Nuclearity of a nonnegative definite integral kernel on a separable metric space

The aim of this paper is to characterize the nuclearity of an integral operator, defined by a continuous non-negative definite square integrable kernel on a separable metric space, in terms of the integrability of the trace of the kernel function. Nuclearity here plays a role forU-statistics.     

Side‐chain crystallization behavior of graft copolymers consisting of an amorphous main chain and crystalline side chains. II. Poly(n‐hexyl methacrylate)‐graft‐poly(ethylene glycol)

The phase behavior and crystallization of graft copolymers consisting of poly(n‐hexyl methacrylate) (PHMA) as an amorphous main chain and poly(ethylene glycol) (PEG) as crystallizable side chains (HMAx with 15 ≤ x ≤ 73, where x represents the weight percentage of PEG) were investigated. Small‐angle X‐ray scattering profiles measured above the melting temperature of PEG suggested that a microdomain structure with segregated PHMA and PEG domains was formed in HMA40 and HMA46. This phase behavior was qualitatively described by a calculated phase diagram based on the mean‐field theory. Because of the segregation of PEG into microdomains, the crystallization temperature of the PEG side chains in HMAx was higher than that in poly(methyl acrylate)‐graft‐poly(ethylene glycol) having a similar value of x, which was considered to be in a disordered state above the melting temperature. In HMAx with x ≤ 40, PEG crystallization was strongly restricted, probably because the PEG microdomains were isolated in the PHMA matrix. As a result, the growth of PEG spherulite was not observed because the PEG crystallization occurred after vitrification of the PHMA segregated domains. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 129–137, 2007     

Basic study of the gelation of dimethacrylate‐type crosslinking agents

An investigation was made of the gelation of dimethacrylate‐type crosslinking agents in view of an application for separation media. The study mainly centered on a crosslinking agent, glycerol dimethacrylate (GDMA), which is relatively hydrophilic because of a hydroxyl group in the middle of its structure. The gelation of GDMA was compared with that of other hydrophobic crosslinking agents such as ethylene glycol dimethacrylate and 1,6‐hexanediol dimethacrylate. The diluents used in the study were toluene, toluene with methanol, and cyclohexanol. The gelation was observed in real time with a charge coupled device camera and dynamic light scattering (DLS). Also, the separated dry gels were extensively characterized with scanning electron microscopy, BET (N₂ absorption and desorption isotherm), and Fourier transform infrared. DLS analysis showed a stronger molecular interaction of GDMA gelation in toluene, whereas this interaction was much weaker in an alcoholic solvent such as toluene with methanol or cyclohexanol. This indicated that GDMA gelation might proceed through hydrogen bonding as well as a crosslinking reaction of vinyl groups. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 949–958, 2006     

Glycopolymeric inhibitors of β‐glucuronidase. III. Configurational effects of hydroxy groups in pendant glyco‐units in polymers upon inhibition of β‐glucuronidase

Two kinds of new glycopolymers, (P(VB‐1‐GlcaH‐co‐AAm), 9 ) and (P(VB‐1‐Glco‐co‐AAm), 10 ), were synthesized through the radical copolymerization of styrene derivatives bearing pendant D ‐glucaric and D ‐gluconic moieties, N‐(p‐vinylbenzyl)‐1‐D ‐glucaramide (VB‐1‐GlcaH, 7 ), and N‐(p‐vinylbenzyl)‐D ‐gluconamide (VB‐1‐Glco, 8 ), with acrylamide (AAm). Glycopolymer 9 bearing the pendant glucaric moiety at the first position inhibited the hydrolysis of a model compound for xenobiotics‐β‐glucuronide conjugates, p‐nitrophenyl β‐D ‐glucuronide, uncompetitively, in contrast to the competitive inhibition in the presence of the corresponding isomeric glycopolymer bearing the pendant D ‐glucaric unit at the sixth position (P(VB‐6‐GlcaH‐co‐AAm), 3 ) reported in our previous article. On the other hand, another copolymer 10 bearing the gluconic moiety was found not to inhibit the hydrolysis as well as the corresponding copolymer bearing pendant gulonic unit (P(VB‐6‐Glco‐co‐AAm), 4 ). These results indicate that the hydrolysis is influenced not only by existence of pendant carboxyl units but also by the direction on the linkage of the glyco‐units to the polymer frame. Therefore the configurational position of hydroxy groups in pendant glyco‐units in macromolecular inhibitors may be essential for the interaction with β‐glucuronidase. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4895–4903, 2006     

Spectrophotometric determination of anthracycline anticancer agents with aluminum(III) and chromazurol S in a nonionic surfactant micellar medium.

A simple and highly sensitive spectrophotometric method for the determination of anthracycline anticancer agents, such as Daunorubicin hydrochloride (DAU), was established by using aluminum(III) and Chromazurol S (CAS) in a nonionic surfactant micellar medium. In the case of determination of DAU, the apparent molar absorptivity was 1.3 x 10(5) dm3 mol(-1) cm(-1) at 615 nm. Beer's law was obeyed in the concentration range of 0.028 - 2.82 microg ml(-1) for DAU. Owing to no need for solvent extraction, this method could be applied to assays of DAU and related drugs in pharmaceutical preparations.     

Spurious Shell Closures in the Relativistic Mean Field Model

Following a previous systematic theoretical study of the ground-state properties of over 7000 nuclei from the proton drip line to the neutron drip line in the relativistic mean field model [Prog. Theor. Phys. 113 （2005） 785], which is in fair agreement with existing experimental data, we observe a few spurious shell closures, i.e. proton shell closures at Z = 58 and Z = 92. These spurious shell closures are found to persist in all the effective forces of the relativistic mean field model, e.g. TMA, NL3, PKDD and DD-ME2.     

On the dimension to represent a graph by a unit distance graph

It is proved that if a graphG has maximum degreed, then its vertices can be represented by distinct unit vectors inR ^2d so that two vectors are orthogonal if and only if the corresponding vertices are adjacent. As a corollary it follows that if a graph has maximum degreed, then it is isomorphic to a unit distance graph inR ^2d.     

A threshold for the size of random caps to cover a sphere

Consider a unit sphere on which are placed N random spherical caps of area 4p(N). We prove that if % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% qGSbGaaeyAaiaab2gaaaWaaeWaaeaacaWGWbWaaeWaaeaacaWGobaa% caGLOaGaayzkaaGaai4Taiaad6eacaGGVaGaaeiBaiaab+gacaqGNb% Gaaeiiaiaad6eaaiaawIcacaGLPaaacqGH8aapcaaIXaaaaa!454E!\[\overline {{\rm{lim}}} \left( {p\left( N \right)\cdotN/{\rm{log }}N} \right) < 1\], then the probability that the sphere is completely covered by N caps tends to 0 as N , and if % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaWaaaeaaca% qGSbGaaeyAaiaab2gaaaWaaeWaaeaacaWGWbWaaeWaaeaacaWGobaa% caGLOaGaayzkaaGaai4Taiaad6eacaGGVaGaaeiBaiaab+gacaqGNb% Gaaeiiaiaad6eaaiaawIcacaGLPaaacqGH+aGpcaaIXaaaaa!4551!\[\underline {{\rm{lim}}} \left( {p\left( N \right)\cdotN/{\rm{log }}N} \right) > 1\], then for any integer n>0 the probability that each point of the sphere is covered more than n times tends to 1 as N .