Help


[permalink] [id link]
+
Page "learned" ¶ 1279
from Brown Corpus
Edit
Promote Demote Fragment Fix

Some Related Sentences

analysis and vector
In mathematics, more specifically in functional analysis, a Banach space ( pronounced ) is a complete normed vector space.
The analysis of linear systems is possible because they satisfy a superposition principle: if u ( t ) and w ( t ) satisfy the differential equation for the vector field ( but not necessarily the initial condition ), then so will u ( t ) + w ( t ).
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure ( e. g. inner product, norm, topology, etc.
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.
The basic and historically first class of spaces studied in functional analysis are complete normed vector spaces over the real or complex numbers.
More generally, functional analysis includes the study of Fréchet spaces and other topological vector spaces not endowed with a norm.
He had made advances in the areas of analysis, foundations and logic, made many contributions to the teaching of calculus and also contributed to the fields of differential equations and vector analysis.
Inner product spaces generalize Euclidean spaces ( in which the inner product is the dot product, also known as the scalar product ) to vector spaces of any ( possibly infinite ) dimension, and are studied in functional analysis.
Functional analysis studies the infinite-dimensional version of the theory of vector spaces.
# Multivariate regression analysis attempts to determine a formula that can describe how elements in a vector of variables respond simultaneously to changes in others.
Normed vector spaces are central to the study of linear algebra and functional analysis.
Oliver Heaviside FRS ( ( 18 May 1850 – 3 February 1925 ) was a self-taught English electrical engineer, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, invented mathematical techniques to the solution of differential equations ( later found to be equivalent to Laplace transforms ), reformulated Maxwell's field equations in terms of electric and magnetic forces and energy flux, and independently co-formulated vector analysis.
In 1884 he recast Maxwell's mathematical analysis from its original cumbersome form ( they had already been recast as quaternions ) to its modern vector terminology, thereby reducing twelve of the original twenty equations in twenty unknowns down to the four differential equations in two unknowns we now know as Maxwell's equations.
Banach's dissertation, completed in 1920 and published in 1922, formally axiomatized the concept of a complete normed vector space and laid the foundations for the area of functional analysis.
His 1867 Elementary Treatise of Quaternions included extensive treatment of the nabla or del operator and is very close to modern vector analysis.
The first half of Gibbs's Elements of Vector Analysis, published in 1881, presents what is essentially the modern system of vector analysis.
Vector calculus ( or vector analysis ) is a branch of mathematics concerned with differentiation and integration of vector fields, primarily in 3 dimensional Euclidean space The term " vector calculus " is sometimes used as a synonym for the broader subject of multivariable calculus, which includes vector calculus as well as partial differentiation and multiple integration.
Phylogenetic analysis identified seven genotypes of yellow fever viruses, and it is assumed that they are differently adapted to humans and to the vector Aedes aegypti.

analysis and relationships
From an analysis of relationships and diversities within the Asterales and with their superorders, estimates of the age of the beginning of the Asterales have been made, which range from 116 Mya to 82Mya.
* Regression analysis – techniques for analyzing the relationships between several variables in the data
The outcome of a cladistic analysis is a cladogram – a tree-shaped diagram ( dendrogram ) that represents a phylogenetic hypothesis, a hypothesis on evolutionary relationships.
Factor analysis is used to summarize relationships among a large set of variables or test questions, develop theories about mental constructs such as self-efficacy or anxiety, and assess the reliability and validity of test scores.
Econometric analysis may also be classified on the basis of the number of relationships modeled.
While a member of the Institute of Social Research, Marcuse developed a model for critical social theory, created a theory of the new stage of state and monopoly capitalism, described the relationships between philosophy, social theory, and cultural criticism, and provided an analysis and critique of German fascism.
The practical implementation of multivariate statistics to a particular problem may involve several types of univariate and multivariate analysis in order to understand the relationships between variables and their relevance to the actual problem being studied.
# Canonical correlation analysis finds linear relationships among two sets of variables ; it is the generalised ( i. e. canonical ) version of bivariate correlation.
But there is no reason why e. g. species identified using phenetics cannot subsequently be subjected to cladistic analysis, to determine their evolutionary relationships.
Some radical feminists are explicitly avowed Marxists, and attempt to explore relationships between patriarchal and class analysis.
* Regression analysis, a statistical technique for estimating the relationships among variables.
This theoretical approach is focused on the analysis of ideologically based movements, usually in terms of leader-follower relationships.
Second, based on cognitive linguistics ' analysis of figurative language, he argues that the reasoning we use for such abstract topics as warfare, economics, or morality is somehow rooted in the reasoning we use for such mundane topics as spatial relationships.
The analysis of people's relationships with the means of production is one element that stands at the basis of Marxism.
Allegations of surreptitious international relationships, mainly with Argentina ( Gelli repeatedly suggested that he was a close friend of Juan Perón ) and with some people suspected of affiliation with the American Central Intelligence Agency were also partly confirmed ; but soon a political debate overtook the legal level of the analysis.
* Ross J, Jiang H, Kanost MR, Wang Y. Serine proteases and their homologs in the Drosophila melanogaster genome: an initial analysis of sequence conservation and phylogenetic relationships.
These relationships are discussed in dimensional analysis.
Many cultural studies scholars employed Marxist methods of analysis, exploring the relationships between cultural forms ( the superstructure ) and that of the political economy ( the base ).
Key elements of an effective environmental scientist include the ability to relate space, and time relationships as well as quantitative analysis.
Regression analysis producing statistically significant negative relationships indicates that two individuals can be less genetically alike than two random ones on average ( Hamilton 1970, Nature & Grafen 1985 Oxford Surveys in Evolutionary Biology ).
Spike's skills of analysis allowed him to realize Willow was barely holding it together after Oz's departure even though Giles and Buffy thought she was doing better, to be the first to see through Tara's abusive and controlling family, forced Buffy and Angel to admit that they were more than " just friends " and identify when and why some relationships, such as between Buffy and Riley, are not meant to last, masterfully feeding Riley's insecurities in an effort to sabotage his relationship with Buffy, so Spike can pursue her.
In recent years hagfish have become of special interest for genetic analysis investigating the relationships among chordates.
These topological relationships allow complex spatial modelling and analysis to be performed.
Since the beginning of his career, he has devoted himself to the analysis of social-economic relationships within human communities.

0.387 seconds.