Higher order duality in multiobjective fractional programming with support functions

In this paper a new class of higher order (F,ρ,σ)-type I functions for a multiobjective programming problem is introduced, which subsumes several known studied classes. Higher order Mond-Weir and Schaible type dual programs are formulated for a nondifferentiable multiobjective fractional programming problem where the objective functions and the constraints contain support functions of compact convex sets in Rn. Weak and strong duality results are studied in both the cases assuming the involved functions to be higher order (F,ρ,σ)-type I. A number of previously studied problems appear as special cases.     

Proton Transfer Isomerization of Pyrazole in the Ground State： σ vs π Mechanism and Water Assisting Effect

The proton transfer isomerization of pyrazole and the water assisting effect by looping 1 to 4 water molecules on the singlet state potential energy surface have been investigated by using hybrid density functional theory method （B3PW91） with a 6-311＋＋G^＊＊ basis set. Two mechanisms were proposed to explain the mono- and multi-water assisting effects, respectively. The reactants and products of all groups have been characterized on their potential energy surfaces. For the isomerizafion of monomolecule pyrazole, the isomeriz＇ation energy barrier is 46.4 kcal·mol^-1. For the monohydration assisting mechanism, the reactant complex is connected to the product complex via two saddle points. The corresponding isomerization barriers are 46.7and 23.0 kcal·mol^-1, respectively. As to the multihydration assisting mechanism, the isomerization barriers are 12.0, 10.9 and 13.14 kcal·mol^-1 accordingly, when the number of water molecules is 2, 3 and 4, respectively. The multihydration assisting isomerization can occur in water-dominated environments, for example, in the organism, and thereby is crucial to energy transference. The deproton and dehydrogen energies of monomolecule pyrazole and various hydrated pyrazoles were calculated and then found much bigger than the isomerization barriers of their relative complexes, suggesting the impossibility of deprotonation or dehydrogenation. The isomerization of pyrazole is a proton-coupling-electron-migration process, but two different mechanisms are noticed, viz. σ- and π-type mechanisms. The π-bond of pyrazole participates in isomerization in the π-type mechanism, whereas only o-electron takes part in isomerization in the σ-type mechanism.     

Synthesis and Characterization of [XeOXe]2+ in the Adduct‐Cation Salt, [CH3CN‐ ‐ ‐XeOXe‐ ‐ ‐NCCH3][AsF6]2

Acetonitrile and [FXeOXe‐ ‐ ‐FXeF][AsF₆] react at ?60 °C in anhydrous HF (aHF) to form the CH₃CN adduct of the previously unknown [XeOXe]²⁺ cation. The low‐temperature X‐ray structure of [CH₃CN‐ ‐ ‐XeOXe‐ ‐ ‐NCCH₃][AsF₆]₂ exhibits a well‐isolated adduct‐cation that has among the shortest Xe?N distances obtained for an sp‐hybridized nitrogen base adducted to xenon. The Raman spectrum was fully assigned by comparison with the calculated vibrational frequencies and with the aid of ¹⁸O‐enrichment studies. Natural bond orbital (NBO), atoms in molecules (AIM), electron localization function (ELF), and molecular electrostatic potential surface (MEPS) analyses show that the Xe?O bonds are semi‐ionic whereas the Xe?N bonds may be described as strong electrostatic (σ‐hole) interactions.     

Kinetic study of nucleophilic reactivity of heterocyclic amines with 4,6-dinitrobenzofuroxan in acetonitrile

The reaction kinetics of 4,6-dinitrobenzofuroxan with five heterocyclic amines was investigated spectrophotometrically (UV–Vis) in acetonitrile at 20 °C. It was observed that the rate constants of these reactions increased as follows: 2-aminopyrimidine > 2-aminothiazole > 2-aminobenzothiazole > 5-amino-3,4-dimethylisoxazole > 2-amino-5-trifluoromethyl-1,3,4-thiadiazole. Further, second-order rate constants (k₁) pertaining to the C–N and C–C bond forming step of these complexation processes fit to the three parameter equation log k (20 °C) = s_N (N + E), allowing the determination of the nucleophilicity parameters (N) of the five heterocyclic amines. The heterocyclic amines were subsequently ranked on the comprehensive nucleophilicity scale defined by Mayr et al. (2003), providing a direct comparison of n-, π-, and σ-nucleophiles.     

Eigenfunction statistics on quantum graphs

We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for which such a model was proposed by Berry in 1977. The autocorrelation functions we calculate for an individual quantum graph exhibit a universal component, which completely determines a Gaussian Random Wave Model, and a system-dependent deviation. This deviation depends on the graph only through its underlying classical dynamics. Classical criteria for quantum universality to be met asymptotically in the large graph limit (i.e. for the non-universal deviation to vanish) are then extracted. We use an exact field theoretic expression in terms of a variant of a supersymmetric σ model. A saddle-point analysis of this expression leads to the estimates. In particular, intensity correlations are used to discuss the possible equidistribution of the energy eigenfunctions in the large graph limit. When equidistribution is asymptotically realized, our theory predicts a rate of convergence that is a significant refinement of previous estimates. The universal and system-dependent components of intensity correlation functions are recovered by means of an exact trace formula which we analyse in the diagonal approximation, drawing in this way a parallel between the field theory and semiclassics. Our results provide the first instance where an asymptotic Gaussian Random Wave Model has been established microscopically for eigenfunctions in a system with no disorder.     

Cooperative interaction between π-hole and single-electron σ-hole interactions in O2S···NCX···CH3 and O2Se···NCX···CH3 complexes (X = F,Cl, Br and I)

Ab initio calculations are performed to analyse the cooperative effects between π-hole and single-electron σ-hole interactions in O₂S···NCX···CH₃ and O₂Se···NCX···CH₃ complexes, where X = F, Cl, Br and I. These effects are investigated in terms of geometric and energetic features of the complexes, which are computed by UMP2/aug-cc-pVTZ(-PP) method. Our results indicate that the shortening of the each π-hole bond distance in the complexes is dependent on the strength of the σ-hole interaction. The maximum and minimum energetic cooperativity values correspond to the most and least stable complexes studied in the present work. The cooperativity between both types of interaction is chiefly caused by the electrostatic effects. The topological analysis, based on the quantum theory of atoms in molecules, is used to characterise the interactions and analyse their enhancement with varying electron density at bond critical points.     

Solution to Nonlinear Parabolic Equations Related to the P-Laplacian

Consider the following Cauchy problem:u_t = div(|▽u ~m |~ p-2▽u~m),(x,t) ∈ST=R~N ×(0,T),u(x,0) = μ,x ∈R~N,where 1相似文献   

A density functional theory study of the Cu+·(CO)n (n = 1–3) complexes

Density functional theory calculations, with an effective core potential for the copper ion, and large polarized basis set functions have been used to construct the potential energy surface of the Cu⁺·(CO)_n (n = 1–3) complexes. A linear configuration is obtained for the global minimum of the Cu⁺·CO and Cu⁺·(CO)₂ complexes with a bond dissociation energy (BDE) of 35.9 and 40.0 kcal mol^-1, respectively. For the Cu⁺·(CO)₃ complex, a trigonal planar geometry is obtained for the global minimum with a BDE of 16.5 kcal mol^?1. C-coordinated copper ion complexes exhibit stronger binding energy than O-coordinated complexes as a result of C_lp → 4s σ-donation. The computed sequential BDEs of Cu⁺·(CO)_n (n = 1–4) complexes agree well with experimental findings, in which the electrostatic energy and σ-donation play an important role in the observed trend.     

On Products of Property b1

In this note,we present that:(1)Let X=σ{Xα:α∈A} be|A|-paracompact (resp.,hereditarily |A|-paracompact).If every finite subproduct of {Xα:α∈A} has property b1 (resp.,hereditarily property b1),then so is X.(2) Let X be a P-space and Y a metric space.Then,X×Y has property b1 iff X has property b1.(3) Let X be a strongly zero-dimensional and compact space.Then,X×Y has property b1 iff Y has property b1.