Families of log canonically polarized varieties

Determining the number of singular fibers in a family of varieties over a curve is a generalization of Shafarevich’s Conjecture and has implications for the types of subvarieties that can appear in the corresponding moduli stack. We consider families of log canonically polarized varieties over \({\mathbb {P}^1}\) , i.e. families \({g:(Y, D) \to \mathbb {P}^1}\) where D is an effective snc divisor and the sheaf \({\omega_{Y/\mathbb {P}^1}(D)}\) is g-ample. After first defining what it means for fibers of such a family to be singular, we show that with the addition of certain mild hypotheses (the fibers have finite automorphism group, \({\mathcal {O}_Y(D)}\) is semi-ample, and the components of D must avoid the singular locus of the fibers and intersect the fibers transversely), such a family must either be isotrivial or contain at least 3 singular fibers.     

Ultrasound-assisted lipase-catalyzed transesterification of soybean oil in organic solvent system

This work reports the transesterification of soybean oil with ethanol using two commercial immobilized lipases under the influence of ultrasound irradiation. The experiments were performed in an ultrasonic water bath, following a sequence of experimental designs to assess the effects of temperature, enzyme and water concentrations, oil to ethanol molar ratio and output irradiation power on the reaction yield. Results show that ultrasound-assisted lipase-catalyzed transesterification of soybean oil with ethanol might be a potential alternative route to conventional alkali-catalyzed method, as high reaction yields (∼90 wt.%) were obtained at mild irradiation power supply (∼100 W), and temperature (60 °C) in a relatively short reaction time, 4 h, using Lipozyme RM IM as catalyst. The repeated use of the catalyst under the optimum experimental condition resulted in a decay in both enzyme activity and product conversion after two cycles. The use of Novozym 435 led to lower conversions (about 57%) but the enzyme activity was stable after eight cycles of use, showing, however, a reduction in product conversion after the forth cycle.     

Entropic Separations of Mixtures of Aromatics by Selective Face‐to‐Face Molecular Stacking in One‐Dimensional Channels of Metal–Organic Frameworks and Zeolites

Separation of challenging mixtures using metal–organic frameworks can be achieved by an entropy‐driven mechanism, where one of the components can arrange into a “face‐to‐face” stacking, thus reducing its “footprint” and reaching a higher saturation loading.     

Insights into amine-based CO<Subscript>2</Subscript> capture: an ab initio self-consistent reaction field investigation

Ab initio many-body perturbation theory (MP2/6-311++G(,dp)), density functional theory (B3LYP/6-31++G(d,p)) and self-consistent reaction field (IEF-PCM UA HF/6-31G(d)) calculations have been used to study the CO₂ capture reagents NH₃, 2-hydroxyethylamine (MEA), diaminoethane (EN), 2-amino-1-propanol (2A1P), diethanolamine (DEA), N-methyl-2-hydroxyethylamine (N-methylMEA), 2-amino-2-methyl-1-propanol (AMP), trishydroxymethylaminomethane (tris), piperazine (PZ) and piperidine (PD). This study involved full conformational searches of the capture amines in their native and protonated forms, and their carbamic acid and carbamate derivatives. Using this data, we were able to compute Boltzmann-averaged thermodynamic values for the amines, carbamates and carbamic acid derivatives, as well as equilibrium constants for a series of ‘universal’ aqueous capture reactions. Important findings include (i) relative pK _a values for the carbamic acid derivatives are a useful measure of carbamate stability, due to a particular chemical resonance which is also manifest in short computed N–CO₂H bonds at both levels of theory, (ii) the computational results for sterically hindered amines such as AMP and tris are consistent with these species forming carbamates which readily hydrolyse and (iii) the amine-catalysed reaction between OH⁻ and CO₂ to generate bicarbonate correlates with amine pK _a. Thermodynamic data from the ab initio computations predicts that the heterocycles PD and PZ and the acyclic sorbent EN are good choices for a capture solvent. AMP and tris perform poorly in comparison.     

Kinetic analysis of the phenyl-shift reaction in β-O-4 lignin model compounds: a computational study

The phenyl-shift reaction for the β-radical of phenethyl phenyl ether (PhCH(2)C?HOPh, β-PPE) is an integral step in the pyrolysis of PPE, which is a model compound for the β-O-4 linkage in lignin. We investigated the influence of natural occurring substituents (hydroxy, methoxy) on the reaction rate by calculating relative rate constants using density functional theory in combination with transition state theory, including anharmonic correction for low-frequency modes. The phenyl-shift reaction proceeds through an oxaspiro[2.5]octadienyl radical intermediate and the overall rate constants were computed invoking the steady-state approximation (its validity was confirmed). Substituents on the phenethyl ring have only little influence on the rate constants. If a methoxy substituent is located in the para position of the phenyl ring adjacent to the ether oxygen, the energies of the intermediate and second transition state are lowered, but the overall rate constant is not significantly altered. This is a consequence of the dominating first transition from reactant to intermediate in the overall rate constant. In contrast, o- and di-o-methoxy substituents significantly accelerate the phenyl-migration rate compared to β-PPE.     

Entanglement thresholds for displaying the quantum nature of teleportation

A protocol for transferring an unknown single qubit state evidences quantum features when the average fidelity of the outcomes is, in principle, greater than 2/3$2/3$. We propose to use the probabilistic and unambiguous state extraction scheme   as a mechanism to redistribute the fidelity in the outcome of the standard teleportation when the process is performed with an X$X$-state as a noisy quantum channel. We show that the entanglement of the channel is necessary but not sufficient in order for the average fidelity f_X$f_X$ to display quantum features, i.e., we find a threshold C_X$C_X$ for the concurrence of the channel. On the other hand, if the mechanism for redistributing fidelity is successful then we find a filterable outcome with average fidelity f_X,0$f_{X,0}$ that can be greater than f_X$f_X$. In addition, we find the threshold concurrence of the channel C_X,0$C_{X,0}$ in order for the average fidelity f_X,0$f_{X,0}$ to display quantum features and surprisingly, the threshold concurrence C_X,0$C_{X,0}$ can be less than C_X$C_X$. Even more, we find some special cases for which the threshold values become zero.     

Correlated one-particle method: numerical results

In a previous paper a correlated one-particle method was formulated, where the effective Hamiltonian was composed of the Fock operator and a correlation potential. The objective was to define a correlated one-particle theory that would give all properties that can be obtained from a one-particle theory. The Fock-space coupled-cluster method was used to construct the infinite-order correlation potential, which yields correct ionization potentials (IP's) and electron affinities (EA's) as the negative of the eigenvalues. The model, however, was largely independent of orbital choice. To exploit the degree of freedom of improving the orbitals, the Brillouin-Brueckner condition is imposed, which leads to an effective Brueckner Hamiltonian. To assess its numerical properties, the effective Brueckner Hamiltonian is approximated through second order in perturbation. Its eigenvalues are the negative of IP's and EA's correct through second order, and its eigenfunctions are second-order Brueckner orbitals. We also give expressions for its energy and density matrix. Different partitioning schemes of the Hamiltonian are used and the intruder state problem is discussed. The results for ionization potentials, electron affinities, dipole moments, energies, and potential curves are given for some sample molecules.     

Simultaneous Determination of Two Antibiotics in Tablets by Spectrophotometry and Principal Component Regression (PCR) Analysis. An Advanced Undergraduate Experiment Involving Chemometrics

An advanced analytical chemistry laboratory experiment involving the simultaneous determination of the antibiotics sulfamethoxazole and trimethoprime in commercial tablets is described. It involves the following steps: (1) preparation of nine calibration mixtures and the recording of their absorption spectra in the region 200–320 nm, (2) dissolution of the tablet contents and the recording of spectrophotometrics data, and (3) processing the data with the multivariate calibration technique of principal component regression (PCR). The theory of PCR is discussed, and a Visual Basic program is made available for data processing. The latter program allows students to obtain and save relevant statistical information (root-mean-square deviation, correlation coefficient, and relative error of prediction), as well as calibrate spectral factors and spectral residuals for each test sample. This program helps to illustrate the PCR technique in detail. The reagents used are of low cost and nontoxic; the experiment is simple and provides students with insight into a the real practice of integrating chemistry, instrumentation and computer techniques.     

A Theoretical Study of the Reductive Elimination of CH3EH3 from cis‐[Pt(CH3)(EH3)(PH3)2] (E = Si,Ge) in the Presence of Acetylene

The reaction mechanism of the elimination of CH₃EH₃ from the platinum complexes cis‐[Pt(CH₃) · (EH₃)(PH₃)₂] (E = Si, Ge) in the presence of acetylene has been studied using gradient‐corrected DFT calculations at the B3LYP level. The reaction proceeds in two steps. The first step is the formation of the acetylene complex [Pt(CH₃)(HCCH)(EH₃)(PH₃)] which occurs in a associative/dissociate pathway via the five‐coordinated intermediate [Pt(CH₃)(HCCH)(EH₃)(PH₃)₂]. The rate‐determining step is the elimination of CH₃EH₃ via a four‐coordinated transition state. The alternative mechanism via direct dissociation from the five‐coordinated intermediates has higher activation barriers. The calculated activation energies of the model reactions are in good agreement with experimental results. The silyl complex has a lower barrier for the elimination reaction than the germyl complex. The calculated transition states show that the reason for the lower barrier is the strength of the nascending C–Si bond, which is higher than the C–Ge bond. The results are in agreement with the postulated mechanism of Ozawa et al. (Organometallics, 1998 , 17, 1018).