# on 22-Feb-2018 (Thu)

#### Annotation 1731577384204

 #fourier-analysis When the function space has an interval as the domain, the bilinear form may be the integral of the product of functions over the interval: The functions f and g are orthogonal when this integral is zero: As with a basis of vectors in a finite-dimensional space, orthogonal functions can form an infinite basis for a function space.

Orthogonal functions - Wikipedia
ia (Redirected from Orthogonal function) Jump to: navigation, search In mathematics, orthogonal functions belong to a function space which is a vector space (usually over R) that has a bilinear form. <span>When the function space has an interval as the domain, the bilinear form may be the integral of the product of functions over the interval: ⟨ f , g ⟩ = ∫ f ( x ) g ( x ) d x . {\displaystyle \langle f,g\rangle =\int f(x)g(x)\,dx.} The functions f and g are orthogonal when this integral is zero: ⟨ f , g ⟩ = 0. {\displaystyle \langle f,\ g\rangle =0.} As with a basis of vectors in a finite-dimensional space, orthogonal functions can form an infinite basis for a function space. Suppose {f n }, n = 0, 1, 2, … is a sequence of orthogonal functions. If f n has positive support then ⟨ f n

#### Flashcard 1732485451020

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#sprectral-theorem #stochastics
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the Karhunen–Loève theorem represents [...] as an infinite linear combination of orthogonal functions

a stochastic process

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d> Jump to: navigation, search In the theory of stochastic processes, the Karhunen–Loève theorem (named after Kari Karhunen and Michel Loève), also known as the Kosambi–Karhunen–Loève theorem   is a representation of a stochastic process as an infinite linear combination of orthogonal functions, analogous to a Fourier series representation of a function on a bounded interval. <html>

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Karhunen–Loève theorem - Wikipedia
Karhunen–Loève theorem - Wikipedia Karhunen–Loève theorem From Wikipedia, the free encyclopedia (Redirected from Karhunen–Loeve expansion) Jump to: navigation, search In the theory of stochastic processes, the Karhunen–Loève theorem (named after Kari Karhunen and Michel Loève), also known as the Kosambi–Karhunen–Loève theorem   is a representation of a stochastic process as an infinite linear combination of orthogonal functions, analogous to a Fourier series representation of a function on a bounded interval. The transformation is also known as Hotelling Transform and Eigenvector Transform, and is closely related to Principal Component Analysis (PCA) technique widely used in image processing

#### Flashcard 1736027540748

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#stochastics
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If the parameter constant of the Poisson process is replaced with [...] , the resulting process is called an inhomogeneous or nonhomogeneous Poisson process
some non-negative integrable function of status measured difficulty not learned 37% [default] 0

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If the parameter constant of the Poisson process is replaced with some non-negative integrable function of , the resulting process is called an inhomogeneous or nonhomogeneous Poisson process, where the average density of points of the process is no longer constant. <

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Stochastic process - Wikipedia
sses.  The homogeneous Poisson process can be defined and generalized in different ways. It can be defined such that its index set is the real line, and this stochastic process is also called the stationary Poisson process.   <span>If the parameter constant of the Poisson process is replaced with some non-negative integrable function of t {\displaystyle t} , the resulting process is called an inhomogeneous or nonhomogeneous Poisson process, where the average density of points of the process is no longer constant.  Serving as a fundamental process in queueing theory, the Poisson process is an important process for mathematical models, where it finds applications for models of events randoml

#### Flashcard 1736251673868

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#poisson-process #stochastics
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In a Poisson process, [...] is a random variable with a Poisson distribution.
the number of points in a region of finite size

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Its name (Poisson Process) derives from the fact that if a collection of random points in some space forms a Poisson process, then the number of points in a region of finite size is a random variable with a Poisson distribution.

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Poisson point process - Wikipedia
oint processes, some of which are constructed with the Poisson point process, that seek to capture such interaction.  The process is named after French mathematician Siméon Denis Poisson despite Poisson never having studied the process. <span>Its name derives from the fact that if a collection of random points in some space forms a Poisson process, then the number of points in a region of finite size is a random variable with a Poisson distribution. The process was discovered independently and repeatedly in several settings, including experiments on radioactive decay, telephone call arrivals and insurance mathematics.   T

#### Flashcard 1738468887820

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#spanish
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Se informó que City [...] de la carrera después de negarse a cumplir con el precio de venta del Arsenal y las demandas salariales de Sánchez.
se retiró

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Se informó que City se retiró de la carrera después de negarse a cumplir con el precio de venta del Arsenal y las demandas salariales de Sánchez. Mourinho, sin embargo, ha desestimado los reclamos. </

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Mourinho: Alexis no llegó al Manchester United por dinero
el Manchester United sobre Manchester City no estuvo motivada por el dinero. United y City se enfrentaron cara a cara por el chileno este mes con el delantero moviéndose a Old Trafford y Henrikh Mkhitaryan firmando por el Arsenal a cambio. <span>Se informó que City se retiró de la carrera después de negarse a cumplir con el precio de venta del Arsenal y las demandas salariales de Sánchez. Mourinho, sin embargo, ha desestimado los reclamos. Lleva ESPN a todos lados Si quieres recibir alertas del Futbol Europeo, descarga la App ahora. espn.com/app » Él dijo en una conferencia de prensa el jueves: "Sé que si otros club

#### Flashcard 1738566405388

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#measure-theory #stochastics
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In the Cantor devil's staircase, the lengths of the removed intervals add up to [...].
one

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This distribution attributes probability zero to each of the intervals removed, and the lengths of these intervals add up to one. So all of the probability is concentrated on the Cantor set C ∞ , which is what the measure-theoretic jargon calls a set of Lebesgue measure zero, Lebesgue measure being the measure-th

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#### Flashcard 1738585017612

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#measure-theory #stochastics
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the new real analysis started with the PhD thesis of [...] (1902)
Henri Lebesgue

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What Kolmogorov did was to say that the new real analysis that had started with the PhD thesis of Henri Lebesgue (1902) and had been rapidly generalized to integrals of real-valued functions on arbitrary spaces by Radon, Fr´echet, and others (called Lebesgue integration or abstract integration) sh

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#### Flashcard 1739058187532

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#bayesian-network
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In Bayesian networks each node represents a variable with [...]
a probability distribution

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ayesian network) represent variables that are conditionally independent of each other. Each node is associated with a probability function that takes, as input, a particular set of values for the node's parent variables, and gives (as output) <span>the probability (or probability distribution, if applicable) of the variable represented by the node. <span><body><html>

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Bayesian network - Wikipedia
ed acyclic graph (DAG). For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases. <span>Formally, Bayesian networks are DAGs whose nodes represent variables in the Bayesian sense: they may be observable quantities, latent variables, unknown parameters or hypotheses. Edges represent conditional dependencies; nodes that are not connected (there is no path from one of the variables to the other in the Bayesian network) represent variables that are conditionally independent of each other. Each node is associated with a probability function that takes, as input, a particular set of values for the node's parent variables, and gives (as output) the probability (or probability distribution, if applicable) of the variable represented by the node. For example, if m {\displaystyle m} parent nodes represent m {\displaystyle m} Boolean variables

#### Flashcard 1739414965516

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#kalman-filter
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In Kalman filter [...] variables have Gaussian distributions.
all latent and observed

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The underlying model of Kalman filter is similar to a hidden Markov model except that the state space of the latent variables is continuous and all latent and observed variables have Gaussian distributions.

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Kalman filter - Wikipedia
stimate in the special case that all errors are Gaussian-distributed. Extensions and generalizations to the method have also been developed, such as the extended Kalman filter and the unscented Kalman filter which work on nonlinear systems. <span>The underlying model is similar to a hidden Markov model except that the state space of the latent variables is continuous and all latent and observed variables have Gaussian distributions. Contents [hide] 1 History 2 Overview of the calculation 3 Example application 4 Technical description and context 5 Underlying dynamical system model 6 Details 6.1 Predict

#### Flashcard 1744250473740

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#dot-product
Question
[...] takes two equal-length sequences of numbers and returns a single number.
dot product

or scalar product

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In mathematics, the dot product or scalar product [note 1] is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single number.

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Dot product - Wikipedia
ia Jump to: navigation, search "Scalar product" redirects here. For the abstract scalar product, see Inner product space. For the product of a vector and a scalar, see Scalar multiplication. <span>In mathematics, the dot product or scalar product [note 1] is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used and often called inner product (or rarely projection product); see also inner product s

#### Flashcard 1744261483788

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#calculus
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differential calculus concerns [...]
rates of change and slopes of curves

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Calculus has two major branches, differential calculus (concerning rates of change and slopes of curves),  and integral calculus (concerning accumulation of quantities and the areas under and between curves).  These two branches are related to each other by the fundamental th

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Calculus - Wikipedia
small pebble', used for counting and calculations, as on an abacus)  is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. <span>It has two major branches, differential calculus (concerning rates of change and slopes of curves),  and integral calculus (concerning accumulation of quantities and the areas under and between curves).  These two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. Generally, modern calculus is considered to have been

#### Flashcard 1759615257868

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#dual-space
Question
A dual vector space has the vector space structure of [...].
pointwise addition and scalar multiplication by constants

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In mathematics, any vector space V has a corresponding dual vector space consisting of all linear functionals on V, together with the vector space structure of pointwise addition and scalar multiplication by constants.

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Dual space - Wikipedia
Dual space - Wikipedia Dual space From Wikipedia, the free encyclopedia Jump to: navigation, search In mathematics, any vector space V has a corresponding dual vector space (or just dual space for short) consisting of all linear functionals on V, together with the vector space structure of pointwise addition and scalar multiplication by constants. The dual space as defined above is defined for all vector spaces, and to avoid ambiguity may also be called the algebraic dual space. When defined for a topological vector space, ther

#### Flashcard 1759925898508

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#topology
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A topology must satisfy axioms of [...12...]
inclusion, complete under infinite union and finit intersection

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A topological space is an ordered pair (X, τ), where X is a set and τ is a collection of subsets of X, satisfying the following axioms:  The empty set and X itself belong to τ. Any (finite or infinite) union of members of τ still belongs to τ. The intersection of any finite number of members of τ still belongs to τ.

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Topological space - Wikipedia
three-point set {1,2,3}. The bottom-left example is not a topology because the union of {2} and {3} [i.e. {2,3}] is missing; the bottom-right example is not a topology because the intersection of {1,2} and {2,3} [i.e. {2}], is missing. <span>A topological space is an ordered pair (X, τ), where X is a set and τ is a collection of subsets of X, satisfying the following axioms:  The empty set and X itself belong to τ. Any (finite or infinite) union of members of τ still belongs to τ. The intersection of any finite number of members of τ still belongs to τ. The elements of τ are called open sets and the collection τ is called a topology on X. Examples[edit source] Given X = {1, 2, 3, 4}, the collection τ = {{}, {1, 2, 3, 4}} of only the two subsets of X required by the axioms forms a topology of X, the trivial topology (

#### Annotation 1759930354956

 In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.

Partially ordered set - Wikipedia
] The Hasse diagram of the set of all subsets of a three-element set {x, y, z}, ordered by inclusion. Sets on the same horizontal level are incomparable with each other. Some other pairs, such as {x} and {y,z}, are also incomparable. <span>In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a binary relation indicating that, for certain pairs of elements in the set, one of the elements precedes the other in the ordering. The word &qu

#### Flashcard 1759932452108

Tags
#has-images
Question
a [...] formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.
[unknown IMAGE 1759935859980]
partially ordered set

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In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.

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Partially ordered set - Wikipedia
] The Hasse diagram of the set of all subsets of a three-element set {x, y, z}, ordered by inclusion. Sets on the same horizontal level are incomparable with each other. Some other pairs, such as {x} and {y,z}, are also incomparable. <span>In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a binary relation indicating that, for certain pairs of elements in the set, one of the elements precedes the other in the ordering. The word &qu

#### Flashcard 1759937957132

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SADR is the initialism for [...]

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#### Annotation 1759968365836

 To fill that property we did the following: r Tenant referral program: Current tenants get \$100 for referring a new tenant to us. r Open houses: We invited the community to check out our im- provements and enticed them to live there. r Special for Soldiers: We were near a military base, so this was a natural. r Banners: We put them up in the entryway to the complex. r Corporate outreach program (again, through the human re- sources departments). r Flyers at the laundromats, hair salons, and nail salons. r Ads in the local college newspaper. r Ads in ethnic newspapers. r Classified ads. r Strong tenant retention program: Once the good ones are in, we work to keep them in. Not one of these programs was responsible for the majority of leads, but together, they brought in the traffic and allowed us to fill the complex.

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#### Annotation 1759969938700

 Expect to get higher occupancy than surrounding properties, but base your financial projec- tions on the more conservative average occupancy for the area.

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#### Annotation 1759972035852

 Properties with high vacancies are an opportunity. Having only one kind of marketing solution is a problem.

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#### Annotation 1759973608716

 Whenever you take over a property, there will be tenant turnover. People leave for all sorts of reasons: r They don’t know what’s going to happen and don’t want to stick around to find out. r They hear rumors. r They just know you’ll be raising rents. Expect it.

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#### Annotation 1759985405196

 Si Neymar no quiere quedarse a la sombra de Messi debería cambiar de deporte

Unknown title
orts Juegos Olímpicos Olimpismo Paralímpicos Rugby Toros Turf Volvo Ocean Race Champions League Champions LeagueAsí reaccionó el exjugador del Arsenal y del Barça ante la comparación entre los dos Thierry Henry: "<span>Si Neymar no quiere quedarse a la sombra de Messi debería cambiar de deporte" Redacción Marca Compartir en Facebook Compartir en Twitter Enviar por email 21/02/2018 10:15 CET In English 273 comentarios Comentar Thierry Henry compartió tres temporadas

#### Flashcard 1759987502348

Question
Si Neymar no quiere quedarse a la [...] de Messi debería cambiar de deporte
sombra

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Si Neymar no quiere quedarse a la sombra de Messi debería cambiar de deporte

#### Original toplevel document

Unknown title
orts Juegos Olímpicos Olimpismo Paralímpicos Rugby Toros Turf Volvo Ocean Race Champions League Champions LeagueAsí reaccionó el exjugador del Arsenal y del Barça ante la comparación entre los dos Thierry Henry: "<span>Si Neymar no quiere quedarse a la sombra de Messi debería cambiar de deporte" Redacción Marca Compartir en Facebook Compartir en Twitter Enviar por email 21/02/2018 10:15 CET In English 273 comentarios Comentar Thierry Henry compartió tres temporadas

#### Annotation 1759994580236

 #spectral-analysis The set of all possible eigenvalues of a linear operator D is sometimes called its spectrum, which may be discrete, continuous, or a combination of both.

Eigenfunction - Wikipedia
he solutions to Equation (1) may also be subject to boundary conditions. Because of the boundary conditions, the possible values of λ are generally limited, for example to a discrete set λ 1 , λ 2 , ... or to a continuous set over some range. <span>The set of all possible eigenvalues of D is sometimes called its spectrum, which may be discrete, continuous, or a combination of both.  Each value of λ corresponds to one or more eigenfunctions. If multiple linearly independent eigenfunctions have the same eigenvalue, the eigenvalue is said to be degenerate and the ma

#### Annotation 1760002444556

 #spectral-analysis Depending on whether the spectrum is discrete or continuous, the eigenfunctions can be normalized by setting the inner product of the eigenfunctions equal to either a Kronecker delta or a Dirac delta function, respectively.

Eigenfunction - Wikipedia
ition always holds for λ i ≠ λ j . For degenerate eigenfunctions with the same eigenvalue λ i , orthogonal eigenfunctions can always be chosen that span the eigenspace associated with λ i , for example by using the Gram-Schmidt process.  <span>Depending on whether the spectrum is discrete or continuous, the eigenfunctions can be normalized by setting the inner product of the eigenfunctions equal to either a Kronecker delta or a Dirac delta function, respectively.   For many Hermitian operators, notably Sturm-Liouville operators, a third property is Its eigenfunctions form a basis of the function space on which the operator is defined [

#### Annotation 1760008736012

 #stochastics In mathematics, the Kronecker delta is a function of two variables that equals 1 if the variables are equal, and 0 otherwise:

Kronecker delta - Wikipedia
pedia Kronecker delta From Wikipedia, the free encyclopedia Jump to: navigation, search Not to be confused with the Dirac delta function, nor with the Kronecker symbol. <span>In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers. The function is 1 if the variables are equal, and 0 otherwise: δ i j = {

#### Flashcard 1760011619596

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#stochastics
Question

the Kronecker delta is a function of two variables that [...]

equals 1 if the variables are equal, and 0 otherwise:

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In mathematics, the Kronecker delta is a function of two variables that equals 1 if the variables are equal, and 0 otherwise:

#### Original toplevel document

Kronecker delta - Wikipedia
pedia Kronecker delta From Wikipedia, the free encyclopedia Jump to: navigation, search Not to be confused with the Dirac delta function, nor with the Kronecker symbol. <span>In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers. The function is 1 if the variables are equal, and 0 otherwise: δ i j = {

#### Flashcard 1760013192460

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#stochastics
Question

the [...] is a function of two variables that equals 1 if the variables are equal, and 0 otherwise:

Kronecker delta

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In mathematics, the Kronecker delta is a function of two variables that equals 1 if the variables are equal, and 0 otherwise:

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Kronecker delta - Wikipedia
pedia Kronecker delta From Wikipedia, the free encyclopedia Jump to: navigation, search Not to be confused with the Dirac delta function, nor with the Kronecker symbol. <span>In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers. The function is 1 if the variables are equal, and 0 otherwise: δ i j = {

#### Annotation 1760016076044

 #fourier-analysis When a function space has an interval as the domain, the integral of the product of functions as the bilinear form The functions f and g are orthogonal when this integral is zero Orthogonal functions - Wikipedia
Orthogonal functions - Wikipedia Orthogonal functions From Wikipedia, the free encyclopedia Jump to: navigation, search In mathematics, orthogonal functions belong to a function space which is a vector space (usually over R) that has a bilinear form. When the function space has an interval as the domain, the bilinear form may be the integral of the product of functions over the interval: ⟨ f , g ⟩ = ∫ f ( x ) ¯ g ( x ) d x . {\displaystyle \langle f,g\rangle =\int {\overline {f(x)}}g(x)\,dx.} The functions f and g are orthogonal when this integral is zero: ⟨ f , g ⟩ = 0. {\displaystyle \langle f,\ g\rangle =0.} As with a basis of vectors in a finite-dimensional space, orthogonal functions can form an infinite basis for a function space. Suppose {f n }, n = 0, 1, 2, … is a sequence of ort

#### Flashcard 1760022629644

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#fourier-analysis
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The functions f and g are orthogonal when [...inner product...] status measured difficulty not learned 37% [default] 0

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When a function space has an interval as the domain, the integral of the product of functions as the bilinear form The functions f and g are orthogonal when this integral is zero

#### Original toplevel document

Orthogonal functions - Wikipedia
Orthogonal functions - Wikipedia Orthogonal functions From Wikipedia, the free encyclopedia Jump to: navigation, search In mathematics, orthogonal functions belong to a function space which is a vector space (usually over R) that has a bilinear form. When the function space has an interval as the domain, the bilinear form may be the integral of the product of functions over the interval: ⟨ f , g ⟩ = ∫ f ( x ) ¯ g ( x ) d x . {\displaystyle \langle f,g\rangle =\int {\overline {f(x)}}g(x)\,dx.} The functions f and g are orthogonal when this integral is zero: ⟨ f , g ⟩ = 0. {\displaystyle \langle f,\ g\rangle =0.} As with a basis of vectors in a finite-dimensional space, orthogonal functions can form an infinite basis for a function space. Suppose {f n }, n = 0, 1, 2, … is a sequence of ort

#### Annotation 1760026037516

 #spectral-analysis The set of all possible eigenvalues of a linear operator D is sometimes called its spectrum

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The set of all possible eigenvalues of a linear operator D is sometimes called its spectrum, which may be discrete, continuous, or a combination of both. 

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Eigenfunction - Wikipedia
he solutions to Equation (1) may also be subject to boundary conditions. Because of the boundary conditions, the possible values of λ are generally limited, for example to a discrete set λ 1 , λ 2 , ... or to a continuous set over some range. <span>The set of all possible eigenvalues of D is sometimes called its spectrum, which may be discrete, continuous, or a combination of both.  Each value of λ corresponds to one or more eigenfunctions. If multiple linearly independent eigenfunctions have the same eigenvalue, the eigenvalue is said to be degenerate and the ma

#### Flashcard 1760027610380

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#spectral-analysis
Question
[...] of a linear operator D is sometimes called its spectrum
The set of all possible eigenvalues

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The set of all possible eigenvalues of a linear operator D is sometimes called its spectrum

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Eigenfunction - Wikipedia
he solutions to Equation (1) may also be subject to boundary conditions. Because of the boundary conditions, the possible values of λ are generally limited, for example to a discrete set λ 1 , λ 2 , ... or to a continuous set over some range. <span>The set of all possible eigenvalues of D is sometimes called its spectrum, which may be discrete, continuous, or a combination of both.  Each value of λ corresponds to one or more eigenfunctions. If multiple linearly independent eigenfunctions have the same eigenvalue, the eigenvalue is said to be degenerate and the ma

#### Flashcard 1760029183244

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#spectral-analysis
Question
The set of all possible eigenvalues of a linear operator D is sometimes called its [...]
spectrum

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The set of all possible eigenvalues of a linear operator D is sometimes called its spectrum

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Eigenfunction - Wikipedia
he solutions to Equation (1) may also be subject to boundary conditions. Because of the boundary conditions, the possible values of λ are generally limited, for example to a discrete set λ 1 , λ 2 , ... or to a continuous set over some range. <span>The set of all possible eigenvalues of D is sometimes called its spectrum, which may be discrete, continuous, or a combination of both.  Each value of λ corresponds to one or more eigenfunctions. If multiple linearly independent eigenfunctions have the same eigenvalue, the eigenvalue is said to be degenerate and the ma

Article 1760037571852

English words
#english

sad or miserable in appearance: don't look so woebegone, Joanna. ternary adjective composed of three parts. • Mathematics using three as a base. a soft modelling material, used especially by children: I made a snake by rolling out plasticine an acrobatic movement in which a person turns head over heels in the air or on the ground and lands or finishes on their feet: a backward somersault from sobre ‘above’ + saut ‘leap’. castanets is small concave pieces of wood, ivory, or plastic, joined in pairs by a cord and clicked together by the fingers as a rhythmic accompaniment to Spanish dancing. principality is a state ruled by a prince. from Latin principalis ‘first, original’ a genre of crime film or fiction characterized by cynicism, fatalism, and moral ambiguity: his film proved that a Brit could do noir as darkly as any American. the husband of an adulteress, often regarded as an object of derision: jokes in literature about elderly cuckolds and misers are rife. (originally in Hinduism and Buddhism)

#### Annotation 1760043076876

 separation of variables solves ordinary and partial differential equations by allowing one to rewrite an equation so that each of two variables occurs on a different side of the equation.

Separation of variables - Wikipedia
People [show] Isaac Newton Leonhard Euler Émile Picard Józef Maria Hoene-Wroński Ernst Lindelöf Rudolf Lipschitz Augustin-Louis Cauchy John Crank Phyllis Nicolson Carl David Tolmé Runge Martin Wilhelm Kutta v t e <span>In mathematics, separation of variables (also known as the Fourier method) is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation. Contents [hide] 1 Ordinary differential equations (ODE) 1.1 Alternative notation 1.2 Example 2 Partial differential equations 2.1 Example: homogeneous case 2.2 Example:

#### Flashcard 1760046222604

Question

separation of variables solves ordinary and partial differential equations by allowing one to rewrite an equation so that [...].

each of two variables occurs on a different side of the equation

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separation of variables solves ordinary and partial differential equations by allowing one to rewrite an equation so that each of two variables occurs on a different side of the equation.

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Separation of variables - Wikipedia
People [show] Isaac Newton Leonhard Euler Émile Picard Józef Maria Hoene-Wroński Ernst Lindelöf Rudolf Lipschitz Augustin-Louis Cauchy John Crank Phyllis Nicolson Carl David Tolmé Runge Martin Wilhelm Kutta v t e <span>In mathematics, separation of variables (also known as the Fourier method) is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation. Contents [hide] 1 Ordinary differential equations (ODE) 1.1 Alternative notation 1.2 Example 2 Partial differential equations 2.1 Example: homogeneous case 2.2 Example:

#### Flashcard 1760047795468

Question

[...] solves ordinary and partial differential equations by allowing one to rewrite an equation so that each of two variables occurs on a different side of the equation.

separation of variables

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separation of variables solves ordinary and partial differential equations by allowing one to rewrite an equation so that each of two variables occurs on a different side of the equation. </spa

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Separation of variables - Wikipedia
People [show] Isaac Newton Leonhard Euler Émile Picard Józef Maria Hoene-Wroński Ernst Lindelöf Rudolf Lipschitz Augustin-Louis Cauchy John Crank Phyllis Nicolson Carl David Tolmé Runge Martin Wilhelm Kutta v t e <span>In mathematics, separation of variables (also known as the Fourier method) is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation. Contents [hide] 1 Ordinary differential equations (ODE) 1.1 Alternative notation 1.2 Example 2 Partial differential equations 2.1 Example: homogeneous case 2.2 Example:

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 You must shop the competition in person, to see how their property compares to yours: Where are they strong and weak? How can you make your property better? And—most important—what are they charging? Do this before you close on the property.

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 Get the exterior of the property looking good. Do all repairs, paint the exterior, improve the landscaping, improve the lighting, and restripe or blacktop the parking lot. Whatever you need to do to show the tenants that times have changed and new ownership has a new attitude, do it.