Shiqiang Zhang — Page 2

arXiv2018

Description of Stability for Two and Three-Dimensional Linear Time-Invariant Systems Based on Curvature and Torsion

This paper focuses on using curvature and torsion to describe the stability of linear time-invariant system. We prove that for a two-dimensional system $\dot{r}(t)= Ar(t)$, (i) if there exists an initial value, such that zero is not the limit of curvature of trajectory as $t\to+\infty$, then the zero solution of the system is stable; (ii) if there exists an initial value, such that the limit of curvature of trajectory is infinity as $t\to+\infty$, then the zero solution of the system is asymptotically stable. For a three-dimensional system, (i) if there exists a measurable set whose Lebesgue measure is greater than zero, such that for all initial values in this set, zero is not the limit of curvature of trajectory as $t\to+\infty$, then the zero solution of the system is stable; (ii) if the coefficient matrix is invertible, and there exists a measurable set whose Lebesgue measure is greater than zero, such that for all initial values in this set, the limit of curvature of trajectory is infinity as $t\to+\infty$, then the zero solution of the system is asymptotically stable; (iii) if there exists a measurable set whose Lebesgue measure is greater than zero, such that for all initial values in this set, zero is not the limit of torsion of trajectory as $t\to+\infty$, then the zero solution of the system is asymptotically stable.

math.OC↗

arXiv2017

In vitro Demonstration of Cancer Inhibiting Properties from Stratified Self-Organized Micro-Discharge Plasma-Liquid Interface

Experiments have revealed a nontrivial cancer-inhibiting capability of liquid media treated by the plasma jet capable of forming thinly stratified self-organized patterns at a plasma-liquid interface. A pronounced cancer depressing activity towards at least two kinds of human cancer cells, namely breast cancer MDA-MB-231 and human glioblastoma U87 cancer lines, was demonstrated. After a short treatment at the thinly stratified self-organized plasma-liquid interface pattern, the cancer inhibiting media demonstrate well pronounced depression and apoptosis activities towards tumor cells, not achievable without interfacial stratification of plasma jet to thin (of several um) current filaments, which therefore play a pivotal (yet still not completely clear) role in building up the cancer inhibition properties. Moreover, thinly stratified, self-organized interfacial discharge is capable to efficiently control the ROS and RNS concentrations in the cancer-inhibiting media, and in particular, abnormal ROS/RNS ratios not achievable in discharges which do not form stratified thin-filament patterns could be obtained. These results were explained in terms of interaction of thin plasma filaments of the self-organized pattern with gas and liquid, where the unusual interaction conditions (i.e., high surface-to-volume ratios etc.) cause accumulation of ROS, RNS and other species in unusual ratios and concentrations, thus forming potentially efficient anti-cancer cocktail. Our funding could be extremely important for handling the cancer proliferation problem, and hence, it should be brought to light to attract due attention of the researchers and explore the possible potential of this approach in tackling the challenging problem of high cancer-induced mortality and rising morbidity trends.

physics.med-ph↗