Moments of the probability density functions of error terms in divisor problems

We derive an explicit formula for the moments of the probability density function of a class of functions. An application of this shows that the density function of the error term in the Pilz divisor problem is asymmetric.

     

PHOTOTOXICITY OF (1H-INDENYL)THIOPHENES

The (1 H -indenyl)thiophene derivatives 2 and 3 were recently reported to be excellent singlet oxygen sensitizers. comparable to α-terthienyl (1). The phototoxicity of these compounds was compared, using human erythrocytes, Aedes aegypti mosquito larvae. Daphnia magna . and fish (fathead minnows, Pimephales promelas ). The known ranking of the photooxidation properties was found to be a good predictor of phototoxic properties in erythrocytes and mosquito larvae but not in daphnias. All three compounds photosensitized the cleavage of supercoiled pBR322 DNA to the same extent.     

Modification of the structure and properties of poly(vinylidene fluoride–trifluoroethylene) 56/44 mol % copolymer by a proton‐irradiation treatment

The effects of high‐energy proton irradiation on the structure and properties of 56/44 mol % poly(vinylidene fluoride–trifluoroethylene) copolymer were studied with differential scanning calorimetry (DSC), X‐ray diffraction (XRD), relative permittivity, and polarization hysteresis measurements. Copolymer films prepared by hot compression molding were irradiated with a broad range of proton dosages (10–107 Mrad) at room temperature. The DSC results showed that the ferroelectric transition was strongly affected by the proton dosages. The XRD data indicated the reduction of polar ordering in the copolymer by the proton‐irradiation treatment. From the relative permittivity and polarization behavior, the copolymer film was found to be converted from a normal ferroelectric material to a relaxor ferroelectric material as the proton dosage was increased to 50 Mrad. The electrostrictive coefficient of the 56/44 mol % copolymer was enhanced after irradiation, and the optimized proton dosage for attaining the highest electrostrictive strain response was determined. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2334–2339, 2005     

Laser spectroscopy measurements of neutron-rich tellurium isotopes by COMPLIS

Laser spectroscopy based on resonant ionization of laser-desorbed atoms has been used to study the neutron-rich tellurium isotopes with the COMPLIS facility at ISOLDE-CERN. Isotope shifts and hyperfine structures of several neutron-rich Te isotopes: ^120?136Te and ^{123 m?133 m}Te have been measured. From the hyperfine structure we have extracted magnetic and quadrupole moments. Changes in the mean square charge radii have been deduced and their comparison with the known data for the other elements near Z?=?50 is presented. The experimental δ?<?r ²> values are compared with those obtained from relativistic mean field calculations.     

A Lower Bound for the Dimension of Trivariate Spline Spaces

We consider trivariate C^r spline spaces of degree d defined on arbitrary tetrahedral partitions. A lower bound for the dimension of trivariate spline spaces over arbitrary tetrahedral partitions for d > r is computed. This is the first general lower bound known.     

Classification of Integral Expanding Matrices and Self-Affine Tiles

   Abstract. Let T be a self-affine tile that is generated by an expanding integral matrix A and a digit set D . It is known that many properties of T are invariant under the Z -similarity of the matrix A . In [LW1] Lagarias and Wang showed that if A is a 2 × 2 expanding matrix with |det(A)| = 2 , then the Z -similar class is uniquely determined by the characteristic polynomial of A . This is not true if |det(A)| > 2. In this paper we give complete classifications of the Z -similar classes for the cases |det(A)| =3, 4, 5 . We then make use of the classification for |det(A)| =3 to consider the digit set D of the tile and show that μ(T) >0 if and only if D is a standard digit set. This reinforces the conjecture in [LW3] on this.     

Convenient expressions for computing the exact annual cost of a continuous-review (<Emphasis Type="Italic">Q</Emphasis>,<Emphasis Type="Italic">R</Emphasis>) system with backordering

For a continuous-review order-quantity reorder point system, the ‘average on-hand inventory level’ (‘AOI’) is often computed by the approximate Hadley–Whitin expression, while the exact AOI is given by a double integral that appears daunting to both students and practitioners. This paper presents exact AOI expressions that are simple enough to be executed by the most basic business softwares. Numerical examples are provided to illustrate the ease of using these expressions as well as the necessity of using them in situations where the standard Hadley–Whitin approximation becomes too inaccurate.     

Economic freedom ranking of 161 countries in year 2000: a minimum disagreement approach

Since 1995, the Heritage Foundation has published the economic freedom index for countries throughout the world. The fundamental challenge is how to objectively measure economic freedom so that the index can be fair, credible and has the least disagreements among all countries. In this paper, we propose a new approach to construct economic freedom ranking which minimizes disagreements among countries. The mathematical model consists of two stages: (1) calculate the set of weights for each country which would give each country the best ranking, and (2) aggregation of ranks from all countries to minimize their disagreements. We apply the model to the data set of year 2000 on Economic Freedom from the Heritage Foundation, and find that the minimum disagreements from the proposed ranking improves by 9%.     

Ca2+‐Induced Oxygen Generation by FeO42− at pH 9–10

Although FeO₄^2? (ferrate(IV)) is a very strong oxidant that readily oxidizes water in acidic medium, at pH 9–10 it is relatively stable (<2 % decomposition after 1 h at 298 K). However, FeO₄^2? is readily activated by Ca²⁺ at pH 9–10 to generate O₂. The reaction has the following rate law: d[O₂]/dt=k_Ca[Ca²⁺][FeO₄^2?]². ¹⁸O‐labeling experiments show that both O atoms in O₂ come from FeO₄^2?. These results together with DFT calculations suggest that the function of Ca²⁺ is to facilitate O–O coupling between two FeO₄^2‐ions by bridging them together. Similar activating effects are also observed with Mg²⁺ and Sr²⁺.     

Palladium‐Catalyzed Arylation of Carbasugars Enables the Discovery of Potent and Selective SGLT2 Inhibitors

Selective inhibition of the transporter protein sodium‐glucose cotransporter 2 (SGLT2) has emerged as a promising way to control blood glucose level in diabetes patients. Reported herein is a short and convergent synthetic route towards some small‐molecule SGLT2 inhibitors by a chemo‐ and diastereospecific palladium‐catalyzed arylation reaction. This synthetic strategy enabled the discovery of two highly selective and potent SGLT2 inhibitors, thereby paving the way towards the development of carbasugar SGLT2 inhibitors as potential antidiabetic/antitumor agents.