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* If N data points of the form ( Y, X ) are observed, where N < k, most classical approaches to regression analysis cannot be performed: since the system of equations defining the regression model is underdetermined, there is not enough data to recover β.
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If and N
If Af denotes the space of N times continuously differentiable functions, then the space V of solutions of this differential equation is a subspace of Af.
** If the set A is infinite, then there exists an injection from the natural numbers N to A ( see Dedekind infinite ).
Let ( m, n ) be a pair of amicable numbers with m < n, and write m = gM and n = gN where g is the greatest common divisor of m and n. If M and N are both coprime to g and square free then the pair ( m, n ) is said to be regular, otherwise it is called irregular or exotic.
If ( m, n ) is regular and M and N have i and j prime factors respectively, then ( m, n ) is said to be of type ( i, j ).
If A is expressed as an N × N matrix, then A < sup >†</ sup > is its conjugate transpose.
If the program hasn't halted yet, then it never will, since its contribution to the halting probability would affect the first N bits.
If S is an arbitrary set, then the set S < sup > N </ sup > of all sequences in S becomes a complete metric space if we define the distance between the sequences ( x < sub > n </ sub >) and ( y < sub > n </ sub >) to be, where N is the smallest index for which x < sub > N </ sub > is distinct from y < sub > N </ sub >, or 0 if there is no such index.
If the expression that defines the DFT is evaluated for all integers k instead of just for, then the resulting infinite sequence is a periodic extension of the DFT, periodic with period N.
If a filter is implemented using, for instance, biquad stages using op-amps, N / 2 stages will be needed.
# If the remainder from dividing N by 6 is not 2 or 3 then the list is simply all even numbers followed by all odd numbers ≤ N
If f: M → N is any function, then we have f id < sub > M </ sub >
If we neglect the possibility of overlapping states, which is valid if the temperature is high, then the number of times we count each state is approximately N < nowiki >!</ nowiki >.
If the molecule is symmetrical, e. g. N < sub > 2 </ sub >, the band is not observed in the IR spectrum, but only in the Raman spectrum.
# If M, N ∈ Λ, then ( M N ) ∈ Λ
If the alphabet consists of alternative symbols, each symbol represents a message consisting of N bits.
If μ is a positive measure, then N is null ( or zero measure ) if its measure μ ( N ) is zero.
If μ is not a positive measure, then N is μ-null if N is | μ |- null, where | μ | is the total variation of μ ; equivalently, if every measurable subset A of N satisfies μ ( A )
If and data
If he found data that fitted his general plan, he used it and counted his sources trustworthy.
If 16 scanlines of continuous graphical data are written to a character-block-aligned portion of the screen then they will appear as a continuous block in most modes but in the two non-continuous modes they will be displayed as two blocks of 8 scanlines, separated in the middle by two blank scanlines.
If the next data item is not available when it is needed, the codec has no choice but to produce silence or guess — and if the data is late, it is useless, because the time period when it should have been converted to a signal has already passed.
If the tree contains data, we can simply simultaneously store it in a consecutive array in preorder.
If products designed for the new standard can receive, read, view or play older standards or formats, then the product is said to be backward-compatible ; examples of such a standard include data formats and communication protocols.
If dynamic re-routing is established, even if one or more nodes depart and abandon a downloading file, for example, the remaining nodes should still have the data needed to complete the download.
If there is little rearrangement of radiosity objects in the scene, the same radiosity data may be reused for a number of frames, making radiosity an effective way to improve on the flatness of ray casting, without seriously impacting the overall rendering time-per-frame.
If preserving the original quality of the stream is more important than eliminating the correspondingly larger data sizes, lossless codecs are preferred.
If the disk was not otherwise prepared with a custom format, ( e. g. for data disks ), 664 blocks would be free after formatting, giving 664 × 254 = 168, 656 bytes ( or almost 165 kB ) for user data.
If the location specified is incorrect, this will cause the computer to write the data to some other part of the program.
If requested data is contained in the cache ( cache hit ), this request can be served by simply reading the cache, which is comparatively faster.
If sender0 has code ( 1, – 1 ) and data ( 1, 0, 1, 1 ), and sender1 has code ( 1, 1 ) and data ( 0, 0, 1, 1 ), and both senders transmit simultaneously, then this table describes the coding steps:
If the checksums match, the data was almost certainly not altered.
If integration via the bus is achieved, the data warehouse, through its two data marts, will not only be able to deliver the specific information that the individual data marts are designed to do, in this example either " Sales " or " Production " information, but can deliver integrated Sales-Production information, which, often, is of critical business value.
If the data to be compressed is analog ( such as a voltage that varies with time ),
If a database cannot tolerate even such smaller probability of data loss, then the RAID group itself is replicated ( mirrored ).
If a database cannot tolerate even such smaller probability of data loss, then the RAID group itself is replicated ( mirrored ).
The report to the European Parliament of 2001 states: " If UKUSA states operate listening stations in the relevant regions of the earth, in principle they can intercept all telephone, fax and data traffic transmitted via such satellites.
If empirical data reach significance under the appropriate statistical formula, the research hypothesis is supported.
If we are to specify this doctor's normality in sensory terms, we must make reference to a second doctor who, when inspecting the sense organs of the first doctor, would himself have to have the sense data a normal observer has when inspecting the sense organs of a subject who is a normal observer.
If and points
If the points aren't thrown all the way, the Turnout cannot be locked, and in turn, the signal cannot be cleared.
If **ya is the multiple secant of **zg which passes through Af and **yb is the simple secant of **zg which passes through Af, and if Af are the points in which **ya meets **zg, and if Af is the image of Af on the generator **yb, it follows that the image of the line Af is Af.
If the score reaches 20-all, then the game continues until one side gains a two point lead ( such as 24 – 22 ), up to a maximum of 30 points ( 30 – 29 is a winning score ).
If the hand value exceeds 21 points, it busts, and all bets on it are immediately forfeit.
* The Lusternik – Schnirelmann theorem: If the sphere S < sup > n </ sup > is covered by n + 1 open sets, then one of these sets contains a pair ( x, − x ) of antipodal points.
If a bubble touches identically-colored bubbles, forming a group of three or more, those bubbles — as well as any bubbles hanging from them — are removed from the field of play, and points are awarded.
If the thumb points in the direction of the 4th substitutent, the enantiomer is R. Otherwise, it's S.
If one chooses an infinite number of distinct points in the unit interval, then there must be some accumulation point in that interval.
If they are successful, they receive two points, if they are not, then they receive zero points.
If they make what would normally be a field goal, they score one point ; what would normally be a touchdown scores two points ( a " two-point conversion ").
If the ball hits the upright above the cross-bar before going through, it is not considered a dead ball, and the points are scored.
If he didn't meet Pitman, Severin points out that Defoe, upon submitting even a draft of a novel about a castaway to his publisher, would undoubtedly have learned about Pitman's book published by his father, especially since the interesting castaway had previously lodged with them at their former premises.
If the difference in vapor pressure between the two components A and B is large ( generally expressed as the difference in boiling points ), the mixture in the beginning of the distillation is highly enriched in component A, and when component A has distilled off, the boiling liquid is enriched in component B.
If air is heated in a region it will expand in all directions such that the velocity field points outward from that region.
If a dachshund is brindled on a dark coat and has tan points, it will have brindling on the tan points only.
If we reciprocate such a polyhedron about its intersphere, the dual polyhedron will share the same edge-tangency points and so must also be canonical ; it is the canonical dual, and the two together form a canonical dual compound.
* If a circle passing through two of the input points doesn't contain any other of them in its interior, then the segment connecting the two points is an edge of a Delaunay triangulation of the given points.
If the equator is projected outward to the celestial sphere, forming the celestial equator, it crosses the ecliptic at two points known as the equinoxes.
If there is a grain of historical truth behind these legends, it may be that Suizei's bare narrative points to one of the chieftains of four clans of the Unebi region who disputed among themselves in the struggle to achieve hegemeony in the Yamato area.
If it is assumed that social change is not only affected, but in some points of view, directed by the advancement of technology, is it ethical to hold these technologies from certain people?
If any part of the ball reaches any part of the imaginary vertical plane transected by this line while in-bounds and in possession of a player whose team is striving toward that end of the field, this is considered a touchdown and scores six points for the team whose player has advanced the ball to, or recovered the ball in, this position.
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