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851.
852.
We extend the applicability of Newton’s method for approximating a solution of a nonlinear operator equation in a Banach space setting using nondiscrete mathematical induction concept introduced by Potra and Ptak. We obtain new sufficient convergence conditions for Newton’s method using Lipschitz and center-Lipschitz conditions instead of only the Lipschitz condition used in F.A.Potra, V.Ptak, Sharp error bounds for Newton’s process, Numer. Math., 34 (1980), 63–72, and F.A.Potra, V.Ptak, Nondiscrete Induction and Iterative Processes, Research Notes in Mathematics, 103. Pitman Advanced Publishing Program, Boston, 1984. Under the same computational cost as before, we provide: weaker sufficient convergence conditions; tighter error estimates on the distances involved and more precise information on the location of the solution. Numerical examples are also provided in this study. 相似文献
853.
854.
In ([11]), we have studied quadratic Leibniz algebras that are Leibniz algebras endowed with symmetric, nondegenerate, and associative (or invariant) bilinear forms. The nonanticommutativity of the Leibniz product gives rise to other types of invariance for a bilinear form defined on a Leibniz algebra: the left invariance, the right invariance. In this article, we study the structure of Leibniz algebras endowed with nondegenerate, symmetric, and left (resp. right) invariant bilinear forms. In particular, the existence of such a bilinear form on a Leibniz algebra 𝔏 gives rise to a new algebra structure ☆ on the underlying vector space 𝔏. In this article, we study this new algebra, and we give information on the structure of this type of algebras by using some extensions introduced in [11]. In particular, we improve the results obtained in [22]. 相似文献
855.
Saúl A. Blanco 《Journal of Algebraic Combinatorics》2013,38(3):585-596
We define the shortest path poset SP(u,v) of a Bruhat interval [u,v], by considering the shortest u–v paths in the Bruhat graph of a Coxeter group W, where u,v∈W. We consider the case of SP(u,v) having a unique rising chain under a reflection order and show that in this case SP(u,v) is a Gorenstein? poset. This allows us to derive the nonnegativity of certain coefficients of the complete cd-index. We furthermore show that the shortest path poset of an irreducible, finite Coxeter group exhibits a symmetric chain decomposition. 相似文献
856.
High pressure experimental studies show that in certain mesogenic materials, the nematic-smectic A (N-Sm A) transition temperature
TAN exhibits nonlinear pressure dependence. As a consequence, the material
shows reentrant phenomena that is a phase sequence nematic — smectic A — reentrant nematic appears. The
characteristic features of this phenomenon have been addressed here within
the framework of Landau-de-Gennes theory, where the coupling between nematic
and smectic A order parameters (γ, λeff) plays an important role. The cubic coupling γ is chosen to be negative in order to form Sm A phase whereas the biquadratic
coupling λeff is made large and positive to obtain reentrant behaviour. In the present work, we incorporate the pressure dependence in
the theory through γ and λeff which justifies the experimental pressure dependence in the reentrant transition temperature
. The pressure dependence of γ and λeff are employed in the calculation of excess specific heat capacity near the reentrant transition. The computed heat capacity
shows strong pressure dependence near the reentrant transition which
can be confirmed from high pressure measurement. 相似文献
857.
Two sets of microemulsions, cyclohexane- and water-rich ones, were prepared with the following n-alkanols as cosurfactants: n-propanol, n-butanol, n-pentanol, and n-hexanol. The results showed the influence of the alkyl chain length of the n-alkanol on the permselectivity properties of the pervaporation technique in the breakdown of the microemulsions. The variations of the total flux rate J and the enrichment factor beta were in parallel with the effect of the cosurfactant on the swelling extent of the PDMS membrane. 相似文献
858.
Koubachi J El Kazzouli S Berteina-Raboin S Mouaddib A Guillaumet G 《The Journal of organic chemistry》2007,72(20):7650-7655
A new and efficient method for the synthesis of 2,3,6-trisubstituted imidazo[1,2-a]pyridine derivatives using a microwave-assisted one-pot, two-step Suzuki/heteroarylation or one-pot, three-step cyclization/Suzuki/heteroarylation was developed. Polysubstituted compounds are obtained in good yield from 2-amino-5-halogenopyridines, 2-halogenocarbonyl derivatives, boronic acids, and heteroaryl bromides. 相似文献
859.
Peach MJ Tellgren EI Sałek P Helgaker T Tozer DJ 《The journal of physical chemistry. A》2007,111(46):11930-11935
The bond length alternation (BLA), the highest-occupied-lowest-unoccupied (HO-LU) orbital energy gap, and the corresponding excitation energy are determined for trans-polyacetylene (PA) and polyyne (PY) using density functional theory. Results from the Coulomb-attenuated CAM-B3LYP functional are compared with those from the conventional BHHLYP and B3LYP hybrid functionals. BLA values and HO-LU gaps are determined using both finite oligomer and infinite chain calculations, subject to periodic boundary conditions. TDDFT excitation energies are determined for the oligomers. The oligomer excitation energies and HO-LU gaps are then used, in conjunction with the infinite chain HO-LU gap, to estimate the infinite chain excitation energy. Overall, BHHLYP and CAM-B3LYP give BLA values and excitation energies that are larger and more accurate than those obtained using B3LYP. The results highlight the degree to which excitation energies can be approximated using the HO-LU gaps-at the infinite limit, this approximation works well for B3LYP, but not for the other functionals, where the HO-LU gap is significantly larger. The study provides further evidence for the high-quality theoretical predictions that can be obtained from the CAM-B3LYP functional. 相似文献
860.
Two new 3D copper(II) azido isomers, [Cu(N3)(nic)]infinity (1 and 2) (nic = nicotinate), have been synthesized and characterized. To the best of our knowledge, 1 is the first metal azido complex showing rutile-type topology, while 2 is a chiral compound obtained by spontaneous resolution upon crystallization. 相似文献