On zonoids whose polars are zonoids

Zonoids whose polars are zonoids cannot have proper faces other than vertices or facets. However, there exist non-smooth zonoids whose polars are zonoids. Examples in ℝ and ℝ are given. Supported in part by the United States-Israel Binational Science Foundation.     

The crystal structure of the inorganic surface films formed on Mg and Li intercalation compounds and the electrode performance

A crystallographic approach was applied to elucidate the influence of the nature of the surface films on the electrochemical behavior of Li and Mg intercalation compounds. This paper presents two examples: (1) protection of graphite electrodes by Li₂CO₃ surface films, and (2) the unique electrochemical behavior of Mg-containing Chevrel phases (MgCP) obtained by different synthetic routes. In the former case, the elucidation of the protection mechanism and the explanation of the high performance of such protected electrodes are based on the analysis of possible Li-ion motion in the carbonate crystal structure. In the latter case, a combination of synthesis, electrochemistry and XRD analysis was used to explain an unusual phenomenon: the difference between the excellent electrochemical behavior of the Chevrel phase (CP) based on Cu-leached Cu₂Mo₆S₈ (CuCP), and the poor electrochemical activity of the high-temperature synthesized MgCP, with the same phase composition. It is shown that this phenomenon is caused by MgO formation on the surface of the latter material. The different surface chemistry of the MgCPs obtained by the two different synthetic routes was substantiated by revealing the correlation between the electrochemical activity and the chemical stability of these materials under ambient atmosphere conditions. Dedicated to Prof. Mikhail A. Vorotyntsev on the occasion of his 60th birthday.     

Self-avoiding walks on random fractal environments

Self-avoiding random walks (SAWs) are studied on several hierarchical lattices in a randomly disordered environment. An analytical method to determine whether their fractal dimensionD _saw is affected by disorder is introduced. Using this method, it is found that for some lattices,D _saw is unaffected by weak disorder; while for othersD _saw changes even for infinitestimal disorder. A weak disorder exponent is defined and calculated analytically [ measures the dependence of the variance in the partition function (or in the effective fugacity per step)vL on the end-to-end distance of the SAW,L]. For lattices which are stable against weak disorder (<0) a phase transition exists at a critical valuev=v ^* which separates weak- and strong-disorder phases. The geometrical properties which contribute to the value of are discussed.     

Amplified DNA sensing and immunosensing by the rotation of functional magnetic particles

Amplified chemiluminescent detection of DNA-complementary DNA or of antigen-antibody interactions is accomplished in the presence of rotating functionalized magnetic particles.     

Studies of the Synthesis of Diethyl Cyclopropylphosphonate and Its Thio and Seleno Analogs

Two methods for the synthesis of unsubstituted diethyl cyclopropylphosphonate are described. One method is a reaction between cyclopropylmagnesium bromide and diethyl chlorophosphite to give diethyl cyclopropylphosphonite, followed by oxidation with sodium periodate to the corresponding phosphonate. Alternatively, diethyl cyclopropylphosphonite was reacted with elemental sulfur or selenium to give the thio and seleno analogs, respectively. The second method involves exclusive 1,3‐elimination of HBr from diethyl 3‐bromopropylphosphonate. This method can be directed to either the 1,2‐ or the 1,3‐elimination reaction, leading to propenylphosphonate or cyclopropylphosphonate, depending on the solvent used.     

Correlation between Ferromagnetic Layer Easy Axis and the Tilt Angle of Self Assembled Chiral Molecules

The spin–spin interactions between chiral molecules and ferromagnetic metals were found to be strongly affected by the chiral induced spin selectivity effect. Previous works unraveled two complementary phenomena: magnetization reorientation of ferromagnetic thin film upon adsorption of chiral molecules and different interaction rate of opposite enantiomers with a magnetic substrate. These phenomena were all observed when the easy axis of the ferromagnet was out of plane. In this work, the effects of the ferromagnetic easy axis direction, on both the chiral molecular monolayer tilt angle and the magnetization reorientation of the magnetic substrate, are studied using magnetic force microscopy. We have also studied the effect of an applied external magnetic field during the adsorption process. Our results show a clear correlation between the ferromagnetic layer easy axis direction and the tilt angle of the bonded molecules. This tilt angle was found to be larger for an in plane easy axis as compared to an out of plane easy axis. Adsorption under external magnetic field shows that magnetization reorientation occurs also after the adsorption event. These findings show that the interaction between chiral molecules and ferromagnetic layers stabilizes the magnetic reorientation, even after the adsorption, and strongly depends on the anisotropy of the magnetic substrate. This unique behavior is important for developing enantiomer separation techniques using magnetic substrates.     

Derivatives of the L-cosine transform

The L^p-cosine transform of an even, continuous function is defined by

     

Truthful mechanism design via correlated tree rounding

A powerful algorithmic technique for truthful mechanism design is the maximal-in-distributional-range (MIDR) paradigm. Unfortunately, many such algorithms use heavy algorithmic machinery, e.g., the ellipsoid method and (approximate) solution of convex programs. In this paper, we present a correlated rounding technique for designing mechanisms that are truthful in expectation. It is elementary and can be implemented quickly. The main property we rely on is that the domain offers fractional optimum solutions with a tree structure. In auctions based on the generalized assignment problem, each bidder has a publicly known knapsack constraint that captures the subsets of items that are of value to him. He has a private valuation for each item and strives to maximize the value of assigned items minus payment. For this domain we design a truthful 2-approximate MIDR mechanism for social welfare maximization. It avoids using the ellipsoid method or convex programming. In contrast to some previous work, our mechanism achieves exact truthfulness. In restricted-related scheduling with selfish machines, each job comes with a public weight, and it must be assigned to a machine from a public job-specific subset. Each machine has a private speed and strives to maximize payments minus workload of jobs assigned to it. Here we design a mechanism for makespan minimization. This is a single-parameter domain, but the approximation status of the optimization problem is similar to unrelated machine scheduling: The best known algorithm obtains a (non-truthful) 2-approximation for unrelated machines, and there is 1.5-hardness. Our mechanism matches this bound with a truthful 2-approximation.