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From this, further mathematical and thermodynamic reasoning leads to another relation between classical calorimetric quantities.
From 1950 to 1955, Simon studied mathematical economics and during this time, together with David Hawkins, discovered and proved the Hawkins – Simon theorem on the “ conditions for the existence of positive solution vectors for input-output matrices.
From ancient times through the Middle Ages, bursts of mathematical creativity were often followed by centuries of stagnation.
From this point on he developed a mathematical approach to expressions of symmetry in his art works.
From this, physically discernible concepts were isolated from the mathematical complexity.
From a purely mathematical viewpoint, the Dirac delta is not strictly a function, because any extended-real function that is equal to zero everywhere but a single point must have total integral zero.
From this point on, Condorcet shifted his focus from the purely mathematical to philosophy and political matters.
From a mathematical point of view, a function of n arguments can always be considered as a function of one single argument which is an element of some product space.
From a mathematical standpoint, an unused gene ( selectively neutral ) has a steadily decreasing probability of retaining potential functionality over time.
From 1911 he collaborated with J. E. Littlewood, in extensive work in mathematical analysis and analytic number theory.
From the perspective of the mathematical modeller, " flocking " is the collective motion of a large number of self-propelled entities and is a collective animal behavior exhibited by many living beings such as birds, fish, bacteria, and insects.
From 1822 to 1872, he frequently communicated papers to the Royal Society, many of them on mathematical subjects.
From there analogy was understood as identity of relation between any two ordered pairs, whether of mathematical nature or not.
From his experimental work with Hodgkin, Huxley developed a set of differential equations that provided a mathematical explanation for nerve impulses — the " action potential ".
* Moses Schönfinkel, 1924, " Über die Bausteine der mathematischen Logik ," translated as " On the Building Blocks of Mathematical Logic " in From Frege to Gödel: a source book in mathematical logic, 1879 – 1931, Jean van Heijenoort, ed.
From 1912 to 1917, he wrote and published seven papers on mathematical theories of climate both on the Earth and on the other planets.
From a mathematical view the Z-transform can also be viewed as a Laurent series where one views the sequence of numbers under consideration as the ( Laurent ) expansion of an analytic function.
From a mathematical perspective, the diagrams are a concise way to represent multilinear functions and functions between representations of matrix groups.
From the perspective of the mathematical modeller, it is an emergent behaviour arising from simple rules that are followed by individuals and does not involve any central coordination.
From 1716 to 1718, Swedenborg published a scientific periodical entitled Daedalus Hyperboreus (" The Northern Daedalus "), a record of mechanical and mathematical inventions and discoveries.
From 1972 onwards, with the launch and growing use of scientific calculators, most mathematical tables went out of use.
From 1919 to June 1921, Emil pursued mostly mathematical studies at Leipzig.
From his letters, it is clear he was treated like royalty by the Japanese mathematical community, and was charmed by the country.
From a mathematical point of view, soap films are considered as minimal surfaces.

From and viewpoint
From a mechanical viewpoint, up to 99 % of the energy delivered by the rider into the pedals is transmitted to the wheels, although the use of gearing mechanisms may reduce this by 10 – 15 %.
From an economics viewpoint, there is a clear trade-off between cost per copy and cost of the printer.
From the viewpoint of the ancient Greeks, a person's public life was not separated from their private life, and Greeks did not distinguish between the two worlds according to the modern western conception.
From the modern viewpoint, there is essentially only one Euclidean space of each dimension.
From the viewpoint of European history the Guinea Coast is associated mainly with slavery.
From a metanarrative viewpoint, Tolkien's Arda is itself a subcreation designed to honour the true stories of the real world.
From that viewpoint, she is seen as one who betrayed the indigenous people by siding with the Spaniards.
From the viewpoint of any single unaccelerated observer, mass can neither be created or destroyed, and special relativity does not change this understanding.
From this viewpoint, the A-law and μ-law algorithms ( G. 711 ) used in traditional PCM digital telephony can be seen as a very early precursor of speech encoding, requiring only 8 bits per sample but giving effectively 12 bits of resolution.
From the program developer's viewpoint, this constitutes the routine caller's portion of the contract.
From a viewpoint in the LMC, the Milky Way would be a spectacular sight.
From a philosophical viewpoint, this theory of matter-waves has contributed greatly to the ruin of the atomism of the past.
From Hitler's viewpoint, it was better to wait until the Z Plan was complete before going to war with the United States.
From this viewpoint, the null space of A is the same as the solution set to the homogeneous system.
From the viewpoint of the investor, however, the Dutch Auction would be more effective at price discovery, and potentially result in a lower offering price.
From this viewpoint there are no distances, but collinearity and ratios of distances on any line are preserved.
From the viewpoint of the ancient Chinese, the Purple Forbidden Enclosure lies in the middle of the sky and is circled by all the other stars.
From this viewpoint, Richard's paradox results from treating a construction in the metatheory ( the enumeration of all statements in the original system that define real numbers ) as if that construction could be conducted in the original system.
From a predicative viewpoint it is not valid to quantify over all real numbers in the process of generating a new real number, because this is believed to lead to a vicious-circle problem in the definitions.
From a spot near the western cliffs of the headland he saw "... the grandest and most pleasing prospects which my eyes ever surveyed, in front of a boundless Ocean ..." That viewpoint, later dubbed " Clark's Point of View ," can be accessed by a hiking trail from Indian Beach in Ecola State Park.
From a cultural viewpoint such a resident could be completely " local " and indistinguishable from citizens.
From the north viewpoint on the summit of Mount Walker, at 2804 feet, are vista views of Mount Jupiter, Buckhorn Mountain, Mount Constance, Mount Baker and the town of Quilcene.
From an economic viewpoint, Radhanite Trade dominance was being usurped by coordinated Christian and Islamic forced-conversions, and torture, compelling Jewish scholars to understand nascent economic threats.

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