Smooth sets for borel equivalence relations and the covering property for σ-ideals of compact sets

This thesis is divided into three chapters. In the first chapter we study the smooth sets with respect to a Borel equivalence realtion E on a Polish space X. The collection of smooth sets forms σ-ideal. We think of smooth sets as analogs of countable sets and we show that an analog of the perfect set theorem for Σ¹₁ sets holds in the context of smooth sets. We also show that the collection of Σ¹₁ smooth sets is ∏¹₁ on the codes. The analogs of thin sets are called sparse sets. We prove that there is a largest ∏¹₁ sparse set and we give a characterization of it. We show that in L there is a ∏¹₁ sparse set which is not smooth. These results are analogs of the results known for the ideal of countable sets, but it remains open to determine if large cardinal axioms imply that ∏¹₁ sparse sets are smooth. Some more specific results are proved for the case of a countable Borel equivalence relation. We also study I(E), the σ-ideal of closed E-smooth sets. Among other things we prove that E is smooth iff I(E) is Borel.

In chapter 2 we study σ-ideals of compact sets. We are interested in the relationship between some descriptive set theoretic properties like thinness, strong calibration and the covering property. We also study products of σ-ideals from the same point of view. In chapter 3 we show that if a σ-ideal I has the covering property (which is an abstract version of the perfect set theorem for Σ¹₁ sets), then there is a largest ∏¹₁ set in I^int (i.e., every closed subset of it is in I). For σ-ideals on 2^ω we present a characterization of this set in a similar way as for C₁, the largest thin ∏¹₁ set. As a corollary we get that if there are only countable many reals in L, then the covering property holds for Σ¹₂ sets.

On an embedding property of generalized Carter subgroups

If E and F are saturated formations, we say that E is strongly contained in F if for any solvable group G with E-subgroup, E, and F-subgroup, F, some conjugate of E is contained in F. In this paper, we investigate the problem of finding the formations which strongly contain a fixed saturated formation E.

Our main results are restricted to formations, E, such that E = {G|G/F(G) ϵT}, where T is a non-empty formation of solvable groups, and F(G) is the Fitting subgroup of G. If T consists only of the identity, then E=N, the class of nilpotent groups, and for any solvable group, G, the N-subgroups of G are the Carter subgroups of G.

We give a characterization of strong containment which depends only on the formations E, and F. From this characterization, we prove:

If T is a non-empty formation of solvable groups, E = {G|G/F(G) ϵT}, and E is strongly contained in F, then

(1) there is a formation V such that F = {G|G/F(G) ϵV}.

(2) If for each prime p, we assume that T does not contain the class, S_p’, of all solvable p’-groups, then either E = F, or F contains all solvable groups.

This solves the problem for the Carter subgroups.

We prove the following result to show that the hypothesis of (2) is not redundant:

If R = {G|G/F(G) ϵS_r’}, then there are infinitely many formations which strongly contain R.

Uptake and intracytoplasmic storage of pigmented particles by human CD34+stromal cells/telocytes: endocytic property of telocytes

We studied the phagocytic-like capacity of human CD34+ stromal cells/telocytes (TCs). For this, we examined segments of the colon after injection of India ink to help surgeons localize lesions identified at endoscopy. Our results demonstrate that CD34+ TCs have endocytic properties (phagocytic-like TCs: phTCs), with the capacity to uptake and store India ink particles. phTCs conserve the characteristics of TCs (long, thin, bipolar or multipolar, moniliform cytoplasmic processes/telopodes, with linear distribution of the pigment) and maintain their typical distribution. Likewise, they are easily distinguished from pigment-loaded macrophages (CD68+ macrophages, with oval morphology and coarse granules of pigment clustered in their cytoplasm). A few c-kit/CD117+ interstitial cells of Cajal also incorporate pigment and may conserve the phagocytic-like property of their probable TC precursors. CD34+ stromal cells in other locations (skin and periodontal tissues) also have the phagocytic-like capacity to uptake and store pigments (hemosiderin, some components of dental amalgam and melanin). This suggests a function of TCs in general, which may be related to the transfer of macromolecules in these cells. Our ultrastructural observation of melanin-storing stromal cells with characteristics of TCs (telopodes with dichotomous branching pattern) favours this possibility. In conclusion, intestinal TCs have a phagocytic-like property, a function that may be generalized to TCs in other locations. This function (the ability to internalize small particles), together with the capacity of these cells to release extracellular vesicles with macromolecules, could close the cellular bidirectional cooperative circle of informative exchange and intercellular interactions.

Structural change of laser-irradiated Ge2Sb2Te5 films studied by electrical property measurement

Sheet resistance of laser-irradiated Ge2Sb2Te5 thin films prepared by magnetron sputtering was measured by the four-point probe method. With increasing laser power the sheet resistance undergoes an abrupt drop from 10(7) to 10(3) Omega/square at about 580 mW. The abrupt drop in resistance is due to the structural change from amorphous to crystalline state as revealed by X-ray diffraction (XRD) study of the samples around the abrupt change point. Crystallized dots were also formed in the amorphous Ge2Sb2Te5 films by focused short pulse laser-irradiated, the resistivities at the crystallized dots and the non-crystallized area are 3.375 x 10(-3) and 2.725 Omega m, sheet resistance is 3.37 x 10(4) and 2.725 x 10(7) Omega/square respectively, deduced from the I-V Curves that is obtained by conductive atomic force microscope (C-AFM). (C) 2008 Elsevier B.V. All rights reserved.

Coincidence point theorems in quasi-metric spaces without assuming the mixed monotone property and consequences in G-metric spaces

In this paper, we present some coincidence point theorems in the setting of quasi-metric spaces that can be applied to operators which not necessarily have the mixed monotone property. As a consequence, we particularize our results to the field of metric spaces, partially ordered metric spaces and G-metric spaces, obtaining some very recent results. Finally, we show how to use our main theorems to obtain coupled, tripled, quadrupled and multidimensional coincidence point results.

Upconversion fluorescence property of Er3+/Yb3+-codoped novel bismuth-germanium glass

Infrared-to-visible upconversion fluorescence property of Er3+/Yb3+ codoped novel bismuth-germanium glass under 975 nm LD excitation has been studied. Intense green and red emissions centered at 525, 546 and 657 nm, corresponding to the transitions H-2(11/2) -> I-4(15/2), S-4(3/2) -> I-4(15/2), and F-4(9/2) -> I-4(15/2), respectively, were observed at room temperature. The quadratic dependence of the 525, 546 and 657 nm emissions on excitation power indicates that a two-photon absorption process occurs. The structure of the bismuth-germanium glass has been investigated by peak-deconvolution of FT-Raman spectrum, and the structural information was obtained from the peak wavenumbers. This novel bismuth-germanium glass with low maximum phonon energy (similar to 750 cm(-1)) can be used as potential host material for upconversion lasers. (c) 2005 Elsevier Ltd. All rights reserved.

Property studies of optical waveguide formed by 6.0 MeV carbon ion implantation into Nd : silicate glass

Nd:silicate glass was implanted at room temperature by 6.0 MeV C3+ ions with a dose of 2.0 x 10(15) ions cm(-2). A waveguide with thickness of about 6.3 mu m was formed. The prism-coupling method was used to observe the dark modes of the waveguide at 633 nm and 1539 nm, respectively. There are three dark modes at 633 nm, of which one is the enhanced-index mode. The propagation loss of the enhanced-index mode in the waveguide measured at 633 nm is 0.42 dB cm(-1) after annealing at 217 degrees C for 35 min. The reflectivity calculation method was applied to simulate the refractive index profiles in the waveguide. The mode optical near-field output at 633 nm was presented.

Study on the hydrolytic property and thermal stability of LiAlO2 substrate

The hydrolytic property and thermal stability of LiAlO2 (LAO), important factors for its application, were examined by AFM and X-ray rocking curve. We found that H2O may be deleterious for LAO surface polishing when the root mean square (RMS) value is less than 1 nm. However, when the RMS value is more than 1 nm it may be useful for LAO polishing. (100)-plane LAO substrates are annealed in the range of 850-900 degrees C in flux N-2, Slick AlN layer probably is produced on the substrate surface. M-plane GaN layer has grown on the substrate by metal-organic chemical vapor deposition (MOCVD) method. Theses results show that LiAlO2 crystal is a promising substrate of fabricating high-efficiency LEDs by MOCVD. (c) 2006 Elsevier B.V. All rights reserved.

High temperature annealing effect on structure, optical property and laser-induced damage threshold of Ta2O5 films

Ta2O5 films were deposited by conventional electron beam evaporation method and then annealed in air at different temperature from 873 to 1273 K. It was found that the film structure changed from amorphous phase to hexagonal phase when annealed at 1073 K, then transformed to orthorhombic phase after annealed at 1273 K. The transmittance was improved after annealed at 873 K, and it decreased as the annealing temperature increased further. The total integrated scattering (TIS) tests and AFM results showed that both scattering and root mean square (RMS) roughness of films increased with the annealing temperature increasing. X-ray photoelectron spectroscopy (XPS) analysis showed that the film obtained better stoichiometry and the O/Ta ratio increased to 2.50 after annealing. It was found that the laser-induced damage threshold (LIDT) increased to the maximum when annealed at 873 K, while it decreased when the annealing temperature increased further. Detailed damaged models dominated by different parameters during annealing were discussed. (C) 2008 Elsevier B. V. All rights reserved.

Approximate Solutions by Truncated Taylor Series Expansions of Nonlinear Differential Equations and Related Shadowing Property with Applications

This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial condition. The class of differential equations is assumed to be approximated by well-posed truncated Taylor series expansions up to a certain order obtained about certain, in general nonperiodic, sampling points t(i) is an element of [t(0), t(J)] for i = 0, 1, . . . , J of the solution. Two examples are provided.