Since the separation of variables in this case involves dividing by y, we must check if the constant function y = 0 is a solution of the original equation.

Since Imbolc is immediately followed ( on 2 February ) by Candlemas ( Irish Lá Fhéile Muire na gCoinneal " feast day of Mary of the Candles ", Welsh Gŵyl Fair y Canhwyllau ), Irish imbolc is sometimes rendered as " Candlemas " in English translation ; e. g. iar n-imbulc, ba garb a ngeilt translated as " after Candlemas, rough was their herding ".

Since terms of linear equations cannot contain products of distinct or equal variables, nor any power ( other than 1 ) or other function of a variable, equations involving terms such as xy, x < sup > 2 </ sup >, y < sup > 1 / 3 </ sup >, and sin ( x ) are nonlinear.

Since this force varies with the position of the charge and by Coloumb's Law it is defined at all points in space, is a continuous function of the charge's position ( x, y, z ).

The transfer principle states that true first order statements about R are also valid in * R. For example, the commutative law of addition, x + y = y + x, holds for the hyperreals just as it does for the reals ; since R is a real closed field, so is * R. Since for all integers n, one also has for all hyperintegers H. The transfer principle for ultrapowers is a consequence of Łoś ' theorem of 1955.

Since at least the time of Ramon y Cajal, psychologists have speculated that the brain stores memory by altering the strength of connections between neurons that are simultaneously active.

Since we know the column, x, the pixel's row, y, is given by rounding this quantity to the nearest integer:

Since neither x nor y can equal zero ( if k is non-zero ), the graph will never cross either axis.

Since they are even, they can be written as x = 2a and y = 2b respectively for integers a and b. Then the sum.

Since there was only one king of Tyre with this hypocoristicon in the 9th century BC, Cross restores the name to pmy ( y ) tn or p ‘ mytn, which is rendered in the Greek tradition as Pygmalion.

* Since we can predict with virtual certainty that " y is not in f ( x )" after the first dart is thrown, and since this prediction is valid no matter what the first dart does, we should be able to make this prediction before the first dart is thrown.

* Since " y is not in f ( x )" is predictably true, by the symmetry of the order in which the darts were thrown ( hence the name " axiom of symmetry ") we should also be able to predict with virtual certainty that " x is not in f ( y )".

Since the late 20th century, Hidalgo y Costilla ’ s " cry of independence " has become emblematic of Mexican independence.

Since they are even, they can be written as x = 2a and y = 2b respectively for integers a and b. Then the sum.

Since trees are combined only when the degrees of their roots are equal, it must have been that y < sub > i </ sub > also had degree at least i-1 at the time it became a child of x.

Since the heights of all the y < sub > i </ sub > are strictly less than that of x, we can apply the inductive hypothesis to them to get size ( y < sub > i </ sub >) ≥ F < sub > c < sub > i </ sub >+ 2 </ sub > ≥ F < sub >( i − 2 )+ 2 </ sub > = F < sub > i </ sub >.

Since 1993, academic organizations in Latin America like ENRED – Foro de Redes de América Latina y el Caribe, discussed the need of a register for Latin America.

Since 2000, she has been a co-host on Aquí y Ahora ( Here and Now ) which is a 20 / 20 news type program on Univision.

Since 2000, RIAA also awards Los Premios de Oro y De Platino to recordings of which over 50 % of the content is in the Spanish language.

Since 1874, the Navy's Hydrographic and Oceanographic Service (" SHOA ", as acronym of " Servicio Hidrográfico y Oceanográfico de la Armada ") has been the Chilean official authority on drawing and publishing nautical charts of the South Pacific Ocean for Military and Civil navigation.

Since in oral languages the elements of sound are for the most part produced linearly in time ( that is, in a word like cat the a sound comes after the c sound, and the t sound comes after that ), they can generally be easily written in a linear ( one-dimensional ) writing system such as an alphabet.

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 we are assuming circular motion, let r ( t ) = R · u < sub > r </ sub >, where R is a constant ( the radius of the circle ) and u < sub > r </ sub > is the unit vector pointing from the origin to the point mass.

Since we've assumed that we can infallibly identify programs for computing squares, we can determine whether t, which depends on a and i, is such a program, and that for every a and i ; thus we have obtained a program that decides whether program a halts on input i. Note that our halting-decision algorithm never executes t, but only passes its description to the squaring-identification program, which by assumption always terminates ; since the construction of the description of t can also be done in a way that always terminates, the halting-decision cannot fail to halt either.

Since the first widespread promotion of t ' ai chi ch ' uan's health benefits by Yang Shaohou, Yang Chengfu, Wu Chien-ch ' uan, and Sun Lutang in the early 20th century, it has developed a worldwide following among people with little or no interest in martial training, for its benefit to health and health maintenance.

Since the space concept doesn ’ t necessarily have to be economical in the traditional sense, it allows the enrichment to exceed that which would be acceptable for a terrestrial system.

Since a convolutional code doesn't use blocks, processing instead a continuous bitstream, the value of t applies to a quantity of errors located relatively near to each other.

Since, the inequality could be satisfied for sufficiently small m. The sum of series first converges to the value of φ ( t ) with arbitrary high accuracy if m is small enough, and left part of the strong inequality is satisfied.

* Since im t

Since T dependns on x ' and t only through the combination, we have:

Since W ( t < sub > 1 </ sub >)

Since we can ’ t know what knowledge will be most needed in the future, it is senseless to try to teach it in advance.

Since B is also a matrix with polynomials in t as entries, one can for each i collect the coefficients of in each entry to form a matrix B < sub > i </ sub > of numbers, such that one has

Since great love, as well as the actual act of committing evil, both create the ability to break the power of Darkness, it was the opportune time to “ win his brother back ” and Christ ’ s death didn ’ t have to be.

Since the power dissipated by a resistor is the amount of energy used ( electrical work applied ) per unit time, the total energy consumed and dissipated in time t is:

Since the product of units is a unit and since ring homomorphisms respect products, we may and will assume that S is a submonoid of the multiplicative monoid of R, i. e. 1 is in S and for s and t in S we also have st in S. A subset of R with this property is called a multiplicatively closed set or, shortly, multiplicative set.

Since D is diagonal, raising it to power, just involves raising each element on the diagonal to the power t. This is much easier to do and to understand than raising A to power t, since A is usually not diagonal.

Since t is the curve length, the curvature, can be expressed as:

Since the light travels the same path at the same rate going both out and back for the observer in this scenario, the coordinate time of the event of the light signal being reflected for the observer t < sub > E </ sub > is.

Since a and n are coprime, this implies that a has an inverse element a < sup >- 1 </ sup > and we can multiply both sides of the congruence with a < sup >- t </ sup >, yielding a < sup > s-t </ sup > ≡ 1 ( mod n ).

Since the Supreme Court's decision of that year this is more doubtful ; ;

( Since the time-span of the nation-state coincides roughly with the separate existence of the United States as an independent entity, it is perhaps natural for Americans to think of the nation as representative of the highest form of order, something permanent and unchanging.

Since it is not far from Viareggio, he will visit Puccini's house, as he never fails to do, to pay his respects to the memory of the composer of La Boheme, which he considers one of Puccini's masterpieces.

Since attack serves to stimulate interest in broadcasts, I added to my opening statement a sentence in which I claimed that German youth seemed to lack the enthusiasm which is a necessary ingredient of anger, and might be classified as uninterested and bored rather than angry.

Since the air is a continuum, the network of communication remains intact regardless of the positions or motions of the points ( the people ) in the net.

Since the hazards of poor communication are so great, p can be justified as a habitable site only on the basis of unusual productivity such as is made available by a waterfall for milling purposes, a mine, or a sugar maple camp.

Since the difficulty of drawing the net is great, we will merely discuss it.

Since a civilizational crisis involves also a crisis in private interests and in the ruling class, reaction is normally found among those who feel themselves to be among the ruling class.

Since civilizational change is the most difficult to perceive and analyze, it seldom is given adequate attention.

Since the slogans have little application to reality and are sanctimonious to boot, the applause is faint even in areas of the world where we should expect to find the greatest affection for free government.

Since more is known about Quiney than about any other acquaintance of Shakespeare in Stratford, his career may be followed to its sudden end in 1602.

Since the great flood of these dystopias has appeared only in the last twelve years, it seems fairly reasonable to assume that the chief impetus was the 1949 publication of Nineteen Eighty-Four, an assumption which is supported by the frequent echoes of such details as Room 101, along with education by conditioning from Brave New World, a book to which science-fiction writers may well have returned with new interest after reading the more powerful Orwell dystopia.

Since Laos is of no more purely military value to Moscow itself than it is to Washington, this approach might be expected to head off Mr. Khrushchev for the moment.

Since little is known about autism, and almost nothing has been written for the layman, we'd like to share one experienced mother's comments.

Since the work is done by hand, the only limitation, it is said, `` is that of human conception ''.

Since the apparatus is new, it requires experimentation and changes in technique.

Since the obvious is not always true, the Republican National Committee wisely analyzed its defeat of last autumn and finds that it occurred, as suspected, in the larger cities.

Since he has just shown who is top dog, he may not be ready to receive this highest honor in the gift of the Soviet people.

Since appeals to morality, to humanity, and to sanity have had such small effect, perhaps our last recourse is the deterrent example.

Since the goal of our international planners is a World Government, this Atlantic Community would mark a giant step in that direction for, once American economic autonomy is absorbed, a larger grouping is a question of time.