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Another representation of loop-erased random walk stems from solutions of the discrete Laplace equation.
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Another and representation
Another definition of the Bessel function, for integer values of, is possible using an integral representation:
Another integral representation is:
Another way to define the Bessel functions is the Poisson representation formula and the Mehler-Sonine formula:
Another common representation of the Dhrystone benchmark is the DMIPS ( Dhrystone MIPS ) obtained when the Dhrystone score is divided by 1757 ( the number of Dhrystones per second obtained on the VAX 11 / 780, nominally a 1 MIPS machine ).
Another explanation is that Punch ’ s treatment of his shrewish wife, as well as others, is so exaggerated that it is clearly not a representation of good behavior, but more of a commentary on how we all have felt toward someone at one time or another, especially a significant other.
Another is that the formal representation of such points, the Kronecker delta function is unphysical, because it cannot be normalized.
Another choice would be to replace each letter with its binary representation, transpose that, and then convert the new binary string into the corresponding ASCII characters.
) Another interchange format, intended to be more compact, easier to parse, and unique for any abstract S-expression, is the " canonical representation " which only allows verbatim strings, and prohibits whitespace as formatting outside strings.
Another useful representation is available by means of double Taylor expansion of e < sup >( ln x − μ )< sup > 2 </ sup >/( 2σ < sup > 2 </ sup >)</ sup >.
Another application of the SVD is that it provides an explicit representation of the range and null space of a matrix M. The right-singular vectors corresponding to vanishing singular values of M span the null space of M.
Another common representation is in ( North ), ( East ) and ( Down ) coordinates.
Another possible representation is the State transition table.
Another way of putting it is that the Poincaré group is a group extension of the Lorentz group by a vector representation of it.
Another matrix representation for a graph is the incidence matrix.
Another early representation is in a mosaic in the Church of San Pietro in Vincoli ( Rome, Italy ), probably made in the year 682.
Another rearrangement shows that the Jacobi identity is equivalent to the following identity between the operators of the adjoint representation:
Another achievement in robotics was the discovery of new approaches for robot spatial representation such as 3D occupancy grids.
Another early representation theorem is now known as Stone's representation theorem for distributive lattices ( the name honors Marshall Harvey Stone, who first proved it ).
Another representation for rotations in 3D space is the quaternions.
Another early cloister, that of the abbey of Saint-Riquier ( 790-99 ), took a triangular shape, with chapels at the corners, in conscious representation of the Trinity.
Another representation of Kamadhenu shows her with the body of a white Zebu cow, crowned woman's head, colourful eagle wings and a peacock's tail.
Another case of Stone duality is Birkhoff's representation theorem stating a duality between finite partial orders and finite distributive lattices.
Another representation of similar formulas, but using n-vector instead of latitude / longitude to describe the positions, is found by means of 3D vector algebra, i. e. utilizing the dot product, cross product, or a combination:
Another popular representation of is Ivo between a rich man and a poor one.
Another and random
Another factor in addition to the packing shape and surface area that affects the performance of random or structured packing is the liquid and vapor distribution entering the packed bed.
Another reason can be seen by looking at the formula for the kurtosis of the sum of random variables.
Another example has Alice and Bob both choosing a key at random, and then contacting each other to compare the depth of each notch on their keys.
Another example is the WWE's Royal Rumble match, which involves thirty participants in a random and unknown order.
Another type of reality programming features hidden cameras rolling when random passers-by encounter a staged situation.
Another reason for random jitter to have a distribution like this is due to the central limit theorem.
* David DeLaney's random arkhive Another collection of posts from the newsgroup, saved for various reasons or none at all.
Another variation of the self-fulfilling prophecy can be seen in " The Tale of Attaf ", where Harun al-Rashid consults his library ( the House of Wisdom ), reads a random book, " falls to laughing and weeping and dismisses the faithful vizier " Ja ' far ibn Yahya from sight.
Another difficulty for developers was with the performance limitations of the earliest DATAPAKs which used a serial-access internal architecture, as opposed to random access.
Another basic type of a stochastic process is a random field, whose domain is a region of space, in other words, a random function whose arguments are drawn from a range of continuously changing values.
Another crack in this belief system has been produced by quantum mechanical events such that the same sequence of causal events ( or causal factors ) regularly produces different effects ( i. e., results ), but the results may repeat themselves in some random ( unknowable ) sequence.
Another useful distinction is between traits that are likely to be adaptations ( such as the nose ) vs. those that are byproducts of adaptations ( such the white color of bones ), or are due to random variation ( non-adaptive variation in, say, nose shape or size ).
Another prototypical feature of the Langevin equation is the occurrence of the damping coefficient λ in the correlation function of the random force.
Another way to use the probabilistic method is by calculating the expected value of some random variable.
Another drawback is the performance limitations preventing flash from matching the response times and, in some cases, the random addressability offered by traditional forms of RAM.
) Another version — later verified by Bentley — holds that two Pomona students on a summer grant project in 1964 hypothesized that 47 occurred far more often in nature than random number distribution would explain.
) Another common reformulation is simply a deterministic Turing machine with an added tape full of random bits called the random tape.
Another barrier to widespread application of BEAM technology is the perceived random nature of the ' nervous network ', which requires new techniques to be learned by the builder to successfully diagnose and manipulate the characteristics of the circuitry.
Another variation of the self-fulfilling prophecy can be seen in " The Tale of Attaf ", where Harun al-Rashid consults his library ( the House of Wisdom ), reads a random book, " falls to laughing and weeping and dismisses the faithful vizier " Ja ' far ibn Yahya from sight.
Another way of stating things is that with probability 1 − 0. 014 = 0. 986, a simple random sample of 55 students would have a mean test score within 4 units of the population mean.
Another model, which generalizes Gilbert's random graph model, is the random dot-product model.
Another way to use this is to play four random cards, and almost no one will call your bluff.
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