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sequence and equations
The sequence of equations ( 6 ) can be solved for Af when Af is known, and clearly Af, the maximization being over all admissible 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

sequence and may
The sequence may involve a sharp contrast: for example, a quiet meditative sway of the body succeeded by a violent leap ; ;
We may carry this sequence one step further and say that at seventy he was a poet at the height of his powers, wanting only the impetus of two tragedies, one personal, the other national, to loose those powers in poetry.
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.
In the second type, a researcher may conduct the gene test by comparing the sequence of DNA bases in a patient's gene to disease in healthy individuals or their progeny.
However, traditional films have frequently had much of the same sort of the issues to deal with ; film shoots may last several months and as scenes are frequently shot out of story sequence, footage shot weeks apart may be edited together as part of the same day's action in the completed film.
A formal grammar defines ( or generates ) a formal language, which is a ( usually infinite ) set of finite-length sequences of symbols ( i. e. strings ) that may be constructed by applying production rules to another sequence of symbols which initially contains just the start symbol.
A rule may be applied to a sequence of symbols by replacing an occurrence of the symbols on the left-hand side of the rule with those that appear on the right-hand side.
( In some instances a player may choose to stop the jumping sequence part way, in order to impede the opponent's progress, or to align pieces for planned future moves.
When scientists transfer a gene from one cell into another cell in order to express the new genetic material as a protein in the recipient cell, the cDNA will be added to the recipient ( rather than the entire gene ), because the DNA for an entire gene may include DNA that does not code for the protein or that interrupts the coding sequence of the protein ( e. g., introns ).
If so, it is unclear how much Tatian may have borrowed from this previous author in determining his own narrative sequence of Gospel elements.
The use of a sequence of experiments, where the design of each may depend on the results of previous experiments, including the possible decision to stop experimenting, is within the scope of Sequential analysis, a field that was pioneered by Abraham Wald in the context of sequential tests of statistical hypotheses.
Each element may be an atom or another sequence.
; object: A generic datatype which may contain any of the above ( i. e. atom, sequence or integer ) and which may be changed to another type during run-time.
A sequence may contain a collection of any types, and this can be sliced ( to take a subset of the data in a sequence ) and concatenated in expressions with no need for special functions.
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 >
It may have its own internal control sequence unit ( not to be confused with the CPUs main control unit ), some registers, and other internal units such as a sub-ALU or FPU, or some smaller, more specific components.
The same letter ( or sequence of letters ) may be pronounced in different ways when it occurs in different positions within a word.
In addition to jumps performed singly, jumps may also be performed in combination or in sequence.
Spins may be performed individually or in a sequence combining different types of spins.
A typical chord sequence, usually called the " Andalusian cadence " may be viewed as in a modified Phrygian: in E the sequence is Am – G – F – E.

sequence and be
The sequence of movements in a Cunningham dance is unlike any sequence to be seen in life.
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.
More importantly, several of the more advanced of the less developed countries have found through experience that they must plan their own complex investment programs for at least 5 years forward and tentatively for considerably more than that if they are to be sure that the various interdependent activities involved are all to take place in the proper sequence.
How and at what stage and in what sequence are other governments to be consulted??
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 ; ;
The only requirements on dictionary information made by the text-lookup operation are that each form represented by the dictionary be available for lookup in the text-form list and that information for each form be available in a sequence identical with the sequence of the forms.
By studying high speed movies made of this type of failure, the sequence of relationships as schematically illustrated in Fig. 9 could be observed.
If, in preparing that shot for the inevitable showing to your friends, you interrupt the sequence to paste in a few frames of the child's grandmother watching this event, you have begun to be an artist in film ; ;
In later Pahlavi papyri, up to half of the remaining graphic distinctions of these twelve letters were lost, and the script could no longer be read as a sequence of letters at all, but instead each word had to be learned as a whole — that is, they had become logograms as in Egyptian Demotic.
While there is no generally accepted formal definition of " algorithm ," an informal definition could be " a set of rules that precisely defines a sequence of operations.
Thus, an algorithm can be considered to be any sequence of operations that can be simulated by a Turing-complete system.
DNA sequence analysis indicated that Liliales should be divided into at least Liliales, Asparagales and Dioscoreales.
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 reason for the term " colloquially ", is that the sum or product of a " sequence " of cardinals cannot be defined without some aspect of the axiom of choice.
The following formulas can be used to update the mean and ( estimated ) variance of the sequence, for an additional element.

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