Semi-continuityIn mathematical analysis, semicontinuity (or semi-continuity) is a property of extended real-valued functions that is weaker than continuity. An extended real-valued function is upper (respectively, lower) semicontinuous at a point if, roughly speaking, the function values for arguments near are not much higher (respectively, lower) than A function is continuous if and only if it is both upper and lower semicontinuous.
Modulus of continuityIn mathematical analysis, a modulus of continuity is a function ω : [0, ∞] → [0, ∞] used to measure quantitatively the uniform continuity of functions. So, a function f : I → R admits ω as a modulus of continuity if and only if for all x and y in the domain of f. Since moduli of continuity are required to be infinitesimal at 0, a function turns out to be uniformly continuous if and only if it admits a modulus of continuity. Moreover, relevance to the notion is given by the fact that sets of functions sharing the same modulus of continuity are exactly equicontinuous families.
Foundations of mathematicsFoundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics. In this latter sense, the distinction between foundations of mathematics and philosophy of mathematics turns out to be vague. Foundations of mathematics can be conceived as the study of the basic mathematical concepts (set, function, geometrical figure, number, etc.
Improper integralIn mathematical analysis, an improper integral is an extension of the notion of a definite integral to cases that violate the usual assumptions for that kind of integral. In the context of Riemann integrals (or, equivalently, Darboux integrals), this typically involves unboundedness, either of the set over which the integral is taken or of the integrand (the function being integrated), or both. It may also involve bounded but not closed sets or bounded but not continuous functions.
Multiple integralIn mathematics (specifically multivariable calculus), a multiple integral is a definite integral of a function of several real variables, for instance, f(x, y) or f(x, y, z). Integrals of a function of two variables over a region in (the real-number plane) are called double integrals, and integrals of a function of three variables over a region in (real-number 3D space) are called triple integrals. For multiple integrals of a single-variable function, see the Cauchy formula for repeated integration.
Gothic languageGothic is an extinct East Germanic language that was spoken by the Goths. It is known primarily from the Codex Argenteus, a 6th-century copy of a 4th-century Bible translation, and is the only East Germanic language with a sizeable text corpus. All others, including Burgundian and Vandalic, are known, if at all, only from proper names that survived in historical accounts, and from loanwords in other languages such as Portuguese, Spanish, Catalan, Occitan and French. As a Germanic language, Gothic is a part of the Indo-European language family.
Determination of the day of the weekThe determination of the day of the week for any date may be performed with a variety of algorithms. In addition, perpetual calendars require no calculation by the user, and are essentially lookup tables. A typical application is to calculate the day of the week on which someone was born or a specific event occurred. In numerical calculation, the days of the week are represented as weekday numbers. If Monday is the first day of the week, the days may be coded 1 to 7, for Monday through Sunday, as is practiced in ISO 8601.
1996 in musicThis is a list of notable events in music that took place in the year 1996. 1996 in British music 1996 in Norwegian music 1996 in South Korean music 1996 in classical music 1996 in country music 1996 in heavy metal music 1996 in hip hop music 1996 in Latin music 1996 in jazz January 8 – Robert Hoskins is found guilty and convicted on five charges of assault, stalking, and threatening to kill Madonna.
ISO week dateThe ISO week date system is effectively a leap week calendar system that is part of the ISO 8601 date and time standard issued by the International Organization for Standardization (ISO) since 1988 (last revised in 2019) and, before that, it was defined in ISO (R) 2015 since 1971. It is used (mainly) in government and business for fiscal years, as well as in timekeeping. This was previously known as "Industrial date coding". The system specifies a week year atop the Gregorian calendar by defining a notation for ordinal weeks of the year.
Mesoamerican Long Count calendarThe Mesoamerican Long Count calendar is a non-repeating base-20 and base-18 calendar used by several pre-Columbian Mesoamerican cultures, most notably the Maya. For this reason, it is often known as the Maya Long Count calendar. Using a modified vigesimal tally, the Long Count calendar identifies a day by counting the number of days passed since a mythical creation date that corresponds to August 11, 3114 BCE in the proleptic Gregorian calendar. The Long Count calendar was widely used on monuments.
