一类单调算子的新不动点定理

利用单调迭代法、数学归纳法以及序差距的性质,在半序Banach空间中探究不具有紧性、连续性以及任何凹凸性的单调算子不动点存在以及惟一性问题,得出其新不动点定理,这些结果对相关结论进行了推广,使其适用范围更广,同时将该结论应用于求解Volterra型积分方程组问题中.     

Complete set of periodic solutions of a discontinuous recurrence equation

A nonlinear three-term recurrence relation arising from seeking the steady states of a cellular neural network with bang‐bang control is studied. We show that each solution is periodic and its prime period can be determined by three of its consecutive terms. By means of this periodicity property, we may then solve the steady state problem which to our knowledge is not solved by other means.     

On Newton’s method for solving equations containing Fréchet-differentiable operators of order at least two

We provide sufficient conditions for the semilocal convergence of Newton’s method to a locally unique solution of a nonlinear operator equation containing operators that are Fréchet-differentiable of order at least two, in a Banach space setting. Numerical examples are also provided to show that our results apply to solve nonlinear equations in cases earlier ones cannot [J.M. Gutiérrez, A new semilocal convergence theorem for Newton’s method, J. Comput. Appl. Math. 79(1997) 131-145; Z. Huang, A note of Kantorovich theorem for Newton iteration, J. Comput. Appl. Math. 47 (1993) 211-217; F.A. Potra, Sharp error bounds for a class of Newton-like methods, Libertas Mathematica 5 (1985) 71-84].     

Twist‐dependent stacking energy of base‐pair steps in B‐DNA geometry: A density functional theory approach

Stacking energy of all the 10 unique DNA base‐pair steps (bp step) are calculated using density functional theory within the ultrasoft pseudopotential plane wave method and local density approximation for the exchange‐correlation functional. We have studied the dependence of stacking energy on twist angle, an aspect found difficult to explain using classical theory. We have found that the twist angle for different bp steps at stacking energy minimum matches extremely well with the values of average twist obtained from B‐DNA crystal structure data. This indicates that the use of a proper quantum chemical method to calculate the π‐π electronic interactions may explain stacking energy without incorporating hydrophobic interaction through solvent or effect of backbone through pseudobond. From the twist angle‐dependent stacking energy profile, we have also generated the probability distributions of twist for all the bp steps and calculated the variance of the distribution. Our calculated variances show similar trend to that of the experimental data for which sufficient numbers of data are available. The TA, AT, and CG doublets show large variances among the 10 possible bp steps, indicating their maximum flexibility. This might be the case of unusual deformation observed at the TATA‐box while binding to TBP protein. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Novel electrochemical biosensor based on functional composite nanofibers for sensitive detection of p53 tumor suppressor gene

A novel electrochemical biosensor based on functional composite nanofibers for sensitive hybridization detection of p53 tumor suppressor using methylene blue (MB) as an electrochemical indicator is developed. The carboxylated multi-walled carbon nanotubes (MWNTs) doped nylon 6 (PA6) composite nanofibers (MWNTs–PA6) was prepared using electrospinning, which served as the nanosized backbone for pyrrole (Py) electropolymerization. The functional composite nanofibers (MWNTs–PA6–PPy) used as supporting scaffolds for ssDNA immobilization can dramatically increase the amount of DNA attachment and the hybridization sensitivity. The biosensor displayed good sensitivity and specificity. The target wild type p53 sequence (wtp53) can be detected as low as 50 fM and the discrimination is up to 57.5% between the wtp53 and the mutant type p53 sequence (mtp53). It holds promise for the early diagnosis of cancer development and monitoring of patient therapy.     

Protection‐Group‐Free Synthesis of Sequence‐Defined Macromolecules via Precision λ‐Orthogonal Photochemistry

An advanced light‐induced avenue to monodisperse sequence‐defined linear macromolecules via a unique photochemical protocol is presented that does not require any protection‐group chemistry. Starting from a symmetrical core unit, precision macromolecules with molecular weights up to 6257.10 g mol^?1 are obtained via a two‐monomer system: a monomer unit carrying a pyrene functionalized visible light responsive tetrazole and a photo‐caged UV responsive diene, enabling an iterative approach for chain growth; and a monomer unit equipped with a carboxylic acid and a fumarate. Both light‐induced chain growth reactions are carried out in a λ‐orthogonal fashion, exciting the respective photosensitive group selectively and thus avoiding protecting chemistry. Characterization of each sequence‐defined chain (size‐exclusion chromatography (SEC), high‐resolution electrospray ionization mass spectrometry (ESI‐MS), and NMR spectroscopy), confirms the precision nature of the macromolecules.     

Dependence of electronic and optical properties of multilayer SiC and GeC on stacking sequence and external electric field

The electronic and optical properties of different stacked multilayer SiC and GeC are investigated with and without external electric field (EEF). The band gaps of multilayer SiC and GeC are found smaller than that of monolayer SiC and GeC due to the interlayer coupling effect. When EEF is applied, the direct band gaps (ΔK–M) of multilayer SiC and direct band gaps (ΔK–K) of multilayer GeC all turn to indirect band gaps (ΔK–G) as the band at the G point drops dramatically toward zero. The imaginary part ε₂(ω)s of multilayer SiC and GeC show that new absorption peaks between 2–5 eV appear when the polarized direction is perpendicular to the layer plane, and new absorption peaks in infrared region appear as the EEF is higher than a certain point when the polarized direction is parallel to the layer plane. Our calculations reveal that different stacking sequences and EEF can provide a wide tunable band structures and optical properties for multilayer SiC and GeC.     

Quadrilaterals,extremal quasiconformal extensions and Hamilton sequences

The relationship between Strebel boundary dilatation of a quasisymmetric function h of the unit circle and the dilatation indicated by the change in the modules of the quadrilaterals with vertices on the circle intrigues many mathematicians. It had been a conjecture for some time that the dilatations Ko（h） and K1（h） of h are equal before Anderson and Hinkkanen disproved this by constructing concrete counterexamples. The independent work of Wu and of Yang completely characterizes the condition for Ko（h） = K1 （h） when h has no substantial boundary point. In this paper, we give a necessary and sufficient condition to determine the equality for h admitting a substantial boundary point.     

生成模型在蛋白质序列设计中的应用

蛋白质是一切生命体的物质基础,是生命活动的主要承担者,参与各种生理功能的调节.设计具有特定功能的蛋白质在蛋白质工程、生物医药、材料科学等领域具有重要意义.蛋白质序列设计的目标是设计能够折叠成期望结构并具有相应功能的氨基酸序列,是所有理性蛋白质工程的核心问题,具有极其重要的研究和应用潜力.随着蛋白质序列数据的指数型增长和...