Since the wavenumber k, is the inverse of wavelength ( k = 1 / λ ) the previous equation can be rewritten as

Since equations ( 1 ) through ( 4 ) above cannot be satisfied simultaneously when the hidden variable, λ, takes the same value in each equation, GHSZ proceed by allowing λ to take different values in each equation.

Since the entries of the matrix are ( linear or constant ) polynomials in λ, the determinant is also a polynomial in λ.

Since the right hand side depends only on x and the left hand side only on t, both sides are equal to some constant value − λ.

Since the set of complex numbers λ with | λ |< sup > 2 </ sup > = 1 form the unit circle in the complex plane, it follows that for each point m in S < sup > 2 </ sup >, the inverse image p < sup >− 1 </ sup >( m ) is a circle, i. e., p < sup >− 1 </ sup > m ≅ S < sup > 1 </ sup >.

Since we can think of the projection map G → G / B as a principal B-bundle, for each C < sub > λ </ sub > we get an associated fiber bundle L < sub >- λ </ sub > on G / B ( note the sign ), which is obviously a line bundle.

Since λ < λ + 1 and − λ − 1 < − λ, without any loss of generality we can assume the highest weight is λ ( if it's − λ − 1, just redefine a new λ ’ as − λ − 1 ) and the lowest weight would then have to be − λ.

Since C is algebraically closed, J is guaranteed to have eigenvalues which satisfy λ < sup > 2 </ sup >

Since it is shorter than λ / 4 the T antenna has a high capacitive reactance.

Since 1944 he has also conducted regularly at the San Francisco Opera, where he made his debut with a memorable performance of Verdi's Falstaff.

Since 1954 the Negro's desire for social justice has led to an ironically anarchical rebellion.

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 1953 California has led the nation in enacting guarantees that public business shall be publicly conducted, but not until this year did the lawmakers in Sacramento plug the remaining loopholes in the Brown Act.

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 it was issued in the spring of 1611, the King James Version has been most generally considered the most poetic and beautiful of all translations of the Bible.

Since the Connally amendment has the effect of giving the same right to the other party to a dispute with the United States, it also prevents us from using the court effectively.

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 then nothing has happened to save the life of Pope.

Since accurate base maps are necessary for any planning program, the first step taken by the planning division to implement the long-range state plan has been to prepare two series of base maps -- one at a scale of 1 inch to a mile, and the second a series of 26 sheets at a scale of 1 inch to 2000 feet, covering the entire state.

Since then, there has been a notable increase in the number of stations and also the accumulation of additional data and the development of new techniques for using it, leading to a better understanding of propagation phenomena.

Since the Industrial Revolution, when factories emerged, this classical pattern has been followed.

Since Af are linearly independent functions and the exponential function has no zeros, these R functions Af, form a basis for the space of solutions.

Since C is rational, this correspondence has K coincidences, each of which implies a line of the pencil which meets its image.

Since the course, one member has lost her husband.

Since her bereavement this individual has reported to the writer on numerous occasions about how helpful the class discussions were to her in this adjustment crisis.

Since on the one hand school desegregation has come in Virginia hand-in-glove with pupil assignment, shall we support the plan??

Since this book is concerned only incidentally with railroad rates, it will not attempt to analyze the methods by which the staff of the Interstate Commerce Commission has estimated out-of-pocket costs and apportioned residue costs.

Since that time the telegraph office has shifted in location from the railroad station at the Depot and shops at the Center back to the town clerk's office and drugstore at the Village.

Since 1948 the working headquarters has been the Department of Geology and Mineralogy.

Since the removal force is a function of coating thickness, a differential transformer pickup has been incorporated into the instrument to accurately measure film thickness.

Since the mid 1950s, when urethane foam first made its appearance in the American market, growth has been little short of fantastic.

Since interviewing is the basic therapeutic and diagnostic instrument of modern psychiatry, the recording of interviews for playbacks and study has been a boost of Redstone proportions in new research and training.

Since 1949, the St. Louis club has been below on May 1 just four times.

Since 1927, fewer than a dozen men have made serious runs at Babe Ruth's record and each, in turn, has been thwarted.

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 only known way to solve that problem requires factoring the modulus, the difficulty of Integer factorization is generally regarded as providing security.

Since the only known way to solve that problem is to factor the modulus, it is generally regarded that the difficulty of integer factorization provides a conditional security proof for the Blum Blum Shub algorithm.

Since the denominator becomes unity if length is doubled, the elastic modulus becomes the stress induced in the material, when the sample of the material turns double of its original length on applying external force.

Since arithmetic and geometric means are equal iff the variables are constant, see, inequality of arithmetic and geometric means, we establish the claim of unit modulus.

Since K depends on the modulus of elasticity and the allowable compressive stress parallel to the grain, it can be seen that this arbitrary limit would vary with the species of the timber.

Since moduli of continuity are required to be infinitesimal at 0, a function turns out to be uniformly continuous if and only if it admits a modulus of continuity.

Since the modulus k is close to zero, the period K can be expanded in powers of k ; to lowest order, this expansion yields