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 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 12th century, courts have had parallel and co-equal authority to make law -- " legislating from the bench " is a traditional and essential function of courts, which was carried over into the U. S. system as an essential component of the " judicial power " specified by Article III of the U. S. constitution.

A set S is called countable if there exists an injective function f from S to the natural numbers Since there is an obvious bijection between and it makes no difference whether one considers 0 to be a natural number of not.

: Since the result is a function of, this function can be defined as.

Since tangents and inverse tangents are both continuous, our identification function is a homeomorphism between the real line and the unit circle without ∞.

Since such life utilised strong nuclear forces instead of electromagnetic interactions, it was posited that life might function millions of times faster than typical on Earth.

Since these devices are used to run countless different types of programs, these CPU designs are not specifically targeted at one type of application or one function.

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 μ is a function of x, we cannot simplify any further directly.

Since all structural levels of the protein determines its function, the protein can no longer perform its function once it has been denatured.

Since the latter is valid over the entire cycle, this gave Clausius the hint that at each stage of the cycle, work and heat would not be equal, but rather their difference would be a state function that would vanish upon completion of the cycle.

Since 2001, 40 non-natural amino acids have been added into protein by creating a unique codon ( recoding ) and a corresponding transfer-RNA: aminoacyl – tRNA-synthetase pair to encode it with diverse physicochemical and biological properties in order to be used as a tool to exploring protein structure and function or to create novel or enhanced proteins.

Since its inception it has broadened to find applications in many other areas, including statistical inference, natural language processing, cryptography, neurobiology, the evolution and function of molecular codes, model selection in ecology, thermal physics, quantum computing, plagiarism detection and other forms of data analysis.

Since the identity element of a monoid is unique, one can alternately define the identity function on M to be this identity element.

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 the names of functions are largely a convenience, the lambda calculus has no means of naming a function.

Since any fluorescence image is made up of a large number of such small fluorescent light sources, the image is said to be " convolved by the point spread function ".

Since the energy of the photoelectrons emitted is exactly the energy of the incident photon minus the material's work function or binding energy, the work function of a sample can be determined by bombarding it with a monochromatic X-ray source or UV source, and measuring the kinetic energy distribution of the electrons emitted.

Since each sample is a random variable, the sample mean is a function of random variables and hence a random variable itself, whose distribution can be computed and properties determined.

Since there is a one-to-one correspondence between Borel regular measures in the interval and functions of bounded variation ( that assigns to each function of bounded variation the corresponding Lebesgue-Stieltjes measure, and the integral with respect to the Lebesgue-Stieltjes measure agrees with the Riemann-Stieltjes integral for continuous functions ), the above stated theorem generalizes the original statement of F. Riesz.

Since this variable is not passed as a parameter but can be altered, the results of subsequent calls to the function can differ even if the parameters are identical.

Since the validity of all subsequent planning depends on the accuracy of the basic inventory information, great care is being taken that the inventory is as complete as possible.

Since the psychiatric interview, like any other interview, depends on communication, it is significant to note that the therapist in this interview was a man of marked skill and long experience.

Since the activity of antibacterials depends frequently on its concentration, in vitro characterization of antibacterial activity commonly includes the determination of the minimum inhibitory concentration and minimum bactericidal concentration of an antibacterial.

Since this depends on a choice of orientation, curl is a chiral operation.

Since the value of this energy depends on the shapes and positions of the conductors and dielectrics, the Casimir effect manifests itself as a force between such objects.

Since construction of the Aswan Dam, agriculture in the Nile valley depends on irrigation.

Since collecting depends on the interests of the individual collector, it may deal with almost any subject.

Since the potential energy depends on the spatial arrangement of the particles, the kinetic energy will also depend on the spatial configuration to conserve energy.

Since the quality of most services depends largely on the quality of the individuals providing the services, it is true that " people costs " are a high component of service costs.

Since Macau has little arable land and few natural resources, it depends on mainland China for most of its food, fresh water, and energy imports.

Since a macro virus depends on the application rather than the operating system, it can infect a computer running any operating system to which the targeted application has been ported.

Since neodymium coloration depends upon " forbidden " f-f transitions deep within the atom, there is relatively little influence on the color from the chemical environment, so the color is impervious to the thermal history of the glass.

Since it depends only on the basic mechanic of betting in rounds, strip poker can be played with any form of poker ; however, it is usually based on simple variants with few betting rounds, like five card draw.

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 it only depends on two of the observations, it is most useful in representing the dispersion of small data sets.

Since the current available depends on the state of charge of the dry cell, a multimeter usually has an adjustment for the ohms scale to zero it.

Since the E1 component of nuclear EMP depends on the prompt gamma ray output, which was only 0. 1 % of yield in Starfish Prime but can be 0. 5 % of yield in pure fission weapons of low yield, a 10 kiloton bomb can easily be 5 x 8 % = 40 % as powerful as the 1. 44 megaton Starfish Prime at producing EMP.

Since the field inside a parallel plate capacitor depends linearly on the potential, the index of refraction depends linearly on the field ( for crystals where Pockels effect dominates ), and the phase depends linearly on the index of refraction, the phase modulation must depend linearly on the potential applied to the EOM.

Since this scheme depends on the difference between successive phases, it is termed differential phase-shift keying ( DPSK ).

Since temperature in principle also depends on altitude, one needs a second equation to determine the pressure as a function of height, as discussed in the next section.

Since thrust depends on both the amount of gas moved and the velocity, we can generate high thrust by accelerating a large mass of gas by a small amount, or by accelerating a small mass of gas by a large amount.

Since good tracking depends on the exact distance between the rotating drum and the fixed control / audio head reading the linear tracks, which usually varies by a couple of micrometers between machines due to manufacturing tolerances, most VCRs offer tracking adjustment, either manual or automatic, to correct such mismatches.