Generalized reinhardt domains

In this paper we investigate a class of Lie group actions on , the so-calledpolar actions, that naturally generalize the standard actions. For a domain invariant under such an action (i.e., a generalized Reinhardt domain) we characterize the invariant plurisubharmonic functions and determine the envelope of holomorphy in geometric terms. For a generalized Reinhardt domain containing the origin of we also compute its automorphism group. Supported in part by NSF Grant 8602020     

Rare numbers

Suppose thatX ₁,X ₂,... is a sequence of iid random variables taking values inZ ⁺. Consider the random sequenceA(X)(X ₁,X ₂,...). LetY _n be the number of integers which appear exactly once in the firstn terms ofA(X). We investigate the limit behavior ofn ^–(1–) Y _n for [0, 1].     

Gap-Free Set Partitions

A set partition is called “gap-free” if its block sizes form an interval. In other words, there is at least one block of each size between the smallest and largest block sizes. Let B(n) and G(n), respectively, denote the number of partitions and the number of gap-free partitions of the set [n]. We prove that      

Reactions of (di)manganese carbonyl ions with 1,4,7-trimethyl-1,4,7-triazacyclononane (Me3TACN) in the gas phase

The gas-phase reactions of a series of (di)manganese carbonyl positive ions with 1,4,7-trimethyl-1,4,7-triazacyclononane (Me(3)TACN) have been examined with the aid of Fourier transform ion cyclotron resonance (FTICR) mass spectrometry. The monomanganese carbonyl ions, [Mn(CO)(n)](+) (n = 2-5), react predominantly by ligand exchange and to a minor extent by electron transfer with the formation of the radical cation of Me(3)TACN. For the [Mn(CO)(n)](+) (n = 2-4) ions, the ligand exchange results in the exclusive formation of a [Mn(Me(3)TACN)](+) complex, whereas small amounts of [Mn(CO)(Me(3)TACN)](+) ions are also generated in the reactions of the [Mn(CO)(5)](+) ion. The [Mn(2)(CO)(n)](+) ions (n = 2, 4 and 5) react also by competing electron transfer and ligand exchange. The reaction of the [Mn(2)(CO)(2)](+) and [Mn(2)(CO)(4)](+) ions is associated with cleavage of the Mn--Mn bond as evidenced by the pronounced formation of [Mn(Me(3)TACN)](+) ions. For [Mn(2)(CO)(5)](+), the ligand exchange leads mainly to the formation of [Mn(2)(CO)(n)(Me(3)TACN)](+) (n = 1-3) ions. These primary product ions react subsequently by the incorporation of a second Me(3)TACN molecule to afford [Mn(2)(CO)(Me(3)TACN)(2)](+) and [Mn(2)(CO)(2)(Me(3)TACN)(2)](+) ions. Both of these latter species incorporate an oxygen molecule with formation of ions with the assigned composition of [Mn(2)(O(2))(CO)(Me(3)TACN)(2)](+) and [Mn(2)(O(2))(CO)(2)(Me(3)TACN)(2)](+).     

The role of angular momentum in collision-induced vibration-rotation relaxation in polyatomics

Vibrational relaxation of the 6(1) level of S(1)((1)B(2u)) benzene is analyzed using the angular momentum model of inelastic processes. Momentum-(rotational) angular momentum diagrams illustrate energetic and angular momentum constraints on the disposal of released energy and the effect of collision partner on resultant benzene rotational excitation. A kinematic "equivalent rotor" model is introduced that allows quantitative prediction of rotational distributions from inelastic collisions in polyatomic molecules. The method was tested by predicting K-state distributions in glyoxal-Ne as well as J-state distributions in rotationally inelastic acetylene-He collisions before being used to predict J and K distributions from vibrational relaxation of 6(1) benzene by H(2), D(2), and CH(4). Diagrammatic methods and calculations illustrate changes resulting from simultaneous collision partner excitation, a particularly effective mechanism in p-H(2) where some 70% of the available 6(1)-->0(0) energy may be disposed into 0-->2 rotation. These results support the explanation for branching ratios in 6(1)-->0(0) relaxation given by Waclawik and Lawrance and the absence of this pathway for monatomic partners. Collision-induced vibrational relaxation in molecules represents competition between the magnitude of the energy gap of a potential transition and the ability of the colliding species to generate the angular momentum (rotational and orbital) needed for the transition to proceed. Transition probability falls rapidly as DeltaJ increases and for a given molecule-collision partner pair will provide a limit to the gap that may be bridged. Energy constraints increase as collision partner mass increases, an effect that is amplified when J(i)>0. Large energy gaps are most effectively bridged using light collision partners. For efficient vibrational relaxation in polyatomics an additional requirement is that the molecular motion of the mode must be capable of generating molecular rotation on contact with the collision partner in order to meet the angular momentum requirements. We postulate that this may account for some of the striking propensities that characterize polyatomic energy transfer.     

Evidence for specific solvation of two halocarbene amides

Laser flash photolysis (LFP, 308 nm) of endo-10-halo-10'-N,N-dimethylcarboxamidetricyclo[4.3.1.0]-deca-2,4-diene (1Cl and 1F) releases indan and halocarbene amide (2Cl and 2F). Although the carbenes are not UV-vis active, they react rapidly with pyridine to form ylides (4Cl, 4F), which are readily detected in LFP experiments (lambda(max) = 450 nm). Dioxane decreases the observed rate of carbene reaction with pyridine in CF(2)ClCFCl(2). Small amounts of THF decrease the observed rate of reaction of carbene 2F with pyridine but increase the rate of reaction of carbene 2Cl with pyridine. LFP (266 nm) of dienes 1Cl and 1F in CF(2)ClCFCl(2) with IR detection produces carbenes 2Cl and 2F with carbonyl vibrations at 1635 and 1650 cm(-1), respectively. In dioxane or THF solvent, LFP produces the corresponding ether ylides (5Cl, 5F) by capture of carbenes 2Cl and 2F. The ylides have broad carbonyl vibrations between 1560 and 1610 cm(-1). The addition of a small amount of dioxane in CFCl(2)CF(2)Cl extends the lifetime of the carbene. This observation, together with the ether-induced retardation of the rates of carbene capture by tetramethylethylene and pyridine, is evidence for solvation of the carbene by dioxane.     

GlyNet: a multi-task neural network for predicting protein–glycan interactions

Advances in diagnostics, therapeutics, vaccines, transfusion, and organ transplantation build on a fundamental understanding of glycan–protein interactions. To aid this, we developed GlyNet, a model that accurately predicts interactions (relative binding strengths) between mammalian glycans and 352 glycan-binding proteins, many at multiple concentrations. For each glycan input, our model produces 1257 outputs, each representing the relative interaction strength between the input glycan and a particular protein sample. GlyNet learns these continuous values using relative fluorescence units (RFUs) measured on 599 glycans in the Consortium for Functional Glycomics glycan arrays and extrapolates these to RFUs from additional, untested glycans. GlyNet''s output of continuous values provides more detailed results than the standard binary classification models. After incorporating a simple threshold to transform such continuous outputs the resulting GlyNet classifier outperforms those standard classifiers. GlyNet is the first multi-output regression model for predicting protein–glycan interactions and serves as an important benchmark, facilitating development of quantitative computational glycobiology.

GlyNet, a neural net model of glycan-protein binding strengths. Given a glycan it outputs binding to each of several protein samples. Reproducing glycan array data, it extrapolates the binding of untested glycans against the protein samples.     

The work function of hydrothermally synthesized UO2 and the implications for semiconductor device fabrication

The photoelectric work function of nearly stoichiometric (111) and (100) hydrothermally grown UO₂ was measured to be 6.28 ± 0.36 eV and 5.80 ± 0.36 eV, respectively. Candidate metals for electrical contacts are identified for both rectifying and non‐rectifying contacts based on work function, lattice compatibility, and electrical conductivity.     

Magnetic resonance imaging of acoustic streaming: absorption coefficient and acoustic field shape estimation

In this study, magnetic resonance imaging (MRI) is used to visualize acoustic streaming in liquids. A single-shot spin echo sequence (HASTE) with a saturation band perpendicular to the acoustic beam permits the acquisition of an instantaneous image of the flow due to the application of ultrasound. An average acoustic streaming velocity can be estimated from the MR images, from which the ultrasonic absorption coefficient and the bulk viscosity of different glycerol-water mixtures can be deduced. In the same way, this MRI method could be used to assess the acoustic field and time-average power of ultrasonic transducers in water (or other liquids with known physical properties), after calibration of a geometrical parameter that is dependent on the experimental setup.     

Detection of unexploded ordnance by PGNAA based borehole-logging

The performance of a borehole-logging system, based on prompt-gamma-neutron-activation-analysis (PGNAA), for explosive detection was studied by Monte-Carlo simulations. The prompt gamma of nitrogen, which is a constituent of common explosive, was used to identify the unexploded ordnance (UXO). Our results show that the minimum counting time depends on the soil moisture, the cladding thickness and the explosive composition. In conjunction with the standard detection by magnetometry, the PGNAA is a promising analytical technique for definitive identification of deep buried UXOs.