Lyapunov stabilityVarious types of stability may be discussed for the solutions of differential equations or difference 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 Aleksandr Lyapunov. In simple terms, if the solutions 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 said to be asymptotically stable (see asymptotic analysis).
Stability theoryIn mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance.
Lyapunov functionIn the theory of ordinary differential equations (ODEs), Lyapunov functions, named after Aleksandr Lyapunov, are scalar functions that may be used to prove the stability of an equilibrium of an ODE. Lyapunov functions (also called Lyapunov’s second method for stability) are important to stability theory of dynamical systems and control theory. A similar concept appears in the theory of general state space Markov chains, usually under the name Foster–Lyapunov functions.
LinearizationIn mathematics, linearization is finding the linear approximation to a function at a given point. The linear approximation of a function is the first order Taylor expansion around the point of interest. In the study of dynamical systems, linearization is a method for assessing the local stability of an equilibrium point of a system of nonlinear differential equations or discrete dynamical systems. This method is used in fields such as engineering, physics, economics, and ecology.
Linear independenceIn the theory of vector spaces, a set of vectors is said to be if there exists no nontrivial linear combination of the vectors that equals the zero vector. If such a linear combination exists, then the vectors are said to be . These concepts are central to the definition of dimension. A vector space can be of finite dimension or infinite dimension depending on the maximum number of linearly independent vectors. The definition of linear dependence and the ability to determine whether a subset of vectors in a vector space is linearly dependent are central to determining the dimension of a vector space.
Marginal stabilityIn the theory of dynamical systems and control theory, a linear time-invariant system is marginally stable if it is neither asymptotically stable nor unstable. Roughly speaking, a system is stable if it always returns to and stays near a particular state (called the steady state), and is unstable if it goes farther and farther away from any state, without being bounded. A marginal system, sometimes referred to as having neutral stability, is between these two types: when displaced, it does not return to near a common steady state, nor does it go away from where it started without limit.
The Last LectureThe Last Lecture is a 2008 New York Times best-selling book co-authored by Randy Pausch —a professor of computer science, human-computer interaction, and design at Carnegie Mellon University in Pittsburgh, Pennsylvania—and Jeffrey Zaslow of the Wall Street Journal. The book extends the September 2007 lecture by Pausch entitled "Really Achieving Your Childhood Dreams". The Last Lecture is renowned for its witty humor, despite encompassing Pausch's farewell to his loved ones due to his terminal pancreatic cancer.
BIBO stabilityIn signal processing, specifically control theory, bounded-input, bounded-output (BIBO) stability is a form of stability for signals and systems that take inputs. If a system is BIBO stable, then the output will be bounded for every input to the system that is bounded. A signal is bounded if there is a finite value such that the signal magnitude never exceeds , that is For discrete-time signals: For continuous-time signals: For a continuous time linear time-invariant (LTI) system, the condition for BIBO stability is that the impulse response, , be absolutely integrable, i.
Dudleian lecturesThe Dudleian lectures are a series of prestigious lectures on religion at Harvard University, where they are the oldest endowed lectureship. They were held annually and without interruption from 1755 to 1857 when they were suspended by the board of trustees "in order that the Fund, now in their judgment insufficient to support the charge of the same, may accumulate." They began again in 1888. The lectures were endowed by Paul Dudley in 1750 with a sum of £133 6s 8d.
Linear mapIn mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism. If a linear map is a bijection then it is called a .
USS LST-546USS LST-546 was a United States Navy in commission from 1944 to sometime between 1946 and 1952. From 1952 until 1972 she served in a non-commissioned status in the Military Sea Transportation Service and Military Sealift Command as USNS LST-546 (T-LST-546). LST-546 was laid down on 20 December 1943 at Evansville, Indiana, by the Missouri Valley Bridge & Iron Co; launched on 16 February 1944; sponsored by Mrs. W. J. Barbrick; and commissioned on 27 March 1944. LST-546 saw no combat action in World War II.
Halley LecturesThe Halley Lectures are a series of annual public lectures hosted by the University of Oxford, in memory of the astronomer Edmond Halley. Currently, some podcasts of the lectures can be found through the Oxford Physics Public Lectures These lectures aim to promote public understanding and engagement with science, mathematics, and related fields, and to inspire new generations of researchers and students to pursue careers in these areas.
Alfred and EmilyAlfred and Emily is a book by Doris Lessing in a new hybrid form. Part fiction, part notebook, part memoir, it was first published in 2008. The book is based on the lives of Lessing's parents. Part one is a novella, a fictional portrait of how her parents' lives might have been without the interruption of the First World War. Part two is a retelling of how her parents' lives really developed. The novella begins in England in 1902, when Alfred and Emily meet at a cricket match.
USS LST-557USS LST-557 was a United States Navy in commission from 1944 to 1946. LST-557 was laid down on 8 February 1944 at Evansville, Indiana, by the Missouri Valley Bridge and Iron Company. She was launched on 11 April 1944, sponsored by Mrs. Edward J. Baechle, and commissioned on 5 May 1944. During World War II, LST-557 was assigned to the Pacific Theater of Operations. She participated in the capture and occupation of the southern Palau Islands in September and October 1944.
Notebook for Anna Magdalena BachThe title Notebook for Anna Magdalena Bach (Notenbüchlein für Anna Magdalena Bach) refers to either of two manuscript notebooks that the German Baroque composer Johann Sebastian Bach presented to his second wife, Anna Magdalena. Keyboard music (minuets, rondeaux, polonaises, chorales, sonatas, preludes, musettes, marches, gavottes) makes up most of both notebooks, and a few pieces for voice (songs, and arias) are included. The Notebooks provide a glimpse into the domestic music of the 18th century and the musical tastes of the Bach family.
USS LST-279USS Berkeley County (LST-279) was an built for the United States Navy during World War II. Named for counties in South Carolina and West Virginia, she was the only U.S. Naval vessel to bear the name. LST-279 was laid down on 2 July 1943 at Ambridge, Pennsylvania by the American Bridge Company; launched on 19 September 1943; sponsored by Miss Marion Ruth Warsack; and commissioned at New Orleans, Louisiana on 25 October 1943. After fitting out at the Naval Station Algiers, New Orleans, LST-279 loaded supplies and ammunition before proceeding to St.
The French DispatchThe French Dispatch (titled onscreen as The French Dispatch of the Liberty, Kansas Evening Sun) is a 2021 American anthology comedy drama film written, directed, and produced by Wes Anderson from a story he conceived with Roman Coppola, Hugo Guinness, and Jason Schwartzman. It features an expansive ensemble cast and follows three different storylines as the French foreign bureau of the fictional Liberty, Kansas Evening Sun newspaper publishes its final issue.
USS LST-325USS LST-325 is a decommissioned tank landing ship of the United States Navy, now docked in Evansville, Indiana, US. Like many of her class, she was not named and is properly referred to by her hull designation (LSTs in service after July 1955 were named after U.S. counties and parishes). The ship was listed on the U.S. National Register of Historic Places in 2009. The property was added to the National Register of Historic Places (NRHP) on 24 June 2009 and the listing was announced as the featured listing in the National Park Service's weekly list of 2 July 2009.
Rankine LectureThe Rankine lecture is an annual lecture organised by the British Geotechnical Association named after William John Macquorn Rankine, an early contributor to the theory of soil mechanics. This should not be confused with the biennial BGA Géotechnique Lecture. The Rankine Lecture is held in March each year. In even-numbered years, the lecturer is from the UK. In odd-numbered years, the lecturer is from outside the UK. Each lecture is usually published in Géotechnique.
Tom Friedman (artist)Tom Friedman (born 1965) is an American conceptual sculptor. He was born in St. Louis, Missouri and received a BFA in graphic illustration from Washington University in St. Louis (1988) and an MFA in sculpture from the University of Illinois at Chicago (1990.). As a conceptual artist he works in diverse media including sculpture, painting, drawing, video, and installation. For over twenty years, Friedman has been investigating the viewer/object relationship, and "the space in between.
