In particular, a DCT is a Fourier-related transform similar to the discrete Fourier transform ( DFT ), but using only real numbers.

Density functional theory ( DFT ) is a quantum mechanical modelling method used in physics and chemistry to investigate the electronic structure ( principally the ground state ) of many-body systems, in particular atoms, molecules, and the condensed phases.

The above re-indexing is then substituted into the formula for the DFT, and in particular into the product nk in the exponent.

If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.

Evidence is plentiful that early and later also he has been indebted to the Gothic romancers, who deal in extravagant horror, to the symbolists writing at the end of the preceding century, and in particular to the stream-of-consciousness novelists, Henry James and James Joyce among them.

Ptolemy's problem is to forecast where, against the inverted bowl of night, some particular light will be found at future times.

The strongest appeal of the Copernican formulation consisted in just this: ideally, the justification for dealing with special problems in particular ways is completely set out in the basic ' rules ' of the theory.

The `` conventional '' image of a particular time and place is not necessarily congruent with the image of the facts as established over the years by scholarly and scientific research.

The symposium provides an opportunity to confront the self with specific statements which were made at particular times by identifiable communicators who were addressing definite audiences -- and throughout several hundred pages everyone is talking about the same key symbol of identification.

But there is one in particular which, it seems to me, deserves special attention.

At Sounion there is a group of beautiful columns, the ruins of a temple to Poseidon, of particular interest at that time, as active reconstruction was in progress.

Each will decide on his own course somewhere between these two extreme cases according to the sense of responsibility which is determined for him by the particular circumstances of his own life.

In Plato's mind there is an irresolvable conflict between the poet and the philosopher, because the poet imitates only particular objects and is incapable of rising to the first level of abstraction, much less the highest level of ideal forms.

The wisdom of granting such tax exemptions is another matter, but this particular instance is, in my opinion, completely satisfactory.

It makes no difference what part of the world is involved, what form of regime, what particular issue.

Molotov, in particular, is being charged with all kinds of sins -- especially with wanting to cut down free public services, to increase rents and fares ; ;

It would seem, then, that movable property and equipment is not taxed as a whole but that certain types are taxed in towns where this is bound to be expedient for that particular kind of personal property.

It is not clear, however, whether they are thinking of all movable property or only of boats, trailers, aircraft or certain other types of personal property whose assessment would be advantageous to their particular towns.

If the resulting difference for the particular State is less or more than these extremes, the State's allotment percentage must be raised or lowered to the appropriate extreme.

Determine if the particular State's unadjusted allotment ( result obtained in item 11 above ) is greater than its maximum allotment, and if so lower its unadjusted allotment to its maximum allotment.

Determine if the particular State's unadjusted allotment ( result obtained in item 11 above ) is less than its minimum ( base ) allotment, and if so raise its unadjusted allotment to its minimum allotment.

If the resulting difference for the particular State is less or more than these extremes, the State's Federal share must be raised or lowered to the appropriate extreme.

For this reason, the more uncertain skywave service was denominated `` secondary '' in our rules, as compared to the steadier, more reliable groundwave `` primary service '', and, for both skywave service and skywave interference, signal strength is expressed in terms of percentage of time a particular signal-intensity level is exceeded -- 50 percent of the time for skywave service, 10 percent of the time for skywave interference.

The exercise I shall discuss in this -- the first of a new series of articles on muscle definition-specialization of a particular body part -- is the One Leg Lunge.

The latter in particular has spread widely, and there are now over a hundred Camphill communities and other anthroposophical homes for children and adults in need of special care in about 22 countries around the world.

An " ideal beauty " is an entity which is admired, or possesses features widely attributed to beauty in a particular culture, for perfection.

The more widely a particular law was recognized, the more weight it held, whereas purely local customs were generally subordinate to law recognized in a plurality of jurisdictions.

The signal for formation of a regional centromere appears to be " epigenetic "-a widely used term that in this instance most likely refers to a particular set of post-translational modifications of the histone proteins, or different histone variants being present.

In particular, the new design did not include many of the addressing modes that were intended to make programs smaller in memory, a technique that was widely used on other DEC machines and CISC designs in general.

The term became more widely assimilated into English by the mid 1950s, with long-term expatriates in significant numbers from other particular countries or regions also being referred to as a diaspora.

In particular, it has remained in broad use in the embedded computing world, though the recently developed EEMBC benchmark suite, HINT, Stream, and even Bytemark are widely quoted and used, as well as more specific benchmarks for the memory subsystem ( Cachebench ), TCP / IP ( TTCP ), and many others.

A relationship with Albanian in particular has been advanced by Zecharia Mayani, as well as earlier writers such as Ascoli, 1877, E. Schneider, 1889, Thomopoulos, 1912, Buonamici, 1919 ; but Albanian is known to be an Indo-European language, and widely considered in linguistics to be an isolate.

This belief is widely accepted in the United States, Europe, Australia and other Western nations, and was recognized as an important value by many Western philosophers throughout history, in particular since the Enlightenment.

It is widely planted throughout the Columbia Valley AVA but has earned particular notice from plantings grown in Walla Walla, Red Mountain and the Horse Heaven Hills.

Of particular significance are the various introductory sections – as well as the introduction to the work itself – these are widely quoted in other works on the Mishnah, and on the Oral law in general.

The timing of festivals, and the rites celebrated, may vary from climate to climate, and will also vary ( sometimes widely ) depending upon which particular pagan religion the adherent subscribes to ( see Wheel of the Year ).

Laudanum was originally the sixteenth-century term for a medicine associated with a particular physician that was widely well-regarded, but became standardized as " tincture of opium ," a solution of opium in ethanol, which Paracelsus has been credited with developing.

One particular polymerase, from the thermophilic bacterium, Thermus aquaticus ( Taq ) ( PDB 1BGX, EC 2. 7. 7. 7 ) is of vital commercial importance due to its use in the polymerase chain reaction, a widely used technique of molecular biology.

In particular, due to its location straddling the erstwhile border between east and west, it was widely perceived as a " linking element ," reconnecting the two halves of the city in a way that was symbolic as well as physical, helping to heal the historical wounds by providing an exciting new mecca attracting Berliners from both sides of the former divide.

The outbreak of the First World War, and in particular its conclusion, made it clear to many academics that some kind of world court was needed, and it was widely expected that one would be established.

The most widely pursued possibilities for quantum gravity phenomenology include violations of Lorentz invariance, imprints of quantum gravitational effects in the Cosmic Microwave Background ( in particular its polarization ), and decoherence induced by fluctuations in the space-time foam.

" Among radical feminists, the view became widely held that, thus far, the sexual freedoms gained in the sexual revolution of the 1960s — in particular, the decreasing emphasis on monogamy — had been largely gained by men at women's expense.

Sales tax rates vary widely among jurisdictions, from 0 % to 16 %, and may vary within a jurisdiction based on the particular goods or services taxed.

The word tachyon has become widely recognized to such an extent that it can impart a science-fictional connotation even if the subject in question has no particular relation to superluminal travel ( a form of technobabble, akin to positronic brain ).

In particular, he is widely recognized as having been the architect of the Prussian education system which was used as a model for education systems in countries such as the United States and Japan.

Several yeasts, in particular S. cerevisiae, have been widely used in genetics and cell biology.

While Hungarian notation can be applied to any programming language and environment, it was widely adopted by Microsoft for use with the C language, in particular for Microsoft Windows, and its use remains largely confined to that area.

In particular, use of Hungarian notation was widely evangelized by Charles Petzold's " Programming Windows ", the original ( and for many readers, the definitive ) book on Windows API programming.