Some notable mathematicians include Archimedes of Syracuse, Leonhard Euler, Carl Gauss, Johann Bernoulli, Jacob Bernoulli, Aryabhata, Brahmagupta, Bhaskara II, Nilakantha Somayaji, Omar Khayyám, Muhammad ibn Mūsā al-Khwārizmī, Bernhard Riemann, Gottfried Leibniz, Andrey Kolmogorov, Euclid of Alexandria, Jules Henri Poincaré, Srinivasa Ramanujan, Alexander Grothendieck, David Hilbert, Alan Turing, von Neumann, Kurt Gödel, Joseph-Louis Lagrange, Georg Cantor, William Rowan Hamilton, Carl Jacobi, Évariste Galois, Nikolay Lobachevsky, Rene Descartes, Joseph Fourier, Pierre-Simon Laplace, Alonzo Church, Nikolay Bogolyubov and Pierre de Fermat.

Given an isolated physical system, the allowed states of this system ( i. e. the states the system could occupy without violating the laws of physics ) are part of a Hilbert space H. Some properties of such a space are

Some but not all of the above generalize to normal operators on infinite-dimensional Hilbert spaces.

Some strategies used in Advanced Bionics and MED-EL devices make use of fine structure presentation by implementing the Hilbert Transform in the signal processing path, while ACE strategies depends mainly on the Short Time Fourier Transform.

Some of his earlier work related to the Discrete Hilbert Transform dates back to lectures he gave in Göttingen.

Some authors prefer to use Hilbert – Schmidt operators rather than trace class operators.

Some authors denote it by σ, so the Hilbert space tensor product in the section above would be

Some buildings have been aerodynamically designed so that convection via ducts and interior spaces eliminates any need for electric fans.

Some questions are still unanswered, such as the inclusion in the BCI repertoire of some characters ( currently about 24 ) that are already encoded in the UCS ( like digits, punctuation signs, spaces and some markers ), but whose unification may cause problems due to the very strict graphical layouts required by the published Bliss reference guides.

Some branches of mathematics such as algebraic geometry, typically influenced by the French school of Bourbaki, use the term quasi-compact for the general notion, and reserve the term compact for topological spaces that are both Hausdorff and quasi-compact.

Some computer systems allow file names to contain spaces ; others do not.

Some models supported separate instruction and data spaces for an effective virtual address size of 128 kB within a physical address size of up to 4 MB.

Some authors consider merely finitely additive probability spaces, in which case one just needs an algebra of sets, rather than a σ-algebra.

Some of the notable mathematical concepts named after Banach include Banach spaces, Banach algebras, the Banach – Tarski paradox, the Hahn – Banach theorem, the Banach – Steinhaus theorem, the Banach-Mazur game, the Banach – Alaoglu theorem and the Banach fixed-point theorem.

Some systems, such as the Burroughs B5500, use segmentation instead of paging, dividing virtual address spaces into variable-length segments.

Some changes, such as the abolition of segregated dining spaces, had already been instituted for some time and had been met with disapproval from the older generation.

Some practitioners argue that " texts " do not have to be confined to printed texts, but can include artifacts such as objects, physical spaces, and the like.

Some aspects of privately owned spaces, such as building facades or domestic gardens, also contribute to public space and are therefore also considered by urban design theory.

Some of these phonemes occupy large spaces in the anatomical vowel triangle ( actually a trapezoid ) of tongue positions.

Some spaces say " roll again ," giving an extra roll of the die to the player.

Some sidewalks may be used as social spaces with sidewalk cafes, markets by busking musicians.

Some of the neighbourhoods constructed after 2000 which are densely built-up often lack green spaces.

Some agoraphobics have a fear of open spaces.

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Some critics argue that these galleries are self-defeating, in that their dramatic interior spaces distract the eye from the paintings they are supposed to exhibit.

Some studies have shown that a lack of neighborhood recreational spaces including natural environment leads to lower levels of personal satisfaction and higher levels of obesity, linked to lower overall health and well being.

Some scholars romanize Japanese sentences by inserting spaces only at phrase boundaries ( i. e., " taiyō-ga higashi-no sora-ni noboru "), treating an entire phrase as a single word.

Some of them are well gardened playgrounds or resting spaces while others, like Lac Beauchamp Park, are relatively wild green areas which often merge with the woods and fields of the surrounding municipalities.

Some numerical applications, such as Monte Carlo methods and exploration of high-dimensional data spaces, require generation of uniformly distributed random orthogonal matrices.

Some residents enjoy biking around the vast spaces north of the town ; at night, avid stargazers bring their telescopes to marvel at the universe.

Some, she knew, looked upon Thompson almost as a saint, but others read in `` The Hound Of Heaven '' what they took to be the confessions of a great sinner, who, like Oscar Wilde, had -- as one pious writer later put it -- thrown himself `` on the swelling wave of every passion ''.

Some retailing, of course, always spreads with the population -- grocery stores, drugstores, local haberdasheries and dress shops, candy stores and the like.

Some, like the British and the French, maintain an elaborate system of personal contacts and have experts constantly studying special areas of the American scene.

Some national languages like Finnish, Turkish, Serbo-Croatian ( Serbian, Croatian and Bosnian ) and Bulgarian have a very regular spelling system with a nearly one-to-one correspondence between letters and phonemes.

Some of the persons listed are, like Korzybski, polymaths and several categories apply to them.

Some consider this more of a short story collection ; Milne didn't like it and considered The Day's Play as his first book.

Some fruit segments ( like those in Daucus spp.

Some, like Rambert, are exiles in double measure since they are not only cut off from those they want to be with but they do not have the luxury of being in their own homes.

Some others, like in Europe wanted republican independence as the French and Americans.

Some scholars argue Plato drew upon memories of past events such as the Thera eruption or the Trojan War, while others insist that he took inspiration from contemporary events like the destruction of Helike in 373 BC or the failed Athenian invasion of Sicily in 415 – 413 BC.

Some operations may change the state of the ADT ; therefore, the order in which operations are evaluated is important, and the same operation on the same entities may have different effects if executed at different times — just like the instructions of a computer, or the commands and procedures of an imperative language.

Some, like Hernando De Soto, argue that much of the poverty in the Third World countries is caused by the lack of Western systems of laws and well-defined and universally recognized property rights.

Some acids like tariric acid contains an alkyne group.

Some authors see a centralized peer – review process as less relevant and publish on their home pages or on unreviewed sites like arXiv.

Some systems are vacuum-insulated, acting something like large thermos bottles.

Some scenes, like Evil Ash walking along the graveyard while his skeleton minions come to life, blended stop-motion animation with live skeletons that were mechanically rigged, with prosthetics and visual effects.

Some encrusting bryozoan colonies with mineralized exoskeletons look very like small corals.

Some companies such as Topdeck Travel were set up to specifically use buses to drive the hippie trail or travel to places like north Africa.

Some properties of this notation are convenient since we are dealing with linear operators and composition acts like a ring multiplication.

Some old characters, like The Three Bears and Little Plum, have more recently made a return.

Some black activists were also offended, claiming Clinton used his knowledge of black culture to exploit black people like no other president before for political gain, while not serving black interests.

Some local Radio stations promote the ideals of the people identifying with Boer / Afrikaner people, like Radio Rosestad ( in Bloemfontein ), Overvaal Stereo and Radio Pretoria.

Some of these early SIMD specifications like HP's Multimedia Acceleration eXtensions ( MAX ) and Intel's MMX were integer-only.