Reducibility and nonreducibility between equivalence relations

We show that, for , the relation of -equivalence between infinite sequences of real numbers is Borel reducible to the relation of -equivalence (i.e., the Borel cardinality of the quotient is no larger than that of ), but not vice versa. The Borel reduction is constructed using variants of the triadic Koch snowflake curve; the nonreducibility in the other direction is proved by taking a putative Borel reduction, refining it to a reduction map that is not only continuous but `modular,' and using this nicer map to derive a contradiction.

     

Hematoporphyrin as a photosensitizer of tumors

Abstract— The ability of hematoporphyrin (Hp) to act as a photosensitizer of cells in vitro or in vivo is a matter of dispute, while hematoporphyrin derivative (Hpd), a mixture of porphyrins including hematoporphyrin, has been consistently found to be an effective photosensitizer both in vitro and in vivo. Until recently the actual component of the Hpd mixture responsible for these effects had not been identified. We have found that those preparations of Hp which contain, as an impurity, a porphyrin similar to that found to be responsible for the tumor photosensitizing ability of Hpd, may be effective photosensitizers of tumors but are generally of low efficacy. This material accounts for the entire photosensitizing activity of both Hp and Hpd in the SMT-F mammary carcinoma in DBA/2 HeHa mice.     

Structure-activity relationship of new octaethylporphyrin-based benzochlorins as photosensitizers for photodynamic therapy

An in vitro and in vivo structure-activity relationship study was carried out on a series of benzochlorins with variable lipophilicity. The structural features evaluated in this study include the length of the alkyl or fluoroalkyl groups attached to the six-member exocyclic ring either by an ether or by a carbon-carbon bond. In preliminary in vitro (radiation-induced fibrosarcoma [RIF] cells) and in vivo screening (C3H mice, bearing RIF tumors), all Zn (II) benzochlorins were found to be effective. However, benzochlorins bearing alkyl groups with carbon-carbon bonds showed enhanced efficacy compared with the related alkyl ether analogs. A comparative intracellular localization study of the newly synthesized benzochlorins with Rhodamine-123 indicated that the effective photosensitizers localize in mitochondria, and a displacement study with PK11195 showed their partial affinity for the peripheral benzodiazepine receptor (PBR). Interestingly, compared with the Zn(II) benzochlorin that was found to be quite effective in vivo, the corresponding free-base analog produced less photosensitizing activity and was found to localize in lysosomes. A comparative study with dansyl-proline confirmed the binding of the effective benzochlorins to Site II of human serum albumin (HSA). However, no direct correlation was observed between the binding constant values (to HSA or to PBR) of benzochlorins and their photosensitizing ability.     

Exclusion limits on the WIMP-nucleon cross section from the cryogenic dark matter search

The Cryogenic Dark Matter Search (CDMS) employs Ge and Si detectors to search for weakly interacting massive particles (WIMPs) via their elastic-scattering interactions with nuclei while discriminating against interactions of background particles. CDMS data, accounting for the neutron background, give limits on the spin-independent WIMP-nucleon elastic-scattering cross section that exclude unexplored parameter space above 10 GeV/c2 WIMP mass and, at >75% C.L., the entire 3sigma allowed region for the WIMP signal reported by the DAMA experiment.     

The effects of sample preparation methods on the variability of the electrospray ionization response for model drug compounds

A post-column infusion system was developed in order to analyze suppression of electrospray ionization (ESI) tandem mass spectrometry response in the presence of endogenous plasma interferences. By enabling direct detection of these interfering components, this experimental system was used to analyze the ability of several common extraction procedures to remove endogenous plasma components that cause changes in the ESI response of model drug substances. Methyl-t-butyl ether (MTBE) liquid-liquid, Oasis and Empore solid-phase, and acetonitrile (ACN) protein precipitation sample preparation methods were tested using the post-column infusion system. In all cases, ACN protein precipitation samples showed the greatest amount of ESI response suppression while liquid-liquid extracts demonstrated the least. In addition, the three test compounds, phenacetin, caffeine, and a representative Merck compound, demonstrated that ESI response suppression is compound dependent. Suppression was greatest with caffeine, the most polar analyte, and the smallest for the Merck compound, the least polar analyte. Copyright 1999 John Wiley & Sons, Ltd.     

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Gamma-ray spectroscopy with relativistic exotic heavy-ions

Feasibility of gamma-ray spectroscopy at relativistic energies with exotic heavy-ions and new generation of germanium detectors (segmented Clover) is discussed. An experiment with such detector array and radioactive is discussed.     

Evaluation of the magnetic moments of radium isotopes

Using the relativistic linked cluster many-body perturbation procedure we have obtained the hyperfine field at the nucleus of the Ra⁺ ion in the²S_1/2 ground state. There is good agreement between the calculated magnetic moment of²¹³Ra and the results of a recent Zeeman measurement by the collinear laser beam technique. Detailed comparison is carried out between our result and earlier ones.     

Percolative transport in the vicinity of charge-order ferromagnetic transition in a hole-doped manganite

We report measurements of non-linear charge transport in epitaxial (La_1−x Pr _x )_0.7Ca_0.3MnO₃ thin films fabricated on (100) oriented SrTiO₃ single crystals by pulsed laser deposition. The end members of this series, namely Pr_0.7Ca_0.3MnO₃ and La_0.7Ca_0.3MnO₃ are canonical charge-ordered (CO) and ferromagnetic manganites, respectively. The onset of the CO state in Pr_0.7Ca_0.3MnO₃ is manifested by a pronounced insulating behavior below ∼ 200 K. The CO state remains stable even when a large (∼ 2×10⁵ V/cm) electric field is applied across the thin film samples. However, on substitution of Pr with La, a crossover from the highly resistive CO state to a state of metallic character is observed at relatively low electric fields. The current-voltage characteristics of the samples at low temperatures show hysteretic and history dependent effects. The electric field driven charge transport in the system is modelled on the basis of an inhomogeneous medium consisting of ferromagnetic metallic clusters dispersed in a CO background.     

Finite Left-Distributive Algebras and Embedding Algebras

We consider algebras with one binary operation · and one generator (monogenic) and satisfying the left distributive lawa·(b·c)=(a·b)·(a·c). One can define a sequence of finite left-distributive algebrasA_n, and then take a limit to get an infinite monogenic left-distributive algebraA_∞. Results of Laver and Steel assuming a strong large cardinal axiom imply thatA_∞is free; it is open whether the freeness ofA_∞can be proved without the large cardinal assumption, or even in Peano arithmetic. The main result of this paper is the equivalence of this problem with the existence of a certain algebra of increasing functions on natural numbers, called anembedding algebra. Using this and results of the first author, we conclude that the freeness ofA_∞is unprovable in primitive recursive arithmetic.