Since the time of the ancient Greeks, humans have been aware of this mathematical idea. Golden ratio is an irrational number that is symbolized by the Greek numeral phi (φ). One can find this ratio everywhere. It is ...Since the time of the ancient Greeks, humans have been aware of this mathematical idea. Golden ratio is an irrational number that is symbolized by the Greek numeral phi (φ). One can find this ratio everywhere. It is in nature, art, architecture, human body, etc. But this symbolism can result in a strong connection with mathematical nature. In this paper we will be discussing the connection between Fibonacci sequence (a series of numbers where every number is equal to the sum of two numbers before it) and Golden ratio. Secondly, how this mathematical idea shows up in a nature, such as sunflower and human DNA.展开更多
In this paper we discuss the uniqueness and existence of solution to a real gas flow network by employing graph theory. A directed graph is an efficient way to represent a gas network. We consider steady state real ga...In this paper we discuss the uniqueness and existence of solution to a real gas flow network by employing graph theory. A directed graph is an efficient way to represent a gas network. We consider steady state real gas flow network that includes pipelines, compressors, and the connectors. The pipelines and compressors are represented as edges of the graph and the interconnecting points are represented as nodes of the graph representing the network. We show that a unique solution of such a system exists. We use monotonicity property of a mapping to proof uniqueness, and the contraction mapping theorem is used to prove existence.展开更多
We consider a continuum model for the evolution of an epitaxially-strained dislocation-free anisotropic thin solid film on isotropic deformable substrate in the absence of vapor deposition. By using a thin film approx...We consider a continuum model for the evolution of an epitaxially-strained dislocation-free anisotropic thin solid film on isotropic deformable substrate in the absence of vapor deposition. By using a thin film approximation we derived a nonlinear evolution equation. We examined the nonlinear evolution equation and found that there is a critical film thickness below which every film thickness is stable and a critical wave number above which every film thickness is stable.展开更多
文摘Since the time of the ancient Greeks, humans have been aware of this mathematical idea. Golden ratio is an irrational number that is symbolized by the Greek numeral phi (φ). One can find this ratio everywhere. It is in nature, art, architecture, human body, etc. But this symbolism can result in a strong connection with mathematical nature. In this paper we will be discussing the connection between Fibonacci sequence (a series of numbers where every number is equal to the sum of two numbers before it) and Golden ratio. Secondly, how this mathematical idea shows up in a nature, such as sunflower and human DNA.
文摘In this paper we discuss the uniqueness and existence of solution to a real gas flow network by employing graph theory. A directed graph is an efficient way to represent a gas network. We consider steady state real gas flow network that includes pipelines, compressors, and the connectors. The pipelines and compressors are represented as edges of the graph and the interconnecting points are represented as nodes of the graph representing the network. We show that a unique solution of such a system exists. We use monotonicity property of a mapping to proof uniqueness, and the contraction mapping theorem is used to prove existence.
文摘We consider a continuum model for the evolution of an epitaxially-strained dislocation-free anisotropic thin solid film on isotropic deformable substrate in the absence of vapor deposition. By using a thin film approximation we derived a nonlinear evolution equation. We examined the nonlinear evolution equation and found that there is a critical film thickness below which every film thickness is stable and a critical wave number above which every film thickness is stable.
