Specifically, a function f is periodic with period P if the graph of f is invariant under translation in the x-direction by a distance of P. This definition of periodic can be extended to other geometric shapes and patterns, such as periodic tessellations of the plane.

Specifically, the antenna gain, or power gain of an antenna is defined as the ratio of the intensity ( power per unit surface ) radiated by the antenna in the direction of its maximum output, at an arbitrary distance, divided by the intensity radiated at the same distance by a hypothetical isotropic antenna.

Specifically, a small-world network is defined to be a network where the typical distance L between two randomly chosen nodes ( the number of steps required ) grows proportionally to the logarithm of the number of nodes N in the network, that is:

Specifically, in a Cuban television interview days after the shootdown took place, Roque, from within Cuba, stated, " I personally have violated air space, specifically the last was on January 9, 1996. where I got a call the day before to participate in a flight to Havana where thousands of leaflets were going to be released from a height of more than 9, 500 feet at a distance of less than 10 miles from the coast.

Specifically, exercises that may be prescribed include keeping eyes fixated on a specific target while moving the head, moving to the head right to left at two targets at a significant distance apart, walking while keeping eyes fixated on a specific target, and walking while keeping eyes fixated on a specific target while also turning the head in different directions.

Specifically, humans all need a certain amount of personal space, also thought of as distance or privacy ; people also desire a certain amount of closeness with others, or affiliation.

Specifically, a formal theorem is always the last formula of a derivation in some formal system each formula of which is a logical consequence of the formulas which came before it in the derivation.

Specifically, duration can be formulated as the first derivative of the price with respect to the interest rate, and convexity as the second derivative ( see: Bond duration closed-form formula ; Bond convexity closed-form formula ).

Specifically, the net profit formula in authors ' contracts does not correspond to the net profit formula of generally accepted accounting principles that the movie studios use when creating their financial statements that are reported to the U. S. Securities and Exchange Commission and to the investing public.

Specifically, umpires were now given the power — and the responsibility — to intervene if they considered a bowler was deliberately aiming at a batsman with intent to injure.

Specifically, given that this is a circularly polarized plane wave, these vectors indicate that the electric field, from plane to plane, has a constant strength while its direction steadily rotates.

Specifically, if one freezes a right-handed wave in time, when one curls the fingers of one ’ s right hand around the helix, the thumb will point in the direction which the helix progresses given that sense of rotation.

Specifically, if the amplitude of the transmitted signal is restricted to the range of ... + A volts, and the precision of the receiver is ± ΔV volts, then the maximum number of distinct pulses M is given by

Specifically, given two quantities, p and q, and a rational number m / n we can say that the ratio of p to q is less than, equal to, or greater than m / n when np is less than, equal to, or greater than mq respectively.

Specifically, the symbol F in a formal language is a functional symbol if, given any symbol X representing an object in the language, F ( X ) is again a symbol representing an object in that language.

Specifically, a 1716 inventory of the musical instrument collection is signed " Bartolommeo Cristofori Custode ", indicating that Cristofori had been given the title of custodian of the collection.

Specifically, even if the British legislature or judiciary changed English common law on a given point, that change is not binding on American authorities.

" Specifically, " no war is just, unless it is entered upon after an official demand for satisfaction has been submitted or warning has been given and a formal declaration made.

Specifically, given g ∈ G, ρ ( g ) is the linear map on V determined by its action on the basis by right translation by g < sup >− 1 </ sup >, i. e.

Specifically, it is the density altitude at which flying in a clean configuration, at the best rate of climb airspeed for that altitude and with all engines operating and producing maximum continuous power, will produce a given rate of climb ( usually 100 feet per minute climb or 30 meters per minute, and 500 feet per minute climb for jet airplanes ).

Specifically, Keynes proposed that new evidence e is irrelevant to a proposition, given old evidence q, if and only if p / q & e

Specifically, if Q is a submodule of some other module, then it is already a direct summand of that module ; also, given a submodule of a module Y, then any module homomorphism from this submodule to Q can be extended to a homomorphism from all of Y to Q.

Specifically we were given a boolean function whose input is 1 bit, and asked if it is constant.

Specifically the fund is to be used to ( 1 ) underwrite the Fritz London Memorial Prize, given in recognition of outstanding contributions in Low Temperature Physics and ( 2 ) provide support for the London Memorial Lectures at Duke University.

Specifically, power is given as total ( not per-phase ) power, and voltage is line-to-line voltage.

Specifically, in Europe in 1991, as part of the “ Action Master Elite ” sub-group, a figure named Omega Spreem was released ; the “ Defense Base ” function given to the character indicates that the toy is intended to be a new version of Omega Supreme himself, but the misspelled name and garish orange and pink paint job leave the toy as something of an oddity overall.

Specifically, given an algebra A over a ring or a field K, a K-derivation is a K-linear map D: A → A that satisfies Leibniz's law:

Specifically, C < sub > 1 </ sub > is also given by

Specifically, he attended a number of informal lectures given by D. T.

Specifically, given a sequence of cohomology groups H < sup > k </ sup >( X ; R ) on X with coefficients in a commutative ring R ( typically R is Z < sub > n </ sub >, Z, Q, R, or C ) one can define the cup product, which takes the form

Specifically, it is given by the state transition function.

Specifically, the separation index is given as follows:

Specifically, it allows one to efficiently find all intervals that overlap with any given interval or point.

Specifically, at speeds of OC-3 and above, the cost of segmentation and reassembly ( SAR ) hardware makes ATM less competitive for IP than Packet Over SONET ( POS ); because of its fixed 48-byte cell payload, ATM is not suitable as a data link layer directly underlying IP ( without the need for SAR at the data link level ) since the OSI layer on which IP operates must provide a maximum transmission unit ( MTU ) of at least 576 bytes.

Specifically, a male secondary school enrollment 10 % above the average reduced the chance of a conflict by about 3 %, while a growth rate 1 % higher than the study average resulted in a decline in the chance of a civil war of about 1 %.

Specifically, the above argument would become a fallacious ad baculum if the conclusion stated:

Specifically, it is claimed that above the ecosystem level a landscape level exists which is generated and identifiable by high interaction intensity between ecosystems, a specific interaction frequency and, typically, a corresponding spatial scale.

Specifically, draw a diagonal line connecting two points on the diagram so that every other point is either on or to the right and above it.

Specifically, the total lead used in electronics makes up only 2 % of world lead consumption, while 90 % of lead is used for batteries ( covered by the battery directive, as mentioned above, which requires recycling and limits the use of mercury and cadmium, but does not restrict lead ).

Specifically, he dictated that only soldiers holding the rank of Colonel or above should be permitted to wear silk and velvet, and that Captains and all ranks below should " make do with fustian and spend the remaining money on their arms.

Specifically, it is bordered by Gowi Mountain ( 495 m above sea level ) on the south, Seondo Mountain ( 380 m ) and Ongnyeo Peak ( 215 m ) on the west, and Gumi Mountain ( 594 m ) on the north.

Specifically, he will evaluate the lesion for the criteria mentioned above, except of course for the final criterion of spreading, which can only be diagnosed at a follow-up examination, should one be necessary.

Specifically, Mt Michael is situated 3750 metres above sea level while Mt Tabletop is at 3, 686 metres.

Specifically it refers to an axe being placed at the base of a tree just above the roots, which would be the final action before beginning to chop down the tree.