Analysis of the maximum entropy principle “debate”

Jaynes's maximum entropy principle (MEP) is analyzed by considering in detail a recent controversy. Emphasis is placed on the inductive logical interpretation of probability and the concept of total knowledge. The relation of the MEP to relative frequencies is discussed, and a possible realm of its fruitful application is noted.     

Existence of the Møller wave operators for V(r)=γ sin(μrα)rβ

We prove the existence of the Møller wave operators and the unitarity of the S operator for quantum mechanical potential scattering by potentials of the form

This includes the Special case $\text{V(r) =}\text{sin}\text{(r)}\text{r}$.     

Determination of Aroma Compounds from Alcoholic Beverages in Spiked Blood Samples by Means of Dynamic Headspace GC–MS

Some aroma compounds found in alcoholic beverages are characteristic of a certain beverage (i.e. 2,4-decadienoic acid ethyl ester is characteristic of pear spirit and 5-butyltetrahydro-4-methylfuran-2-on “whiskey lactone” is characteristic of aged spirits like whiskey). These substances were detectable in beverages but not in blood samples. The aim of this investigation was to find a sensitive sampling technique for aroma compounds in whole blood samples. This technique may be used in forensic toxicology for examination of drinking claims. The method comprises dynamic headspace sampling using a purge and trap concentrator, followed by quantitative gas chromatography–mass spectrometry (dynamic HS–GC–MS). The influence of sample preparation, trap adsorbents and sample temperature as well as desorption time and purge time on the quality of the analytical results were investigated. The following optimal parameters were determined: stirred and diluted whole blood sample without salt addition, use of Carbotrap C as trap material, sample temperature at 80 °C, desorption time 20 min and purge time 30 min. These optimal parameters were used for the determination of detection limits (LOD). The LOD of aroma compounds by means of dynamic headspace sampling were compared with the results of conventional sampling: the static headspace technique. Limits of detection for the aroma compounds with conventional static headspace GC are in the range 400–10,000 μg L^?1. Dynamic headspace–GC was found to be a more sensitive sampling technique for most of the aroma compounds investigated (e.g. C₄–C₈ ethyl esters, benzoic acid ethyl ester, linalool oxide and 4-ethylguaiacol) with detection limits between 1 and 50 μg L^?1, but there were also limits to the sampling of substances with lower volatility like decanoic acid ethyl ester, 2,4-decadienoic acid ethyl ester, eugenol and whiskey lactone with detection limits of about 1,000 μg L^?1.     

Structural properties of ultra-small thorium and uranium dioxide nanoparticles embedded in a covalent organic framework

We report the structural properties of ultra-small ThO₂ and UO₂ nanoparticles (NPs), which were synthesized without strong binding surface ligands by employing a covalent organic framework (COF-5) as an inert template. The resultant NPs were used to observe how structural properties are affected by decreasing grain size within bulk actinide oxides, which has implications for understanding the behavior of nuclear fuel materials. Through a comprehensive characterization strategy, we gain insight regarding how structure at the NP surface differs from the interior. Characterization using electron microscopy and small-angle X-ray scattering indicates that growth of the ThO₂ and UO₂ NPs was confined by the pores of the COF template, resulting in sub-3 nm particles. X-ray absorption fine structure spectroscopy results indicate that the NPs are best described as ThO₂ and UO₂ materials with unpassivated surfaces. The surface layers of these particles compensate for high surface energy by exhibiting a broader distribution of Th–O and U–O bond distances despite retaining average bond lengths that are characteristic of bulk ThO₂ and UO₂. The combined synthesis and physical characterization efforts provide a detailed picture of actinide oxide structure at the nanoscale, which remains highly underexplored compared to transition metal counterparts.

ThO₂ and UO₂ nanoparticles synthesized using a COF-5 template exhibit unpassivated surfaces and provide insight into nanoscale properties of actinides.     

A DFT analysis of the vibrational spectra of nitrobenzene

Raman and FTIR, spectra of nitrobenzene, nb, and its isotopomers, nb-¹⁵N, nb-¹³C₆ and nb-d₅, were obtained and the fundamental vibrational modes assigned with the aid of a B3LYP/6-311+G** calculation, without the need for scaling of the force constants. The changes in vibrational coupling between the nitro and benzene groups upon certain isotopic substitutions are well modelled by the calculation, which is able to reproduce the isotopic shifts in frequencies for the nitro vibrations, as well as changes in IR intensities.     

Studies of the reactions between indole-2,3-diones (isatins) and 2-aminobenzylamine

Reflux of equimolecular amounts 2-aminobenzylamine and isatins in acetic acid produced indolo[3,2-c]quinolin-6-ones in good yields. A proposed mechanism involving initial formation of a spiro compound is given. This isolable intermediate subsequently rearranges via a sequential isocyanate ring opening and a cyclisation process to a urea derivative which finally cyclized to the indolo[3,2-c]quinolin-6-ones. The urea derivative could be prepared separately and cyclized selectively to indolo[3,2-c]quinolin-6-one. Reaction of N-acetylisatin with 2-aminobenzylamine at room temperature yielded the 1,4-benzodiazepinone 3-(2-acetamidophenyl)-1,5-dihydro-1,4-benzodiazepin-2-one whereas its isomer 2(2-acetamidophenyl)-4,5-dihydro-1,4-benzodiazepin-3-one was obtained from 2-(2-acetylaminophenyl)-N-(2-aminobenzyl)-2-oxoacetamide in acetic acid at room temperature.The previously unknown linear isomer of indolo[3,2-c]quinolin-6-one, i.e. indolo[2,3-b]quinolin-11-one, has been prepared by thermal (260°C) cyclization of methyl 2-phenylamino indole-3-carboxylate, which in turn was prepared in two steps from methyl indole-3-carboxylate.     

Ab initio studies on Al(+)(H(2)O)(n), HAlOH(+)(H(2)O)(n-1), and the size-dependent H(2) elimination reaction

We report computational studies on Al(+)(H(2)O)(n), and HAlOH(+)(H(2)O)(n-1), n = 6-14, by the density functional theory based ab initio molecular dynamics method, employing a planewave basis set with pseudopotentials, and also by conventional methods with Gaussian basis sets. The mechanism for the intracluster H(2) elimination reaction is explored. First, a new size-dependent insertion reaction for the transformation of Al(+)(H(2)O)(n), into HAlOH(+)(H(2)O)(n-1) is discovered for n > or = 8. This is because of the presence of a fairly stable six-water-ring structure in Al(+)(H(2)O)(n) with 12 members, including the Al(+). This structure promotes acidic dissociation and, for n > or = 8, leads to the insertion reaction. Gaussian based BPW91 and MP2 calculations with 6-31G* and 6-31G** basis sets confirmed the existence of such structures and located the transition structures for the insertion reaction. The calculated transition barrier is 10.0 kcal/mol for n = 9 and 7.1 kcal/mol for n = 8 at the MP2/6-31G** level, with zero-point energy corrections. Second, the experimentally observed size-dependent H(2) elimination reaction is related to the conformation of HAlOH(+)(H(2)O)(n-1), instead of Al(+)(H(2)O)(n). As n increases from 6 to 14, the structure of the HAlOH(+)(H(2)O)(n-1) cluster changes into a caged structure, with the Al-H bond buried inside, and protons produced in acidic dissociation could then travel through the H(2)O network to the vicinity of the Al-H bond and react with the hydride H to produce H(2). The structural transformation is completed at n = 13, coincident approximately with the onset of the H(2) elimination reaction. From constrained ab initio MD simulations, we estimated the free energy barrier for the H(2) elimination reaction to be 0.7 eV (16 kcal/mol) at n = 13, 1.5 eV (35 kcal/mol) at n = 12, and 4.5 eV (100 kcal/mol) at n = 8. The existence of transition structures for the H(2) elimination has also been verified by ab initio calculations at the MP2/6-31G** level. Finally, the switch-off of the H(2) elimination for n > 24 is explored and attributed to the diffusion of protons through enlarged hydrogen bonded H(2)O networks, which reduces the probability of finding a proton near the Al-H bond.     

Synthesis and characterization of platinum(II) and (IV) complexes containing hexamethyleneimine ligand: crystal structure of [Pt(hexamethyleneimine)2(cyclobutanedicarboxylato)]·H2O

A series of new platinum(II) and platinum(IV) complexes of the type [Pt^II(HMI)₂X] (where HMI=hexamethyleneimine, X=dichloro, sulfato, 1,1-cyclobutanedicarboxylato [CBDCA], oxalato, methylmalonato, or tatronato) and [Pt^IV(HMI)₂Y₂Cl₂] (where Y=hydroxo, acetato, or chloro) were synthesized and characterized by infrared (IR) spectroscopy, ¹³C and ¹⁹⁵Pt nuclear magnetic resonance (NMR) spectroscopy and elemental analysis. Among the complexes synthesized, [Pt^II(hexamethyleneimine)₂(1,1-cyclobutanedicarboxylato)]·H₂O was examined by single-crystal X-ray diffraction. The slightly distorted square planar coordination environment of the platinum metal includes the amino group of the hexamethyleneimine (HMI) molecule and the oxygen atoms of the carboxylato ligand. The cyclobutanedicarboxylic acid (CBDCA) molecule adopts six-member chelating rings with platinum. Hydrogen bonding plays an important part in holding the crystal lattice together.     

EXCITATION ENERGY TRANSFER IN THE CRYPTOPHYTES. FLUORESCENCE EXCITATION SPECTRA AND PICOSECOND TIME-RESOLVED EMISSION SPECTRA OF INTACT ALGAE AT 77 K

Excitation spectra of chlorophyll- a (Chl- a ) fluorescence in intact cells of Cryptomonas ovata, Chroomonas pauciplastida and Chroomonas salina were determined at 77 K. For all species the excitation spectra for emission from Chl- a associated with photosystem II (PSII) showed increased contributions by a carotenoid (493 nm) and phycobiliproteins, and decreased contributions by carotenoid (417 nm, 505 nm) and Chl- a (445 nm) as compared to excitation spectra for emission from Chl- a associated with photosystem I (PSI). Excitation spectra of C. salina and C. ovata showed an increased contribution by Chl- c ² to PSII Chl- a fluorescence emission. In all three species the absorbance band positions of Chl- a , as determined from the excitation spectra, were similar to those previously described in green plants. green algae and phycobilisome-containing organisms. Time-resolved 77 K fluorescence emission spectra of C. ovata and C. salina showed successive emission from both phycoerythrin and Chl- c ², PSII Chl- a , and PSI Chl- a. C. pauciplastida showed successive emission from phycocyanin, PSII Chl- a , and PSI Chl- a. Spectral red-shifts with time were observed for the phycobiliprotein peaks in all three species. The fluorescence decay of phycoerythrin in C. ovata and C. salina was faster than that of phycocyanin in C. pauciplastida. The results are discussed in relation to the organization of the antenna pigments of PSII and PSI in the cryptophyte algae.     

Deactivation of silica surfaces with a silanol-terminated polysiloxane; structural sharacterization by inverse gas chromatography and solid-state NMR

Retention gape deactivated with Silicone OV-1701-OH show good chromatographic performance and remarkable stability against water induced stationary phase degradrdation. In an attempt to better understand the findamentals off the deactivation process using silanol terminated polysiloxanes, a fumed silica was deactivated with Silicon OV-1701-OH. In contrast to fused silic capillaries, fumed silica (Aerosil A-200) can be studied by ²⁹Si cross-polarization magic-angle-spinning (CPMAS) NMR, thus serving as a model substrate for fused silica. Retention data from inverse gas chromatography at infinite dilurion and ²⁹Si CP MAS NMR data of five Aerosil phases, differing in residual silanol surface concentration, are correlated with the aim of validating this approach for stationary phase characterization. A comparatively detailed model of the deactivating polymer layer that explains the observed absorption activities is deduced. Surface silanols are shown to play a key role in the polymer layer, the structure of which is of primary importance for the absorption behavior after deactivation. Contrary to common belief, the absolute silanol surface concentration after deativation is only of secondary importance for the overall absorption activity. High silanol surface concentrations enhance degradation of the polysiloxane chains into small cyclic fragments as well as subsequent absorption and immobolization to the silica substrate surface. The mobility of linear polysiloxane chains in the kHz regime (as determined bby NMR cross-polarization dynamics) appears to determine the extent which the residual silanols are accessible for analytes. It is therefore anticipated that there is an optimum silanol surface concentration of fused silica surfaces to be deactivated with silanol terminated polysiloxanes; it should be lazrge enough to adsord polymer fragments, but not large to avoid excessive residual silanol activity.