P-harmonic obstacle problems

We prove an extension theorem for Sobolev functions which plays an important role in the partial regularity theory of vector valued functions which minimize degenerate variational integrals subject to some nonlinear side conditions in the image space.     

Detection of hepatocarcinoma in rats by integration of the fluorescence spectrum: Experimental model

The incorporation of spectroscopic techniques into diagnostic procedures may greatly improve the chances for precise diagnostics. One promising technique is fluorescence spectroscopy, which has recently been used to detect many different types of diseases. In this work, we use laser-induced tissue fluorescence to detect hepatocarcinoma in rats using excitation light at wavelengths of 443 and 532 nm. Hepatocarcinoma was induced chemically in Wistar rats. The collected fluorescence spectrum ranges from the excitation wavelength up to 850 nm. A mathematical procedure carried out on the spectrum determines a figure of merit value, which allows the detection of hepatocarcinoma. The figure of merit involves a procedure which evaluates the ratio between the backscattered excitation wavelength and the broad emission fluorescence band. We demonstrate that a normalization allowed by integration of the fluorescence spectra is a simple operation that may allow the detection of hepatocarcinoma.     

Fractal strings as an alternative justification for El Naschie''s cantorian spacetime and the fine structure constant

Beginning with the most general fractal strings/sprays construction recently expounded in the book by Lapidus and Frankenhuysen, it is shown how the complexified extension of El Naschie's cantorian-fractal spacetime model belongs to a very special class of families of fractal strings/sprays whose scaling ratios are given by suitable pinary (pinary, p prime) powers of the Golden Mean. We then proceed to show why the logarithmic periodicity laws in Nature are direct physical consequences of the complex dimensions associated with these fractal strings/sprays. We proceed with a discussion on quasi-crystals with p-adic internal symmetries, von Neumann's Continuous Geometry, the role of wild topology in fractal strings/sprays, the Banach-Tarski paradox, tesselations of the hyperbolic plane, quark confinement and the Mersenne-prime hierarchy of bit-string physics in determining the fundamental physical constants in Nature.     

Approximating the single source unsplittable min-cost flow problem

In the single source unsplittable min-cost flow problem, commodities must be routed simultaneously from a common source vertex to certain destination vertices in a given graph with edge capacities and costs; the demand of each commodity must be routed along a single path so that the total flow through any edge is at most its capacity. Moreover, the total cost must not exceed a given budget. This problem has been introduced by Kleinberg [7] and generalizes several NP-complete problems from various areas in combinatorial optimization such as packing, partitioning, scheduling, load balancing, and virtual-circuit routing. Kolliopoulos and Stein [9] and Dinitz, Garg, and Goemans [4] developed algorithms improving the first approximation results of Kleinberg for the problem of minimizing the violation of edge capacities and for other variants. However, known techniques do not seem to be capable of providing solutions without also violating the cost constraint. We give the first approximation results with hard cost constraints. Moreover, all our results dominate the best known bicriteria approximations. Finally, we provide results on the hardness of approximation for several variants of the problem. Received: August 23, 2000 / Accepted: April 20, 2001?Published online October 2, 2001     

Enhanced four-wave mixing in mercury isotopes, prepared by stark-chirped rapid adiabatic passage

We demonstrate significant enhancement of four-wave mixing in coherently driven mercury isotopes to generate vacuum-ultraviolet radiation at 125 nm. The enhancement is accomplished by preparation of the mercury atoms in a state of maximum coherence, i.e. maximum nonlinear-optical polarization, driven by Stark-chirped rapid adiabatic passage (SCRAP). In this technique, a pump laser at 313 nm excites the two-photon transition between the ground state 6s²¹S₀ and the target state 7s ¹S₀ in mercury. A strong, off-resonant radiation field at 1064 nm generates dynamic Stark shifts. These Stark shifts serve to induce a rapid adiabatic passage process on the two-photon transition. During the process a coherent superposition of the two states is established, which enhances the nonlinear-optical polarization in the medium to the maximum possible value. The maximum coherence permits efficient four-wave mixing of a pump laser and an additional probe laser at 626 nm. The efficiency is further enhanced, as the SCRAP process allows to stimulate the complete set of different mercury isotopes to participate in the frequency conversion process. This enlarges the effective atomic density of the medium. Thus, we observe the generation of vacuum-ultraviolet radiation at 125 nm enhanced by more than one order of magnitude with respect to conventional frequency conversion. Parallel to the frequency conversion process, we monitored the evolution of the population in the medium by laser-induced fluorescence. These data demonstrate efficient coherent population transfer by SCRAP.     

Correlated and non-correlated growth kinetics of pentacene in the sub-monolayer regime

We present a study of the growth kinetics of pentacene monolayer islands on SiO₂ in the submonolayer regime by using Atomic Force Microscopy (AFM). Two distinct growth modes, namely correlated growth (CG) and non-correlated growth (NCG), have been identified by Voronoi tesselation. These two modes are characterized by different island growth kinetics. In the case of correlated growth, the average island size 〈A〉 scales with deposition time t i.e. 〈A〉 ∝ t whereas for non-correlated growth, 〈A〉 ∝ t². The CG and NCG regimes are defined by the level of re-evaporation which determines the capture zones around the islands: Wigner-Seitz cells for CG and coronas of width λ_D (λ_D is the mean diffusion distance on SiO₂ before re-evaporation) for NCG. A simple model is proposed to reproduce the experimental growth kinetics in both modes.     

Studies on pre-hump and main fractions of cellulose-2,5-acetate in acetone

Technical cellulose-2.5-acetates (CA 2.5) were characterized regarding their carbohydrate composition in comparison to the raw material. The association of the CA 2.5 samples in acetone was studied by size exclusion chromatography (SEC) using various acetone grades and styrene divinylbenzene copolymer columns. In HPLC grade acetone with and without addition of 1% water up to three different pre-humps eluted in front of the main fraction of the polymer. The evaluation of the main peak by light scattering measurements resulted in high molar masses indicating that for these technical CA 2.5 samples even the main fraction is not dissolved without association. No pre-humps or association phenomena were observed after addition of 1 ppm LiBr to HPLC grade acetone or with p.a. grade acetone. In addition pre-hump enriched and pre-hump free fractions were isolated by fractionated precipitation. The carbohydrate composition of these fractions was determined and correlated with their association pattern in SEC investigations.