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Since tangent vectors to a general manifold can be defined as derivations it is natural to think of them as directional derivatives.
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Since and tangent
Since two curves of symbol Af on Q intersect in Af points, it follows that there are Af lines of Af which are tangent to Aj.
Since the map d restricts to 0 on I < sub > x </ sub >< sup > 2 </ sup > ( the reader should verify this ), d descends to a map from I < sub > x </ sub > / I < sub > x </ sub >< sup > 2 </ sup > to the dual of the tangent space, ( T < sub > x </ sub > M )< sup >*</ sup >.
Since at this stress the slope of the material's stress-strain curve, E < sub > t </ sub > ( called the tangent modulus ), is smaller than that below the proportional limit, the critical load at inelastic buckling is reduced.
Since the string vibrates from the bridge only as far as the tangent, multiple keys with multiple tangents can be assigned to the same string.
Since the line of sight is a tangent to the Earth, it is perpendicular to the radius at the horizon.
Since the collision only imparts force along the line of collision, the velocities that are tangent to the point of collision do not change.
Since streamlines are tangent to the velocity vector of the flow, the value of the stream function must be constant along a streamline.
( Since the manifold metric is always assumed to be regular, the compatibility condition implies linear independence of the partial derivative tangent vectors.
Since is a simple node, the tangent cone to this point is mapped to a conic under the double cover.
Since Hermann Minkowski's foundation for spacetime study in 1908, the concept of points in a spacetime plane being hyperbolic-orthogonal to a timeline ( tangent to a World line ) has been used to define simultaneity of events relative to the timeline.
Since Q is tangent to the unit semicircle centered at the origin, the two semicircles represent parallel hyperbolic lines.
Since the tangent of 45 degrees is 1, the radius of the 70 % ring would be equal to the height of the shadow-casting rod.
Since the work of Malfatti, there has been a significant amount of work on methods for constructing Malfatti's three tangent circles ; Richard K. Guy writes that the literature on the problem is " extensive, widely scattered, and not always aware of itself ".
Since the line is tangent to the original function at the point, the derivative can be seen as a way to find the best linear approximation of a function.
Since light gun entered service after the introduction of Field Artillery Computer Equipment ( FACE ) it never, unlike Abbot, had gun rules ( large slide rule like instruments used at each gun to convert range in metres to tangent elevation in mils, taking account of muzzle velocity ).
Since the invention of calculus, the slope of the tangent line can be found easily using implicit differentiation.
Since and vectors
Since virtually every calculation in quantum mechanics involves vectors and linear operators, it can involve, and often does involve, bra-ket notation.
Since there are infinitely many vectors in the basis, this is an infinite-dimensional Hilbert space.
Since the complex numbers can be multiplied giving another complex number, this identification provides a means to " multiply " vectors.
Since at a minimum the starting code address vector must always be valid on reset, systems commonly included some nonvolatile memory ( e. g. ROM ) starting at address zero to contain the vectors and bootstrap code.
Since the column vectors of A are the row vectors of the transpose of A ( denoted here by A < sup > T </ sup >), column rank of A equals row rank of A is equivalent to saying that the rank of a matrix is equal to the rank of its transpose, i. e. rk ( A ) = rk ( A < sup > T </ sup >).
Since there is a slight spread in the incoming wavelengths of the incoming X-ray beam, the values of | F ( q )| can be measured only for q vectors located between the two spheres corresponding to those radii.
Since is one of the basis vectors in the overlap is
Since is a positive semi-definite operator, it has a spectral decomposition such that where are orthonormal vectors.
Since the vectors are collinear ( parallel, and lie on the same line )-only the magnitudes of the vectors are necessary, hence non-bold letters are used for magnitudes, and because the motion is along a straight line, the problem effectively reduces from three dimensions to one.
Since U and V * are unitary, the columns of each of them form a set of orthonormal vectors, which can be regarded as basis vectors.
Since a plane can be defined in several ways ( e. g., by vectors or points in them, or by their normal vectors ), there are several equivalent definitions of a dihedral angle.
Since modern processors can operate fast on vectors this increases the speed.
Since only the relative phase between the coefficients of the two basis vectors has any physical meaning, we can take the coefficient of to be real and non-negative.
Since the vectors form a basis for, the maps form a basis for.
Since the resulting velocity vectors are based on cross-correlating the intensity distributions over small areas of the flow, the resulting velocity field is a spatially averaged representation of the actual velocity field.
Since it is often desirable to work with more than one basis for a vector space, it is of fundamental importance in linear algebra to be able to easily transform coordinate-wise representations of vectors and linear transformations taken with respect to one basis to their equivalent representations with respect to another basis.
Since HEK cells express a number of adenoviral genes, they can be used to propagate adenoviral vectors in which these genes ( typically, E1 and E3 ) are deleted, such as AdEasy.
Since the lengths of vectors and the angles between them are defined through the inner product, orthogonal transformations preserve lengths of vectors and angles between them.
Since and general
Since independence from Portugal in 1975, a number of Angolan students continued to be admitted every year at high schools, polytechnical institutes, and universities in Portugal, Brazil and Cuba through bilateral agreements ; in general, these students belong to the Angolan elites.
Since the 1951 general election, the party system has been dominated by the personalist Antigua Labour Party ( ALP ), dominated by the Bird family, particularly Prime Ministers Vere and Lester Bird.
Since the start of the " Special Period " in 1991 ( energy shortages caused by the loss of the Soviet Union as a trading partner ), hitchhiking and carpooling have become important parts of Cuba's transportation system and society in general.
Since the end of the Cold War, the focus of civil defense has largely shifted from military attack to emergencies and disasters in general.
Since Cauchy sequences can also be defined in general topological groups, an alternative to relying on a metric structure for defining completeness and constructing the completion of a space is to use a group structure.
Since the 3rd edition, the Britannica has enjoyed a popular and critical reputation for general excellence.
Since Ōtomo had weak political support from his maternal relatives, the general wisdom of the time held that it was not a good idea for him to ascend to the throne, yet Tenji was obsessed with the idea.
Since classical general relativity and quantum mechanics seem to be incompatible at such energies, from a theoretical point of view this situation is not tenable.
Since the proteins remain in the native state they may be visualised not only by general protein staining reagents but also by specific enzyme-linked staining.
Since the 2005 general election the government has floated the idea of voluntary mergers of local councils, avoiding a costly reorganisation but achieving desired reform.
Since the 19th century it has become associated with the wider culture of Scotland in general, or with Celtic ( and more specifically Gaelic ) heritage even more broadly.
Since the institution of a democratic form of government in 2002, Mali's relations with the West in general and the United States in particular have improved significantly.
Since independence, general elections have been held in 1966, 1971, 1976, 1981, 1987, 1992, 1996, 1998, 2003 and 2008.
Since Major's election as leader, Kinnock spent the end of 1990 and most of 1991 putting pressure on Major to hold the election that year, but Major had held out and insisted that there would be no general election in 1991.
Since the general animation renaissance headlined by the likes of Who Framed Roger Rabbit and The Little Mermaid at the end of the 1980s and the beginning of the 1990s, there have been an increasing number of traditional stop motion feature films, despite advancements with computer animation.
Since a general solution is quite difficult, various simplifying assumptions are used to represent the actual system.
Since there is no real consensus about where to draw the exact line between Spaghetti Westerns and other Eurowesterns ( or other Westerns in general ) one cannot say which one of the films mentioned so far really was the first Spaghetti Western.
Since man had access to fire, Zeus devised woman as a general punishment, in trade.
Since thin clients are cheap, they offer a low risk of theft in general, and are easy to replace if stolen or broken.
Since that time, the Labour and Conservatives parties have been dominant, with the Liberal Democrats also holding a significant number of seats and increasing their share of the vote in parliamentary general elections in the four elections 1992.
Since the general public understands denomination much more readily than association of congregations, the distinction is generally elided in conversation.
Since 1910, the governor general was also always made the Chief Scout for Canada, which was renamed Chief Scout of Canada after 1946 and again in 2011 as Patron Scout.
Since 1968, Powell had been an increasingly frequent visitor to Northern Ireland, and in keeping with his general British nationalist viewpoint, he sided strongly with the Ulster Unionists in their desire to remain a constituent part of the United Kingdom.
Since 1993, he has been the general director of the National Aerospace Agency of Republic of Kazakhstan.
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