Importance of Internet Banking Essay Example for Free

Importance of Internet Banking Essay From Wikipedia, the free encyclopedia Jump to: navigation, search This article is about asymptotic stability of nonlinear systems. For stability of linear systems, see exponential stability. Various types of stability may be discussed for the solutions of differential equations describing dynamical systems. The most important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Lyapunov. In simple terms, if all solutions of the dynamical system that start out near an equilibrium point stay near forever, then is Lyapunov stable. More strongly, if is Lyapunov stable and all solutions that start out near converge to , then is asymptotically stable. The notion of exponential stability guarantees a minimal rate of decay, i. e. , an estimate of how quickly the solutions converge. The idea of Lyapunov stability can be extended to infinite-dimensional manifolds, where it is known as structural stability, which concerns the behavior of different but nearby solutions to differential equations. Input-to-state stability (ISS) applies Lyapunov notions to systems with inputs. Contents [hide] †¢1 History †¢2 Definition for continuous-time systems o2. 1 Lyapunovs second method for stability †¢3 Definition for discrete-time systems †¢4 Stability for linear state space models †¢5 Stability for systems with inputs †¢6 Example †¢7 Barbalats lemma and stability of time-varying systems †¢8 References †¢9 Further reading †¢10 External links [edit] History Lyapunov stability is named after Aleksandr Lyapunov, a Russian mathematician who published his book The General Problem of Stability of Motion in 1892. 1] Lyapunov was the first to consider the modifications necessary in nonlinear systems to the linear theory of stability based on linearizing near a point of equilibrium. His work, initially published in Russian and then translated to French, received little attention for many years. Interest in it started suddenly during the Cold War (1953-1962) period when the so-called Second Method of Lyapunov was found to be applicable to the stability of aerospace guidance systems which typically contain strong nonlinearities not treatable by other methods. A large number of publications appeared then and since in the control and systems literature.More recently the concept of the Lyapunov exponent (related to Lyapunovs First Method of discussing stability) has received wide interest in connection with chaos theory. Lyapunov stability methods have also been applied to finding equilibrium solutions in traffic assignment problems. [7] [edit] Definition for continuous-time systems Consider an autonomous nonlinear dynamical system , where denotes the system state vector, an open set containing the origin, and continuous on . Suppose has an equilibrium . 1. The equilibrium of the above system is said to be Lyapunov stable, if, for every , there exists a such that, if , then , for every . 2. The equilibrium of the above system is said to be asymptotically stable if it is Lyapunov stable and if there exists such that if , then . 3. The equilibrium of the above system is said to be exponentially stable if it is asymptotically stable and if there exist such that if , then , for . Conceptually, the meanings of the above terms are the following: 1. Lyapunov stability of an equilibrium means that solutions starting close enough to the equilibrium (within a distance from it) remain close enough forever (within a distance from it). Note that this must be true for any that one may want to choose. 2. Asymptotic stability means that solutions that start close enough not only remain close enough but also eventually converge to the equilibrium. 3. Exponential stability means that solutions not only converge, but in fact converge faster than or at least as fast as a particular known rate .

Knights and Thier Role In Medieval Society Essay -- European History

Knights and their role in medieval society. Knights were an integral part of medieval society. They originally began with primitive warriors such as the Mongols who fought on horseback for added speed and power, but quickly advanced to chivalrous gentleman such as the Normans. Much has been written about medieval knights with the most famous being a series of legends about King Arthur and his Knights of the Round Table. Arthur and his knights were the ultimate example of what a perfect knight should have been. They were brave and skilful in battle, but merciful to their enemies once vanquished. They were courteous to ladies, and never ate or drank to excess. Knights associated in groups which they called orders. They vowed loyalty to the king they fought under and formed military org...

Chemical bond Essay

Answer the following questions in your own words, using complete sentences. Based on your observations in the lab, categorize each unidentified compound as ionic or covalent. Explain in one or two sentences why you categorized the compounds the way that you did. (5 points) Based on my observations in the lab I categorized Substance A and Substance C as an ionic bonds because the solids don‘t conduct electricity but when in liquid state and aqueous solutions, electricity was conducted. I categorized  substances B and D as covalent bonds because the solids conduct electricity but the liquid state and aqueous solution do not. Explain, in your own words, the differences between ionic and covalent bonding that account for the differences in their melting points. (4 points) Ionic bonds typically have much higher melting points than covalent bonds because of their crystal-like structures. The bondage is much more complex and requires higher heat to break than a covalent whose bonds are broken relatively easy. In order to conduct an electrical current, a substance must have charged particles (ions or electrons) that are free-moving (able to move about throughout the sample). Why do you think ionic compounds are not able to conduct electricity as solids, even though they can as liquids and in solution? (2 points) I think ionic compounds can’t conduct electricity as solids because the particle are all packed together and have no room to move freely as opposed to the particle when in liquid state or solutions. Based on your research and observations, why do you think pure (distilled) water does not conduct electricity but tap water usually does? (2 points) I think this is because tap water contains more ions than distilled water allowing it to conduct electricity. I also think the minerals that dissolve in the water have a lot to do with the conductivity.

Chicano Essay Definition - 1067 Words

The word Chicano involves more than just a cultural identification. There has been a continuity of a discussion of its origins, it meanings, its purpose and its affirmations throughout generations. Through oral history, scattered essays, Chicano studies courses and personal relationships, I have evolved my usage of the word Chicano, as many in history have. Through experience I have learned that social, geographical and economical elements have twisted and turned the meaning according to the moral judgments of the class or national origin. I will utilize my knowledge and life experience as a Chicana to the word Chicano. I did this to illustrate the assignments topic, in that outside factors have a significant effect on the usage and†¦show more content†¦Chicanos felt that as a nation, the history has had some significant Chicano influence that also needed to be recognized and taught within our school system. They also felt that the institutions that let this country function like law enforcement, government and education, were set up to systematically work against the Chicano. This was their way to identify themselves with the struggle against such entities. My grandfather first told me a story about the origins of the word Chicano with the prime intent on steering me away from using the word to identify myself. He said to me that Mexicans joke about the history of the word Chicano through this story. In Mexico, there has existed for long time a small population of Asian descent, primarily from Japanese decent. In Spanish, the word for pig is Cochinitos, and after time the word became shortened, and Mexican farmers started to use the name chinito to refer to a pig. Chinito is also used to refer to people of Asian ancestry, primarily rooting from the term Chinamen which is Chino. Adding the -into at the end of Chino is slang to reference to something smaller than the original noun. 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