Additive Hermitian idempotent preservers between operator algebras

Let L be an additive map between (real or complex) matrix algebras sending $n\times n$ Hermitian idempotent matrices to $m\times m$ Hermitian idempotent matrices. We show that there are nonnegative integers $p,q$ with $n(p+q)=r\le m$ and an $m\times m$ unitary matrix U such that$L(A)=U[(I_p?A)\oplus (I_q?A^t)\oplus 0_{m?r}]U^{?},\text{for any}n\times n\text{Hermitian}A\text{with rational trace}.$ We also extend this result to the (complex) von Neumann algebra setting, and provide a supplement to the Dye-Bunce-Wright Theorem asserting that every additive map of Hermitian idempotents extends to a Jordan ?-homomorphism.     

A Closed‐Loop Control Strategy for Producing Nitrile Rubber of Uniform Chemical Composition in a Semibatch Reactor: A Simulation Study

To improve the quality of industrial nitrile rubbers, the copolymer chemical composition, p_A(t), should ideally be kept constant along the reaction. This work proposes a closed‐loop control strategy for the semibatch operation of the reactor with the aim of regulating p_A(t) within a reduced range of variability. The proposed strategy is evaluated by simulating a mathematical model of the process. To this effect, a simplified mathematical model of the reaction is first derived and then utilized to obtain a suboptimal control law and a soft‐sensor that estimates the polymerization rates. The suboptimal control law is compensated by adding a term proportional to errors in p_A(t). The simulated example considers the production of the low‐composition AJLT grade, with the copolymerization reaction represented by a detailed mathematical model adjusted to an industrial plant. Due to the high performance of the soft‐sensor, the simulation results suggest that the proposed closed‐loop strategy is efficient to adequately regulate p_A(t) in spite of structural and parametric uncertainties, while other quality variables remained practically unaffected.     

Some extensions of the operator entropy type inequalities

In this paper, we define the generalised relative operator entropy and investigate some of its properties such as subadditivity and homogeneity. As application of our result, we obtain the information inequality. In continuation, we establish some reverses of the operator entropy inequalities under certain conditions by using the Mond–Pe?ari? method.     

Equivalences among Z2s-linear Hadamard codes

The ${\mathbb{Z}}_{2^s}$-additive codes are subgroups of ${\mathbb{Z}}_{2^s}^n$, and can be seen as a generalization of linear codes over ${\mathbb{Z}}_2$ and ${\mathbb{Z}}_4$. A ${\mathbb{Z}}_{2^s}$-linear Hadamard code is a binary Hadamard code which is the Gray map image of a ${\mathbb{Z}}_{2^s}$-additive code. A partial classification of these codes by using the dimension of the kernel is known. In this paper, we establish that some ${\mathbb{Z}}_{2^s}$-linear Hadamard codes of length $2^t$ are equivalent, once $t$ is fixed. This allows us to improve the known upper bounds for the number of such nonequivalent codes. Moreover, up to $t=11$, this new upper bound coincides with a known lower bound (based on the rank and dimension of the kernel). Finally, when we focus on $s\in \{2,3\}$, the full classification of the ${\mathbb{Z}}_{2^s}$-linear Hadamard codes of length $2^t$ is established by giving the exact number of such codes.     

Sufficient Conditions for a Digraph to be Supereulerian

A (di)graph is supereulerian if it contains a spanning eulerian sub(di)graph. This property is a relaxation of hamiltonicity. Inspired by this analogy with hamiltonian cycles and by similar results in supereulerian graph theory, we analyze a number of sufficient Ore type conditions for a digraph to be supereulerian. Furthermore, we study the following conjecture due to Thomassé and the first author: if the arc‐connectivity of a digraph is not smaller than its independence number, then the digraph is supereulerian. As a support for this conjecture we prove it for digraphs that are semicomplete multipartite or quasitransitive and verify the analogous statement for undirected graphs.     

A novel chaotic image encryption scheme using DNA sequence operations

In this paper, we propose a novel image encryption scheme based on DNA (Deoxyribonucleic acid) sequence operations and chaotic system. Firstly, we perform bitwise exclusive OR operation on the pixels of the plain image using the pseudorandom sequences produced by the spatiotemporal chaos system, i.e., CML (coupled map lattice). Secondly, a DNA matrix is obtained by encoding the confused image using a kind of DNA encoding rule. Then we generate the new initial conditions of the CML according to this DNA matrix and the previous initial conditions, which can make the encryption result closely depend on every pixel of the plain image. Thirdly, the rows and columns of the DNA matrix are permuted. Then, the permuted DNA matrix is confused once again. At last, after decoding the confused DNA matrix using a kind of DNA decoding rule, we obtain the ciphered image. Experimental results and theoretical analysis show that the scheme is able to resist various attacks, so it has extraordinarily high security.     

OCS分子在128 nm附近的光解动力学研究：S(3PJ=2,1,0)、S(1D2)以及S(1S0)产物通道

本文利用时间切片离子成像技术对OCS分子进行了真空紫外波段的光解动力学研究. 在四个光解光波长(从129.32到126.08 nm)下测量了硫原子解离产物S(³P_J=2,1,0)、S(¹D₂)、S(¹S₀)的速度影像，并从中清晰地发现了四个主要的解离产物通道：S(³P_J=2,1,0)+CO(X¹Σ⁺)，S(³P_J=2,1,0)+CO(A³π)，S(¹D₂)+CO(X¹Σ⁺)和S(¹S₀)+CO(X¹Σ⁺). 在实验影像中，产物CO分子的部分振动态结构能够得到分辨. 实验还获取解离产物总平动能谱，产物分支比和角分布. 对实验结果进行分析显示除绝热解离通道S(³P_J=2,1,0)+CO(A³π)之外，在其他三个产物通道中非绝热效应都起到非常重要的作用.