零积决定的矩阵代数

本文研究了零积决定的矩阵代数A=Mn(B)的条件及分类问题.利用基矩阵及巧妙对线性映射T进行构造和扩充,用初等矩阵的方法.获得了较为简单直接的新的证明(对于文献[1]中一系列的问题),并还对其遗留的问题n=2的情形给予一并解决,推广了文献[1]中的结论.     

Soliton Solutions to Coupled Integrable Dispersionless Equations

In this paper, by introducing a new transformation, the bilinear form of the coupled integrable dispersionless （CID） equations is derived. It will be shown that this bilineax form is easier to perform the standard Hirota process. One-, two-, and three-soliton solutions are presented. Furthermore, the N-soliton solutions axe derived.     

一类非线性发展方程的精确解

利用hirota双线性法,得到(3+1)维孤子方程、(3+1)维KP-Boussinesq方程、(2+1)维修正Caudrey-Dodd-Gibbon-Kotera-S awada方程、Hirota-Satsuma浅水波方程的精确解,并做出一部分解的图形,进一步研究解的结构和性质.     

Lump and interaction solutions to the (3+1)-dimensional Burgers equation

The(3+1)-dimensional Burgers equation, which describes nonlinear waves in turbulence and the interface dynamics,is considered. Two types of semi-rational solutions, namely, the lump–kink solution and the lump–two kinks solution, are constructed from the quadratic function ansatz. Some interesting features of interactions between lumps and other solitons are revealed analytically and shown graphically, such as fusion and fission processes.     

Novikov algebras carrying an invariant Lorentzian symmetric bilinear form

In this note, we shall classify Novikov algebras that admit an invariant Lorentzian symmetric bilinear form.     

The anharmonic effect study of coupled Morse oscillators for the unimolecular reaction

The importance of anharmonic effect in dissociation of molecular systems especially clusters has been noted. In this paper, we shall study the effect of coupled anharmonic oscillator of the standard bilinear form (SBF) Morse oscillator (MO) potential on unimolecular reaction. We shall use the systematic theoretical approach, YL method, proposed by Yao and Lin (YAO L, et. al. J Phys Chem A, 2007, 111(29): 6722-6729), which can evaluate anharmonic effects on the rate constants based on the transition state theory. In treating the anharmonic effect with the Morse oscillator potential on unimolecular reactions under collision-free conditions by using the RRKM (Rice-Ramsperger-Kassel-Marcus) theory, the in-verse Laplace transformation of the partition functions was used to obtain the total amount of state and density of state by using the first-order and the second-order approximations of the saddle-point method. To demonstrate the anharmonic effect of the SBF Morse model, we choose some model systems and a real reaction as examples.     

Oligonucleotides Containing 7‐Deaza‐2′‐deoxyinosine as Universal Nucleoside: Synthesis of 7‐Halogenated and 7‐Alkynylated Derivatives,Ambiguous Base Pairing,and Dye Functionalization by the Alkyne–Azide ‘Click’ Reaction

Oligonucleotides containing 7‐deaza‐2′‐deoxyinosine derivatives bearing 7‐halogen substituents or 7‐alkynyl groups were prepared. For this, the phosphoramidites 2b – 2g containing 7‐substituted 7‐deaza‐2′‐deoxyinosine analogues 1b – 1g were synthesized (Scheme 2). Hybridization experiments with modified oligonucleotides demonstrate that all 2′‐deoxyinosine derivatives show ambiguous base pairing, as 2′‐deoxyinosine does. The duplex stability decreases in the order C_d>A_d>T_d>G_d when 2b – 2g pair with these canonical nucleosides (Table 6). The self‐complementary duplexes 5′‐d(F⁷c⁷I‐C)₆, d(Br⁷c⁷I‐C)₆, and d(I⁷c⁷I‐C)₆ are more stable than the parent duplex d(c⁷I‐C)₆ (Table 7). An oligonucleotide containing the octa‐1,7‐diyn‐1‐yl derivative 1g , i.e., 27 , was functionalized with the nonfluorescent 3‐azido‐7‐hydroxycoumarin ( 28 ) by the Huisgen–Sharpless–Meldal cycloaddition ‘click’ reaction to afford the highly fluorescent oligonucleotide conjugate 29 (Scheme 3). Consequently, oligonucleotides incorporating the derivative 1g bearing a terminal C?C bond show a number of favorable properties: i) it is possible to activate them by labeling with reporter molecules employing the ‘click’ chemistry. ii) Space demanding residues introduced in the 7‐position of the 7‐deazapurine base does not interfere with duplex structure and stability (Table 8). iii) The ambiguous pairing character of the nucleobase makes them universal probes for numerous applications in oligonucleotide chemistry, molecular biology, and nanobiotechnology.     

Structural Properties of Hachimoji Nucleic Acids and Their Building Blocks: Comparison of Genetic Systems with Four,Six and Eight Alphabets

Expansion of the genetic alphabet is an ambitious goal. A recent breakthrough has led to the eight-base (hachimoji) genetics having canonical and unnatural bases. However, very little is known on the molecular-level features that facilitate the candidature of unnatural bases as genetic alphabets. Here we amalgamated DFT calculations and MD simulations to analyse the properties of the constituents of hachimoji DNA and RNA. DFT reveals the dominant syn conformation for isolated unnatural deoxyribonucleosides and at the 5′-end of oligonucleotides, although an anti/syn mixture is predicted at the nonterminal and 3′-terminal positions. However, isolated ribonucleotides prefer an anti/syn mixture, but mostly prefer anti conformation at the nonterminal positions. Further, the canonical base pairing combinations reveals significant strength, which may facilitate replication of hachimoji DNA. We also identify noncanonical base pairs that can better tolerate the substitution of unnatural pairs in RNA. Stacking strengths of 51 dimers reveals higher average stacking stabilization of dimers of hachimoji bases than canonical bases, which provides clues for choosing energetically stable sequences. A total of 14.4 μs MD simulations reveal the influence of solvent on the properties of hachimoji oligonucleotides and point to the likely fidelity of replication of hachimoji DNA. Our results pinpoint the features that explain the experimentally observed stability of hachimoji DNA.     

Integrable couplings of fractional L‐hierarchy and its Hamiltonian structures

Based on a general isospectral problem of fractional order, a fractional bilinear form variational identity, the new integrable coupling of fractional L‐hierarchy and the Hamiltonian structures of the integrable coupling of fractional L‐hierarchy are obtained. Copyright © 2016 John Wiley & Sons, Ltd.     

Time-dependent Calculations for Two-proton Decay Width with Schematic Density-dependent Contact Pairing Interaction

We calculate the two-proton decay width of the 6Be nucleus employing the schematic densitydependent contact potential for the proton-proton pairing interaction. The decay width is calculated with a time-dependent method, in which the two-proton emission is described as a time-evolution of a threebody meta-stable state. Model-dependence of the two-proton decay width has been shown by comparing the results obtained with the two different pairing models, schematic density-dependent contact and Minnesota interactions, which have zero and finite ranges, respectively.