On the theta completions for maximal subalgebras

Let L be a finite dimensional Lie algebra. Then for a maximal subalgebra M of L, a 𝜃-completion for M is a subalgebra C of L such that CM and M_L?C and C∕M_L contains no non-zero ideal of L∕M_L, properly. And a 𝜃-completion C of M is said to be a strong 𝜃-completion, if C = L or there exists a subalgebra B of L such that C be maximal in B and B is not a 𝜃-completion for M. These are analogous to the concepts of 𝜃-completion and strong 𝜃-completion of a maximal subgroup of a finite group. Now, we consider the influence of these concepts on the structure of a finite dimensional Lie algebra.     

Water increases rates of epoxidation by Mn(III)porphyrins/imidazole/IO4(-) in CH2Cl2. Analogy with peroxidase and chlorite dismutase

Manganese(III)-meso-tetraphenylporphyrin [Mn(TPP)] and manganese(III)-meso-tetrakis(pentafluorophenyl)porphyrin [Mn(TPFPP)] catalyse the epoxidation of cyclooctene by IO(4)(-) in the presence of excess imidazoles, in both dry CH(2)Cl(2) and CH(2)Cl(2) saturated with H(2)O. The reaction rates of the electron deficient Mn(TPFPP) are a factor 24 less than those of Mn(TPP); however, the former increases 15-30 times in the presence of water, while those of Mn(TPP) do so by a factor of 2-3. The most striking catalytic enhancement caused by the addition of water was observed with 2-methylimidazole and Mn(TPFPP). As deprotonation of imidazoles may play a significant role in the presence of water, we found that manganese(III)-meso-tetrakis(phenyl-4-sulfonato)porphyrin [Mn(TPPS)] decreases the NH proton pK(a) of axially coordinated imidazole from 14.2 to 9.5. We conclude that the imidazole ligand is partially deprotonated in the presence of water. The latter enables the solvation of imidazolium ions that are formed simultaneously. The imidazolate form of the co-catalyst is a much stronger donor than the imidazole itself, providing electron density to Mn(III) and thus promoting oxygen transfer. The failure of N-methylimidazole to increase the reaction rates upon addition of water supports this hypothesis. A functionally related deprotonation has been shown to occur in horseradish peroxidase (J. S. de Ropp, V. Thanabal, G. N. La Mar, J. Am. Chem. Soc. 1985, 107, 8270-8272) and in chlorite dismutase (B. R. Goblirsch, B. R. Streit, J. L. Dubois, C. M. Wilmot, J. Biol. Inorg. Chem. 2010, 15, 879-888). Mn(III)porphyrins in combination with imidazoles and water constitute a functional biomimetic model of peroxidases.     

The extent of molecular orientation at liquid/vapor interface of pyridine and its alkyl derivatives by molecular dynamics simulation

In this paper, molecular dynamics simulation was performed to investigate the liquid∕vapor interfacial structure of neat polar liquids. Large-scale ensembles of liquid pyridine and its alkyl derivatives, 4-methylpyridine and 4-ethylpyridine, were simulated by classical molecular dynamics at 298 K. For the liquid system of low polarity, the surface density profile of the atoms meet exactly at the middle of interfacial region, and atoms of hydrophobic nature can be hardly discriminated from hydrophilic ones in either vapor or liquid sides. For a liquid system of high polarity, the density profile of atoms with different nature is highly discriminated all over the interfacial region, and as the polarity increases, a dense region of atomic density is clearly developed in the subsurface region. The recognized bivariate method was also used to study the molecular orientational distribution quantitatively. Orientational analysis of the three liquid systems indicates that the pyridine ring plane in the outmost surface tends to be vertical. Its tendency in the innermost interfacial region is parallel. The orientational states available to 4-ethylpyridine and pyridine are discriminated by predicting the possibility of a bisector-wise tumbling for the ring plane in pyridine and a side-wise tumbling in 4-ethylpyridine. The orientational distribution maps explain the trend of experimental surface tension and surface entropy. As the dipole moment of these liquids increases with the alkyl chain length, the surface structural profile changes from a regular definite one to a surface of complex atomic structure involving a dense phase near the interface. The development of dense region in alkyl derivatives is the result of segregation of molecules due to the alkyl group, which is captured and discriminated by molecular dynamics simulation even when the length of a short alkyl chain is increased by one carbon atom.     

Faltings’ local–global principle for finiteness dimension of cofinite modules

Archiv der Mathematik - Let R denote a commutative Noetherian ring, $$\mathfrak {a}$$ an ideal of R, and M an $$\mathfrak {a}$$ -cofinite R-module. The purpose of this article is to show that for a...     

FFT-based convolution algorithm for fast and precise numerical evaluating diffracted field by photon sieve

FFT-based convolution is proposed to numerical solve Fresnel–Kirchhoff integral in Fresnel regime carefully and in a very shorter time in comparison to direct solving convolution. To show its capability, the algorithm was implemented to evaluate amplitude of a diffracted plane wave at the focal plane of photon sieves with different focal lengths. The calculated amplitudes are completely the same calculated via convolving operation but has advantageous of taking very very shorter time. The calculation was also repeated using single-FFT algorithm that produce same result for all ranges either below or upper the sampling criteria and different results in comparison to the other two methods.     

Artificial Protein Crosstalk with a Molecule that Exchanges Binding Partners

Drawing inspiration from allosteric signaling enzymes, whose catalytic and regulatory units are non-covalently linked, we have devised a method to establish unnatural, effector-mediated enzyme activation within native cells. The feasibility of this approach is demonstrated by introducing a synthetic regulatory unit (sRU) onto glycogen synthase kinase 3 (GSK-3) through non-covalent means. Our study reveals that this synthetic regulator mediates an unnatural crosstalk between GSK-3 and lactate dehydrogenase A (LDHA), whose expression is regulated by cellular oxygen levels. Specifically, with this approach, the constitutively active GSK-3 is transformed into an activable enzyme, whereas LDHA is repurposed as an unnatural effector protein that controls the activity of the kinase, making it unnaturally dependent on the cell‘s hypoxic response. These findings demonstrate a step toward imitating the function of effector-regulated cell-signaling enzymes, which play a key biological role in mediating the response of cells to changes in their environment. In addition, at the proof-of-principle level, our results indicate the potential to develop a new class of protein inhibitors whose inhibitory effect in cells is dictated by the cell‘s environment and consequent protein expression profile.     

Kinetic Study of Radical Polymerization v. Determination of Reactivity Ratio in Copolymerization of Acrylonitrile and Itaconic Acid by 1H‐NMR

Many reports exist in the literature about the application of ¹H and ¹³C‐NMR techniques to analyze the copolymer structure and composition and also determination of reactivity ratios. In this work, on‐line ¹H‐NMR spectroscopy has been applied to identify reactivity ratios of itaconic acid and acrylonitrile in the solution phase (DMSO as the solvent) and in the presence of AIBN as the radical initiator. All the peaks corresponding to the existing protons were assigned quietly. Therefore, the kinetics of the copolymerization reaction was investigated by studying the variation of integral of two characteristic peaks regarding each monomer. The obtained data were used to find the reactivity ratios of acrylonitrile and itaconic acid by linear least‐squares methods such as Finemann‐Ross, inverted Finemann‐Ross, Mayo‐Lewis, Kelen‐Tudos, extended Kelen‐Tudos and Mao‐Huglin. In addition, a non‐linear least‐square method (Tidwell‐ Mortimer) was used at low conversions. Extended Kelen‐ Tudos and Mao‐Huglin were applied to determine reactivity ratio values at high conversions as well.     

Self-propagating assembly of a molecular-based multilayer

Accelerated growth of a molecular-based material that is an active participant in its continuing self-propagated assembly has been demonstrated. This nonlinear growth process involves diffusion of palladium into a network consisting of metal-based chromophores linked via palladium.