Since the energy levels of electrons in atoms are discrete, each element and each molecule emits and absorbs its own characteristic frequencies.

Since there is generally a clear separation between the browser and the plug-in, the results are discrete objects embedded within a webpage.

( Since the sub-structure is usually represented in the computer by a set of integer variables with constraints, these problems can be viewed as special cases of constraint satisfaction or discrete optimization ; but they are usually formulated and solved in a more abstract setting where the internal representation is not explicitly mentioned.

Since is discrete and

Terminal objects in a category C may also be defined as limits of the unique empty diagram ∅ → C. Since the empty category is vacuously a discrete category, a terminal object can be thought of as an empty product ( a product is indeed the limit of the discrete diagram

Since it is of the discrete form, then the absorption coefficient and CD of the line are given by

Since Rader's algorithm only depends upon the periodicity of the DFT kernel, it is directly applicable to any other transform ( of prime order ) with a similar property, such as a number-theoretic transform or the discrete Hartley transform.

Since there is generally a clear separation between the browser and the plug-in, the results are discrete objects embedded within a webpage.

Since displays have a discrete number of points, the frequency span measured is also discretized.

Since T is compact, the topology on the dual group is that of uniform convergence, which turns out to be the discrete topology.

Since every map from a discrete space is continuous, the topological homomorphisms between discrete groups are exactly the group homomorphisms between the underlying groups.

Since topological groups are homogeneous, one need only look at a single point to determine if the topological group is discrete.

Since the only Hausdorff topology on a finite set is the discrete one, a finite Hausdorff topological group must necessarily be discrete.

Since the intensity function of a digital image is only known at discrete points, derivatives of this function cannot be defined unless we assume that there is an underlying continuous intensity function which has been sampled at the image points.

Since a digital computer is a discrete system, the Laplace transform is replaced with the Z-transform.

Since the early days, it has been recognized that the PIC method is susceptible to error from so-called discrete particle noise.

Since BGL ( R )< sup >+</ sup > is path connected and K < sub > 0 </ sub >( R ) discrete, this definition doesn't differ in higher degrees and also holds for n = 0.

Since the term was first coined by archaeologists, further excavation and analysis has indicated that it consisted of several discrete cultures such as the Hembury and the Abingdon cultures ; and that " Windmill Hill culture " is too general a term.

Since his retirement from the Puerto Rico Supreme Court, he announced that he would abstain from political activity for one year, and on March 14, 2006 announced that within a month would begin attending New Progressive Party of Puerto Rico meetings, as former party president, to provide discrete advice.

Since a discrete signal is a sequence ( merely a series of symbols ; typically, numbers ) it contains no direct information as to determine the frequency of the corresponding continuous signal.

Since pH is defined as the negative logarithm of the concentration of hydronium ions, acids thus have pHs of less than 7.

Since the attenuation is defined as proportional to the logarithm of the ratio between and, where is the power at point and respectively.

Since the absorbance of a sample is measured as a logarithm, it is directly proportional to the thickness of the sample and to the concentration of the absorbing material in the sample.

Since illumination and reflectance combine multiplicatively, the components are made additive by taking the logarithm of the image intensity, so that these multiplicative components of the image can be separated linearly in the frequency domain.

Since E < sub > m </ sub > is small compared to E *, a Taylor series expansion can be performed on the latter logarithm around the energy E *.

Since this is the logarithm of, we can see that itself is a Gaussian distribution.

( Since this is a quotient of logarithms, the base of the logarithm chosen is irrelevant.

Since the company under review is supplying what we are here regarding as only one kind of service, we might suppose that the problem of total cost apportionment would be very simple ; ;

Since an objective viewer might well conclude that this is not a situation that would often arise, the film's extensive discussion of the problem seems, at best, superfluous.

Since all problems in NP can be reduced to this problem it follows that for all problems in NP we can construct a non-deterministic Turing machine that decides the complement of the problem in polynomial time, i. e., NP is a subset of co-NP.

The proof of this fact relies on an algorithm which, given the first n digits of Ω, solves Turing's halting problem for programs of length up to n. Since the halting problem is undecidable, Ω can not be computed.

Since the brain effects of hypoglycemia, termed neuroglycopenia, determine whether a given low glucose is a " problem " for that person, most doctors use the term hypoglycemia only when a moderately low glucose level is accompanied by symptoms or brain effects

Since Syria built a dam on the Euphrates, the flow of water has been considerably diminished and flooding was no longer a problem in the mid-1980s.

Since M-theory is thought to operate in 11 dimensions this problem then becomes very difficult.

Since then, dams have been constructed to ameliorate the problem.

Since uplift and erosion are more or less in equilibrium in the Himalaya, rapid uplift is balanced by annual increments of cubic kilometers of sediments washing down from the mountains, then on the plains settling out of suspension on vast alluvial fans or inland deltas over which rivers meander and change course at least every few decades, causing some experts to question whether manmade embankments can contain the problem of flooding.

Since late 2004, he has suffered from a reemergence of his focal dystonia which has affected his ability to draw for lengthy periods on paper, though it causes no real problem now that he draws the comic on a graphics tablet.

Since the dawn of computing, the sorting problem has attracted a great deal of research, perhaps due to the complexity of solving it efficiently despite its simple, familiar statement.

Since the relevant parallel commitment is only that good can co-exist with an omniscient, omnipotent and omnimalevolent being, not that it is plausible that they should do so, the theist who is responding to the problem of evil need not be committing themselves to something they are likely to think is false.

Since they do not have any complicated boot images, the problem of boot image control is centralized to the server.

Since the tertiary structure of proteins is an important problem in biochemistry, and since structure determination is relatively difficult, protein structure prediction has been a long-standing problem.

Since the Laplace operator appears in the heat equation, one physical interpretation of this problem is as follows: fix the temperature on the boundary of the domain according to the given specification of the boundary condition.

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 Amiga's hardware was more or less fixed ( unlike today's PC industry, where arbitrary combinations of hardware can be put together ), there was competition to test the limits of that hardware and perform theoretically " impossible " feats by refactoring the problem at hand.

Since null alleles are a technical problem and sampling effects that occur during mating are a real biological property of a population, it is often very important to distinguish between them if excess homozygotes are observed.

* Since L is NP-complete, and hence the hardest in class NP, also problem H is at least as hard as NP, but H does not have to be in NP and hence does not have to be a decision problem ( even if it is a decision problem, it need not be in NP );

* Since NP-complete problems transform to each other by polynomial-time many-one reduction ( also called polynomial transformation ), all NP-complete problems can be solved in polynomial time by a reduction to H, thus all problems in NP reduce to H ; note, however, that this involves combining two different transformations: from NP-complete decision problems to NP-complete problem L by polynomial transformation, and from L to H by polynomial Turing reduction ;