Various generalizations of the Cauchy – Schwarz inequality exist in the context of operator theory, e. g. for operator-convex functions, and operator algebras, where the domain and / or range of φ are replaced by a C *- algebra or W *- algebra.

Various generalizations capture in an abstract form this idea of curvature as a measure of holonomy ; see curvature form.

Various generalizations of the Lie derivative play an important role in differential geometry.

Various generalizations and reinterpretations of the connection form were formulated subsequent to Cartan's initial work.

Various generalizations of Euler's problem are known ; these generalizations add linear and inverse cubic forces and up to five centers of force.

Various ideas from real analysis can be generalized from real space to general metric spaces, as well as to measure spaces, Banach spaces, and Hilbert spaces.

Various international treaties attempt to reduce pollution caused by environmental threats such as oil spills, marine debris, and the incineration of toxic wastes at sea.

# Various basic foodstuffs such as rice, sugar, wheat, cooking oil and butter ( the Salex Group enjoys a de facto monopoly on imports of wheat, sugar, flour, butter and cooking oil.

Various manufacturers started producing PCI busboards for the A1200 and A4000, allowing standard Amiga computers to use PCI cards such as Voodoo graphic cards, Sound Blaster sound cards, 10 / 100 Ethernet cards, and TV tuner cards.

Various historical sources such as Martin Ewans, E. J.

Various historical sources such as Martin Ewans, E. J.

Various smaller communities, such as the Old Catholic and Independent Catholic Churches, include the word Catholic in their title, and share much in common with Roman Catholicism but are no longer in communion with the See of Rome.

Various cults and religions, such as Danza del Cordon and Afro-Cuban religion, incorporate Taíno spiritual practices.

Various examples include personal finance authors and writers such as Robert Kiyosaki, Suze Orman, Jean Chatzky, and Jim Cramer as well as fitness personalities such as Richard Simmons, Jane Fonda, Suzanne Somers, and Tamilee Webb.

Various pastors and other religious figures and activists such as Rick Warren, Al Sharpton and Jesse Jackson campaigned for various social and political causes have achieved celebrity status in mainstream media as well.

Various equivalent notions of compactness, such as sequential compactness and limit point compactness, can be developed in general metric spaces.

Various results in probability theory about expected values, such as the strong law of large numbers, will not work in such cases.

Various conventions of the detective genre were standardized during the Golden Age, and in 1929 some of them were codified by writer Ronald Knox in his ' Decalogue ' of rules for detective fiction, among them to avoid supernatural elements, all of which were meant to guarantee that, in Knox's words, a detective story " must have as its main interest the unravelling of a mystery ; a mystery whose elements are clearly presented to the reader at an early stage in the proceedings, and whose nature is such as to arouse curiosity, a curiosity which is gratified at the end.

Various attempts have been made to address this problem, many of them gathering under banners such as post-relational or NoSQL.

Various concepts based on length, such as the arc length of curves, area of plane regions, and volume of solids all possess natural analogues in Riemannian geometry.

Various modern compiler static code analysis techniques ( such as elimination of dead code: for example, code which uses the processor but produces internal results which are not used or output ) make the use and design of synthetic benchmarks more difficult.

Various styles dictate the curve of the fingers and thumb, as do the style of piece ; a more pronounced curve and lighter hold on the bow is used for virtuoso or more delicate pieces, while a flatter curve and sturdier grip on the bow sacrifices some power for easier control in strokes such as detaché, spiccato, and staccato.

Various collections of such recipes have been published in book form in Esperanto, e. g. Internacie kuiri (“ Cooking Internationally ”) by Maria Becker-Meisberger, published by FEL ( Flemish Esperanto League ), Antwerp 1989, ISBN 90-71205-34-7, Manĝoj el sanigaj plantoj (“ Healthy Vegetable Dishes ”) by Zlata Nanić, published by BIO-ZRNO, Zagreb 2002, ISBN 953-97664-5-1.

Various internet laws generally regard any message or post that threatens, harasses, or degrades another user as cyber harassment and as such can be considered criminal in some jurisdictions.

Various reasons have been suggested for the resistance to the Celsius system in the U. S., including the larger size of each degree Celsius ( resulting in the need for decimals where integer Fahrenheit degrees were adequate for much non-technical work ), the lower zero point in the Fahrenheit system ( which reduces the number of negative signs when measurements such as weather data were averaged ), and the more intuitive alignment of its 0-100 scale to the ordinary range of outdoor temperatures seen in most of the U. S. ( e. g., 0 ° F

Various tangibles and intangibles such as national or international advertising, training and other support services are commonly made available by the franchisor.

Various political Muslim leaders since have styled themselves Caliph and served as dynastic heads of state, sometimes in addition to another title, such as the Ottoman Sultan.

Various factors such as low pH, high CO < sub > 2 </ sub > and high 2, 3 BPG at the level of the tissues favor the taut form, which has low oxygen affinity and releases oxygen in the tissues.

Various scholars on early Wiccan history, such as Ronald Hutton, Philip Heselton, and Leo Ruickbie concur that witchcraft's early rituals, as devised by Gardner, contained much from Crowley's writings such as the Gnostic Mass.

Various methods of pulsing, scanning, and displaying these sound waves are used to detect submarines, map ocean floors, and even communicate under water.

Various of the apartments are of the terrace type, being on the ground floor so that entrance is direct.

Various theorists have differing, though similar, legal philosophies which are considered to fall under " anarcho-capitalism.

Various designs exist and many are home produced from lead or improvised with heavy objects.

Various symbol sets are used to represent numbers in the Hindu-Arabic numeral system, all of which evolved from the Brahmi numerals.

Various markets are held in the Market Hall, for example: Tuesdays – retail market, which also stretches into the town hall car park and temporarily the Cattle Market, while Brewery Yard car park is regenerated ; Wednesday – flea market ; 4th Thursday of the month a farmers ' market ; Friday – retail market ; Saturday – retail market ( also in the town hall car park ); 3rd Sunday of the month – antique fair ; 2nd Saturday – craft fair.

Various conflicting accounts are given in Classical Greek mythology of the birth of Artemis and her twin brother, Apollo.

Various violations are generally called " fouls ".

Various ordinances and laws are decreed.

* Various: several short sources, none of which have much connection to each other, and are fairly independent of the rest of the text.

Various legislations first introduced by the British are still in effect in their modified forms today.

Various types of colloids are recognised: inorganic colloids ( clay particles, silicates, iron oxy-hydroxides, ...), organic colloids ( humic and fulvic substances ).

Various chemical admixtures are also added to achieve varied properties.

Various forms of prepaid electronic toll collection systems are in place which allow quicker collection of toll, usually at a discounted rate, as well as use of dedicated toll plaza lanes ( for ENC system of the electronic toll collection ).

Various orders are in place for 100 locomotives from China and various freight wagons and passenger coaches.

Various theorists are split as to whether the rules are the only determinant of moral behavior or not.

Various careers within the fields of sports and entertainment are commonly associated with celebrity status.

Various examples of celebrity turned entrepreneurs included in the table below are:

Various CVD processes are used for integrated circuits ( ICs ).

Various forms of coercion are distinguished: first on the basis of the kind of injury threatened, second according to its aims and scope, and finally according to its effects, from which its legal, social, and ethical implications mostly depend.

Various muzzle loading arms, to scale ; numbers 1, 10, and 11 are identified as carbines.

Various Shandong snacks are also worth trying.

* Various utilities are provided for converting between Windows and Unix paths and file formats, for handling line ending ( CRLF / LF ) issues, for displaying the DLLs that an executable is linked with, etc.