Order Embeddings with Irrational Codomain: Debreu Properties of Real Subsets

The objective of this paper is to investigate the role of the set of irrational numbers as the codomain of order-preserving functions defined on topological totally preordered sets. We will show that although the set of irrational numbers does not satisfy the Debreu property it is still nonetheless true that any lower (respectively, upper) semicontinuous total preorder representable by a real-valued strictly isotone function (semicontinuous or not) also admits a representation by means of a lower (respectively, upper) semicontinuous strictly isotone function that takes values in the set of irrational numbers. These results are obtained by means of a direct construction. Moreover, they can be related to Cantor’s characterization of the real line to obtain much more general results on the semicontinuous Debreu properties of a wide family of subsets of the real line.      

Grafting onto wool. VIII. Graft copolymerization of methyl methacrylate (MMA) by use of Ce4+ -amine system as redox initiator

In an attempt to determine the role of a variety of amines in ceric-ion-initiated grafting, poly-(methyl methacrylate) was graft copolymerized onto Himachali wool in the presence of a variety of amines that included ammonia, diethylamine (DEA), dipropylamine (DPA), triethylamine (TEA), triethanol amine, and pyridine. All amines (with the exception of DEA) reduced the percent grafting. The reactivity of various amines toward graft copolymerization followed the order: DEA > DPA > NH₃ > TEA > triethanol amine > Py. An explanation based on the basicity, nucleophilicity, and steric requirement of amines is given to explain the observed reactivity order shown by the various amines toward graft copolymerization.     

On the Fourier spectrum of symmetric Boolean functions

We study the following questionWhat is the smallest t such that every symmetric boolean function on κ variables (which is not a constant or a parity function), has a non-zero Fourier coefficient of order at least 1 and at most t?We exclude the constant functions for which there is no such t and the parity functions for which t has to be κ. Let τ (κ) be the smallest such t. Our main result is that for large κ, τ (κ)≤4κ/logκ.The motivation for our work is to understand the complexity of learning symmetric juntas. A κ-junta is a boolean function of n variables that depends only on an unknown subset of κ variables. A symmetric κ-junta is a junta that is symmetric in the variables it depends on. Our result implies an algorithm to learn the class of symmetric κ-juntas, in the uniform PAC learning model, in time n ^o(κ) . This improves on a result of Mossel, O’Donnell and Servedio in [16], who show that symmetric κ-juntas can be learned in time n ^2κ/3.     

Bounded Degree, Triangle Avoidance Graph Games

We consider variants of the triangle-avoidance game first defined by Harary and rediscovered by Hajnal a few years later. A graph game begins with two players and an empty graph on n vertices. The two players take turns choosing edges within K _n , building up a simple graph. The edges must be chosen according to a set of restrictions ${\mathcal{R}}$ . The winner is the last player to choose an edge that does not violate any of the restrictions in ${\mathcal{R}}$ . For fixed n and ${\mathcal{R}}$ , one of the players has a winning strategy. For various games where ${\mathcal{R}}$ includes bounded degree and triangle avoidance, we determine the winner for all values of n.     

Temperature dependent small-angle neutron scattering of CTABr—magnetic fluid emulsion

Small-angle neutron scattering studies have been carried out to check the structural integrity of citryltrimethylammonium bromide (CTABr) micelles in a magnetic fluid for different magnetic fluid concentrations at two different temperatures 303 and 333 K. It is found that the CTABr micelles grow with increasing magnetic fluid concentration and there is a decrease in the micellar size with increase in temperature.     

Spectroscopy of50V with (p,nγ) reaction

Information on the low-lying levels up to ～1.9 MeV excitation of the doubly odd nucleus⁵⁰V has been obtained through the Ge (Li)-Ge (Li) coincidence study with the⁵⁰Ti(p, nγ)⁵⁰V reaction. Branching ratios have been measured and tentative spin-parity assignments have been made. A detailed comparison with other measurements reported recently has also been made. Using the lowest seniority wave functions with (f_7/2) _p ³ (f _7/2) _n ^?1 configuration, energy levels and electromagnetic properties have been calculated. These have been compared with the present and earlier experimental data.     

The photodegradation of cadmium yellow paints in Henri Matisse’s Le Bonheur de vivre (1905–1906)

Evidence for the alteration of the yellow paints in Henri Matisse’s Le Bonheur de vivre (1905–1906, The Barnes Foundation) has been observed since the 1990s. The changes in this iconic work of Matisse’s Fauvist period include lightening, darkening, and flaking of the yellow paints. Handheld X-ray fluorescence (XRF) and multispectral imaging surveys reveal that the degradation is confined to cadmium yellow (CdS) paints. The discoloration of cadmium yellow paints in Impressionist, Post-Impressionist and early modernist work from the 1880s through the 1920s has been ascribed to the photo-oxidative degradation of CdS. Preliminary investigations of the degraded yellow paints in this work involved Cd L_III-edge X-ray Absorption Near Edge Spectroscopy (XANES) at the Stanford Synchrotron Radiation Light Source (SSRL Menlo Park, California) and Scanning Electron Microscopy-energy dispersive X-ray analysis (SEM-EDS) at the Winterthur Museum Scientific Research and Analysis Laboratory. To determine if the visual changes in the paints did in fact indicate photo-oxidative degradation and if different chemistries could be observed for the lightened versus darkened regions, synchrotron radiation-micro Fourier Transform InfraRed (SR-μFTIR) spectroscopy, X-ray Fluorescence (SR-μXRF) mapping and micro X-ray Absorption Near Edge Spectroscopy (μXANES) mapping at the Cd L_III-edge of the altered paint cross-sections were carried out at the European synchrotron radiation facility (ESRF, Grenoble, France) beamline ID-21. The goal is to elucidate the discoloration mechanisms observed in the paint using elemental and speciation mapping. The μXANES mapping and SR-FTIR imaging showed a substantial enrichment of CdCO₃ in the off-white surface crust of the faded/discolored CdS paint. This suggests that the CdCO₃ is present as an insoluble photodegradation product rather than solely a paint filler or starting reagent. Additionally, oxalates and sulfates were found to be concentrated at the alteration surface.     

Observation of inverse Meyer–Neldel rule in thermally activated crystallization of a hybrid composite of phenol formaldehyde

We report the inverse Meyer–Neldel (MN) rule in the thermally activated crystallization of a hybrid composite of phenol formaldehyde using two experimental approaches. In the first experiment, the annealing time dependence of the pre-exponential factor K ₀ and the activation energy of crystallization E _c were studied. In the second experiment, the annealing temperature dependence of the same parameters was investigated. We observed the inverse Meyer–Neldel rule between the pre-exponential factor K ₀ and the activation energy of crystallization E _c in both cases.     

Hybrid systems through natural product leads: an approach towards new molecular entities

Hybrid systems are constructs of different molecular entities, natural or unnatural, to generate functional molecules in which the characteristics of various components are modulated, amplified or give rise to entirely new properties. These hybrids can be designed from carefully selected components either through domain integration of key structural/functional features or via straightforward covalent linkages. Some of the recently reported hybrid systems based on steroid, carbohydrate, C60-fullerene platforms, amongst others, mainly crafted with the object of enhancement of the therapeutical spectrum, will be discussed.