Description of stability for linear time-invariant systems based on the first curvature

This paper focuses on using the first curvature κ(t) of trajectory to describe the stability of linear time-invariant system. We extend the results for two and three-dimensional systems (Wang, Sun, Song et al, arXiv:1808.00290) to n-dimensional systems. We prove that for a system $\text{◂=▸}\dot{r}(t)=\text{◂⋅▸}Ar(t)$, (a) if there exists a measurable set whose Lebesgue measure is greater than zero, such that $\text{◂≠▸}\underset{t\to +\infty }{\lim }\kappa (t)\ne 0$ or $\underset{t\to +\infty }{\lim }\kappa (t)$ does not exist for any initial value in this set, then the zero solution of the system is stable; (b) if the matrix A is invertible, and there exists a measurable set whose Lebesgue measure is greater than zero, such that $\text{◂=▸}\underset{t\to +\infty }{\lim }\kappa (t)=+\infty$ for any initial value in this set, then the zero solution of the system is asymptotically stable.     

A Hydrosilylation Approach to Silicon‐Bridged Functional Dipyrromethanes: Introducing Silicon to A New Arena

Two silylene‐spaced ((E)‐vinylsilyl)anthracene‐dipyrromethane dyads have been designed and synthesized by RhCl(PPh₃)₃‐catalyzed hydrosilylation reactions of 5‐methyl‐5′‐(ethynylaryl)dipyrromethanes with (9‐Anthryl)‐dimethylsilane. The complexation studies of dyads toward different anions have also been performed, which reveal that dyads exhibit a highly selective response towards fluoride anion attributable to both hydrogen‐bonding and pentacoordination phenomena. This dual‐mode fluoride recognition event is unprecedented and may pave the way for future developments in the areas of porphyrinoids, organosilicon, polymer, and supramolecular chemistry.     

Power-of-two sampling in redundancy systems: The impact of assignment constraints

A classical sampling strategy for load balancing policies is power-of-two, where any server pair is sampled with equal probability. This does not cover practical settings with assignment constraints which force non-uniform sampling. While intuition suggests that non-uniform sampling adversely impacts performance, this was only supported through simulations, and rigorous statements have remained elusive. Building on product-form distributions for redundancy systems, we prove the stochastic dominance of uniform sampling for a four-server system as well as arbitrary-size systems in light traffic.     

Entanglement of two distinguishable atoms in a rectangular waveguide: Linear approximation with single excitation

We investigate the entanglement dynamics of two distinguishable two-level systems(TLSs) characterized by energy difference δ located inside a rectangular hollow metallic waveguide of transverse dimensions a and b. The effects of energy difference δ and the inter-TLS distance on the time evolution of the concurrence of the TLSs are examined in the single excitation subspace when the energy separation of the TLS is far away from the cutoff frequencies of the transverse mode.     

Expansion of Photostable Luminescent Radicals by Meta-Substitution

Polychlorinated pyridyldiphenylmethyl radicals having substituents meta to the position bearing the carbon-centered radical (α-carbon) are synthesized. All of them are stable in ambient conditions in solutions and fluorescent in cyclohexane. The fluorescence of the radicals with bromo, phenyl, 4-chlorophenyl, or 2-pyridyl substituents are enhanced in chloroform, while the emission of the radicals with 2-thienyl or 2-furyl substituents are quenched in chloroform. DFT and TD-DFT calculations indicate that the first doublet excited states of the former are locally excited, while the first doublet excited states of the latter are charge transfer states from the π-electron-donating substituent to the accepting radical. The latter also show much higher photostability under 370-nm light irradiation compared with the first reported photostable fluorescent radical, (3,5-dichloro-4-pyridyl)bis(2,4,6-trichlorophenyl)methyl radical (PyBTM), with pronounced bathochromic shifts of the fluorescence.     

Order-Stability in Complex Biological,Social, and AI-Systems from Quantum Information Theory

This paper is our attempt, on the basis of physical theory, to bring more clarification on the question “What is life?” formulated in the well-known book of Schrödinger in 1944. According to Schrödinger, the main distinguishing feature of a biosystem’s functioning is the ability to preserve its order structure or, in mathematical terms, to prevent increasing of entropy. However, Schrödinger’s analysis shows that the classical theory is not able to adequately describe the order-stability in a biosystem. Schrödinger also appealed to the ambiguous notion of negative entropy. We apply quantum theory. As is well-known, behaviour of the quantum von Neumann entropy crucially differs from behaviour of classical entropy. We consider a complex biosystem S composed of many subsystems, say proteins, cells, or neural networks in the brain, that is, S=(Si). We study the following problem: whether the compound system S can maintain “global order” in the situation of an increase of local disorder and if S can preserve the low entropy while other Si increase their entropies (may be essentially). We show that the entropy of a system as a whole can be constant, while the entropies of its parts rising. For classical systems, this is impossible, because the entropy of S cannot be less than the entropy of its subsystem Si. And if a subsystems’s entropy increases, then a system’s entropy should also increase, by at least the same amount. However, within the quantum information theory, the answer is positive. The significant role is played by the entanglement of a subsystems’ states. In the absence of entanglement, the increasing of local disorder implies an increasing disorder in the compound system S (as in the classical regime). In this note, we proceed within a quantum-like approach to mathematical modeling of information processing by biosystems—respecting the quantum laws need not be based on genuine quantum physical processes in biosystems. Recently, such modeling found numerous applications in molecular biology, genetics, evolution theory, cognition, psychology and decision making. The quantum-like model of order stability can be applied not only in biology, but also in social science and artificial intelligence.     

Boussinesq方程行波解的存在性

利用平面动力系统方法的分支理论，研究了Boussinesq方程，通过对Boussinesq方程进行行波变换，得到了相应行波系统的首次积分和平衡点，给出了不同参数条件下的相图，证实了Boussinesq方程存在孤立波解和周期波解。