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( In particular, the exponential map can be used to define abstract index groups.
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particular and exponential
* Conjugate prior, in Bayesian statistics, a family of probability distributions that contains a prior and the posterior distributions for a particular likelihood function ( particularly for one-parameter exponential families )
In particular, it can be seen that the Néel relaxation time is an exponential function of the grain volume, which explains why the flipping probability becomes rapidly negligible for bulk materials or large nanoparticles.
In particular, the exponential generating series F ( x ) of a species F can be defined:
Both the terms " Markov property " and " strong Markov property " have been used in connection with a particular " memoryless " property of the exponential distribution.
* In history of science, some believe that the body of knowledge of any particular science is gradually disproved according to an exponential decay pattern ( see half-life of knowledge ).
A family of distributions is defined by a set of parameters that can be varied, and what makes a family be an exponential family is a particular relationship between the domain of a family of distributions ( the variable over which each distribution in the family is defined ) and the parameters.
( This can be seen by considering what was said above — the support of an exponential family cannot vary depending on a particular parameter.
It is critical, when considering the examples in this section, to remember the discussion above about what it means to say that a " distribution " is an exponential family, and in particular to keep in mind that the set of parameters that are allowed to vary is critical in determining whether a " distribution " is or is not an exponential family.
The functor category D < sup > C </ sup > has all the formal properties of an exponential object ; in particular the functors from E × C → D stand in a natural one-to-one correspondence with the functors from E to D < sup > C </ sup >.
In particular, a very detailed treatment of the EM method for exponential families was published by Rolf Sundberg in his thesis and several papers following his collaboration with Per Martin-Löf and Anders Martin-Löf.
Cell populations go through a particular type of exponential growth called doubling.
In particular, the complete Bell polynomials appear in the exponential of a formal power series:
In a generalized linear model ( GLM ), each outcome of the dependent variables, Y, is assumed to be generated from a particular distribution in the exponential family, a large range of probability distributions that includes the normal, binomial and Poisson distributions, among others.
Hyperbolic discounting is a particular mathematical model devised as an improvement over exponential discounting.
In particular, the one expressing the exponential function ( ) consists of even and odd terms, the former comprise the cosh function (), the latter the sinh function ().
The exponential growth of new technologies, the Internet in particular, has gone hand in hand with the development over the last decade of a global community producing and exchanging goods.
found examples of graphs for which M does indeed grow very fast and is at least as large as a 1 / ε < sup > 1 / 16 </ sup >- level iterated exponential of m. In particular the best bound has level exactly 4 in the Grzegorczyk hierarchy, and so is not an elementary recursive function.
That is, it asks for analogues of the roots of unity, as complex numbers that are particular values of the exponential function ; the requirement is that such numbers should generate a whole family of further number fields that are analogues of the cyclotomic fields and their subfields.
In mathematics, in the field of number theory, the Ramanujan – Nagell equation is a particular exponential Diophantine equation.
particular and map
The game between the Chicago Cubs and St. Louis Cardinals in particular was cited for putting Ryne Sandberg ( as well as the 1984 Cubs in general, who would go on to make their first postseason appearance since 1945 ) " on the map.
Even if the technology to map out every neuron in the brain in real-time were available, and it were known when each neuron was firing, it would still be impossible to know how a particular firing of neurons translates into the observed behavior.
) In particular, every continuous bijective map from a compact space to a Hausdorff space is a homeomorphism.
In particular, these foregrounds are dominated by galactic emissions such as free-free, synchrotron, and dust that emit in the microwave band ; in practice, the galaxy has to be removed resulting in a CMB map that is not a full-sky map.
The Sylow 2-subgroups are either cyclic, which is easy to handle using the transfer map, or generalized quaternion, which are handled with the Brauer – Suzuki theorem: in particular there are no simple groups of 2-rank 1.
* In particular, if V is a normed vector space and if z is any element of V, then there exists a continuous linear map with ψ ( z ) = || z || and || ψ || ≤ 1.
The plight of U. S. Route 66 in particular, whose disappearance from the map in 1985 turned places like Glenrio, Texas and Amboy, California into overnight ghost towns, began to capture public attention with Route 66 associations springing up in every state as concern over preservation of decaying motels and other roadside infrastructure of the neon era came into view.
In particular, the following two conditions are not equivalent in general for a map f between topological spaces X and Y:
In particular, if I has more than one element, the inclusion map R < sub > i </ sub > → R is not ring homomorphism as it does not map the identity in R < sub > i </ sub > to the identity in R.
A first countable, separable Hausdorff space ( in particular, a separable metric space ) has at most the continuum cardinality c. In such a space, closure is determined by limits of sequences and any sequence has at most one limit, so there is a surjective map from the set of convergent sequences with values in the countable dense subset to the points of X.
The brain map of an individual, he argues, can be altered by this activation to create a larger area of the brain activated by a particular type of sensory experience.
The horoscope serves as a stylized map of the heavens over a specific location at a particular moment in time.
The notion of a natural transformation is categorical, and states ( informally ) that a particular map between functors can be done consistently over an entire category.
Informally, a particular map ( esp.
Conversely, a particular map between particular objects may be called an unnatural isomorphism ( or " this isomorphism is not natural ") if the map cannot be extended to a natural transformation on the entire category.
The symbol used on the map for each of these levels at a particular observation time will be for the genus, species, variety, mutation, or cloud motion that is considered most important according to criteria set out by the World Meteorological Organization ( WMO ).
Taken to its extreme, the " epigenetic code " could represent the total state of the cell, with the position of each molecule accounted for in an epigenomic map, a diagrammatic representation of the gene expression, DNA methylation and histone modification status of a particular genomic region.
If a function is harmonic ( that is, it satisfies Laplace's equation ) over a particular space, and is transformed via a conformal map to another space, the transformation is also harmonic.
The mathematics of projection do not permit any particular map projection to be " best " for everything.
particular and can
Second, we can make assistance for particular projects conditional on the consistency of such projects with the program.
A group of native trees or plants which are outstanding in a particular county can be featured at the site.
It supplies local data which are useful in administration and which can be used as a basis for intensive studies in particular situations.
The practical operational problem of lexicostatistics is the establishment of a basic list of items of meaning against which the particular forms or terms of languages can be matched as the medium of comparison.
If he is not told which of four or five readings was meant for him, he can more readily assess each item in a larger frame: `` Does that statement really sound as if it were for me, significant in my particular life??
What we can attempt with some hope of dependable conclusions is to point out the manner in which Christianity entered into particular aspects of the life of the nation.
Tylor in particular laid the groundwork for theories of cultural diffusionism, stating that there are three ways that different groups can have similar cultural forms or technologies: " independent invention, inheritance from ancestors in a distant region, transmission from one race to another.
The specific procedures for appealing, including even whether there is a right of appeal from a particular type of decision, can vary greatly from country to country.
Some appellate courts, particularly supreme courts, have the power of discretionary review, meaning that they can decide whether they will hear an appeal brought in a particular case.
Notably, these alerts can be customized to the particular person's risks.
Speakers from the different states of Austria can easily be distinguished from each other by their particular accents ( probably more so than Bavarians ), those of Carinthia, Styria, Vienna, Upper Austria, and the Tyrol being very characteristic.
In many cases such a selection can be made without invoking the axiom of choice ; this is in particular the case if the number of bins is finite, or if a selection rule is available: a distinguishing property that happens to hold for exactly one object in each bin.
Expanding upon Foucault's position, Alexander Nehamas writes that Foucault suggests " an author [...] is whoever can be understood to have produced a particular text as we interpret it ", not necessarily who penned the text.
While a character with Pattern, Logrus or Conjuration can acquire virtually any object, players can choose to spend character points to obtain objects with particular virtues-unbreakability, or a mind of their own.
In astronomy, a given point on the celestial sphere ( that is, the apparent position of an astronomical object ) can be identified using any of several astronomical coordinate systems, where the references vary according to the particular system.
The term may also refer to the physical region where the electron can be calculated to be, as defined by the particular mathematical form of the orbital.
Zwitterions have minimum solubility at their isolectric point and some amino acids ( in particular, with non-polar side-chains ) can be isolated by precipitation from water by adjusting the pH to the required isoelectric point.
With some simplifications, in particular constant density, they can be given as follows:
The < tt > MixColumns </ tt > step can also be viewed as a multiplication by a particular MDS matrix in a finite field.
A case can be made that discriminatory lines came to be drawn more sharply under Athenian democracy than before or elsewhere, in particular in relation to woman and slaves, as well as in the line between citizens and non-citizens.
Exact ( not asymptotic ) measures of efficiency can sometimes be computed but they usually require certain assumptions concerning the particular implementation of the algorithm, called model of computation.
The back and sides of a particular guitar are typically made of the same wood ; Brazilian or East Indian rosewood and Honduras mahogany are traditional choices, however, maple has been prized for the figuring that can be seen when it is cut in a certain way ( such as " flame " and " quilt " patterns ).
For example, if a program needs 20 hours using a single processor core, and a particular portion of 1 hour cannot be parallelized, while the remaining promising portion of 19 hours ( 95 %) can be parallelized, then regardless of how many processors we devote to a parallelized execution of this program, the minimum execution time cannot be less than that critical 1 hour.
To express even smaller angles, standard SI prefixes can be employed ; in particular, the milliarcsecond, abbreviated mas, is used in astronomy.
0.431 seconds.