Maximum modulus sets in pseudoconvex boundaries

LedD be a strictly pseudoconvex domain in ? ⁿ withC ^∞ boundary. We denote byA ^∞(D) the set of holomorphic functions inD that have aC ^∞ extension to \(\bar D\) . A closed subsetE of ?D is locally a maximum modulus set forA ^∞(D) if for everyp∈E there exists a neighborhoodU ofp andf∈A ^∞(D∩U) such that |f|=1 onE∩U and |f|<1 on \(\bar D \cap U\backslash E\) . A submanifoldM of ?D is an interpolation manifold ifT _p (M)?T _p ^c (?D) for everyp∈M, whereT _p ^c (?D) is the maximal complex subspace of the tangent spaceT _p (?D). We prove that a local maximum modulus set forA ^∞ (D) is locally contained in totally realn-dimensional submanifolds of ?D that admit a unique foliation by (n?1)-dimensional interpolation submanifolds. LetD =D ₁ x ... xD _r ? ? ⁿ whereD _i is a strictly pseudoconvex domain withC ^∞ boundary in ? ⁿ _i ,i=1,…,r. A submanifoldM of ?D ₁×…×?D _r verifies the cone condition if \(II_p (T_p (M)) \cap \bar C[Jn_1 (p),...,Jn_r (p)] = \{ 0\} \) for everyp∈M, wheren _i (p) is the outer normal toD _i atp, J is the complex structure of ? ⁿ , \(\bar C[Jn_1 (p),...,Jn_r (p)]\) is the closed positive cone of the real spaceV _p generated byJ _{n 1}(p),…,J _{n r}(p), and II _p is the orthogonal projection ofT _p (?D) onV _p . We prove that a closed subsetE of ?D ₁×…×?D _r which is locally a maximum modulus set forA ^∞(D) is locally contained inn-dimensional totally real submanifolds of ?D ₁×…×?D _r that admit a foliation by (n?1)-dimensional submanifolds such that each leaf verifies the cone condition at every point ofE. A characterization of the local peak subsets of ?D ₁×…×?D _r is also given.     

Possible side reactions due to water in emulsion polymerization by late transition metal complexes. 1. Water complexation and hydrolysis of the growing chain

The transition metal catalyzed ethylene polymerization in aqueous emulsion has been increasingly successful in the last couple of years. Water however adversely affects the polymerization process by (a) competing with ethylene for the binding site at the metal and (b) hydrolyzing the growing chain. Neutral salicylaldiminato and cationic diimine complexes of Ni and Pd with different substituent patterns are studied here by density functional theory to determine their propensity toward water complexation and hydrolysis of the growing chain. Experimental NMR studies have also been carried out on the protonolysis of the Ni(II)-based Grubbs catalyst. It is found that in general that (a) ethylene coordination is preferred over water coordination for both Ni and Pd catalysts and (b) hydrolysis of the metal alkyl bond is competitive to ethylene insertion.     

Optimizing the structures of minimum and transition state on the free energy surface

Presented here is the application of a scheme for optimizing the structures of minima and transition states on the free energy surface (FES) for a path along a fixed reaction coordinate with the aid of ab initio molecular dynamics (AIMD) simulation. In the direction of the reaction coordinate, the values corresponding to the stationary points were optimized using the quasi-Newton method, in which the gradient of the free energy along the reaction coordinate was obtained by a constraint AIMD method, and the Bofill Hessian update scheme was used. The equilibrium values for the other directions were taken as the corresponding averages in the dynamic simulation. This scheme was applied to several elementary bimolecular addition reactions: (A) BH(3) + H(2)O --> H(2)O.BH(3); (B) BF(3) + NH(3) --> FB(3).NH(3); (C) SO(3) + NH(3) --> O(3)S.NH(3); (D) C(2)H(4) + CCl(2) --> H(4)C(2).CCl(2); (E) Ni(NH(2))(2) + PH(3) --> (NH(2))(2)Ni.PH(3); (F) W(CO)(5) + CO --> W(CO)(6). For reactions A, B, C, and F, no transition state (TS) exists on the potential energy surface (PES). However there is a TS on the FES. This stems from the curvature difference of the PES and -TDeltaS as a function of the reaction coordinate. For all reactions, it is found that the TS shifts toward the complexation product with increasing temperature because of the curvature increase of -TDeltaS. The equilibrium bond distances for the inactive coordinates perpendicular to the reaction coordinate always increase with temperature, which is due to the thermal excitation and anharmonicity of the PES.     

Computer design of thermal sprayed metal powder coatings

An approach to the modeling of the process of the formation of a lamellar structure of thermal coatings, including plasma coatings, at the spraying of metal powders is proposed. The results are presented, which concern the development of the computational algorithm and the program complex for modeling the process of laying the splats in the coating with regard for the topology of its surface, which varies dynamically at the spraying, as well as the formation of a lamellar structure and porosity of the coating. The experimentally verified theoretical solutions are used to predict the scenarios of the formation of splats and rapid prediction of their thicknesses and diameters. The results of computational experiments illustrating the performance of the developed computational technology are presented.     

Characterisation of homogeneous polynomials which are constant on complex-tangential curves in the boundary of the unit ball of

We prove that a complex-tangential curve γ in the boundary of the unit ball of having the property that there exists a homogeneous polynomial P such that P=1 on γ has constant curvature. This implies that a homogeneous polynomial P having the property that there exists a closed complex-tangential curve γ (respectively a totally real 2-dimensional submanifold) in the boundary of the unit ball of such that P=1 on γ (respectively |P|=1 on γ) reduces to a monomial by a unitary chage of variables. These results represent a positive answer to conjectures of H. O. Kim.     

Thiophenylazobenzene: An Alternative Photoisomerization Controlled by Lone‐Pair⋅⋅⋅π Interaction

Azoheteroarene photoswitches have attracted attention due to their unique properties. We present the stationary photochromism and ultrafast photoisomerization mechanism of thiophenylazobenzene (TphAB). It demonstrates impressive fatigue resistance and photoisomerization efficiency, and shows favorably separated (E)‐ and (Z)‐isomer absorption bands, allowing for highly selective photoconversion. The (Z)‐isomer of TphAB adopts an unusual orthogonal geometry where the thiophenyl group is perfectly perpendicular to the phenyl group. This geometry is stabilized by a rare lone‐pair???π interaction between the S atom and the phenyl group. The photoisomerization of TphAB occurs on the sub‐ps to ps timescale and is governed by this interaction. Therefore, the adoption and disruption of the orthogonal geometry requires significant movement along the inversion reaction coordinates (CNN and NNC angles). Our results establish TphAB as an excellent photoswitch with versatile properties that expand the application possibilities of AB derivatives.     

Strongly deformed nuclei near the magic proton shell 82?

The sudden change of the isotope phase shift in the Hg isotopes is explained by studying the deformation energy with the Strutinsky shell correction method. It is shown that going from the spherical isotope ²⁰⁴Hg to the isotope ¹⁸⁴Hg a small negative deformation (up to β₂ = −0.19) is built up. Between the mass numbers 186 and 182 the deformation is shifted through the γ instability valley to larger positive deformations (β₂ ≈ 0.3). The experimentally observed anomaly can be explained with the theoretical isotope shift constant, if this change of ground state deformations is taken into account.     

Frequency spectrum and modes of vibration in circular,convex AT-cut bevelled — Design quartz resonators

In this paper an approximate solution of the problem for the calculation of the frequency spectrum in circular, convex AT-cut bevelled — design quartz resonators, operating in overtones of coupled TS-TT modes of vibration is given. A plot of nondimensional resonance frequency as a function of the plates geometry is made. The graph includes the influence of the bevel on the suppression of the unwanted anharmonic overtones of vibration.