measurements have been performed in order to determine the translational diffusion coefficients of three differently charged fluorescent probes (cationic: rhodamine 6G, neutral: 4-dicyanomethylene-2-methyl-6-p-dimethylaminostyryl-4-H-pyran, DCM, and anionic: fluorescein) dissolved within the common room temperature ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate, [bmim][PF6]. These experiments demonstrate that FCS is a rapid, sensitive, precise (typical RSD from 4-8%), and low-consumption screening tool for the determination of analyte mobility within microliter ionic liquid samples.     

The convergence rate for the strong law of large numbers: General lattice distributions

LetX ₁,X ₂, ... be a sequence of independent random variables with common lattice distribution functionF having zero mean, and let (S _n ) be the random walk of partial sums. The strong law of large numbers (SLLN) implies that for any and >0

Crystal and molecular structure of 1R,3S,5S,7R,10R-3,6,6,10,14-Pentamethyltricyclo[10.3.0.05,7]pentadeca-11,14-diene-1, 10-dihydroxy-2,13-dione (Japodagrol), C20H28O4

A new cytotoxic macrocyclic diterpenoid named Japodagrol, C₂₀H₂₈O₄, has been isolated from the ornamental plantJatropha podagrica, family Euphorbiaceae, grown in Nigeria. The structure of the title compound, C₂₀H₂₈O₄, was solved by X-ray analysis.M _r =332.44, monoclinic space groupC2,a=23.285(4),b=6.5105(12),c=12.505(3) Å,=98.504(17),V=1874.8 ų,Z=4,D _c =1.178 Mg/m³. CuK radiation (graphite crystal monochromator, =1.54184 A), (CuK)=6.13 cm^–1,F(000)=720,T=290 K. Final conventionalR factor=0.035,R _w =0.038 for 3349 observed reflections. The structure was solved with the programDirdif. The 5-membered ring is closed to a half-chair form. The compound contains inter- and intramolecular hydrogen bonds.