On m-Ary Overpartitions

Presently there are a lot of activities in the study of overpartitions, objects that were discussed by MacMahon, and which have recently proven useful in several combinatorial studies of basic hypergeometric series. In this paper we study some similar objects, which we name m-ary overpartitions. We consider divisibility properties of the number of m-ary overpartitions of a natural number, and we prove a theorem which is a lifting to general m of the well-known Churchhouse congruences for the binary partition function. Received October 11, 2004     

A study of the B2 excited state geometries of the metal-metal quadruply bonded compounds Mo2X4(PMe3)4 (X = Cl, Br or I)

The excited state geometries of the metal-metal quadruply bonded compounds Mo₂X₄(PMe₃)₄ (X = Cl, Br or I) have been studied by means of resonance Raman and absorption spectroscopy. A fit of the parameters of a simple theoretical model to the experimental data indicates that the metal-metal bond increases some 10 pm on excitation to the ¹B₂ (δδ^*) state, whereas other geometric changes are small. Furthermore, the phenomenological lifetime factor of the excited state, Γ, is found to be dependent on the vibrational quantum number, ν, of this state.     

Gluon bremsstrahlung in e+e− annihilation: (II). Gluon polarization

The linear and circular polarizations of gluons emitted in electron-positron annihilation, $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→}\text{q}\text{q}\text{g}$, are evaluated, including neutral current and beam polarization effects. For the lower part of the gluon bremsstrahlung spectrum, the linear polarization is found to be large and the plane of polarization to be almost parallel to the q$\text{q}$g event plane. The neutral current induced circular polarization is in the upper part of the gluon spectrum of the order of 10–15% at 40 GeV total energy and reaches ～50% at asymptotic energies.     

The variation in γ-ray multiplicity with nuclear temperature studied in 160Dy

A novel method of obtaining detailed infromation on the level density far above the yrast line is described. The γ-ray multiplicity as a function of excitation energy in ¹⁶⁰Dy is studied by means of the ${}^{161}\text{Dy}\text{(}{}^3\text{He}\text{, α)}{}^{160}\text{Dy}$ reaction.     

Kazama-Yang monopole-fermion bound states: (I). Analytic results

We present explicit, approximate, remarkably precise results for the Kazama-Yang monopole-fermion binding energies and wave functions. The results are valid for the states of lowest angular momentum and for the binding energy M ? E ? M. They agree very well with the numerically calculated values.     

Free radical conformations and conversions in X-irradiated single crystals of L-cysteic acid by electron magnetic resonance and density functional theory studies

Single crystals of L-cysteic acid monohydrate were X-irradiated and studied at 295 K using EPR, ENDOR, and EIE techniques. Three spectroscopically different radicals were observed. These were a deamination radical reduction product (R1), and two oxidation products formed by hydrogen abstraction (radicals R2, R3). R2 and R3 were shown to exhibit the same chemical structure while exhibiting very different geometrical conformations. Cluster DFT calculations at the 6-31G(d,p) level of theory supported the experimental observations for radicals R1 and R2. It was not possible to simulate the R3 radical in any attempted cluster; hence, for this purpose a single molecule approach was used. The precursor radicals for R1, R2, and R3, identified in the low-temperature work on L-cysteic acid monohydrate by Box and Budzinski, were also investigated using DFT calculations. The experimentally determined EPR parameters for the low-temperature decarboxylated cation could only be reproduced correctly within the cluster when the carboxyl group remained in the proximity of the radical. Only one of the two observed low-temperature carboxyl anions (stable at 4 and 48 K) could be successfully simulated by the DFT calculations. Evidence is presented in support of the conclusions that the carboxyl reduction product already is protonated at 4 K and that the irreversible conversion between the two reduction products is brought forward by an umbrella-type inversion of the carboxyl group.     

A High Pressure Operando Spectroscopy Examination of Bimetal Interactions in ‘Metal Efficient’ Palladium/In2O3/Al2O3 Catalysts for CO2 Hydrogenation

CO₂ hydrogenation to methanol has the potential to serve as a sustainable route to a wide variety of hydrocarbons, fuels and plastics in the quest for net zero. Synergistic Pd/In₂O₃ (Palldium on Indium Oxide) catalysts show high CO₂ conversion and methanol selectivity, enhancing methanol yield. The identity of the optimal active site for this reaction is unclear, either as a Pd−In alloy, proximate metals, or distinct sites. In this work, we demonstrate that metal-efficient Pd/In₂O₃ species dispersed on Al₂O₃ can match the performance of pure Pd/In₂O₃ systems. Further, we follow the evolution of both Pd and In sites, and surface species, under operando reaction conditions using X-ray Absorption Spectroscpy (XAS) and infrared (IR) spectroscopy. In doing so, we can determine both the nature of the active sites and the influence on the catalytic mechanism.     

A pH-metric, UV, NMR, and X-ray crystallographic study on arsenous acid reacting with dithioerythritol

The aqueous solutions of arsenous acid with the meso and racemic forms of 1,4-dithiol-butane-2,3-diol, namely, dithioerythritol (dte) and dithiothreitol (dtt), respectively, were titrated pH-metrically in different molar ratios. The p K a values determined for As(OH) 3, and dtt were in good accordance with the literature data, and we determined for the first time the p K a value of dte. The deprotonation steps of both M (As(OH) 3 considered as a central metal ion) and H 2L components dte and dtt (considered as ligands) appeared at a higher pH in the titration curves of the ternary systems (M, H 2L, H (+)) than in the individual component. This unusual observation is explained by the condensation reactions between the reagents taking place in the pH < 8 range. In the solutions of c As(III) > 5.10 (-3) M, the precipitate formed upon mixing the arsenous acid and H 2L solutions in neutral medium, and the formation of the precipitate shifted toward acidic pH on the increase of the total concentrations. This indicated that pH-metry can follow the reactions only in an indirect way. Useful, but not satisfactory, information can be obtained by means of this method alone. Combined with NMR and UV spectroscopic measurements it is revealed that depending on the As(III)/H 2L molar ratio, different complexes form in the solutions. In the species with 1:2 composition, one of the ligands is strongly bound to the arsenic(III) probably via its two thiolate, while the second one is attached only weakly. The crystal structure of an As(III)-dte crystal of 1:1 composition, grown from ethanolic solution, shows that As(III) binds the ligand through its three p-orbitals in a manner similar to that expected in aqueous solution. While the uptake of the second ligand cannot be detected by pH-metry, the decomposition of thioether bonds above pH approximately 10 is confirmed by the change in UV spectra at approximately 265 nm to be a base-consuming process. In such alkaline solutions, most probably, rearrangement of the bonding scheme occurs, resulting in ligands being bound to the arsenic(III) through the oxygen donor atoms.     

Directed Data-Processing Inequalities for Systems with Feedback

We present novel data-processing inequalities relating the mutual information and the directed information in systems with feedback. The internal deterministic blocks within such systems are restricted only to be causal mappings, but are allowed to be non-linear and time varying, and randomized by their own external random input, can yield any stochastic mapping. These randomized blocks can for example represent source encoders, decoders, or even communication channels. Moreover, the involved signals can be arbitrarily distributed. Our first main result relates mutual and directed information and can be interpreted as a law of conservation of information flow. Our second main result is a pair of data-processing inequalities (one the conditional version of the other) between nested pairs of random sequences entirely within the closed loop. Our third main result introduces and characterizes the notion of in-the-loop (ITL) transmission rate for channel coding scenarios in which the messages are internal to the loop. Interestingly, in this case the conventional notions of transmission rate associated with the entropy of the messages and of channel capacity based on maximizing the mutual information between the messages and the output turn out to be inadequate. Instead, as we show, the ITL transmission rate is the unique notion of rate for which a channel code attains zero error probability if and only if such an ITL rate does not exceed the corresponding directed information rate from messages to decoded messages. We apply our data-processing inequalities to show that the supremum of achievable (in the usual channel coding sense) ITL transmission rates is upper bounded by the supremum of the directed information rate across the communication channel. Moreover, we present an example in which this upper bound is attained. Finally, we further illustrate the applicability of our results by discussing how they make possible the generalization of two fundamental inequalities known in networked control literature.     

Non-Isotropic Cusp Conditions and Regularity of the Electron Density of Molecules at the Nuclei

We investigate regularity properties of molecular one-electron densities ρ near the nuclei. In particular we derive a representation