On the variety of triangles for a hyper-Kähler fourfold constructed by Debarre and Voisin

We study the similarities between the Fano varieties of lines on a cubic fourfold, a hyper-Kähler fourfold studied by Beauville and Donagi, and the hyper-Kähler fourfold constructed by Debarre and Voisin in [3]. We exhibit an analog of the notion of “triangle” for these varieties and prove that the 6-dimensional variety of “triangles” is a Lagrangian subvariety in the cube of the constructed hyper-Kähler fourfold.     

自由基浓度测定方法的再验证及其在煤化学中应用

对前人建立的标准曲线法测煤中自由基浓度进行优化,以DPPH标准样品和基准样品的二次积分面积比值为新参数,结果显示新参数标准曲线法的实测值与理论值相对误差都在5%以内;重复性、复现性实验的相对标准偏差都小于3%。将新参数标准曲线法用于分析不同煤化程度煤和新疆黑山煤(HS)沥青质的自由基浓度,发现随着煤化程度增加,其煤中自由基浓度逐渐增大,从低阶褐煤的8.531×10~(17)/g上升到高阶无烟煤3.37899×10~(19)/g;而在HS煤液化过程中,随着加氢液化温度的升高,其沥青质自由基浓度逐渐下降,从290℃的1.5793×10~(18)/g降到450℃的7.410×10~(17)/g,沥青质自由基浓度变化趋势与其产率变化趋势相一致。     

Homogenization of Periodically Heterogeneous Thin Beams

Consider an elastic thin three-dimensional body made of a periodic distribution of elastic inclusions. When both the thickness of the beam and the size of the heterogeneities tend simultaneously to zero the authors obtain three different one-dimensional models of beam depending upon the limit of the ratio of these two small parameters.     

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.