Vertex-disjoint cycles in local tournaments

Let $r$ be a positive integer. The Bermond–Thomassen conjecture states that, a digraph of minimum out-degree at least $2r-1$ contains $r$ vertex-disjoint directed cycles. A digraph $D$ is called a local tournament if for every vertex $x$ of $D$, both the out-neighbours and the in-neighbours of $x$ induce tournaments. Note that tournaments form the subclass of local tournaments. In this paper, we verify that the Bermond–Thomassen conjecture holds for local tournaments. In particular, we prove that every local tournament $D$ with ${\delta }^{+}\left(D\right)\ge 2r-1$ contains $r$ disjoint cycles $C_1,C_2,\dots ,C_r$, satisfying that either $C_i$ has the length at most 4 or is a shortest cycle of the original digraph of $D-C_1-\dots -C_{i-1}$ for $1\le i\le r$.     

Hilbert空间中连续广义标架的和

基于Hilbert空间标架理论，借助算子工具，用己有连续广义标架构造了新连续广义标架，并给出了有限个连续广义标架和构成新连续广义标架的充要条件，为构造连续广义标架提供了新方法。     

Effect of intramolecular crosslinker properties on the mechanochemical fragmentation of covalently folded polymers

The mechanochemical stability of polymers in solution is enhanced if the chains are covalently folded. Under shear forces, the additional bonds absorb mechanical energy and inhibit unfolding, and as a result, slow down fragmentation. However, not all crosslinkers are equal in terms of their properties (length, strength, etc.). In order to understand the role of these added bonds in the polymers' stability under mechanical stress, a thorough study compares the rate of mechanochemistry on single-chain polymer nanoparticles which have been folded with crosslinkers with different lengths, strengths, positioning, and valencies. The usage of bonds with different mechanical strengths in the crosslinkers was found to be the most powerful way to change the mechanochemical fragmentation rate. In addition, positioning and valency also play significant role in the mechanical stabilization mechanism. © 2020 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2020 © 2020 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2020 , 58, 692–703     

连续梁在周期荷载下的动力稳定性简化分析方法

对于一般任意支撑的连续梁结构动力稳定性问题，已有的计算方法求解过程都很复杂，给工程设计带来极大的不便．本文提出了一个简化的分析方法，利用现有的商业软件，只需求得连续梁的自然频率及静力屈曲（失稳）荷载，就可容易得到结构的动力失稳区域，当考虑结构阻尼对不稳定区域的影响时，可将阻尼矩阵表达为Rayleigh阻尼的形式．研究结果表明：采用本文计算方法与已有的理论计算方法得到的连续梁主参数共振的不稳定边界非常吻合，而本文计算方法更为简单，计算结果可靠，计算精度高，可满足工程设计的需要．     

Copper-Photocatalyzed Borylation of Organic Halides under Batch and Continuous-Flow Conditions

The copper-photocatalyzed borylation of aryl, heteroaryl, vinyl and alkyl halides (I and Br) was reported. The reaction proceeded using a new heteroleptic Cu complex under irradiation with blue LEDs, giving the corresponding boronic-acid esters in good to excellent yields. The reaction was extended to continuous-flow conditions to allow an easy scale-up. The mechanism of the reaction was studied and a mechanism based on a reductive quenching (Cu^I/Cu^I*/Cu⁰) was suggested.     

‐Theory for Schrödinger systems

In this article, we study for the ‐realization of the vector‐valued Schrödinger operator . Using a noncommutative version of the Dore–Venni theorem due to Monniaux and Prüss, we prove that the ‐realization of , defined on the intersection of the natural domains of the differential and multiplication operators which form , generates a strongly continuous contraction semigroup on . We also study additional properties of the semigroup such as extension to L¹, positivity, ultracontractivity and prove that the generator has compact resolvent.     

Synergistic Effects of Pseudocolor Imaging,Differentiation, and Square and Logarithmic Conversion on Accuracy of Quantification of Chemical Characteristics Using Test Strips and Similar Products

Test strips and similar products are highly feasible tools for the rapid and approximate determination of chemical characteristics. Although the application of both the quantitative observation of coloration and regression modeling has recently enabled these products to become quantitative tools, their precision and accuracy may be further improved. In this study, the pseudocolor imaging of the coloration image, derivative spectrophotometry-like differentiation of the coloration values, and logarithmic conversion of the raw and derivative values were compared in terms of the precision and accuracy of the quantitative determination of corrosiveness, glucose, nitrate, and pH using the products. The best regression models for the determination were provided by the combination of pseudocolor imaging and differentiation (nitrate and pH); pseudocolor imaging, differentiation, and square-conversion (corrosiveness); or all of the techniques (glucose). When compared to the use of the original 10 raw coloration variables of red-green-blue, cyan-magenta-yellow-key black, and L*a*b* color models only, the above combinations improved the normalized mean absolute error from 14.8% to 3.09% (corrosiveness), 6.33% to 3.15% (glucose), 7.46% to 4.56% (nitrate), and 3.22% to 0.94% (pH). These achievements were largely attributed to the combination of multiple variables that have non-linear and nonmonotonic relationships with the chemical characteristics.