Proof assistantIn computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human-machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer. A recent effort within this field is making these tools use artificial intelligence to automate the formalization of ordinary mathematics.
Pointwise convergenceIn mathematics, pointwise convergence is one of various senses in which a sequence of functions can converge to a particular function. It is weaker than uniform convergence, to which it is often compared. Suppose that is a set and is a topological space, such as the real or complex numbers or a metric space, for example. A net or sequence of functions all having the same domain and codomain is said to converge pointwise to a given function often written as if (and only if) The function is said to be the pointwise limit function of the Sometimes, authors use the term bounded pointwise convergence when there is a constant such that .
Heat kernelIn the mathematical study of heat conduction and diffusion, a heat kernel is the fundamental solution to the heat equation on a specified domain with appropriate boundary conditions. It is also one of the main tools in the study of the spectrum of the Laplace operator, and is thus of some auxiliary importance throughout mathematical physics. The heat kernel represents the evolution of temperature in a region whose boundary is held fixed at a particular temperature (typically zero), such that an initial unit of heat energy is placed at a point at time t = 0.
Compact convergenceIn mathematics compact convergence (or uniform convergence on compact sets) is a type of convergence that generalizes the idea of uniform convergence. It is associated with the compact-open topology. Let be a topological space and be a metric space. A sequence of functions is said to converge compactly as to some function if, for every compact set , uniformly on as . This means that for all compact , If and with their usual topologies, with , then converges compactly to the constant function with value 0, but not uniformly.
Heat transferHeat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes. Engineers also consider the transfer of mass of differing chemical species (mass transfer in the form of advection), either cold or hot, to achieve heat transfer.
Polish spaceIn the mathematical discipline of general topology, a Polish space is a separable completely metrizable topological space; that is, a space homeomorphic to a complete metric space that has a countable dense subset. Polish spaces are so named because they were first extensively studied by Polish topologists and logicians—Sierpiński, Kuratowski, Tarski and others. However, Polish spaces are mostly studied today because they are the primary setting for descriptive set theory, including the study of Borel equivalence relations.
Radius of convergenceIn mathematics, the radius of convergence of a power series is the radius of the largest disk at the center of the series in which the series converges. It is either a non-negative real number or . When it is positive, the power series converges absolutely and uniformly on compact sets inside the open disk of radius equal to the radius of convergence, and it is the Taylor series of the analytic function to which it converges.
Constructive proofIn mathematics, a constructive proof is a method of proof that demonstrates the existence of a mathematical object by creating or providing a method for creating the object. This is in contrast to a non-constructive proof (also known as an existence proof or pure existence theorem), which proves the existence of a particular kind of object without providing an example. For avoiding confusion with the stronger concept that follows, such a constructive proof is sometimes called an effective proof.
University of JordanThe University of Jordan (الجامعة الأردنية), often abbreviated UJ, is a public university located in Amman, Jordan. It was founded in 1962 by royal decree, and it is the largest and oldest institution of higher education in Jordan. It is located in the capital Amman in the Jubaiha area of the University District. It is composed of 20 faculties, and it contains over 95 departments.The university's stated main strategy and rule is to be global and productive in all its educational fields.
Jordan RiverThe Jordan River or River Jordan (نَهْر الْأُرْدُنّ, Nahr al-ʾUrdunn; נְהַר הַיַּרְדֵּן, Nəhar hayYardēn; ܢܗܪܐ ܕܝܘܪܕܢܢ Nahrāʾ Yurdnan), also known as Nahr Al-Sharieat ( نهر الشريعة), is a river in the Middle East that flows roughly north to south through the Sea of Galilee (Hebrew: כנרת Kinneret, Arabic: Bohayrat Tabaraya, meaning Lake of Tiberias) and on to the Dead Sea. Jordan and the Golan Heights border the river to the east, while the West Bank and Israel lie to its west.
Ho Chi Minh CityHo Chi Minh City (abbreviated HCMC), commonly known as Saigon, is the most populous city in Vietnam, with a population of around 9.3 million in 2023. Situated in the Southeast region of Vietnam, the city surrounds the Saigon River and covers about . Saigon was the capital of French Indochina from 1887 to 1902, and again from 1945 until its cessation in 1954. Following the partition of French Indochina, it became the capital of South Vietnam until the fall of Saigon in 1975.
Proof by exhaustionProof by exhaustion, also known as proof by cases, proof by case analysis, complete induction or the brute force method, is a method of mathematical proof in which the statement to be proved is split into a finite number of cases or sets of equivalent cases, and where each type of case is checked to see if the proposition in question holds. This is a method of direct proof. A proof by exhaustion typically contains two stages: A proof that the set of cases is exhaustive; i.e.
