scholarly journals Existence of homoclinic orbit in generalized Liénard type system

Author(s):  
Tohid Kasbi ◽  
Vahid Roomi ◽  
Aliasghar Jodayree Akbarfam
Keyword(s):  
2016 ◽  
Vol 26 (12) ◽  
pp. 1650194 ◽  
Author(s):  
Haijun Wang ◽  
Chang Li ◽  
Xianyi Li

We devote to studying the problem for the existence of homoclinic and heteroclinic orbits of Unified Lorenz-Type System (ULTS). Other than the known results that the ULTS has two homoclinic orbits to [Formula: see text] for [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and two heteroclinic orbits to [Formula: see text] for [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] on its invariant algebraic surface [Formula: see text], formulated in the literature by Yang and Chen [2014], we seize two new heteroclinic orbits of this Unified Lorenz-Type System. Namely, we rigorously prove that this system has another two heteroclinic orbits to [Formula: see text] and [Formula: see text] while no homoclinic orbit when [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text].


Author(s):  
Patricia N. Hackney

Ustilago hordei and Ustilago violacea are yeast-like basidiomycete pathogens ofHordeum vulgare and Silene alba respectively. The mating type system in both species of Ustilago is bipolar, with alleles, A,a, (U.hordei) and a1, a2 (U.violacea) at a single locus. Haploid sporidia maintain the asexual phase by budding, while the sexual phase is initiated by conjugation tube formation between the mating types during budding and conjugation.For observation of budding, sporidia were prepared by culturing the four types on YEG (yeast extract glucose) broth for 24 hours. After centrifugation at 5000g cells were either left unmated or mated in a1/a2,A/a combinations. The sporidia were then mixed 1:1 with 4% agar and the resulting 1mm cubes fixed in 8% gluteraldehyde and post fixed in osmium tetroxide. After dehydration and embedding cubes were thin sectioned with a LKB ultratome and photographed in a Zeiss 9s transmission electron microscope or in an AE1 electron microscope of MK11 1MEV at the High Voltage Electron Microscopy Center of the University of Wisconsin-Madison.


Author(s):  
Rogério Vilain ◽  
Marcelo Pereira ◽  
Nathan Mendes ◽  
katia cordeiro ◽  
anastacio da silva junior
Keyword(s):  

1987 ◽  
Vol 52 (3) ◽  
pp. 663-671 ◽  
Author(s):  
Jiří Hanika ◽  
Vladimír Janoušek ◽  
Karel Sporka

Adsorption data for the impregnation of alumina with an aqueous solution of cobalt dichloride and ammonium molybdate were treated in terms of the Langmuir adsorption isotherm and compared with a mathematical model set up to describe the kinetics of simultaneous impregnation of a support by two components. The effective diffusion coefficients of the two components at 25 °C in a cylindrical particle of alumina were obtained. The validity of the model used was verified qualitatively by comparing the numerical results with the experimental time dependent concentration profiles of the active components in a catalyst particle, measured by electron microanalysis technique.


2021 ◽  
Vol 43 (1) ◽  
pp. 1-73
Author(s):  
David J. Pearce

Rust is a relatively new programming language that has gained significant traction since its v1.0 release in 2015. Rust aims to be a systems language that competes with C/C++. A claimed advantage of Rust is a strong focus on memory safety without garbage collection. This is primarily achieved through two concepts, namely, reference lifetimes and borrowing . Both of these are well-known ideas stemming from the literature on region-based memory management and linearity / uniqueness . Rust brings both of these ideas together to form a coherent programming model. Furthermore, Rust has a strong focus on stack-allocated data and, like C/C++ but unlike Java, permits references to local variables. Type checking in Rust can be viewed as a two-phase process: First, a traditional type checker operates in a flow-insensitive fashion; second, a borrow checker enforces an ownership invariant using a flow-sensitive analysis. In this article, we present a lightweight formalism that captures these two phases using a flow-sensitive type system that enforces “ type and borrow safety .” In particular, programs that are type and borrow safe will not attempt to dereference dangling pointers. Our calculus core captures many aspects of Rust, including copy- and move-semantics, mutable borrowing, reborrowing, partial moves, and lifetimes. In particular, it remains sufficiently lightweight to be easily digested and understood and, we argue, still captures the salient aspects of reference lifetimes and borrowing. Furthermore, extensions to the core can easily add more complex features (e.g., control-flow, tuples, method invocation). We provide a soundness proof to verify our key claims of the calculus. We also provide a reference implementation in Java with which we have model checked our calculus using over 500B input programs. We have also fuzz tested the Rust compiler using our calculus against 2B programs and, to date, found one confirmed compiler bug and several other possible issues.


1994 ◽  
Vol VII (3) ◽  
pp. 250-262 ◽  
Author(s):  
Andrew K. Wright ◽  
Robert Cartwright
Keyword(s):  

2009 ◽  
Vol 19 (06) ◽  
pp. 1931-1949 ◽  
Author(s):  
QIGUI YANG ◽  
KANGMING ZHANG ◽  
GUANRONG CHEN

In this paper, a modified generalized Lorenz-type system is introduced, which is state-equivalent to a simple and special form, and is parameterized by two parameters useful for chaos turning and system classification. More importantly, based on the parameterized form, two classes of new chaotic attractors are found for the first time in the literature, which are similar but nonequivalent in topological structure. To further understand the complex dynamics of the new system, some basic properties such as Lyapunov exponents, Hopf bifurcations and compound structure of the attractors are analyzed and demonstrated with careful numerical simulations.


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