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) to trivial ( romance, games ) can be any kind of imaginative encoding: flowers, game cards, clothes, fans, hats, melodies, birds, etc., in which the sole requisite is the previous agreement of the meaning by both the sender and the receiver.
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The calculation of the Roulette house edge was a trivial exercise ; for other games, this is not usually the case.
While this is a trivial result, deriving similar results for games with rich combinatorial structures is difficult.
While there are only four possible types of payoff symmetric 2x2 games ( of which one is trivial ), the five different best response curves per player allow for a larger number of payoff asymmetric game types.
As the piece delay is implemented client side, a trivial modification was made to the network protocol to prevent TetriFast clients connecting to standard TetriNET games.
trivial and can
We hold safe little jobs illustrating tooth-paste ads or the salacious incidents in trivial novels, and most of our easel painting is nothing but picking the fluff out of the navel so it can be contemplated in greater purity.
For every group G there is a natural group homomorphism G → Aut ( G ) whose image is the group Inn ( G ) of inner automorphisms and whose kernel is the center of G. Thus, if G has trivial center it can be embedded into its own automorphism group.
Capoeira songs can talk about virtually anything, being it about a historical fact, a famous capoeirista, trivial life facts, hidden messages for players, anything.
( In the last step, the summation is trivial if, where it is 1 + 1 +⋅⋅⋅= N, and otherwise is a geometric series that can be explicitly summed to obtain zero.
Chaos theory has been so surprising because chaos can be found within almost trivial systems.
: Note that the equivalence relation generated in this manner can be trivial.
It is frequently the result of the discussion of heated real-world issues such as politics, religion, and philosophy, or of issues that polarise subpopulations, but can also be provoked by seemingly trivial differences.
Evaluating the DFT's sums directly involves N < sup > 2 </ sup > complex multiplications and N ( N − 1 ) complex additions which O ( N ) operations can be saved by eliminating trivial operations such as multiplications by 1.
Configuring a complete programming toolchain from scratch to the point where even trivial programs can be compiled and run can involve substantial amounts of work.
* Merge sort parallelizes well and can achieve close to linear speedup with a trivial implementation ; heapsort is not an obvious candidate for a parallel algorithm.
Some examples of groups that are not Lie groups ( except in the trivial sense that any group can be viewed as a 0-dimensional Lie group, with the discrete topology ), are:
Although this difference is trivial in bulk chemistry calculations, it can result in complete failure in situations where the behavior of individual molecules matters, such as in mass spectrometry and particle physics ( where the mixture of isotopes does not act as an average ).
Naively, you might think that a single number is simpler, but the entire set can be generated by quite a trivial computer program, whereas a single number can be hugely long.
The trivial zeros − 2, − 4, − 6, − 8, ... can be handled separately:
Poincaré's new condition — i. e., " trivial fundamental group "— can be restated as " every loop can be shrunk to a point.
Called the chakravala ( cyclic ) method, it starts by composing any triple ( that is, one which satisfies ) with the trivial triple to get the triple, which can be scaled down to
Apart from the trivial zeros, the Riemann zeta function doesn't have any zero on the right of σ = 1 and on the left of σ = 0 ( neither the zeros can lie too close to those lines ).
However, in the case of a finitely presented group we know that not all the generators can be trivial ( Any individual generator could be, of course ).
trivial or can be clandestine, encrypted and low-power in the presence
In general, cladogram generation algorithms must be implemented as computer programs, although some algorithms can be performed manually when the data sets are trivial ( for example, just a few species and a couple of characteristics ).
This is because they have zero divisors ; this means that two non-zero numbers can be multiplied to obtain a zero result: a trivial example is (< var > e </ var >< sub > 3 </ sub > + < var > e </ var >< sub > 10 </ sub >)×(< var > e </ var >< sub > 6 </ sub > − < var > e </ var >< sub > 15 </ sub >).
trivial and be
( The largest problem that could be solved without the use of the intermediate output and input was two simultaneous equations, a trivial problem.
AMD's older CPUs could simply be set to run at whatever clock speed the user chose on the motherboard, making it trivial to relabel a CPU and sell it as a faster grade than it was originally intended.
* The curve at a fixed offset from a given Bézier curve, often called an offset curve ( lying " parallel " to the original curve, like the offset between rails in a railroad track ), cannot be exactly formed by a Bézier curve ( except in some trivial cases ).
While the structure of diatomic, triatomic or tetra atomic molecules may be trivial, ( linear, angular pyramidal etc.
Likewise, the problem of computing a quantity on a manifold which is invariant under differentiable mappings is inherently global, since any local invariant will be trivial in the sense that it is already exhibited in the topology of R < sup > n </ sup >.
For a finite group, the derived series terminates in a perfect group, which may or may not be trivial.
A " Winning Smile " that makes the hero likable is worth 0 points because of its trivial effect, while a " Charming Song " that inspires one emotion when played might be useful enough to count as Frequent ( 1 point ).
To exclude the trivial ring, the additive identity and the multiplicative identity are required to be distinct.
A path-connected space with a trivial fundamental group is said to be simply connected.
However 1 / 3 cannot be represented exactly by either binary ( 0. 010101 ...) nor decimal ( 0. 333 ....), but in base 3 it is trivial ( 0. 1 or 1 * 3 ^- 1 ).
In other words, if value could be analysed, then such questions and statements would be trivial and obvious.
Since they are anything but trivial and obvious, value must be indefinable.
By proving that there are ( infinitely ) many possible sizes for infinite sets, Cantor established that set theory was not trivial, and it needed to be studied.
*" Homo -" prefix may be used in organic chemistry trivial names to indicate next higher straight chain homolog i. e. one noncyclic carbon more ( and similarly " dihomo -" meaning two noncyclic carbon more ), and is opposite of the prefix " Nor -" which usually means one noncyclic carbon less.
For this application, the hash function must be as insensitive as possible to data capture or transmission errors, and to " trivial " changes such as timing and volume changes, compression, etc.
trivial and any
a treatment effect is then trivial, " the effect of any treatment is
Slightly more generally, any space with a finite topology ( only finitely many open sets ) is compact ; this includes in particular the trivial topology.
* The spectrum of any commutative ring with the Zariski topology ( that is, the set of all prime ideals ) is compact, but never Hausdorff ( except in trivial cases ).
The equality equivalence relation is the finest equivalence relation on any set, while the trivial relation that makes all pairs of elements related is the coarsest.
In Euclidean space R < sup > n </ sup >, or any convex subset of R < sup > n </ sup >, there is only one homotopy class of loops, and the fundamental group is therefore the trivial group with one element.
In keeping with their social orientation, numbers are usually low in magnitude, often under ten, and any arithmetic in the game is typically trivial.
An object without any symmetry has as symmetry group the trivial group only containing this isometry ( symmetry type C < sub > 1 </ sub >).
" This put the Academy in an awkward position, as they felt the paper to be “ inadequate and trivial ,” but they did not want to “ treat her as a professional colleague, as they would any man, by simply rejecting the work .” So Augustin-Louis Cauchy, who had been appointed to review her work, recommended she publish it, and she followed his advice.
The property of separability does not in and of itself give any limitations on the cardinality of a topological space: any set endowed with the trivial topology is separable, as well as second countable, quasi-compact, and connected.
The trivial subgroup of any group is the subgroup
A more trivial approach is to write a program that will make a copy of any stream of data that it is directed to, and then direct it at itself.
Some theorems are " trivial ," in the sense that they follow from definitions, axioms, and other theorems in obvious ways and do not contain any surprising insights.
A topological soliton, also called a topological defect, is any solution of a set of partial differential equations that is stable against decay to the " trivial solution.
When disks were small, this was of little consequence, because the individual allocation block size was trivial, but as disks started to approach the 1 GB mark, the smallest amount of space that any file could occupy ( a single allocation block ) became excessively large, wasting significant amounts of disk space.
In any case, even when viewed as expressions, all that matters about a linear combination is the coefficient of each v < sub > i </ sub >; trivial modifications such as permuting the terms or adding terms with zero coefficient do not give distinct linear combinations.
Writing simple software applications for keylogging can be trivial, and like any nefarious computer program, can be distributed as a trojan horse or as part of a virus.
* In the category of groups, any trivial group is a zero object.
In mathematics, a group G is called free if there is a subset S of G such that any element of G can be written in one and only one way as a product of finitely many elements of S and their inverses ( disregarding trivial variations such as st < sup >− 1 </ sup > = su < sup >− 1 </ sup > ut < sup >− 1 </ sup >).
Any proposal of law in the broadest sense and any proposed treaty is in principle first submitted to the Council of State for legal comment ; this can be limited by formal law, which however only does so for trivial cases ( Article 73 ).
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