Telegram from Ralph Lamberti, Deputy Borough President of Staten Island, to Geraldine Ferraro

Congratulatory telegram from Ralph J. Lamberti, Deputy Borough President of Staten Island, to Geraldine Ferraro. Includes standard response letter from Ferraro, and a data entry sheet.https://ir.lawnet.fordham.edu/vice_presidential_campaign_correspondence_1984_new_york/1266/thumbnail.jp

On a classical spectral optimization problem in linear elasticity

We consider a classical shape optimization problem for the eigenvalues of elliptic operators with homogeneous boundary conditions on domains in the $N$-dimensional Euclidean space. We survey recent results concerning the analytic dependence of the elementary symmetric functions of the eigenvalues upon domain perturbation and the role of balls as critical points of such functions subject to volume constraint. Our discussion concerns Dirichlet and buckling-type problems for polyharmonic operators, the Neumann and the intermediate problems for the biharmonic operator, the Lam\'{e} and the Reissner-Mindlin systems.Comment: To appear in the proceedings of the workshop `New Trends in Shape Optimization', Friedrich-Alexander Universit\"{a}t Erlangen-Nuremberg, 23-27 September 201

Werner states and the two-spinors Heisenberg anti-ferromagnet

We ascertain, following ideas of Arnesen, Bose, and Vedral concerning thermal entanglement [Phys. Rev. Lett. {\bf 87} (2001) 017901] and using the statistical tool called {\it entropic non-triviality} [Lamberti, Martin, Plastino, and Rosso, Physica A {\bf 334} (2004) 119], that there is a one to one correspondence between (i) the mixing coefficient $x$ of a Werner state, on the one hand, and (ii) the temperature $T$ of the one-dimensional Heisenberg two-spin chain with a magnetic field $B$ along the $z-$axis, on the other one. This is true for each value of $B$ below a certain critical value $B_c$. The pertinent mapping depends on the particular $B-$value one selects within such a range

Spectral analysis of the biharmonic operator subject to Neumann boundary conditions on dumbbell domains

We consider the biharmonic operator subject to homogeneous boundary conditions of Neumann type on a planar dumbbell domain which consists of two disjoint domains connected by a thin channel. We analyse the spectral behaviour of the operator, characterizing the limit of the eigenvalues and of the eigenprojections as the thickness of the channel goes to zero. In applications to linear elasticity, the fourth order operator under consideration is related to the deformation of a free elastic plate, a part of which shrinks to a segment. In contrast to what happens with the classical second order case, it turns out that the limiting equation is here distorted by a strange factor depending on a parameter which plays the role of the Poisson coefficient of the represented plate.Comment: To appear in "Integral Equations and Operator Theory

Methanolysis of Poly(lactic Acid) Using Catalyst Mixtures and the Kinetics of Methyl Lactate Production

Polylactic acid (PLA) is a leading bioplastic of which the market share is predicted to increase in the future; its growing production capacity means its end-of-life treatment is becoming increasingly important. One beneficial disposal route for PLA is its chemical recycling via alcoholysis. The alcoholysis of PLA leads to the generation of value-added products alkyl lactates; this route also has potential for a circular economy. In this work, PLA was chemically recycled via methanolysis to generate methyl lactate (MeLa). Four commercially available catalysts were investigated: zinc acetate dihydrate (Zn(OAc)2), magnesium acetate tetrahydrate (Mg(OAc)2), 4-(dimethylamino)pyridine (DMAP), and triazabicyclodecene (TBD). Dual catalyst experiments displayed an increase in reactivity when Zn(OAc)2 was paired with TBD or DMAP, or when Mg(OAc)2 was paired with TBD. Zn(OAc)2 coupled with TBD displayed the greatest reactivity. Out of the single catalyst reactions, Zn(OAc)2 exhibited the highest activity: a higher mol% was found to increase reaction rate but plateaued at 4 mol%, and a higher equivalent of methanol was found to increase the reaction rate, but plateaued at 17 equivalents. PLA methanolysis was modelled as a two-step reversible reaction; the activation energies were estimated at: Ea1 = 25.23 kJ∙mol−1, Ea2 = 34.16 kJ∙mol−1 and Ea-2 = 47.93 kJ∙mol−1

Photo-induced pyridine substitution in cis-[Ru(bpy)(2)(py)(2)]Cl-2 : a snapshot by time-resolved X-ray solution scattering

Determination of transient structures in light-induced processes is a challenging goal for time-resolved techniques. Such techniques are becoming successful in detecting ultrafast structural changes in molecules and do not require the presence of probe-like groups. Here, we demonstrate that TR-WAXS (Time-Resolved Wide Angle X-ray Scattering) can be successfully employed to study the photochemistry of cis-[Ru(bpy)(2)(py)(2)]Cl-2, a mononuclear ruthenium complex of interest in the field of photoactivatable anticancer agents. TR-WAXS is able to detect the release of a pyridine ligand and the coordination of a solvent molecule on a faster timescale than 800 ns of laser excitation. The direct measurement of the photodissociation of pyridine is a major advance in the field of time-resolved techniques allowing detection, for the first time, of the release of a multiatomic ligand formed by low Z atoms. These data demonstrate that TR-WAXS is a powerful technique for studying rapid ligand substitution processes involving photoactive metal complexes of biological interest

Kinetics of Alkyl Lactate Formation from the Alcoholysis of Poly(Lactic Acid)

Alkyl lactates are green solvents that are successfully employed in several industries such as pharmaceutical, food and agricultural. They are considered prospective renewable substitutes for petroleum-derived solvents and the opportunity exists to obtain these valuable chemicals from the chemical recycling of waste poly(lactic acid). Alkyl lactates (ethyl lactate, propyl lactate and butyl lactate) were obtained from the catalysed alcoholysis reaction of poly(lactic acid) with the corresponding linear alcohol. Reactions were catalysed by a Zn complex synthesised from an ethylenediamine Schiff base. The reactions were studied in the 50–130 °C range depending on the alcohol, at autogenous pressure. Arrhenius temperature-dependent parameters (activation energies and pre-exponential factors) were estimated for the formation of the lactates. The activation energies (Ea1, Ea2 and Ea−2) for alcoholysis in ethanol were 62.58, 55.61 and 54.11 kJ/mol, respectively. Alcoholysis proceeded fastest in ethanol in comparison to propanol and butanol and reasonable rates can be achieved in temperatures as low as 50 °C. This is a promising reaction that could be used to recycle end-of-life poly(lactic acid) and could help create a circular production economy

Jensen-Shannon divergence as a measure of distinguishability between mixed quantum states

We discuss an alternative to relative entropy as a measure of distance between mixed quantum states. The proposed quantity is an extension to the realm of quantum theory of the Jensen-Shannon divergence (JSD) between probability distributions. The JSD has several interesting properties. It arises in information theory and, unlike the Kullback-Leibler divergence, it is symmetric, always well defined and bounded. We show that the quantum JSD (QJSD) shares with the relative entropy most of the physically relevant properties, in particular those required for a "good" quantum distinguishability measure. We relate it to other known quantum distances and we suggest possible applications in the field of the quantum information theory.Comment: 14 pages, corrected equation 1