This sequence of equations may be started with the remark that with no process Af there is no profit, i.e., Af.

Thus, the algorithm can be written as a sequence of equations

* The intro sequence for each episode of Pinky and the Brain ( the 1995 spin-off from Animaniacs ), shows The Brain writing equations on a blackboard, one of which is " THX = 1138 ".

In addition to the standard two-dimensional function plots, it can also produce graphs of parametric equations, polar equations, sequence plots, differential equation fields, and three-dimensional ( two independent variable ) functions.

which are a sequence of linear differential equations that can be readily solved with, for instance, Laplace transform, or Integrating factor.

It is straightforward to show from analytic geometry that constructible lengths must come from base lengths by the solution of some sequence of quadratic equations.

He stated that pi was equal to 3, leading to a complex sequence of equations which came up with an answer more accurate than the answer that would have resulted if he did the same sequence of equations, but instead having pi equal to 3. 1415.

The Ramachandran plot utilizes mathematical equations to determine the possible angles of the amino acids within the primary sequence of Protein Z.

Specifically it implies that a sequence generated from the Rössler equations will begin to loop around, start being pulled upwards into the vector, creating the upward arm of a curve that bends slightly inward toward the vector before being pushed outward again as it is pulled back towards the repelling plane.

The AR coefficients can be estimated from the autocorrelation sequence by solving the Yule-Walker equations.

This turns out to be closely related to the discovery that some equations, which are said to be completely integrable, enjoy an infinite sequence of conservation laws.

Conversely, the sequence components are generated from the analysis equations

Both components are orange-hued dwarf ( main sequence ) stars ; the primary is of magnitude 5. 2 and the secondary is of magnitude 6. 1.

Unbound free-floating planetary-mass bodies in the Milky Way may number in the trillions, with 100, 000 objects larger than Pluto for every main-sequence star .< ref > Nomads of the Galaxy, Louis E. Strigari, Matteo Barnabe, Philip J. Marshall, Roger D. Blandford ; estimates 700 objects > 10 < sup >- 6 </ sup > Solar masses (≈ a Mars mass ) per main sequence star between 0. 08 and 1 Solar mass, of which there are billions in the Milky Way .</ ref >

Human genes differ only 1. 6 % on average from their corresponding gorilla genes in their sequence, but there is further difference in how many copies each gene has.

In all, GPCRs can be grouped into 6 classes based on sequence homology and functional similarity:

( In fact, subtracting 1 and dividing the result by 9 always gives a triangular number, the sequence starting with 3, 55, 903, 3727815, ....) This can be reformulated as follows: adding the digits of any even perfect number ( except 6 ), then adding the digits of the resulting number, and repeating this process until a single digit ( called the digital root ) is obtained, always produces the number 1.

The gene spans 20 kb, with a non-coding exon 1 and a very long first intron of 10 kb. The coding sequence contains five regions showing a high degree of conservation in vertebrates, predominantly in exons 2, 5, 6, 7 and 8, but the sequences found in invertebrates show only distant resemblance to mammalian TP53.

On average, only 3 of the 6 base pairs in each consensus sequence is found in any given promoter.

This coincides with the normal order of integer representations, such as the sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

In the structure of Tl < sub > 2 </ sub > Ba < sub > 2 </ sub > CuO < sub > 6 </ sub > ( Tl-2201 ), there is one CuO < sub > 2 </ sub > layer with the stacking sequence ( Tl – O ) ( Tl – O ) ( Ba – O ) ( Cu – O ) ( Ba – O ) ( Tl – O ) ( Tl – O ).

Sequences can be finite, as in this example, or infinite, such as the sequence of all even positive integers ( 2, 4, 6 ,...).

For instance, starting with n = 6, one gets the sequence 6, 3, 10, 5, 16, 8, 4, 2, 1.

The digit sequence is rarely given ; one arrangement is 6 7 5 8 4 3 9 2 0 1 from front ( 6 ) to back ( 1 ).

Instructions were 24 bits long, with 6 bits for the opcode, 4 bits for the " skip " value ( telling how many memory locations to skip to get to the next instruction in program sequence ), and 14 bits for the memory address.

In early days of photography, available shutter speeds were not standardized, though a typical sequence might have been 1 / 10 s, 1 / 25 s, 1 / 50 s, 1 / 100 s, 1 / 200 s and 1 / 500 s. Following the adoption of a standardized way of representing aperture so that each major step exactly doubled or halved the amount of light entering the camera ( 2. 8, 4, 5. 6, 8, 11, 16, etc.

* f < sub > ω + 1 </ sub >( 64 ) > f < sub > ω </ sub >< sup > 64 </ sup >( 6 ) > Graham's number (= g < sub > 64 </ sub > in the sequence defined by g < sub > 0 </ sub >

The firing sequence is odd ( BMW M5, Dodge Viper, Ford 6. 8 V10 ).

* The 5 ' donor site in the intron downstream from exon 6 in the pre-mRNA has a weak agreement with the consensus sequence, and is not bound usually by the U1 snRNP.

On November 6, the 56½ hour countdown sequence began with propellant loading.

The sequence of automorphic numbers begins 1, 5, 6, 25, 76, 376, 625, 9376, ....

Another difference with American skeet is that the sequence to complete the 25 targets in a round of Olympic skeet requires shooters to shoot at doubles, not only in stations 1, 2, 6, and 7, as in American skeet, but also on 3, 4, and 5.

Each Omega station transmitted a sequence of three very low frequency ( VLF ) signals ( 10. 2 kHz, 13. 6 kHz, 11. 333 ... kHz in that order ) plus a fourth frequency which was unique to each of the eight stations.

The first is the chronological sequence that the radio frequencies were allocated to the service: 1 = 162. 550, 2 = 162. 400, 3 = 162. 475, 4 = 162. 425, 5 = 162. 450, 6 = 162. 500, 7 = 162. 525.

And any sequence can not only change its positions in the work but can even be eliminated from it altogether.

When the historian encounters a situation in which he can perceive no visible cause and effect sequence, he should be alert to intuition and unconscious instinct as possible guides.

But first, we must define two terms so that their meaning will be clearly understood: form -- any unique sequence of alphabetic characters that can appear in a language preceded and followed by a space ; ;

This type of presentation is usually accomplished with a camera and a projector or a computer viewing screen which can rapidly cycle through images in a sequence.

Thus, an algorithm can be considered to be any sequence of operations that can be simulated by a Turing-complete system.

There is a wide variety of representations possible and one can express a given Turing machine program as a sequence of machine tables ( see more at finite state machine, state transition table and control table ), as flowcharts ( see more at state diagram ), or as a form of rudimentary machine code or assembly code called " sets of quadruples " ( see more at Turing machine ).

If the method is applied to an infinite sequence ( X < sub > i </ sub >: i ∈ ω ) of nonempty sets, a function is obtained at each finite stage, but there is no stage at which a choice function for the entire family is constructed, and no " limiting " choice function can be constructed, in general, in ZF without the axiom of choice.

The following formulas can be used to update the mean and ( estimated ) variance of the sequence, for an additional element.

Whenever the observer's learning process ( which may be a predictive neural network-see also Neuroesthetics ) leads to improved data compression such that the observation sequence can be described by fewer bits than before, the temporary interestingness of the data corresponds to the number of saved bits.

By sweeping this surface through R < sup > 3 </ sup > as a function of the ion sequence input data, such as via ion-ordering, a volume is generated onto which positions the 2D detector positions can be computed and placed three-dimensional space.

Protein sequence can be determined by Edman degradation, in which the N-terminal residues are hydrolyzed from the chain one at a time, derivatized, and then identified.

Nucleic acid sequence can be determined using gel electrophoresis and capillary electrophoresis.

These programs can compensate for mutations ( exchanged, deleted or inserted bases ) in the DNA sequence, to identify sequences that are related, but not identical.

Shotgun sequencing yields sequence data quickly, but the task of assembling the fragments can be quite complicated for larger genomes.

The expression of many genes can be determined by measuring mRNA levels with multiple techniques including microarrays, expressed cDNA sequence tag ( EST ) sequencing, serial analysis of gene expression ( SAGE ) tag sequencing, massively parallel signature sequencing ( MPSS ), RNA-Seq, also known as " Whole Transcriptome Shotgun Sequencing " ( WTSS ), or various applications of multiplexed in-situ hybridization.

Using the extension of the code, the encoded string 0011001011 can be grouped into codewords as 0 – 011 – 0 – 01 – 011, and these in turn can be decoded to the sequence of source symbols acabc.

If a cabal can be implicated in a sequence of events, there is always the hope, however tenuous, of being able to break the cabal's power – or joining it and exercising some of that power oneself.

However, an open disk is not compact, because a sequence of points can tend to the boundary without getting arbitrarily close to any point in the interior.

Likewise, spheres are compact, but a sphere missing a point is not since a sequence of points can tend to the missing point without tending to any point within the space.

A metric space is called pre-compact or totally bounded if any sequence has a Cauchy subsequence ; this can be generalised to uniform spaces.

This is often exploited in algorithms, both theoretical and applied, where an iterative process can be shown relatively easily to produce a Cauchy sequence, consisting of the iterates.