In this paper, we show how to analyze bifurcation and limit cycles for biological systems by using an algebraic approach based on triangular decomposition, Gröbner bases, discriminant varieties, real solution classification, and quantifier elimination by partial CAD. The analysis of bifurcation and limit cycles for a concrete two-dimensional system, the self-assembling micelle system with chemi...

The influence of thermal cycling on the microstructure, magnetic phase transition and magnetic entropy change of a Gd5Si1.3Ge2.7 thin film up to 1000 cycles is investigated. The authors found that after 1000 cycles a strong reduction of the crystallographic phase responsible for the magnetostructural transition (Orthorhombic II phase) occurs. This is attributed to chemical disorder, caused by t...

an acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. the acyclic chromatic index of a graph $g$ denoted by $chi_a '(g)$ is the minimum number $k$ such that there is an acyclic edge coloring using $k$ colors. the maximum degree in $g$ denoted by $delta(g)$, is the lower bound for $chi_a '(g)$. $p$-cuts introduced in this paper acts as a powerfu...

The molecular motor myosin V has been studied extensively both in bulk and single molecule experiments. Based on the chemical states of the motor, we construct a systematic network theory that includes experimental observations about the stepping behavior of myosin V. We utilize constraints arising from nonequilibrium thermodynamics to determine motor parameters and demonstrate that the motor b...

the paper deals with the analysis of the external factor (solar activity, volcanic eruptions) influence on tree growth at the kola peninsula, northwestern russia. pinus sylvestris l. (scots pine) tree-ring chronologies collected nearby the northern timberline (68.63n, 33.25e) include the oldest (1445-2005 ad) living pine tree found up to date in the kola peninsula. a total of 18 living trees p...

Abstract Many chemical indices have been invented in theoretical chemistry, such as Wiener index, Merrifield-Simmons index, Hosoya index, spectral radius and Randić index, etc. The extremal trees and unicyclic graphs for these chemical indices are interested in existing literature. Let G be a molecular graph (called a cacti), which all of blocks of G are either edges or cycles. Denote G (n, r) ...

While structures and reactivities of many small molecules can be computed efficiently and accurately using quantum chemical methods, heuristic approaches remain essential for modeling complex structures and large-scale chemical systems. Here, we present a heuristics-aided quantum chemical methodology applicable to complex chemical reaction networks such as those arising in cell metabolism and p...