Numerical stabilityIn the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.
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.
Neumann boundary conditionIn mathematics, the Neumann (or second-type) boundary condition is a type of boundary condition, named after Carl Neumann. When imposed on an ordinary or a partial differential equation, the condition specifies the values of the derivative applied at the boundary of the domain. It is possible to describe the problem using other boundary conditions: a Dirichlet boundary condition specifies the values of the solution itself (as opposed to its derivative) on the boundary, whereas the Cauchy boundary condition, mixed boundary condition and Robin boundary condition are all different types of combinations of the Neumann and Dirichlet boundary conditions.
Dirichlet boundary conditionIn the mathematical study of differential equations, the Dirichlet (or first-type) boundary condition is a type of boundary condition, named after Peter Gustav Lejeune Dirichlet (1805–1859). When imposed on an ordinary or a partial differential equation, it specifies the values that a solution needs to take along the boundary of the domain. In finite element method (FEM) analysis, essential or Dirichlet boundary condition is defined by weighted-integral form of a differential equation.
Robin boundary conditionIn mathematics, the Robin boundary condition (ˈrɒbɪn; properly ʁɔbɛ̃), or third type boundary condition, is a type of boundary condition, named after Victor Gustave Robin (1855–1897). When imposed on an ordinary or a partial differential equation, it is a specification of a linear combination of the values of a function and the values of its derivative on the boundary of the domain. Other equivalent names in use are Fourier-type condition and radiation condition.
Numerical analysisNumerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.
Albanian languageAlbanian (endonym: shqipja ʃcipja or gjuha shqipe ˈɟuha ˈʃcipe) is an Indo-European language and an independent branch of that language family. It is the descendant of a Paleo-Balkan language. Albanian is the official language of Albania and Kosovo, and a co-official language in North Macedonia and Montenegro, as well as a recognized minority language of Italy, Croatia, Romania and Serbia. It is also spoken in Greece and by the Albanian diaspora, which is generally concentrated in the Americas, Europe and Oceania.
Culture of AlbaniaAlbanian culture or the culture of Albanians (kultura shqiptare kultuˈɾa ʃcipˈtaɾɛ) is a term that embodies the artistic, culinary, literary, musical, political and social elements that are representative of Albanians. Albanian culture has been considerably shaped by the geography and history of Albania, Kosovo, parts of Montenegro, parts of North Macedonia, and parts of Northern Greece, traditional homeland of Albanians.
Albanian literatureAlbanian literature stretches back to the Middle Ages and comprises those literary texts and works written in Albanian. It may also refer to literature written by Albanians in Albania, Kosovo and the Albanian diaspora particularly in Italy. Albanian occupies an independent branch within the Indo-European family and does not have any other closely related language. The origin of Albanian is not entirely known, but it may be a successor of the ancient Illyrian language.
AlbaniaAlbania (ælˈbeɪniə,_ɔːl- ; Shqipëri or Shqipëria), officially the Republic of Albania (Republika e Shqipërisë), is a country in Southeastern Europe. The country is located in the Balkans on the Adriatic and Ionian Seas within the Mediterranean Sea and shares land borders with Montenegro to the northwest, Kosovo to the northeast, North Macedonia to the east and Greece to the south. Spanning an area of , it displays a varied range of climatic, geological, hydrological and morphological conditions.
DefinitionA definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories: intensional definitions (which try to give the sense of a term), and extensional definitions (which try to list the objects that a term describes). Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions.
Island of stabilityIn nuclear physics, the island of stability is a predicted set of isotopes of superheavy elements that may have considerably longer half-lives than known isotopes of these elements. It is predicted to appear as an "island" in the chart of nuclides, separated from known stable and long-lived primordial radionuclides. Its theoretical existence is attributed to stabilizing effects of predicted "magic numbers" of protons and neutrons in the superheavy mass region.
