Binary Representations of Finite Fields and Their Application to Complexity Theory

Binary representations of finite fields are defined as an injective mapping from a finite field tol-tuples with components in {0, 1} where 0 and 1 are elements of the field itself. This permits one to study the algebraic complexity of a particular binary representation, i.e., the minimum number of additions and multiplications in the field needed to compute the binary representation. The two-way complexity of a binary representation is defined as the sum of the algebraic complexities of the binary representation and of its inverse mapping. Two particular binary representations are studied: the standard representation and the logarithmic representation. A method of surrogate computation is developed and used to deduce relationships between the algebraic complexities of certain functions. The standard representation of a finite field is shown to be among the two-way easiest representations of this field. In particular, the standard representation of a finite field with characteristicpis two-way easy wheneverp− 1 has only small prime factors. For any finite field having a two-way easy binary representation, the algebraic complexity in this field is shown to be essentially equivalent to Boolean circuit complexity. For any finite field, the Boolean circuit complexity of Zech's (or Jacobi's) logarithm is shown to be closely related to the Boolean circuit complexity of the discrete logarithm problem that is used in public-key cryptography.     

Binding energies of hydrogen molecules to isoreticular metal-organic framework materials

Recently, several novel isoreticular metal-organic framework (IRMOF) structures have been fabricated and tested for hydrogen storage applications. To improve our understanding of these materials, and to promote quantitative calculations and simulations, the binding energies of hydrogen molecules to the MOF have been studied. High-quality second-order Moller-Plesset (MP2) calculations using the resolution of the identity approximation and the quadruple zeta QZVPP basis set were used. These calculations use terminated molecular fragments from the MOF materials. For H2 on the zinc oxide corners, the MP2 binding energy using Zn4O(HCO2)6 molecule is 6.28 kJ/mol. For H2 on the linkers, the binding energy is calculated using lithium-terminated molecular fragments. The MP2 results with coupled-cluster singles and doubles and noniterative triples method corrections and charge-transfer corrections are 4.16 kJ/mol for IRMOF-1, 4.72 kJ/mol for IRMOF-3, 4.86 kJ/mol for IRMOF-6, 4.54 kJ/mol for IRMOF-8, 5.50 and 4.90 kJ/mol for IRMOF-12, 4.87 and 4.84 kJ/mol for IRMOF-14, 5.42 kJ/mol for IRMOF-18, and 4.97 and 4.66 kJ/mol for IRMOF-993. The larger linkers are all able to bind multiple hydrogen molecules per side. The linkers of IRMOF-12, IRMOF-993, and IRMOF-14 can bind two to three, three, and four hydrogen molecules per side, respectively. In general, the larger linkers have the largest binding energies, and, together with the enhanced surface area available for binding, will provide increased hydrogen storage. We also find that adding up NH2 or CH3 groups to each linker can provide up to a 33% increase in the binding energy.     

Penning ionization electron spectrometry of hydrogen chloride

An electron spectrometric study has been performed on HCl using metastable helium and neon atoms as well as neon resonance photons. High resolution electron spectra were obtained with two different beam apparatuses for a mixed He(2¹ S, 2³ S) beam, a pure He(2³ S) beam, and, for the first time, state-selected pure Ne(3s ³ P ₂) and pure Ne(3s ³ P ₀) beams, and for NeI resonance photons. For the system He(2³ S)+HCl the vibrational populationsP(υ′) of the formed HCl⁺ (X ²∏ _i , υ′) and HCl⁺ (A ²Ω⁺, υ′) ions are found to differ from the Franck-Condon factors for unperturbed potentials, indicating slight bond stretching in HCl upon He(2³ S) approach. For He(2¹ S)+HCl the vibrational peak shapes and vibrational populations are substantially different from the He(2³ S) case, pointing to an additional, charge exchanged interaction (He⁺+HCl^?) in the entrance channel of the former system. For the first time, we have detected the electrons in both the He(2¹ S)+HCl and He(2³ S)+HCl spectra associated with the major mechanism for the formation of Cl⁺ ions: energy transfer to repulsive HCl** Rydberg states, dissociating toH(1s) and autoionizing Cl**(¹ D ₂ nl) atoms. For both Ne(³ P ₂)+HCl and Ne(³ P ₀)+HCl, the populationsP(υ′) of both final molecular states HCl⁺ (X, A) agree closely with the Franck-Condon factors at the average relative collision energyē _coll=55 meV and, for HCl⁺ (A ²Ω⁺), also atē _coll=130 meV.     

Nucleation and Growth Synthesis of Siloxane Gels to Form Functional,Monodisperse, and Acoustically Programmable Particles

Nucleation and growth methods offer scalable means of synthesizing colloidal particles with precisely specified size for applications in chemical research, industry, and medicine. These methods have been used to prepare a class of silicone gel particles that display a range of programmable properties and narrow size distributions. The acoustic contrast factor of these particles in water is estimated and can be tuned such that the particles undergo acoustophoresis to either the pressure nodes or antinodes of acoustic standing waves. These particles can be synthesized to display surface functional groups that can be covalently modified for a range of bioanalytical and acoustophoretic sorting applications.     

Equilibrium and structural characterization of ofloxacin–cyclodextrin complexation

The enantiomer-specific characterization of ofloxacin–cyclodextrin complexes was carried out by a set of complementary analytical techniques. The apparent stability constants of the ofloxacin enantiomers with 20 different cyclodextrins at two different pH values were determined to achieve good resolution capillary electrophoresis enantioseparation either to establish enantioselective drug analysis assay, or to interpret and design improved host–guest interactions at the molecular level. The cyclodextrins studied differed in the nature of substituents, degree of substitution (DS), charge and purity, allowing a systematic test of these properties on the complexation. The seven-membered beta-cyclodextrin and its derivatives were found to be the most suitable hosts. Highest stability and best enantioseparation were observed for the carboxymethylated-beta-cyclodextrin (DS ~ 3.5). The effect of substitution pattern (SP) was investigated by molecular modeling, verifying that SP greatly affects the complex stability. Induced circular dichroism was observed and found especially significant on carboxymethylated-beta-cyclodextrin. The complex stoichiometry and the geometry of the inclusion complexes were determined by ¹H NMR spectroscopy, including 2D ROESY techniques. Irrespective of the kind of cyclodextrin, the complexation ratio was found to be 1:1. The alfa-cyclodextrin cavity can accommodate the oxazine ring only, whereas the whole tricyclic moiety can enter the beta- and gamma-cyclodextrin cavities. These equilibrium and structural information offer molecular basis for improved drug formulation.     

Evaluation of Redox Activity of Human Myocardium‐derived Mesenchymal Stem Cells by Scanning Electrochemical Microscopy

In this study the redox activity of human myocardium‐derived mesenchymal stem cells (hmMSC) were investigated by redox‐competition (RC‐SECM) and generation‐collection (GC‐SECM) modes of scanning electrochemical microscopy (SECM), using 2‐methylnaphthalene‐1,4‐dione (menadione, MD) as a redox mediator. The redox activity of human healthy and dilated hmMSCs was evaluated by measuring reduction of MD. Measurements were performed by approaching and retracting the UME from the surface of growing hmMSC cells. The current study shows that the RC‐SECM mode can be applied to investigate integrity of cell membranes, whereas the most promising results were observed by using the GC‐SECM mode and applying the Hill's equation for the calculation/fitting of dependencies of electrical current vs menadione concentration. The calculated apparent Michaelis constant (K_M) for the production of menadiol (MDH₂) in the pathological hmMSC cells was 14.4 folds higher compared to that of the healthy hmMSC revealing the lover redox activity of pathological cells. Moreover, the calculated Hill's coefficient n shows a negative cooperative binding between MD and healthy hmMSC and positive cooperative binding between MD and pathological hmMSC. It means that healthy hmMSC is of lower affinity to MD, which is also related to the better membrane integrity of healthy cells. Data of this study demonstrate that SECM can be applied to investigate intracellular redox and membrane changes ongoing in human dilated myocardium‐derived hmMSC in order to improve their functioning and further regenerative potential.     

Variational transition state theory as a tool to determine kinetic selectivity in reactions involving a valley-ridge inflection point

Variational transition state theory has been used to calculate the kinetic isotope effects affecting product ratios in the reaction between (1)O(2) and d(6)-tetramethylethylene. The minimum energy path on the potential energy surface for this process reaches a valley-ridge inflection point and then bifurcates leading to the two final products. Using canonical variational transition state theory, two distinct dynamical bottlenecks were located corresponding to the H- and the D-abstraction, respectively. The calculated KIE at 263 K turns out to be 1.126. Analogously, a H/T KIE of 1.17 at the same temperature has been found for the reaction of (1)O(2) with the tritiated derivative of tetramethylethylene.     

Baryon rapidity loss in relativistic Au + Au collisions

An excitation function of proton rapidity distributions for different centralities is reported from AGS Experiment E917 for Au+Au collisions at 6, 8, and 10.8 GeV/nucleon. The rapidity distributions from peripheral collisions have a valley at midrapidity which smoothly change to distributions that display a broad peak at midrapidity for central collisions. The mean rapidity loss increases with increasing beam energy, whereas the fraction of protons consistent with isotropic emission from a stationary source at midrapidity decreases with increasing beam energy. The data suggest that the stopping is substantially less than complete at these energies.     

Measuring spatial coherence by using a mask with multiple apertures

A simple method to measure the complex degree of spatial coherence of a partially coherent quasi-monochromatic light field is presented. The Fourier spectrum of the far-field interferogram generated by a mask with multiple apertures (small circular holes) is analyzed in terms of classes of aperture pairs. A class of aperture pairs is defined as the set of aperture pairs with the same separation vector. The height of the peaks in the magnitude spectrum determines the modulus of the complex degree of spatial coherence and the corresponding value in the phase spectrum determines the phase of the complex degree of spatial coherence. The method is illustrated with experimental results.     

Cationic organometallic complexes with hexaalkylborazines: I. Synthesis and reactivity of cationic hexamethylborazinerhodium complexes with carbonyl,ethylene and diolefins as ligands

The PF₆ salts of the new cationic hexamethylborazinerhodium(I) complexes of general formula [Rh(Me₃B₃N₃Me₃)(LL′)]⁺ (LL′= 1,5-cyclooctadiene, norbornadiene, tetrafluorobenzobarrelene, trimethyltetrafluorobenzobarrelene, L = L′ = ethylene, CO) have been prepared from the reaction between [RhCl(LL′)]₂, Me₃B₃NMe₃, and AgPF₆ in dichloromethane. These complexes are very labile, undergoing rapid ring ligand exchange in solution with σ and π-donor ligands. The synthesis of [Rh(η⁶-naphthalene)(COD)]PF₆ is also described. The properties and NMR and IR spectroscopic characteristics of the new compounds are briefly discussed.