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In particular, a vector field on a smooth manifold M is a choice of tangent vector at each point of M: this is a section of the tangent bundle of M. Likewise, a 1-form on M is a section of the cotangent bundle.
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particular and vector
In physics, angular momentum, moment of momentum, or rotational momentum is a vector quantity that represents the product of a body's rotational inertia and rotational velocity about a particular axis.
A particular particle within the body in a particular configuration is characterized by a position vector
It is not a vector field because it depends not only on the position of a particular material point, but also on the local orientation of the surface element as defined by its normal vector.
In modern introductory texts to functional analysis, the subject is seen as the study of vector spaces endowed with a topology, in particular infinite dimensional spaces.
In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces ; in particular, they can be used to represent group elements as matrices so that the group operation can be represented by matrix multiplication.
* 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.
* Neutral vector ( statistics ), a multivariate random variable is neutral if it exhibits a particular type of statistical independence seen when considering the Dirichlet distribution
* A " random word " may be parameterized by an integer-valued index into the vocabulary of possible words ; or alternatively as an indicator vector, in which exactly one element is a 1 and the others are 0, with the 1 indexing a particular word into a vocabulary.
If an image stored in one vector file format is converted to another file format that supports all the primitive objects used in that particular image, then the conversion can be lossless.
When only the magnitude and direction of the vector matter, then the particular initial point is of no importance, and the vector is called a free vector.
The three-dimensional real vector q represents a point in reciprocal space, that is, to a particular oscillation in the electron density as one moves in the direction in which q points.
The matrix M may be regarded as a diagonal matrix D that has been re-expressed in coordinates of the basis P. In particular, the one-to-one change of variable y = Pz shows that z < sup >*</ sup > Mz is real and positive for any complex vector z if and only if y < sup >*</ sup > Dy is real and positive for any y '; in other words, if D is positive definite.
Viewed in this light, this construction ( add transforms for each object, restrict maps to commute with these ) is completely general, and does not depend on any particular properties of vector spaces.
The elements of topological vector spaces are typically functions or linear operators acting on topological vector spaces, and the topology is often defined so as to capture a particular notion of convergence of sequences of functions.
In particular, the power cepstrum is often used as a feature vector for representing the human voice and musical signals.
The Poynting vector represents the particular case of an energy flux vector for electromagnetic energy.
The individual variables in a random vector are grouped together because there may be correlations among them — often they represent different properties of an individual statistical unit ( e. g. a particular person, event, etc .).
In linear algebra, this vector is known as the kernel of the dimensional matrix, and it spans the nullspace of the dimensional matrix, which in this particular case is one dimensional.
particular and field
The same argument proves that no subfield of the real field is algebraically closed ; in particular, the field of rational numbers is not algebraically closed.
The field of chemistry uses analysis in at least three ways: to identify the components of a particular chemical compound ( qualitative analysis ), to identify the proportions of components in a mixture ( quantitative analysis ), and to break down chemical processes and examine chemical reactions between elements of matter.
Field automorphisms are important to the theory of field extensions, in particular Galois extensions.
The < tt > MixColumns </ tt > step can also be viewed as a multiplication by a particular MDS matrix in a finite field.
The term argot is also used to refer to the informal specialized vocabulary from a particular field of study, hobby, job, sport, etc.
Ideas from it have proved influential, and have been developed by others, in particular dessins d ' enfants and a new field emerging as anabelian geometry.
The black letter law refers to the basic standard elements for a particular field of law, which are generally known and free from doubt or dispute.
The International Organization for Standardization, ISO, has a special technical committee for cycles, TC149, that has the following scope: " Standardization in the field of cycles, their components and accessories with particular reference to terminology, testing methods and requirements for performance and safety, and interchangeability.
Graduate programs in BME, like in other scientific fields, are highly varied, and particular programs may emphasize certain aspects within the field.
However, Ogden prescribed that any student should learn an additional 150-word list for everyday work in some particular field, by adding a word list of 100 words particularly useful in a general field ( e. g., science, verse, business, etc.
Of particular note, programs that were placed within the top 10 % of all size programs in that field based on an average of the R95 and S95 rank order include Aeronautics, Astrophysics, Biochemistry and Molecular Biophysics, Bioengineering, Biology, Chemical Engineering, Chemistry, Electrical Engineering, Environmental Science and Engineering, Geology, Geophysics, Materials Science, Mechanical Engineering, Physics, Planetary Science, and Social Science ( Economics ).
The term is synonymous with wealth ( commonly denoted as a person with fame and fortune ), implied with great popular appeal, prominence in a particular field, and is easily recognized by the general public.
While people may gain celebrity status as a result of a successful career in a particular field ( primarily in the areas pertaining towards sports and entertainment ), in other cases, people become celebrities due to media attention for their extravagant lifestyle or wealth ( as in the case of a socialite ); for their connection to a famous person ( as in the case of a relative of a famous person ); or even for their misdeeds ( as in the case of a well-known criminal ).
Therefore, there exists a contact force density or Cauchy traction field that represents this distribution in a particular configuration of the body at a given time.
The company organization of each camp had a dual-authority supervisory staff: firstly, Department of War personnel or Reserve officers ( until 1 July 1939 ), a " company commander " and junior officer, who were responsible for overall camp operation, logistics, education and training ; and secondly, ten to fourteen technical service civilians, including a camp " superintendent " and " foreman ," employed by either the Departments of Interior or Agriculture, responsible for the particular field work.
In particular, this field contains all the numbers named in the mathematical constants article, and all algebraic numbers ( and therefore all rational numbers ).
A design pattern in architecture and computer science is a formal way of documenting a solution to a design problem in a particular field of expertise.
An organized collection of design patterns that relate to a particular field is called a pattern language.
) is reserved for those who can prove a particular distinction in the field, usually through a body of published work or the submission of a dissertation.