Synthesis,structure and catalytic properties of Pdii-based bimetallic complexes with ferrocenecarboxylic acid

Novel highly soluble palladium-based complexes with ferrocenecarboxylic acid of general formula [Pd(lut)₂(FcCOO)₂] (lut is 2,6-or 3,4-lutidines) were synthesized and structurally characterized by single-crystal X-ray diffraction. The catalytic oxidation of 1,2-diphenyl-acetylene with these complexes gave dibenzo[a,e]pentalene derivative along with other products.     

Oxidative Addition of Haloheteroarenes to Palladium(0): Concerted versus SNAr‐Type Mechanism

The kinetics of the oxidative additions of haloheteroarenes HetX (X=I, Br, Cl) to [Pd⁰(PPh₃)₂] (generated from [Pd⁰(PPh₃)₄]) have been investigated in THF and DMF and the rate constants have been determined. In contrast to the generally accepted concerted mechanism, Hammett plots obtained for substituted 2‐halopyridines and solvent effects reveal a reaction mechanism dependent on the halide X of HetX: an unprecedented S_NAr‐type mechanism for X=Br or Cl and a classical concerted mechanism for X=I. These results are supported by DFT studies.     

An unprecedented transformation mode in aluminium oxazoline-amido-phenolate complexes

This paper describes the effect of solvent-induced synthetic routes of aluminium pendant oxazoline-amido-phenolate complexes. Treatment of ligand precursor L with AlMe₃ in a 1:1 ratio in diethyl ether yielded the four-coordinated complex (LAlMe)₂. Reaction of ligand precursor L with AlMe₃ in a 1:2 ratio in hexane generated the four-coordinated complex L(AlMe₂)₂. A novel transformation mode occurred from L(AlMe₂)₂ to (LAlMe)₂ when using diethyl ether or tetrahydrofuran as solvent. A density functional theory computational study also supports a plausible mechanism. All results were supported by spectroscopic data and in agreement with single-crystal X-ray diffraction structural analysis.     

Singular Hamiltonian elliptic systems with critical exponential growth in dimension two

We will focus on the existence of nontrivial solutions to the following Hamiltonian elliptic system where are numbers belonging to the interval [0, 2), V is a continuous potential bounded below on by a positive constant and the functions f and g possess exponential growth range established by Trudinger–Moser inequalities in Lorentz–Sobolev spaces. The proof involves linking theorem and a finite‐dimensional approximation.     

Periodic Solutions of Third-order Differential Equations with Finite Delay in Vector-valued Functional Spaces

In this paper, we study the well-posedness of the third-order differential equation with finite delay(P_3): αu'"(t) + u"(t) = Au(t) + Bu'(t) + Fut +f(t)(t ∈ T := [0,2π]) with periodic boundary conditions u(0) = u(2π), u'(0) = u"(2π),u"(0)=u"(2π) in periodic Lebesgue-Bochner spaces Lp(T;X) and periodic Besov spaces B_(p,q)~s(T;X), where A and B are closed linear operators on a Banach space X satisfying D(A) ∩ D(B) ≠ {0}, α≠ 0 is a fixed constant and F is a bounded linear operator from Lp([-2π, 0]; X)(resp. Bp,qs([-2π, 0]; X)) into X, ut is given by ut(s) = u(t + s) when s ∈ [-2π,0]. Necessary and sufficient conditions for the Lp-well-posedness(resp. B_(p,q)~s-well-posedness)of(P_3) are given in the above two function spaces. We also give concrete examples that our abstract results may be applied.     

Norms and lower bounds of some matrix operators on Fibonacci weighted difference sequence space

Norm of an operator T:X→Y is the best possible value of U satisfying the inequality and lower bound for T is the value of L satisfying the inequality where ‖.‖_X and ‖.‖_Y are the norms on the spaces X and Y, respectively. The main goal of this paper is to compute norms and lower bounds for some matrix operators from the weighted sequence space ?_p(w) into a new space called as Fibonacci weighted difference sequence space. For this purpose, we firstly introduce the Fibonacci difference matrix and the space consisting of sequences whose ‐transforms are in .