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An important property of the exponential map is the following lemma of Gauss ( yet another Gauss's lemma ): given any tangent vector v in the domain of definition of exp < sub > p </ sub >, and another vector w based at the tip of v ( hence w is actually in the double-tangent space T < sub > v </ sub >( T < sub > p </ sub > M )) and orthogonal to v, remains orthogonal to v when pushed forward via the exponential map.
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important and property
Recovering the property was much less important ''.
This is an important oncolytic property of CDV, this virus is capable of killing canine lymphoma cells.
Another important property of Bessel's equations, which follows from Abel's identity, involves the Wronskian of the solutions:
This led in 1828 to an important theorem, the Theorema Egregium ( remarkable theorem ), establishing an important property of the notion of curvature.
For the preceding property of unions of non-decreasing sequences of convex sets, the restriction to nested sets is important: The union of two convex sets need not be convex.
Chirality ( handedness ) is a property of asymmetry important in several branches of science.
Such a property is extremely important because it allows one to avoid the difficulties associated with the deprojection and disentanglement of the dark and visible contributions to the rotation curves.
Bit rate is an important property when transmitting video because the transmission link must be capable of supporting that bit rate.
Another important government intervention was the designation in 1982 of an enterprise zone, an area in which businesses were exempt from property taxes and had other incentives, including simplified planning and capital allowances.
This is an important property because it allows the use of a flipping technique.
Some authors also require the domain of the Euclidean function be the entire ring R ; this can always be accommodated by adding 1 to the values at all nonzero elements, and defining the function to be 0 at the zero element of R, but the result is somewhat awkward in the case of K. The definition is sometimes generalized by allowing the Euclidean function to take its values in any well-ordered set ; this weakening does not affect the most important implications of the Euclidean property.
This important property is known as Bézout's identity.
Again, some important graph properties are hereditary with respect to induced subgraphs, which means that a graph has a property if and only if all induced subgraphs also have it.
The fact that the electric charges of electrons and protons seem to cancel each other exactly to extreme precision is essential for the existence of the macroscopic world as we know it, but this important property of elementary particles is not explained in the Standard Model of particle physics.
It was the most ambitious round to date, hoping to expand the competence of the GATT to important new areas such as services, capital, intellectual property, textiles, and agriculture.
By pursuing exclusive publication rights for his own works, he set one of the most important early precedents for regarding music as the intellectual property of the composer.
In scientific research, the behavior of the two fluid phases of helium-4 ( helium I and helium II ), is important to researchers studying quantum mechanics ( in particular the property of superfluidity ) and to those looking at the phenomena, such as superconductivity, that temperatures near absolute zero produce in matter.
) An important property of entropy is that it is maximized when all the messages in the message space are equiprobable ,— i. e., most unpredictable — in which case.
In his important essay The Soul of Man under Socialism from 1891 Wilde defended socialism as the way to guarantee individualism and so he saw that " With the abolition of private property, then, we shall have true, beautiful, healthy Individualism.
The most important property of these wavefunctions is that exchanging any two of the coordinate variables changes the wavefunction by only a plus or minus sign.
An important carbon property is catenation as the ability to form long carbon chains and rings.
In attempts to tackle such attacks on their intellectual property, companies are increasingly keeping important information off network, leaving an " air gap ", with some companies building " Faraday cages " to shield from electromagnetic or cellphone transmissions.
These teachings had more important results upon the orders and their possessions in Bohemia, where the instructions of the " Evangelical master " were followed to the letter in such a way that the noble foundations and practically the whole of the property of the Church were sacrificed.
The most important property of needles is their diameter, which ranges from below 2 to 25 mm ( roughly 1 inch ).
important and exponential
which is valid for < math >| x |< 1 </ math >, is one of the most important examples of a power series, as are the exponential function
Two important special cases of this are the exponential map for a manifold with a Riemannian metric, and the exponential map from a Lie algebra to a Lie group.
The exponential map of a Lie group satisfies many properties analogous to those of the ordinary exponential function, however, it also differs in many important respects.
In probability and statistics, an exponential family is an important class of probability distributions sharing a certain form, specified below.
What is important to note, and what characterizes all exponential family variants, is that the parameter ( s ) and the observation variable ( s ) must factorize ( can be separated into products each of which involves only one type of variable ), either directly or within either part ( the base or exponent ) of an exponentiation operation.
It is important to stress that here we assume that the permanence of each single subject in the epidemic states is a random variable with exponential distribution.
In these fields, the exponential distribution is often more important than the normal distribution.
Like exponential growth and logistic growth, hyperbolic growth is highly nonlinear, but differs in important respects.
# Bob concatenates the exponentials ( g < sup > y </ sup >, g < sup > x </ sup >) ( order is important ), signs them using his asymmetric key B, and then encrypts them with K. He sends the ciphertext along with his own exponential g < sup > y </ sup > to Alice.
important and map
This graph is planar ( it is important to note that we are talking about the graphs that have some limitations according to the map they are transformed from only ): it can be drawn in the plane without crossings by placing each vertex at an arbitrarily chosen location within the region to which it corresponds, and by drawing the edges as curves that lead without crossing within each region from the vertex location to each shared boundary point of the region.
That is to say, correctly generalized maps are those that emphasize the most important map elements while still representing the world in the most faithful and recognizable way.
The level of detail and importance in what is remaining on the map must outweigh the insignificance of items that were generalized, as to preserve the distinguishing characteristics of what makes the map useful and important.
Greenwich Village is generally known as an important landmark on the map of American bohemian culture.
The most important purpose of the political map is to show territorial borders ; the purpose of the physical is to show features of geography such as mountains, soil type or land use including infrastructure such as roads, railroads and buildings.
PET is also an important research tool to map normal human brain and heart function.
An important result regarding the derivative map is the following:
An important reference point along a chromosome, which is a very long and compacted string of DNA and proteins, is the centromere ; the distance from a gene to the centromere is referred to as the gene's locus or map location.
However, advocates of this point of view ignore the many successful and well-adjusted Vietnam veterans who have played important roles in America since the end of the Vietnam War such as Al Gore, Fred Smith ( founder and president of Federal Express ), Colin Powell, John McCain, Craig Venter ( famed for being the first to map the human genome ), and many others.
An important special case is the kernel of a linear map.
A number of varieties and supplementary features are also deemed important enough to have their own weather map symbols.
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 ).
• Waypower: “ Waypower reflects the mental plans or road maps that guide hopeful thought ” There are important versus less important goals that play a part in one ’ s ability to plan through a goal, to map out a plan.
She produced the first genetic map for maize, linking regions of the chromosome with physical traits, and demonstrated the role of the telomere and centromere, regions of the chromosome that are important in the conservation of genetic information.
A map of Kamakura with the approximate location of the most important historical sites.
On at least three occasions, he has nearly fallen off a cliff, and has fallen two of those times, to retrieve something important ( Half of the map in Pooh's Grand Adventure: The Search for Christopher Robin, his locket in The Tigger Movie, and a page of Piglet's scrapbook in Piglet's Big Movie ).
Recent USGS digital US Topo 1: 24, 000 topo maps based on the National Map omit several important geographic details that were featured in the original USGS topographic map series ( 1945-1992 ).
Inside the Independence Room, there are three most important relics from Indonesia's history: the Garuda Pancasila statue, the Nusantara ( Archipelago ) map and the original text of the Proclamation of Independence, which all are kept in the gold plated cases.
The triangular park that has played an important role as a place of community gatherings is also shown on the 1876 map.
It is an important contemporary issue of growing concern as enterprise style organizations employ new technologies to create vast private networks that interconnect with the PSTN in ways that do not map to the logic used to locate callers in the Public Enhanced 9-1-1 system.
This was not always practical and thus Doncaster became an important staging post on the Roman map.
Because of the resistance offered to all European explorers at the time, especially by Senussis Ikhwan, Rohlfs only managed to come back with a few important findings which included an inaccurate first map of the Libyan Desert.
Captain John Smith of Jamestown | John Smith's 1624 map of Bermuda, showing important sites, including the Castle Islands Fortifications, Bermuda | Castle Islands Fortifications.
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