台中新建案預售屋查詢 相關
廣告台北信義計畫區＋大安森林公園＝台中中央公園特區，【華固頂滙】15%超低建蔽，45/53坪. 15%超低建蔽！華固頂滙3243基地完整街廓；中央公園水湳轉運中心旁，擁抱繁華住進自然森活
精選全台搶手好屋，降價宅、景觀宅，近學區商圈物件，智慧搜尋快速匹配，馬上找到理想宅！ 自住宅、店面、廠辦一秒快查，搶手物件不錯過！VR互動、影音帶看、手機APP，找房安心高效率！
搜尋結果
550 Madison Avenue is a postmodern skyscraper on Madison Avenue between 55th Street and 56th Street in New York City. Designed by Philip Johnson and John Burgee with associate architect Simmons Architects, the building was completed in 1984. It is a 647-foot-tall (197-meter), 37-story office tower with a facade made of pink granite.
The 828-metre (2,717 ft) tall Burj Khalifa in Dubai has been the tallest building since 2010. The Burj Khalifa has been classified as megatall. A diagram showing the tallest buildings as of 2024 This is a list of the tallest buildings.Tall buildings, such as skyscrapers, are intended here as enclosed structures with continuously occupiable floors and a height of at least 340 metres (1,120 ft).
Perplexity AI is an AI chatbot-powered research and conversational search engine that answers queries using natural language predictive text.[2][3] Launched in 2022, Perplexity generates answers using sources from the web and cites links within the text response.[4] Perplexity works on a freemium model; the free product uses its Perplexity ...
- Example
- Jacobian Matrix
- Jacobian Determinant
- Inverse
- Critical Points
- Examples
- Other Uses
- See Also
- Further Reading
- External Links
Suppose f : Rn → Rm is a function such that each of its first-order partial derivatives exist on Rn. This function takes a point x ∈ Rn as input and produces the vector f(x) ∈ Rm as output. Then the Jacobian matrix of f is defined to be an m×n matrix, denoted by J, whose (i,j)th entry is J i j = ∂ f i ∂ x j {\textstyle \mathbf {J} _{ij}={\frac {\pa...
The Jacobian of a vector-valued function in several variables generalizes the gradient of a scalar-valued function in several variables, which in turn generalizes the derivative of a scalar-valued function of a single variable. In other words, the Jacobian matrix of a scalar-valued function in several variablesis (the transpose of) its gradient and...
If m = n, then f is a function from Rn to itself and the Jacobian matrix is a square matrix. We can then form its determinant, known as the Jacobian determinant. The Jacobian determinant is sometimes simply referred to as "the Jacobian". The Jacobian determinant at a given point gives important information about the behavior of f near that point. F...
According to the inverse function theorem, the matrix inverse of the Jacobian matrix of an invertible function is the Jacobian matrix of the inverse function. That is, if the Jacobian of the function f : Rn → Rn is continuous and nonsingular at the point p in Rn, then f is invertible when restricted to some neighborhood of pand 1. J f − 1 = J f − 1...
If f : Rn → Rm is a differentiable function, a critical point of f is a point where the rank of the Jacobian matrix is not maximal. This means that the rank at the critical point is lower than the rank at some neighbour point. In other words, let k be the maximal dimension of the open balls contained in the image of f; then a point is critical if a...
Example 1
Consider the function f : R2 → R2, with (x, y) ↦ (f1(x, y), f2(x, y)),given by 1. f ( [ x y ] ) = [ f 1 ( x , y ) f 2 ( x , y ) ] = [ x 2 y 5 x + sin y ] . {\displaystyle \mathbf {f} \left({\begin{bmatrix}x\\y\end{bmatrix}}\right)={\begin{bmatrix}f_{1}(x,y)\\f_{2}(x,y)\end{bmatrix}}={\begin{bmatrix}x^{2}y\\5x+\sin y\end{bmatrix}}.} Then we have 1. f 1 ( x , y ) = x 2 y {\displaystyle f_{1}(x,y)=x^{2}y} and 1. f 2 ( x , y ) = 5 x + sin y {\displaystyle f_{2}(x,y)=5x+\sin y} and the Jacobia...
Example 2: polar-Cartesian transformation
The transformation from polar coordinates (r, φ) to Cartesian coordinates (x, y), is given by the function F: R+ × [0, 2π) → R2with components: 1. x = r cos φ ; y = r sin φ . {\displaystyle {\begin{aligned}x&=r\cos \varphi ;\\y&=r\sin \varphi .\end{aligned}}} 2. J F ( r , φ ) = [ ∂ x ∂ r ∂ x ∂ φ ∂ y ∂ r ∂ y ∂ φ ] = [ cos φ − r sin φ sin φ r cos φ ] {\displaystyle \mathbf {J} _{\mathbf {F} }(r,\varphi )={\begin{bmatrix}{\dfrac {\partial x}{\partial r}}&{\dfrac {\partial x}{\partial...
Example 3: spherical-Cartesian transformation
The transformation from spherical coordinates (ρ, φ, θ) to Cartesian coordinates (x, y, z), is given by the function F: R+ × [0, π) × [0, 2π) → R3with components: 1. x = ρ sin φ cos θ ; y = ρ sin φ sin θ ; z = ρ cos φ . {\displaystyle {\begin{aligned}x&=\rho \sin \varphi \cos \theta ;\\y&=\rho \sin \varphi \sin \theta ;\\z&=\rho \cos \varphi .\end{aligned}}} The Jacobian matrix for this coordinate change is 1. J F ( ρ , φ , θ ) = [ ∂ x ∂ ρ ∂ x ∂ φ ∂ x ∂ θ ∂ y ∂ ρ ∂ y ∂ φ ∂ y ∂ θ ∂ z...
Dynamical systems
Consider a dynamical system of the form x ˙ = F ( x ) {\displaystyle {\dot {\mathbf {x} }}=F(\mathbf {x} )} , where x ˙ {\displaystyle {\dot {\mathbf {x} }}} is the (component-wise) derivative of x {\displaystyle \mathbf {x} } with respect to the evolution parameter t {\displaystyle t} (time), and F : R n → R n {\displaystyle F\colon \mathbb {R} ^{n}\to \mathbb {R} ^{n}} is differentiable. If F ( x 0 ) = 0 {\displaystyle F(\mathbf {x} _{0})=0} , then x 0 {\displaystyle \mathbf {x} _{0}} is a...
Newton's method
A square system of coupled nonlinear equations can be solved iteratively by Newton's method. This method uses the Jacobian matrix of the system of equations.
Regression and least squares fitting
The Jacobian serves as a linearized design matrix in statistical regression and curve fitting; see non-linear least squares. The Jacobian is also used in random matrices, moments, local sensitivity and statistical diagnostics.
Gandolfo, Giancarlo (1996). "Comparative Statics and the Correspondence Principle". Economic Dynamics (Third ed.). Berlin: Springer. pp. 305–330. ISBN 3-540-60988-1.Protter, Murray H.; Morrey, Charles B. Jr. (1985). "Transformations and Jacobians". Intermediate Calculus (Second ed.). New York: Springer. pp. 412–420. ISBN 0-387-96058-9."Jacobian", Encyclopedia of Mathematics, EMS Press, 2001 [1994]Viète. de Moivre. Euler. Fourier. v. t. e. In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles.
Windsor Castle is a royal residence at Windsor in the English county of Berkshire. It is strongly associated with the English and succeeding British royal family, and embodies almost a millennium of architectural history. The original castle was built in the 11th century, after the Norman invasion of England by William the Conqueror. Since the ...
Jeffrey Lionel Dahmer (/ˈdɑːmər/; May 21, 1960 – November 28, 1994), also known as the Milwaukee Cannibal or the Milwaukee Monster,[4] was an American serial killer and sex offender who killed and dismembered seventeen males between 1978 and 1991.[5] Many of his later murders involved necrophilia,[6] cannibalism, and the permanent ...
