Matrix calculus

In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices.  It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single variable, into vectors and matrices that can be treated as single entities.  This greatly simplifies operations such as finding the maximum or minimum of a multivariate function and solving systems of differential equations. The notation used here is commonly used in statistics and engineering, while the tensor index notation is preferred in physics.

Two competing notational conventions split the field of matrix calculus into two separate groups. The two groups can be distinguished by whether they write the derivative of a scalar with respect to a vector as a column vector or a row vector. Both of these conventions are possible even when the common assumption is made that vectors should be treated as column vectors when combined with matrices (rather than row vectors). A single convention can be somewhat standard throughout a single field that commonly uses matrix calculus (e.g. econometrics, statistics, estimation theory and machine learning). However, even within a given field different authors can be found using competing conventions. Authors of both groups often write as though their specific convention were standard. Serious mistakes can result when combining results from different authors without carefully verifying that compatible notations have been used. Definitions of these two conventions and comparisons between them are collected in the layout conventions section.

Scope

Matrix calculus refers to a number of different notations that use matrices and vectors to collect the derivative of each component of the dependent variable with respect to each component of the independent variable. In general, the independent variable can be a scalar, a vector, or a matrix while the dependent variable can be any of these as well. Each different situation will lead to a different set of rules, or a separate calculus, using the broader sense of the term. Matrix notation serves as a convenient way to collect the many derivatives in an organized way.

As a first example, consider the gradient from vector calculus. For a scalar function of three independent variables, , the gradient is given by the vector equation
,

where  represents a unit vector in the  direction for . This type of generalized derivative can be seen as the derivative of a scalar, f, with respect to a vector, , and its result can be easily collected in vector form.

More complicated examples include the derivative of a scalar function with respect to a matrix, known as the gradient matrix, which collects the derivative with respect to each matrix element in the corresponding position in the resulting matrix. In that case the scalar must be a function of each of the independent variables in the matrix. As another example, if we have an n-vector of dependent variables, or functions, of m independent variables we might consider the derivative of the dependent vector with respect to the independent vector. The result could be collected in an m×n matrix consisting of all of the possible derivative combinations. There are, of course, a total of nine possibilities using scalars, vectors, and matrices. Notice that as we consider higher numbers of components in each of the independent and dependent variables we can be left with a very large number of possibilities.

The six kinds of derivatives that can be most neatly organized in matrix form are collected in the following table.

Here, we have used the term "matrix" in its most general sense, recognizing that vectors and scalars are simply matrices with one column and then one row respectively. Moreover, we have used bold letters to indicate vectors and bold capital letters for matrices. This notation is used throughout.

Notice that we could also talk about the derivative of a vector with respect to a matrix, or any of the other unfilled cells in our table. However, these derivatives are most naturally organized in a tensor of rank higher than 2, so that they do not fit neatly into a matrix. In the following three sections we will define each one of these derivatives and relate them to other branches of mathematics. See the layout conventions section for a more detailed table.

Relation to other derivatives

The matrix derivative is a convenient notation for keeping track of partial derivatives for doing calculations. The Fréchet derivative is the standard way in the setting of functional analysis to take derivatives with respect to vectors. In the case that a matrix function of a matrix is Fréchet differentiable, the two derivatives will agree up to translation of notations. As is the case in general for partial derivatives, some formulae may extend under weaker analytic conditions than the existence of the derivative as approximating linear mapping.

Usages

Matrix calculus is used for deriving optimal stochastic estimators, often involving the use of Lagrange multipliers. This includes the derivation of:
 Kalman filter
 Wiener filter
 Expectation-maximization algorithm for Gaussian mixture
 Gradient descent

Notation

The vector and matrix derivatives presented in the sections to follow take full advantage of matrix notation, using a single variable to represent a large number of variables. In what follows we will distinguish scalars, vectors and matrices by their typeface. We will let M(n,m) denote the space of real n×m matrices with n rows and m columns.  Such matrices will be denoted using bold capital letters: A, X, Y, etc.  An element of M(n,1), that is, a column vector, is denoted with a boldface lowercase letter: a, x, y, etc. An element of M(1,1) is a scalar, denoted with lowercase italic typeface: a, t, x, etc. XT denotes matrix transpose, tr(X) is the trace, and det(X) or |X| is the determinant. All functions are assumed to be of differentiability class C1 unless otherwise noted. Generally letters from the first half of the alphabet (a, b, c, ...) will be used to denote constants, and from the second half (t, x, y, ...) to denote variables.

NOTE: As mentioned above, there are competing notations for laying out systems of partial derivatives in vectors and matrices, and no standard appears to be emerging yet.  The next two introductory sections use the numerator layout convention simply for the purposes of convenience, to avoid overly complicating the discussion.  The section after them discusses layout conventions in more detail.  It is important to realize the following:
Despite the use of the terms "numerator layout" and "denominator layout", there are actually more than two possible notational choices involved.  The reason is that the choice of numerator vs. denominator (or in some situations, numerator vs. mixed) can be made independently for scalar-by-vector, vector-by-scalar, vector-by-vector, and scalar-by-matrix derivatives, and a number of authors mix and match their layout choices in various ways.
The choice of numerator layout in the introductory sections below does not imply that this is the "correct" or "superior" choice.  There are advantages and disadvantages to the various layout types.  Serious mistakes can result from carelessly combining formulas written in different layouts, and converting from one layout to another requires care to avoid errors.  As a result, when working with existing formulas the best policy is probably to identify whichever layout is used and maintain consistency with it, rather than attempting to use the same layout in all situations.

Alternatives

The tensor index notation with its Einstein summation convention is very similar to the matrix calculus, except one writes only a single component at a time.  It has the advantage that one can easily manipulate arbitrarily high rank tensors, whereas tensors of rank higher than two are quite unwieldy with matrix notation.  All of the work here can be done in this notation without use of the single-variable matrix notation. However, many problems in estimation theory and other areas of applied mathematics would result in too many indices to properly keep track of, pointing in favor of matrix calculus in those areas.  Also, Einstein notation can be very useful in proving the identities presented here (see section on differentiation) as an alternative to typical element notation, which can become cumbersome when the explicit sums are carried around. Note that a matrix can be considered a tensor of rank two.

Derivatives with vectors

Because vectors are matrices with only one column, the simplest matrix derivatives are vector derivatives.

The notations developed here can accommodate the usual operations of vector calculus by identifying the space M(n,1) of n-vectors with the Euclidean space Rn, and the scalar M(1,1) is identified with R. The corresponding concept from vector calculus is indicated at the end of each subsection.

NOTE: The discussion in this section assumes the numerator layout convention for pedagogical purposes.  Some authors use different conventions.  The section on layout conventions discusses this issue in greater detail.  The identities given further down are presented in forms that can be used in conjunction with all common layout conventions.

Vector-by-scalar

The derivative of a vector , by a scalar x is written (in numerator layout notation) as

In vector calculus the derivative of a vector y with respect to a scalar x is known as the tangent vector of the vector y, . Notice here that y: R1 → Rm.

Example Simple examples of this include the velocity vector in Euclidean space, which is the tangent vector of the position vector (considered as a function of time). Also, the acceleration is the tangent vector of the velocity.

Scalar-by-vector

The derivative of a scalar y by a vector , is written (in numerator layout notation) as

In vector calculus, the gradient of a scalar field y in the space Rn (whose independent coordinates are the components of x) is the transpose of the derivative of a scalar by a vector. In physics, the electric field is the negative vector gradient of the electric potential.

The directional derivative of a scalar function f(x) of the space vector x in the direction of the unit vector u (represented in this case as a column vector) is defined using the gradient as follows.

Using the notation just defined for the derivative of a scalar with respect to a vector we can re-write the directional derivative as
 This type of notation will be nice when proving product rules and chain rules that come out looking similar to what we are familiar with for the scalar derivative.

Vector-by-vector

Each of the previous two cases can be considered as an application of the derivative of a vector with respect to a vector, using a vector of size one appropriately. Similarly we will find that the derivatives involving matrices will reduce to derivatives involving vectors in a corresponding way.

The derivative of a vector function (a vector whose components are functions) , with respect to an input vector, , is written (in numerator layout notation) as

In vector calculus, the derivative of a vector function y with respect to a vector x whose components represent a space is known as the pushforward (or differential), or the Jacobian matrix.

The pushforward along a vector function f with respect to vector v in Rn is given by

Derivatives with matrices
There are two types of derivatives with matrices that can be organized into a matrix of the same size. These are the derivative of a matrix by a scalar and the derivative of a scalar by a matrix. These can be useful in minimization problems found in many areas of applied mathematics and have adopted the names tangent matrix and gradient matrix respectively after their analogs for vectors.

Note: The discussion in this section assumes the numerator layout convention for pedagogical purposes.  Some authors use different conventions.  The section on layout conventions discusses this issue in greater detail.  The identities given further down are presented in forms that can be used in conjunction with all common layout conventions.

Matrix-by-scalar

The derivative of a matrix function Y by a scalar x is known as the tangent matrix and is given (in numerator layout notation) by

Scalar-by-matrix

The derivative of a scalar y function of a p×q matrix X of independent variables, with respect to the matrix X, is given (in numerator layout notation) by

Important examples of scalar functions of matrices include the trace of a matrix and the determinant.

In analog with vector calculus this derivative is often written as the following.

Also in analog with vector calculus, the directional derivative of a scalar f(X) of a matrix X in the direction of matrix Y is given by

It is the gradient matrix, in particular, that finds many uses in minimization problems in estimation theory, particularly in the derivation of the Kalman filter algorithm, which is of great importance in the field.

Other matrix derivatives

The three types of derivatives that have not been considered are those involving vectors-by-matrices, matrices-by-vectors, and matrices-by-matrices. These are not as widely considered and a notation is not widely agreed upon.

Layout conventions

This section discusses the similarities and differences between notational conventions that are used in the various fields that take advantage of matrix calculus. Although there are largely two consistent conventions, some authors find it convenient to mix the two conventions in forms that are discussed below. After this section equations will be listed in both competing forms separately.

The fundamental issue is that the derivative of a vector with respect to a vector, i.e. , is often written in two competing ways.  If the numerator y is of size m and the denominator x of size n, then the result can be laid out as either an m×n matrix or n×m matrix, i.e. the elements of y laid out in columns and the elements of x laid out in rows, or vice versa.  This leads to the following possibilities:
Numerator layout, i.e.  lay out according to y and xT (i.e. contrarily to x).  This is sometimes known as the Jacobian formulation. This corresponds to the m×n layout in the previous example.
Denominator layout, i.e. lay out according to yT and x (i.e. contrarily to y).  This is sometimes known as the Hessian formulation.  Some authors term this layout the gradient, in distinction to the Jacobian (numerator layout), which is its transpose. (However, gradient more commonly means the derivative  regardless of layout.). This corresponds to the n×m layout in the previous example.
A third possibility sometimes seen is to insist on writing the derivative as  (i.e. the derivative is taken with respect to the transpose of x) and follow the numerator layout.  This makes it possible to claim that the matrix is laid out according to both numerator and denominator.  In practice this produces results the same as the numerator layout.

When handling the gradient  and the opposite case  we have the same issues.  To be consistent, we should do one of the following:
If we choose numerator layout for  we should lay out the gradient  as a row vector, and  as a column vector.
If we choose denominator layout for  we should lay out the gradient  as a column vector, and  as a row vector.
In the third possibility above, we write  and  and use numerator layout.

Not all math textbooks and papers are consistent in this respect throughout. That is, sometimes different conventions are used in different contexts within the same book or paper. For example, some choose denominator layout for gradients (laying them out as column vectors), but numerator layout for the vector-by-vector derivative

Similarly, when it comes to scalar-by-matrix derivatives  and matrix-by-scalar derivatives  then consistent numerator layout lays out according to Y and XT, while consistent denominator layout lays out according to YT and X.  In practice, however, following a denominator layout for  and laying the result out according to YT, is rarely seen because it makes for ugly formulas that do not correspond to the scalar formulas.  As a result, the following layouts can often be found:
Consistent numerator layout, which lays out  according to Y and  according to XT.
Mixed layout, which lays out  according to Y and  according to X.
Use the notation  with results the same as consistent numerator layout.

In the following formulas, we handle the five possible combinations  and  separately.  We also handle cases of scalar-by-scalar derivatives that involve an intermediate vector or matrix. (This can arise, for example, if a multi-dimensional parametric curve is defined in terms of a scalar variable, and then a derivative of a scalar function of the curve is taken with respect to the scalar that parameterizes the curve.) For each of the various combinations, we give numerator-layout and denominator-layout results, except in the cases above where denominator layout rarely occurs. In cases involving matrices where it makes sense, we give numerator-layout and mixed-layout results.  As noted above, cases where vector and matrix denominators are written in transpose notation are equivalent to numerator layout with the denominators written without the transpose.

Keep in mind that various authors use different combinations of numerator and denominator layouts for different types of derivatives, and there is no guarantee that an author will consistently use either numerator or denominator layout for all types.  Match up the formulas below with those quoted in the source to determine the layout used for that particular type of derivative, but be careful not to assume that derivatives of other types necessarily follow the same kind of layout.

When taking derivatives with an aggregate (vector or matrix) denominator in order to find a maximum or minimum of the aggregate, it should be kept in mind that using numerator layout will produce results that are transposed with respect to the aggregate.  For example, in attempting to find the maximum likelihood estimate of a multivariate normal distribution using matrix calculus, if the domain is a k×1 column vector, then the result using the numerator layout will be in the form of a 1×k row vector. Thus, either the results should be transposed at the end or the denominator layout (or mixed layout) should be used.

{|class="wikitable"
|+ Result of differentiating various kinds of aggregates with other kinds of aggregates
! colspan=2 rowspan=2 |
! colspan=2 | Scalar y
! colspan=2 | Column vector y (size m×1)
! colspan=2 | Matrix Y (size m×n)
|-
! Notation !! Type
! Notation !! Type
! Notation !! Type
|-
! rowspan=2 | Scalar x
! Numerator
| rowspan=2 style="text-align:center;" |
| rowspan=2 | Scalar
| rowspan=2 style="text-align:center;" |
| Size-m column vector
| rowspan=2 style="text-align:center;" |
| m×n matrix
|-
! Denominator
| Size-m row vector
|
|-
! rowspan=2 | Column vector x(size n×1)
! Numerator
| rowspan=2 style="text-align:center;" |
| Size-n row vector
| rowspan=2 style="text-align:center;" |
| m×n matrix
| rowspan=2 style="text-align:center;" |
| rowspan=2 |
|-
! Denominator
| Size-n column vector
| n×m matrix
|-
! rowspan=2 | Matrix X(size p×q)
! Numerator
| rowspan=2 style="text-align:center;" |
| q×p matrix
| rowspan=2 style="text-align:center;" |
| rowspan=2 |
| rowspan=2 style="text-align:center;" |
| rowspan=2 |
|-
! Denominator
| p×q matrix
|}

The results of operations will be transposed when switching between numerator-layout and denominator-layout notation.

Numerator-layout notation

Using numerator-layout notation, we have:

The following definitions are only provided in numerator-layout notation:

Denominator-layout notation
Using denominator-layout notation, we have:

Identities

As noted above, in general, the results of operations will be transposed when switching between numerator-layout and denominator-layout notation.

To help make sense of all the identities below, keep in mind the most important rules: the chain rule, product rule and sum rule.  The sum rule applies universally, and the product rule applies in most of the cases below, provided that the order of matrix products is maintained, since matrix products are not commutative.  The chain rule applies in some of the cases, but unfortunately does not apply in matrix-by-scalar derivatives or scalar-by-matrix derivatives (in the latter case, mostly involving the trace operator applied to matrices).  In the latter case, the product rule can't quite be applied directly, either, but the equivalent can be done with a bit more work using the differential identities.

The following identities adopt the following conventions:
 the scalars, a, b, c, d, and e are constant in respect of, and the scalars, u, and v are functions of one of x, x, or X;
 the vectors, a, b, c, d, and e are constant in respect of, and the vectors, u, and v are functions of one of x, x, or X;
 the matrices, A, B, C, D, and E are constant in respect of, and the matrices, U and V are functions of one of x, x, or X.

Vector-by-vector identities
This is presented first because all of the operations that apply to vector-by-vector differentiation apply directly to vector-by-scalar or scalar-by-vector differentiation simply by reducing the appropriate vector in the numerator or denominator to a scalar.

{|class="wikitable" style="text-align: center;"
|+ Identities: vector-by-vector
! scope="col" width="150" | Condition
! scope="col" width="10" | Expression
! scope="col" width="100" | Numerator layout, i.e. by y and xT
! scope="col" width="100" | Denominator layout, i.e. by yT and x
|-
| a is not a function of x ||  ||colspan=2|
|-
| ||  || colspan=2|
|-
| A is not a function of x ||  ||  ||
|-
| A is not a function of x ||  ||  ||
|-
| a is not a function of x,u = u(x) ||
| colspan=2|
|-
| v = v(x), u = u(x) ||  ||  ||
|-
| A is not a function of x,u = u(x) ||  ||  ||
|-
| u = u(x), v = v(x) ||
| colspan=2|
|-
| u = u(x) ||  ||  ||
|-
| u = u(x) ||  ||  ||
|}

Scalar-by-vector identities

The fundamental identities are placed above the thick black line.

{|class="wikitable" style="text-align: center;"
|+ Identities: scalar-by-vector
! scope="col" width="150" | Condition
! scope="col" width="200" | Expression
! scope="col" width="200" | Numerator layout,i.e. by xT; result is row vector
! scope="col" width="200" | Denominator layout,i.e. by x; result is column vector
|-
| a is not a function of x ||
|  ||
|-
| a is not a function of x, u = u(x) ||
| colspan=2|
|-
| u = u(x), v = v(x) ||
| colspan=2|
|-
| u = u(x), v = v(x) ||
| colspan=2|
|-
| u = u(x) ||
| colspan=2|
|-
| u = u(x) ||
| colspan=2|
|-
| u = u(x), v = v(x)
|
|
 in numerator layout
|
 in denominator layout
|-
| u = u(x), v = v(x), A is not a function of x
|
|
 in numerator layout
|
 in denominator layout
|-
|
|
|
| , the Hessian matrix
|- style="border-top: 3px solid;"
| a is not a function of x ||     ||  ||
|-
| A is not a function of x b is not a function of x ||  ||  ||
|-
| A is not a function of x ||  ||  ||
|-
| A is not a function of x A is symmetric ||  ||  ||
|-
| A is not a function of x ||  || colspan=2|
|-
| A is not a function of x A is symmetric ||  || colspan=2|
|-
| ||  ||  ||
|-
| a is not a function of x, u = u(x)
|
|
 in numerator layout
|
 in denominator layout
|-
| a, b are not functions of x ||  ||  ||
|-
| A, b, C, D, e are not functions of x ||  ||  ||
|-
| a is not a function of x ||  ||||
|}

Vector-by-scalar identities

{|class="wikitable" style="text-align: center;"
|+ Identities: vector-by-scalar
! scope="col" width="150" | Condition
! scope="col" width="100" | Expression
! scope="col" width="100" | Numerator layout, i.e. by y,result is column vector
! scope="col" width="100" | Denominator layout, i.e. by yT,result is row vector
|-
| a is not a function of x ||  ||colspan=2|
|-
| a is not a function of x,u = u(x) ||
| colspan=2|
|-
| A is not a function of x,u = u(x) ||  ||  ||
|-
| u = u(x) ||
| colspan=2|
|-
| u = u(x), v = v(x) ||
| colspan=2|
|-
| u = u(x), v = v(x) ||
||
||
|-
| rowspan=2|u = u(x) || rowspan=2| ||  ||
|-
|colspan=2|Assumes consistent matrix layout; see below.
|-
| rowspan=2|u = u(x) || rowspan=2| ||  ||
|-
|colspan=2|Assumes consistent matrix layout; see below.
|-
| U = U(x), v = v(x) ||
||
||
|}

NOTE: The formulas involving the vector-by-vector derivatives  and  (whose outputs are matrices) assume the matrices are laid out consistent with the vector layout, i.e. numerator-layout matrix when numerator-layout vector and vice versa; otherwise, transpose the vector-by-vector derivatives.

Scalar-by-matrix identities

Note that exact equivalents of the scalar product rule and chain rule do not exist when applied to matrix-valued functions of matrices.  However, the product rule of this sort does apply to the differential form (see below), and this is the way to derive many of the identities below involving the trace function, combined with the fact that the trace function allows transposing and cyclic permutation, i.e.:

For example, to compute

Therefore,

(For the last step, see the 'Conversion from differential to derivative form' section.)

{|class="wikitable" style="text-align: center;"
|+ Identities: scalar-by-matrix
! scope="col" width="175" | Condition
! scope="col" width="10" | Expression
! scope="col" width="100" | Numerator layout, i.e. by XT
! scope="col" width="100" | Denominator layout, i.e. by X
|-
| a is not a function of X ||
|  ||
|-
| a is not a function of X, u = u(X) ||
| colspan=2|
|-
| u = u(X), v = v(X) ||
| colspan=2|
|-
| u = u(X), v = v(X) ||
| colspan=2|
|-
| u = u(X) ||
| colspan=2|
|-
| u = u(X) ||
| colspan=2|
|-
| rowspan=2|U = U(X) || rowspan=2|
||
||
|-
| colspan=2|Both forms assume numerator layout for
i.e. mixed layout if denominator layout for X is being used.
|- style="border-top: 3px solid;"
| a and b are not functions of X ||
|||
|-
| a and b are not functions of X ||
|||
|-
| a, b and C are not functions of X ||
|||
|-
| a, b and C are not functions of X ||
|||
|- style="border-top: 3px solid;"
| ||  || colspan=2|
|-
| U = U(X), V = V(X) ||  || colspan=2|
|-
| a is not a function of X, U = U(X) ||  || colspan=2|
|-
| g(X) is any polynomial with scalar coefficients, or any matrix function defined by an infinite polynomial series (e.g. eX, sin(X), cos(X), ln(X), etc. using a Taylor series); g(x) is the equivalent scalar function, g′(x) is its derivative, and g′(X) is the corresponding matrix function ||  ||  ||
|-
| A is not a function of X ||      ||  ||
|-
| A is not a function of X ||      ||  ||
|-
| A is not a function of X ||      ||  ||
|-
| A is not a function of X ||      ||  ||
|-
| A, B are not functions of X ||  ||  ||
|-
| A, B, C are not functions of X ||  ||  ||
|-
| n is a positive integer ||      ||  ||
|-
| A is not a function of X, n is a positive integer ||      ||  ||
|-
| ||      ||  ||
|-
| ||      ||  ||
|- style="border-top: 3px solid;"
| ||      ||  ||
|-
| a is not a function of X ||
 ||  ||
|-
| A, B are not functions of X ||       ||  ||
|-
| n is a positive integer ||      ||  ||
|-
| (see pseudo-inverse) ||        ||  ||
|-
| (see pseudo-inverse) ||       ||  ||
|-
| A is not a function of X,X is square and invertible ||  ||  ||
|-
| A is not a function of X,X is non-square,A is symmetric ||  ||  ||
|-
| A is not a function of X,X is non-square,A is non-symmetric ||
|
|
|}

Matrix-by-scalar identities

{|class="wikitable" style="text-align: center;"
|+ Identities: matrix-by-scalar
! scope="col" width="175" | Condition
! scope="col" width="100" | Expression
! scope="col" width="100" | Numerator layout, i.e. by Y
|-
| U = U(x) ||  ||
|-
| A, B are not functions of x, U = U(x) ||  ||
|-
| U = U(x), V = V(x) ||  ||
|-
| U = U(x), V = V(x) ||  ||
|-
| U = U(x), V = V(x) ||  ||
|-
| U = U(x), V = V(x) ||  ||
|-
| U = U(x) ||  ||
|-
| U = U(x,y) ||  ||
|-
| A is not a function of x, g(X) is any polynomial with scalar coefficients, or any matrix function defined by an infinite polynomial series (e.g. eX, sin(X), cos(X), ln(X), etc.); g(x) is the equivalent scalar function, g′(x) is its derivative, and g′(X) is the corresponding matrix function ||  || colspan=2|
|-
| A is not a function of x ||  ||
|}

Further see Derivative of the exponential map.

Scalar-by-scalar identities

With vectors involved

{|class="wikitable" style="text-align: center;"
|+ Identities: scalar-by-scalar, with vectors involved
! scope="col" width="150" | Condition
! scope="col" width="10" | Expression
! scope="col" width="150" | Any layout (assumes dot product ignores row vs. column layout)
|-
| u = u(x) ||  ||
|-
| u = u(x), v = v(x) ||
| colspan=2|
|}

With matrices involved

{|class="wikitable" style="text-align: center;"
|+Identities: scalar-by-scalar, with matrices involved
! scope="col" width="175" | Condition
! scope="col" width="100" | Expression
! scope="col" width="100" | Consistent numerator layout,i.e. by Y and XT
! scope="col" width="100" | Mixed layout,i.e. by Y and X
|-
| U = U(x) ||  || colspan=2|
|-
| U = U(x) ||  || colspan=2|
|-
| U = U(x) ||
| colspan=2 |
|-
| U = U(x) ||  ||
||
|-
| A is not a function of x, g(X) is any polynomial with scalar coefficients, or any matrix function defined by an infinite polynomial series (e.g. eX, sin(X), cos(X), ln(X), etc.); g(x) is the equivalent scalar function, g′(x) is its derivative, and g′(X) is the corresponding matrix function. ||  || colspan=2|
|-
| A is not a function of x ||  || colspan=2|
|}

Identities in differential form

It is often easier to work in differential form and then convert back to normal derivatives.  This only works well using the numerator layout. In these rules, "a" is a scalar.

{|class="wikitable" style="text-align: center;"
|+ Differential identities: scalar involving matrix
! Condition !! Expression !! Result (numerator layout)
|-
| ||  ||
|-
| ||  ||
|-
| ||  ||
|}

{|class="wikitable" style="text-align: center;"
|+ Differential identities: matrix
! Condition !! Expression !! Result (numerator layout)
|-
|A is not a function of X ||  ||
|-
|a is not a function of X ||  ||
|-
| ||  ||
|-
| ||  ||
|-
| (Kronecker product)  ||  ||
|-
| (Hadamard product) ||  ||
|-
| ||  ||
|-
|
|
|
|-
| (conjugate transpose) ||  ||
|-
| n is a positive integer ||  ||
|-
|
|
|
|-
|  is diagonalizable

f is differentiable at every eigenvalue
|
|
|}
In the last row,  is the Kronecker delta and  is the set of orthogonal projection operators that project onto the k-th eigenvector of X.
Q is the matrix of eigenvectors of , and  are the eigenvalues.
The matrix function  is defined in terms of the scalar function  for diagonalizable matrices by
 where  with .

To convert to normal derivative form, first convert it to one of the following canonical forms, and then use these identities:

{|class="wikitable" style="text-align: center;"
|+ Conversion from differential to derivative form
! Canonical differential form !! Equivalent derivative form
|-
|  ||
|-
|  ||
|-
|  ||
|-
|  ||
|-
|  ||
|-
|  ||
|}

Applications
Matrix differential calculus is used in statistics, particularly for the statistical analysis of multivariate distributions, especially the multivariate normal distribution and other elliptical distributions.

It is used in regression analysis to compute, for example, the ordinary least squares regression formula for the case of multiple explanatory variables.

See also

 Derivative (generalizations)
 Product integral
 Ricci calculus

Notes

References

Further reading

External links

Information
 Matrix Reference Manual, Mike Brookes, Imperial College London.
 Matrix Differentiation (and some other stuff), Randal J. Barnes, Department of Civil Engineering, University of Minnesota.
 Notes on Matrix Calculus, Paul L. Fackler, North Carolina State University.
 Matrix Differential Calculus (slide presentation), Zhang Le, University of Edinburgh.
 Introduction to Vector and Matrix Differentiation (notes on matrix differentiation, in the context of Econometrics), Heino Bohn Nielsen.
 A note on differentiating matrices (notes on matrix differentiation), Pawel Koval, from Munich Personal RePEc Archive.
 Vector/Matrix Calculus More notes on matrix differentiation.
 Matrix Identities (notes on matrix differentiation), Sam Roweis.

Category:Matrix theory
Category:Linear algebra
Category:Multivariable calculus


The Kensington Club

The Kensington Club is a private all-male dining club for students of the University of St Andrews.

Founded circa 1739 by Alexander the Laird Balgonie as a social club, the Kensington Club flourished predominately in the late eighteenth and early nineteenth centuries as a retreat for aristocratic and moneyed members of the student population. Renewed interest in the club after a period of decline in the second part of the twentieth century has led to a surge in membership since the early 2000s.

History
Alexander Leslie Laird Balgonie was born around the year 1720, the only son among five children. His father, also named Alexander, lived in the Balgonie Castle, a fortified manor of ancient origin over the bank of the river Leven, east of Glenrothes. The family's claim of descent from the Earls of Leven is disputed. The etymology of the name ‘The Kensington Club’ is unclear.

The policies of the labour governments in the early twentieth century were felt with particular acuteness among the Scottish aristocracy, with their limited ability to generate income. Club fortunes took a downturn and membership began to tail off. With the exception of a brief resurgence in the nineteen seventies, the club remained almost dormant. With the turn of the century interest began once more to escalate, and the Kensington Club once again exists as a social institution within St Andrews. In 2001, in honour of this revival, Raymond, the present Laird of Balgonie, was given honorary membership and made the club patron.

Controversy
In 2018, a series of articles in several newspapers and online publications called into question the legitimacy the majority of the club’s self-reported history, including the above description. The only references to the club’s history seem to have come from unverifiable, self-written publications. Inside sources are quoted as stating that the club was instead founded in the 1970s or more recently, instead of several centuries ago. Further statements claimed that the club’s recent publicity including its annual 'secret garden party' drove it to change its name from Kensington to Jodhpur.

Activities
Private dinners for club members are held biweekly. Etiquette and manners are enforced on the penalty of port.

Club Colours

The club colours are thick red and green stripes divided by a thin white stripe

References

Category:Dining clubs
Category:Clubs and societies in Scotland
Category:1739 establishments in Scotland


Tametraline

Tametraline (CP-24,441) is the parent of a series of chemical compounds investigated at Pfizer that eventually led to the development of sertraline (CP-51,974-1).

Sertraline has been called "3,4-dichloro-tametraline". This is correct but it is an oversimplification in the sense that sertraline is the S,S-isomer whereas tametraline is the 1R,4S-stereoisomer.

1R-Methylamino-4S-phenyl-tetralin is a potent inhibitor of norepinephrine uptake in rat brain synaptosomes, reverses reserpine induced hypothermia in mice, and blocks uptake of 3H-Norepinephrine into rat heart.

Tametraline is a norepinephrine-dopamine reuptake inhibitor.

Indatraline is an indanamine homolog of tetralin-based tametraline, although in the case of indatraline the product is pm-dichlorinated.

Chemistry
Two routes have been previously described, one for aryl moieties containing electron withdrawing groups, and one for electron donating groups:

"As expected, Friedel-Crafts cyclization of the diarylbutyric acid derivatives # to the most reactive ring was observed with little or none of the alternative isomer being detected."

"The KMnO4 oxidation of the 1-aryl-tetralins # was observed to give 4-hydroxy-4-aryltetralones # instead of the expected tetralone # previously reported. As a result of this finding, direct oxidation of Grignard reaction product # was attempted and found to be a more efficient route."

See also .

cis-/trans-Ratio
In the case of 3,4-dichloro product, approximately 50:50 cis-/trans- ratio was achieved, according to the reference.

CAN radical induced dimerization of styrene
"A facile one-pot synthesis of 1-amino-4-aryl-tetralin derivatives by the CAN-induced cyclodimerization of various styrenes in acetonitrile and acrylonitrile is described."

Structure-activity relationship
Certain aromatic substitutients have a potentiating effect (e.g., p-Br), whereas others negate the compound's intrinsic activity.

It is not right to think of the dimethyl analogs as a "prodrug" to the monomethylated drugs (cf. indatraline, "31,345"), but it is correct that it is a "latentiated" form of the drug. This word is from the salsalate page. This was the reason why sertraline was made only as monomethylated because apparently according to the orders the 1° amine is inactive therefore the drug would have a shorter duration of activity.

Enantiopurified trans- and cis-aminotetraline derivatives

(±)-Sertraline is not entirely SERT selective until it has been resolved into the S,S-enantiomer.

In terms of the trans- isomers there is relatively marked separation in the activity between the R,S- and S,R-enantiomers. This stands in contrast to what has been observed in the homologous indamine class where both of the trans- enantiomers possessed significant TRI activity at all three of the monoamine transporters.

Racemic cis- and trans-aminotetraline derivatives

The primary amines are claimed to completely lack any affinity for the transporters.

See also
 Cyproheptadine [4-(5H-dibenz-[a,d]cyclohepten-5-ylidine)-1-methylpiperidine]
 Dasotraline
 Desmethylsertraline
 EXP-561 (1-amino-4-phenylbicyclo[2.2.2]octane)
 JNJ-7925476
 Lometraline
 Nefopam
 Sertraline

References

Category:Amines
Category:Norepinephrine-dopamine reuptake inhibitors
Category:Pfizer brands
Category:Stimulants
Category:Tetralins


Jean Dénarié

Jean Dénarié (born 26 October 1940) is a french biologist, member of the French Academy of sciences since December 2008.

Emeritus research director at the Institut national de la recherche agronomique (INRA), his research has focused on the symbiosis between legumes and nitrogen-fixing bacteria.

Biography
In 1962, Jean Dénarié joined INRA, in the soil microbiology laboratory in Versailles. After 5 years of work, he began to study the symbiosis between legumes and nitrogen-fixing bacteria of the genus rhizobium.

In 1981, Jean Dénaria merged his laboratory with the one run by Pierre Boitard, who used molecular genetic methods to study the interactions between plants and pathogenic microorganisms. The new laboratory is located in Toulouse, in direct affiliation with INRA and CNRS. The research teams are joined by cytologist Georges Truchet and mass spectrometry biochemist Jean-Claude Promé. The team made the major discovery of the Nod factors. The team was able to verify that the purified Nod factors could stimulate the development of the root system. Their discovery makes it possible to increase the yields of soya, groundnut, pea and alfalfa crops. Patents are filed, a partnership with an industrial group is initiated, and in 2004 the production of Rhizobium inoculants enriched with Nod factors begins. In 2011, 2 million hectares of crops were fed with nod1 factors.

Jean Dénarié's work has since focused on the myc factor and its effects on the root and nutritional system of plants.

On 16 December 2008, Jean Dénarié was elected a member of the Academy of Sciences in the Integrative Biology section.

Other functions

    President of the Scientific Commission "Molecular and Cellular Biology" of INRA (1989-1993)
    Co-editor of The Plant Journal (1997-2000)
    Coordinator of the international Human Frontier Science Program project (1992-1995)
    Member of the French Society of Genetics
    Member of the French Society of Plant Biology
    Member of the International Society for Molecular Plant-Microbe Interactions

Prizes and awards

    Officer of the Ordre du Mérite Agricole
    Winner of Grand Prizes from the French Academy of sciences (1993, 2005)
    French citation laureate (1981-1998) from the ISI (Institute for Scientific Information)
    Laurier d'excellence de l'INRA (2007)
    Gold medal of the Académie d'agriculture de France (2011)

References

Category:1940 births
Category:French biologists
Category:Members of the French Academy of Sciences
Category:Living people


Estadio Gasómetro

Estadio Gasómetro was a multi-purpose stadium in the barrio (neighborhood) of Boedo, Buenos Aires, Argentina.

It was the home ground of San Lorenzo before they moved to their new stadium, Estadio Pedro Bidegain, which is sometimes referred to as "Estadio Nuevo Gasómetro" ("New Gasometer"), in 1993. The stadium had a capacity of 75,000 people.

San Lorenzo fans wish to return to their original home, "Viejo Gasómetro" (Old Gasometer), and won a court action saying that Carrefour should sell back the land that their supermarket is now built on.

References

Category:Sports venues in Buenos Aires
Gasometro
Category:Copa América stadiums
Category:Multi-purpose stadiums in Argentina


Sinwonsa

Sinwonsa is a Buddhist temple in the South Chungcheong province in South Korea.
Sinwonsa is located in Yanghwari Gyeryong-myeon Gongju, and one of three main temples in Gyeryong mountain along with Donghaksa and Gapsa. The temple was built by the monk Bodeokhwasang in the 11th year (651) of King Uija's reign of Baekje, and underwent several expansions. Gaeyeonhwasang is said to have renovated the current daeungjeon in 1876.

Jungakdan was built when the royal family respected Gyeryong mountain as three steep mountains with Myohyangsan mountain and Jirisan mountain in the third year (2431 AD) of King Taejo's reign. The religious service for the god of Gyeryong mountain was performed every spring and autumn. The present Jungakdan was expanded in the 16th year of King Gojong's reign.

References

Category:Buddhist temples in South Korea


Ancilla van de Leest

Ancilla van de Leest (Rotterdam, 21 July 1985), born as Linde van de Leest is a Dutch politician, former fetish model, producer, presenter and activist.

Modeling and media career
Van de Leest attended gymnasium in Rotterdam and worked as a waitress when she was discovered by a photographer. She quit school and at eighteen appeared under her birth name as a Playmate in the Dutch edition of men's magazine Playboy in May 2004. Afterwards she moved to Los Angeles for work and adopted the name Ancilla Tilia. In June 2009 Van de Leest appeared on the cover of Dutch Playboy, in a photo session by the photographer and music video director Carli Hermès. In September 2012 she again appeared on the cover of Dutch Playboy. She also appeared twice on the cover of the Dutch edition of FHM, as well as on the covers of Sp!ts, Rotterdams Dagblad, Panorama, Aktueel and Viva. In 2012 Van de Leest ended her career as a model.

Van de Leest appeared in erotic fetish photography, specializing in latex clothes, corsets, high heels and stockings. As a fetish model, she appeared on the cover of Bizarre, Marquis and The Picture.

In November 2013 she appeared in the first episode of the Dutch Popoz comedy series on Comedy Central. From 2008 to 2010 she wrote the "Ask Ancilla" section for the magazine FHM, which eventually became a full-page column that appeared monthly until 2010. In 2011 she wrote a book Aan mijn jongere ik ("To my younger self"). In 2013 she won the BNN's Nationale Reistest (a travel knowledge competition) as the "Famous Dutch person".

Pirate Party

On 26 June 2016 Van de Leest was elected as the top candidate of the Pirate Party of the Netherlands for the Dutch parliamentary elections in 2017.

In interviews Van de Leest indicated that her priorities are aimed at strengthening privacy rights and opposing abolishing cash. She foresees a development in which high costs are imposed on entrepreneurs who use cash in order to stimulate digital currency. This she sees as a privacy undermining development in which a person can be followed on the basis of their payment history. In addition to privacy rights in general, the party specifically focuses on strengthening privacy in the relationship between the government and its citizens, as the government poses a greater risk than corporations of infringing their fundamental rights. In September 2016 she stood up for the victims of a data breach in the town of Almelo.

On 6 April 2017, Ancilla announced that she would be leaving the Pirate Party as front-runner and would instead focus on her own projects. She will be a passive member and is going to continue to give advice to future party members.

References

External links

Category:1985 births
Category:Living people
Category:Dutch activists
Category:Dutch women activists
Category:Dutch female models
Category:People from Rotterdam
Category:De Trap Theater Academy alumni
Category:Pirate Party of the Netherlands politicians


Henry Brutsche

Landsman Henry Brutsche (1846 to December 27, 1880) was a Union Navy sailor who fought in the American Civil War. Brutsche received the country's highest award for bravery during combat, the Medal of Honor, for his action aboard the USS Tacony at Plymouth, North Carolina on 31 October 1864. He was honored with the award on 31 December 1864.

Biography
Brutsche was born in Philadelphia, Pennsylvania in 1846. He enlisted into the United States Navy. He died on 27 December 1880 and his remains are interred at the Lawnview Memorial Park in Rockledge, Pennsylvania.

Medal of Honor citation

See also

List of American Civil War Medal of Honor recipients: A–F

References

External links

Category:1846 births
Category:1880 deaths
Category:People of Pennsylvania in the American Civil War
Category:Union Navy officers
Category:United States Navy Medal of Honor recipients
Category:American Civil War recipients of the Medal of Honor
Category:Military personnel from Philadelphia
Category:Burials at Lawnview Memorial Park


Listed buildings in Catterall

Catterall is a civil parish in the Wyre district of Lancashire, England.  It contains eight listed buildings that are recorded in the National Heritage List for England.  All the listed buildings are designated at Grade II, the lowest of the three grades, which is applied to "buildings of national importance and special interest".  The parish includes the village of Catterall and the surrounding countryside.  The Lancaster Canal and the River Calder run through the parish, and the listed buildings associated with these are bridges and an aqueduct.  The other listed buildings are two medieval cross bases, a farmhouse with an associated barn, and a milestone.
__NOTOC__

Buildings

References

Citations

Sources

Category:Lists of listed buildings in Lancashire
Category:Buildings and structures in the Borough of Wyre


Thomas Mermillod-Blondin

Thomas Mermillod-Blondin (born 3 January 1984) is a former World Cup alpine ski racer from France. Born in Annecy, Haute-Savoie, he primarily competed in super-G, but his best results were in the super combined event: he took five of his six World Cup podiums in combined, with the other coming in super-G. Mermillod-Blondin made his World Cup debut in 2007 and represented France at the 2010 Winter Olympics in Vancouver and the 2011 World Championships. He made a total of 179 World Cup starts in his career. In February 2019 Mermillod-Blondin announced that he would retire from competition following a combined race in Bansko, Bulgaria that month.

World Cup results

Season standings

World Cup podiums
6 podiums – (4 SC, 1 K, 1 SG)

World Championship results

Olympic results

References

External links

 Thomas Mermillod Blondin World Cup standings at the International Ski Federation

 French Ski Team – 2016 men's A team
 Thomas Mermillod-Blondin at Rossignol.com

Category:1984 births
Category:French male alpine skiers
Category:Alpine skiers at the 2010 Winter Olympics
Category:Alpine skiers at the 2014 Winter Olympics
Category:Alpine skiers at the 2018 Winter Olympics
Category:Olympic alpine skiers of France
Category:Living people
Category:Université Savoie-Mont Blanc alumni
Category:People from Annecy


Mito

Mito may refer to:

Places
Mito, Ibaraki, a Japanese city
Mito, Aichi, a Japanese town
Mito, Shimane, a Japanese town
Mitō, Yamaguchi, a Japanese town
Mito District, a district in the province of Concepción, Peru
Mito domain, in the Japanese Edo period

People with the surname
, Japanese model, television personality and singer

Other
Cagiva Mito, an Italian sports motorcycle made by Cagiva
Alfa Romeo MiTo, a mini Italian sports car made by Alfa Romeo between 2008-2018
Vasconcellea candicans, a South American plant
 Mito Uzumaki, a kunoichi from Naruto
 Mito (Hunter × Hunter), a character from the manga series Hunter × Hunter
 Ikumi Mito, a character from Shokugeki no Sōma
Anji Mito, a character from the video game Guilty Gear
Mito, a type of currency in the video game Drift City
Mito House, a branch of the Tokugawa Gosanke clan in Japan
Minimum Interval Take Off
Space Pirate Mito
 Nickname of Brazilian President Jair Bolsonaro

See also

 Art Tower Mito, an arts complex in Mito, Ibaraki, Japan
Miko (disambiguation)
Milo (disambiguation)
MIMO (disambiguation)
Miño (disambiguation)
Mio (disambiguation)
Miso (disambiguation)
MIT (disambiguation)
Mite (disambiguation)
Mitu (disambiguation)

Category:Japanese-language surnames


Cross brace

A Cross brace is the cross-beam connecting between arches that is meant to add rigidity to the construction of mining tunnels. It is often tubular, having a diameter (generally made of lengths of pipes), and modified on the ends with clips or apertures for screw fastening; it serves as a stiffening element for the stability of a design. This brace could also be an ordinary cross-section wooden cross-beam, or even a board.

See also
Cross bracing

Category:Underground mining


Indorama Corporation

Indorama Corporation  is a global manufacturer of Polyethylene, Polypropylene, Polyester Fiber, Spandex filament, Filament as well as Spun Yarns, Fabrics, and Medical Gloves. It has presence in several countries and a major producer of Polyolefins. A multinational organisation with products being shipped to over 90 countries across the globe.

Indorama Corporation started with the establishment of a spun yarn manufacturing plant in 1976 in Indonesia by Mr.Sri Prakash Lohia. Today, Indorama Corp is a leading Asian organization headed by its chairman Mr. Giovanni boelens.

See also
Sri Prakash Lohia
Aloke Lohia
INVIYA® - The New Freedom FiberTM A Part of Indorama Corporation (Singapore)

References

Category:Companies established in 1994
Category:Companies listed on the Stock Exchange of Thailand


1988–89 FC Lokomotiv Gorna Oryahovitsa season

The 1988–89 season was FC Lokomotiv Gorna Oryahovitsa's third season in A PFG.

First-team squad

 18/0
 28/0
 26/1
 30/0
 29/1
 29/10
 3/0
 25/3
 10/1
 24/1
 18/0
 14/1

 12/0
 15/0
 6/1
 26/0
 4/0
 13/4
 10/0
 2/0
 11/1
 10/0
 2/0
 2/0

Fixtures

League

The team is finished 12th after 30 games in his third "A"group's season.

League standings

Cup
Lokomotiv GO dropped after the loss of second divisional Hebаr

1/8 finals

References

External links
 1988–89 A PFG
 Lokomotiv Gorna Oryahovitsa official website

Category:FC Lokomotiv Gorna Oryahovitsa seasons
Lokomotiv Gorna Oryahovitsa


2009 Deildabikar

Deildabikar 2009 was the 14th season of the Icelandic League Cup, a pre-season professional football competition in Iceland. The competition started on 20 February 2009 and concluded on 1 May 2009. FH beat Breiðablik 3–0 in the final and won their fifth League Cup title.

The 24 teams were divided into 4 groups of 6 teams. Every team played every other team of its group once, either home or away. Top 2 teams from each group qualified for the quarter-finals.

Group stage
The games were played from 20 February to 18 April 2009.

Group 1

Group 2

Group 3

Group 4

Knockout stage
Source: ksi.is

Quarterfinals
The games were played on 22, 23 and 24 April 2009.

Semifinals
The games were played on 27 April 2009.

Final

External links
 Deildabikar on rsssf.com

Category:2009 domestic association football cups
Category:2009 in Icelandic football
Category:Deildabikar


Riverside Local School District

Riverside Local School District, formerly named Painesville Township Local School District until July 1, 2007, is a primary/secondary school district in Ohio.

Location
The Riverside Local School District encompasses the following locations of Lake County, Ohio:
Painesville Township, Ohio
Concord Township, Ohio
Leroy Township, Ohio
Grand River, Ohio

Buildings
The Riverside Local School District has one high school campus for both junior and senior high school students, one middle school, and four elementary schools.

High school
Riverside High School is the only high school in the district. Students in grades ten through twelve attend Riverside. On the same campus, and connected to Riverside by the Campus Library, is John R. Williams Junior High School, which encompasses students in grades eight and nine. Students in all grades often take classes in both buildings.

Middle school
Henry F. LaMuth Middle School (Auburn Middle School until around 2000)  is the only middle school in the district. District students in grades 6 and 7 attend LaMuth.
Classes

You will get to pick whether to join band, with Mr. Swisslocki teaching, or choir, with Mr. Allen. Other than the core and music classes, students will also get special classes, art, computer, and gym for 12 weeks each.

Elementary schools
There are four elementary schools in the Riverside Local School District. Each elementary school has students from kindergarten through grade five. Each elementary school is part of the Ohio Reads tutoring program in conjunction with Riverside High School's National Honor Society program and each elementary school's after-school supervision program.
Buckeye Elementary - in Concord
Parkside Elementary - in Concord
Riverview Elementary in Painesville
Melridge Elementary - in Concord.

New Facilities
In November 2016 the residents of Painesville Township voted to approve a bond levy that allows the Riverside Local School District to construct two new elementary schools to replace four older ones. These buildings began construction in early 2018.

Zoning Issues
During the final planning stages of the new Concord Township school the Concord Township Board of Zoning Appeal's heard from the public and decided to deny the permit for the district to build on a plot of land it had purchased. The district later decided to take the Board of Zoning Appeal's to court where they reached a final settlement where the district agreed to change some aspects of its new school including the removal of the planned baseball field as well as meeting with the township and sheriffs for an outdoor security lighting schedule. In return the township agreed to allow the district to build on the plot of land it had purchased.

References

External links
District website

Category:School districts in Ohio
Category:Education in Lake County, Ohio


List of forts in California

This is a list of forts and camps in California, established by military, commercial and other interests.

List

See also
Geography of California
List of forts

Notes

References
 Heizer, Robert F., The Destruction of California Indians, University of Nebraska Press, Lincoln and London, 1993. .

External links
 California State Military Museum List of Camps and Posts

*
Category:Lists of buildings and structures in California
Category:Geography of California
California


HoopWorld

HoopWorld is a 3-on-3 multiplayer arcade basketball game with a kung-fu power-up twist, released in North America on July 19, 2010 and in the PAL region on August 13, 2010 exclusively for WiiWare.  HoopWorld utilizes power-up gameplay, basketball and Kung-fu to create a unique and competitive experience reminiscent of Arch Rivals, NBA Jam, and Power Stone.

Gameplay
 HoopWorld is an action sports basketball game in arcade style where two teams fight each other in order to defend their home courts. The point of the game is to get the highest score possible before match time runs out. The player runs, fights, kicks, steals the ball from opponents, and performs dunks and ball passes to win the match. Mystery Boxes will appear randomly on the court during the match revealing one of eight power-ups that impact game play.

The game comes with three game modes  (Quick Match, Tournament, and Survival) and has four difficulty levels (easy, normal, difficulty, and crazy) that enable the player to unlock teams and courts when played in Tournament mode. HoopWorld is an offline multiplayer game that can be played with 1-2 players. There is also an online leader board allowing players to upload their accumulated scores generated in Tournament mode.  There are six available courts that are set in nature and outdoor locations, such as a jungle, a volcano, a Caribbean island, a Greek village, a desert, and a mystical forest. Each court is defended by its respective team that the player can pick from.

History
HoopWorld was first announced in 2005 for release on XBLA in spring 2006. In September 2006, the game was postponed due to quality and gameplay concerns and Streamline Studios announced engineering support from Spanish developer and publisher Virtual Toys. In 2008, the developers decided to release HoopWorld as a WiiWare title slated for release in 2010. The game launched in North and South America on July 19, 2010, and in Europe, Australia, and New Zealand on August 13, 2010, where it is available for the same amount of 1000 Wii Points under the title HoopWorld BasketBrawl.

Programmer Tommy Refenes of Super Meat Boy fame was a member of the development team.

Reception

HoopWorld has received a variety of reactions from varying media outlets. 1UP cited that the game's controls come with a learning curve, but it does "deliver... its promise of old-school three-on-three fun".

Continuing with the thought of difficulty, RunDLC commented that the AI will make you "scream" at times, but it was still considered to be a "cool new take" on the sport.

Wiiloveit.com praised the game for its "new dimension of gameplay" and "extremely intense" matches. Although the lack of online play was commented on, it was highlighted that the game is "a lot of fun", especially from the standpoint of it being a quality multiplayer game for the service.

IGN mentioned that the control scheme "can take some adjustment" but described HoopWorld overall as one of "the most attractive WiiWare titles" and an "impressive alternative" to the NBA Jam experience that excels beyond nostalgia memories of arcade classics.

See also
List of WiiWare games
List of WiiWare games (North America)

References

External links
 Streamline Studios
 Hoopworld official website
 Virtual Toys

Category:WiiWare games
Category:Wii-only games
Category:Cancelled Xbox 360 games
Category:2010 video games
Category:Basketball video games
Category:Video games developed in the Netherlands
Category:Wii games


Palnissa

Palnissa is a genus of moths of the family Erebidae.

Species
Palnissa spatula Fibiger, 2008

References
  2008: Revision of the Micronoctuidae (Lepidoptera: Noctuoidea). Part 2, Taxonomy of the Belluliinae, Magninae and Parachrostiinae. Zootaxa, 1867: 1-136. Abstract & excerpt

Category:Micronoctuini
Category:Moth genera


George Dawson (Northern Ireland politician)

George Dawson (10 May 1961 – 7 May 2007) was a Northern Irish politician and a member of the Democratic Unionist Party (DUP) since 1979. He was an MLA for East Antrim from November 2003 until his death following a short battle with cancer. He was seen as a potential member of the power-sharing executive of the first minister, the DUP leader Ian Paisley, whose evangelical Protestant and strong unionist beliefs he shared.

Dawson was a founder in 1998, and was until his death the chairman, of the Caleb Foundation, a Christian fundamentalist pressure group. He was also Grand Master of the Independent Orange Order and Treasurer of the Evangelical Protestant Society.

References

External links
 georgedawson.org (archived)

Category:1961 births
Category:2007 deaths
Category:People from Lurgan
Category:Alumni of Queen's University Belfast
Category:Democratic Unionist Party MLAs
Category:Northern Ireland MLAs 2003–2007
Category:Northern Ireland MLAs 2007–2011
Category:Deaths from cancer in Northern Ireland
Category:People educated at Banbridge Academy
Category:Presbyterians from Northern Ireland
Category:Christian creationists
Category:Christian fundamentalists


Sander Kaasjager

Sander Kaasjager (; born 21 June 1985), who plays under the pseudonym Vo0 (pronunciation: ), is a Dutch professional player of the first person shooter games Painkiller, Quake II, Quake III , Quake 4, Quake Live and Quake Champions, and also World of Warcraft. He has won more titles and prize money—over US$250,000—at professional Painkiller tournaments than any other player.

Career
Originally starting with Quake II, Kaasjager later rose to widespread popularity with the release of a self-made highlight montage (or "frag video") from the game Challenge ProMode Arena, which showcases his unique aggressive style of playing.

Kaasjager played Painkiller for esports team Fnatic. Kaasjager won two world championship titles in 2004, one with CPL and one with ESWC,. In 2005, Kaasjager competed in the 2005 CPL World Tour, in which he won at five out of nine stops and earned $223,000. Kaasjager was named the Most Valuable Player of the tour. He played in the finals of the CPL World Tour against Fatal1ty but ended up losing.

When the Cyberathlete Professional League, World Series of Video Games, and other tournaments dropped Painkiller in favor of Quake 4, Kaasjager took a break from professional gaming starting from June 21, 2006 to pursue his studies for the upcoming college semester. He made a comeback to competitive gaming on April 30, 2007, participating in the World of Warcraft competition of the World Series of Video Games representing Fnatic once again.

After retiring, he has been known to play Challenge ProMode Arena, Warsow, QuakeWorld and Quake Live.

Tournament placings

2004
 1st – CPL Extreme Summer Championships 2004 – 1on1 (Dallas, U.S.)
 1st – CPL Extreme Winter Championships 2004 – 1on1 (Dallas, U.S.)
 1st – Electronic Sports World Cup 2004 – 1on1 (Poitiers, France)
 1st – Netgamez 2004B – 1on1 (Nieuwegein, Netherlands)

2005
 2nd – CPL World Tour Grand Finals – 1on1 (New York City)
 3rd – CPL World Tour Stop Chile 2005 – 1on1 (Santiago, Chile)
 1st – CPL World Tour Stop Italy 2005 – 1on1 (Milan, Italy)
 2nd – CPL World Tour Stop Singapore 2005 – 1on1 (Singapore)
 1st – CPL World Tour Stop UK 2005 – 1on1 (Sheffield)
 2nd – CPL World Tour Stop USA 2005 – 1on1 (Dallas)
 1st – CPL World Tour Stop Sweden 2005 – 1on1 (Jönköping)
 1st – CPL World Tour Stop Brazil 2005 – 1on1 (Rio de Janeiro, Brazil)
 2nd – CPL World Tour Stop Spain 2005 – 1on1 (Barcelona)
 1st – CPL World Tour Stop Turkey 2005 – 1on1 (Istanbul)
 1st – CPL World Tour Spain Qualifier 2005 – 1on1 (Istanbul)

2007
 2nd – World Series of Video Games, China – 3on3 (Wuhan, China)

2008
 7th – QuakeCon 2008 Intel Quake Live 1v1 Championship – 1on1 (Dallas, Texas, USA)
 8th – GameGune 2008 – 1on1 (Bilbao, Spain)
 13th – Electronic Sports World Cup Masters of Paris– 1on1 (Paris, France)
 2nd – Electronic Sports World Cup qualifier – 1on1 (Enschede, Netherlands)

2009
 4th – Intel Extreme Masters Season IV American Championship finals, Quake Live – 1on1 (Edmonton, Alberta, Canada)
 1st – Dreamhack Summer CPM, Quake III Championship – 1on1 (Jönköping, Sweden)

2017
 2nd – Quake World Championship 2017: Duel Tournament finals, Quake Champions – 1on1 (Dallas, USA)

Awards
 Most Valuable Player CPL World Tour 2005
 (ESports Award) Newcomer / Breakthrough of the Year 2005

Personal life
Kaasjager was born in Naarden, Netherlands on June 21, 1985. He enrolled in Delft as a student of mechanical engineering but dropped out to focus on gaming. He attended the University of Texas at Dallas and is a member of the UTD Comets men's tennis team. Vo0 has a Bachelor of Science degree in mechanical engineering.

References

External links
 vo0 on e-Sports Earnings
 Team Fnatic

Category:Living people
Category:1985 births
Category:Quake (series) players
Category:Painkiller players
Category:World of Warcraft players
Category:Dutch esports players
Category:People from Naarden
Category:University of Texas at Dallas alumni
Category:Delft University of Technology alumni
Category:Fnatic players
Category:CompLexity Gaming players


Electricity sector in Pakistan

Electricity in Pakistan () is generated, transmitted, distributed, and retail supplied by two vertically integrated public sector utilities: Water and Power Development Authority (WAPDA) for all of Pakistan (except Karachi), and the Karachi Electric (K-Electric) for the city of Karachi and its surrounding areas. There are around 42 independent power producers (IPPs) that contribute significantly in electricity generation in Pakistan.

History
Pakistan electricity sector is a developing market. For years, the matter of balancing the country's supply against the demand for electricity had remained a largely unresolved matter. The country faced significant challenges in revamping its network responsible for the supply of electricity. Electricity generators were seeking a parity in returns for both domestic and foreign investors indicating it to be one of the key issues in overseeing a surge in electricity generation when the country was facing growing shortages. Other problems included lack of efficiency, rising demands for energy, and political instability. Provincial and federal agencies, who are the largest consumers, often do not pay their bills. At one point electricity generation had shrunk by up to 50% due to an over-reliance on fossil fuels. The country was hit by its worst power crisis in 2007 when production fell by 6000 Megawatts and massive blackouts followed suit. Load Shedding and power blackouts had become severe in Pakistan before 2016.

Economic Survey 2017-18 unfolds that Pakistan's installed capacity to generate electricity has surged up to 29,573MW by February 2018 which stood at 22,812MW in June 2013, showing the growth of 30 percent.

Installed capacity
Pakistan's installed capacity to generate electricity has surged up to 33,836 MW by February 2019 which stood at 23,337 MW in 2014, showing the growth of 45 percent in five years.

Electricity Concerns
Although Pakistan has reduced blackouts and increased electricity production significantly, blackouts are still common, and the price of electricity has still increased. Recent tariff have contributed to this increase in prices.

Thermal

Natural Gas

Coal

Hydroelectricity
Pakistan produced 8250 MW of hydropower in 2018 and by 2040, when under construction hydropower projects are completed, this will increase to 29000 MW.

Nuclear

Wind Power

Solar Power

Electricity generation
Electricity – generation: 148.25 GWh (2019)
Electricity – generation by source (2019)
Furnace oil: 14% of total
Natural gas: 31% of total
Coal: 16% of total
Hydroelectric: 29% of total
Nuclear: 4% of total
Renewable (Solar & Wind) : 5% of total
 Others(Bagasse, Waste Heat Recovery etc.) : 1% of total

Electricity consumption
Electricity – consumption: 90.36 GWh (2015-2016)
Electricity – exports: 6.01% (2015-2016)
Electricity – imports: .49% (2015-2016)
Electricity Consumption per Capita  =  971 kWh/Capita (2015-2016)

Governance and sector reform
Recent reforms include the unbundling and corporatization of the Water and Power Development Authority (WAPDA) into 10 regional distribution companies, 4 government-owned thermal power
generation companies and a transmission company, the National Transmission and Despatch Company. The hydropower plants were retained by WAPDA as WAPDA Hydroelectric. All are
fully owned by the government. K-Electric Limited (formally known as Karachi Electric Supply Company), which is responsible for power generation and distribution in the Karachi area, is
listed on the stock exchanges and is privately owned. Privately owned independent power producers generated 53% of the country's power in FY2016.

Effects of natural and man-made disasters
During 2010 Pakistan floods and 2005 Kashmir earthquake power stations, power distribution and transmission and other energy infrastructures were damaged. During the floods and rainfalls the recently constructed Jinnah hydroelectric power plant was flooded in addition to severe damages to transmission and distribution network and installations while several power plants and refineries were threatened by rising waters and had to be shut down. Natural gas field output had to be reduced as the flood waters approached the wells. There has also been some concern by Pakistani nuclear activists over the effect of natural disasters on nuclear plants specially over the Chashma Nuclear Power Plant, since the plant lies over a geological fault.
Due to over reliance of Pakistan on dams for electricity generation, some environmental impacts of dams such as submergence of usable/ecological land and their negative impact on Pakistan's mangrove forests due to loss of river silt load, as well as increased risk of severe floods have become evident.

See also

 List of power stations in Pakistan
 List of electric supply companies in Pakistan
 Water and Power Development Authority
 Economy of Pakistan
 Private Power and Infrastructure Board
 Pakistan Electric Power Company
 Alternative Energy Development Board
 National Electric Power Regulatory Authority
 Karachi Electric Supply Company
 Pakistan national energy policy
 Rolling blackout

References

Further reading
 Robert M. Hathaway, editor, and Michael Kugelman, editor, Powering Pakistan, Oxford University Press, USA (15 January 2010), hardcover, 216 pages


Altamont, Pennsylvania

Altamont is a census-designated place (CDP) in Schuylkill County, Pennsylvania, USA. The population was 2,689 at the 2000 census.

Geography
Altamont is located at  (40.783382, -76.222798).

According to the United States Census Bureau, the CDP has a total area of , all of it land.

Demographics
As of the census of 2000, there were 2,689 people, 305 households, and 203 families living in the CDP. The population density was 2,857.1 people per square mile (1,104.5/km²). There were 329 housing units at an average density of 349.6/sq mi (135.1/km²). The racial makeup of the CDP was 53.63% White, 41.17% African American, 0.04% Native American, 0.63% Asian, 4.31% from other races, and 0.22% from two or more races. Hispanic or Latino of any race were 7.66% of the population.

There were 305 households out of which 20.3% had children under the age of 18 living with them, 51.1% were married couples living together, 9.5% had a female householder with no husband present, and 33.4% were non-families. 30.2% of all households were made up of individuals and 21.6% had someone living alone who was 65 years of age or older. The average household size was 2.31 and the average family size was 2.87.

In the CDP, the population was spread out with 4.4% under the age of 18, 18.0% from 18 to 24, 55.2% from 25 to 44, 14.9% from 45 to 64, and 7.5% who were 65 years of age or older. The median age was 34 years. For every 100 females, there were 668.3 males. For every 100 females age 18 and over, there were 771.5 males.

The median income for a household in the CDP was $23,603, and the median income for a family was $27,375. Males had a median income of $15,372 versus $16,875 for females. The per capita income for the CDP was $12,151. About 5.3% of families and 8.0% of the population were below the poverty line, including 5.0% of those under age 18 and 3.2% of those age 65 or over.

References

Category:Census-designated places in Schuylkill County, Pennsylvania
Category:Census-designated places in Pennsylvania


Młynowo, Greater Poland Voivodeship

Młynowo  is a settlement in the administrative district of Gmina Łobżenica, within Piła County, Greater Poland Voivodeship, in west-central Poland.

References

Category:Villages in Piła County


Mike Mineo

Mike Mineo is an American singer-songwriter and multi-instrumentalist born in Hollywood, Florida. His musical style encompasses avant-garde, pop, folk, soul, and jazz. He has recorded and self-released four albums on his own independent record label Nevernothing Records, LLC. In March 2016 Mike Mineo moved to Nashville, TN to further his music career.

Career
In 2010, Mike Mineo released his first album Eccentricity. The single "Eazy Livin" was well received by college radio and was licensed to iHome for their studio series home entertainment systems. The other single "Peaceful Daze" (also from "Eccentricity") was licensed to the popular E! Television show Khloé & Lamar in season 1 episode 7  "Jamie 9-1-1". In the summer of 2010 he was awarded "Best Male Vocalist" of 2010 by the local weekly paper Broward New Times. On August 17 through October 20 of 2010 he went on tour to support his debut release of "Eccentricity" and played dates throughout the U.S. & Canada. During this tour the press and media started to claim him as a modern-day Frank Zappa In 2011 Mike Mineo formed the group MINEO and released his next album "Beach Season" Their song "Brand New Feeling" was well received by college radio and was featured on Austin Texas's college radio station 93.3 KGSR. This song made the MINEO band become a featured top up and coming artist to look out for in 2011  Both albums were produced by Brent T. Williams a.k.a. Teasley. In late 2013 Mike Mineo released the album "Big Big Star". "Big Big Star" was produced and engineered by Mike Mineo himself at his home in Delray Beach, Florida. "Big Big Star" was mastered by Matthew de Nobrega at Timecode Mastering Studio in Cape Town, South Africa. The same engineer that is known for his work with Die Antwoord. In March 2016 Mike Mineo moved to Nashville, TN and released his 4th album "1".  Mike Mineo was announced as a headliner at the 2016 SunFest  In 2017, Mike Mineo was brought on to open for Steve Miller Band during their Southeast leg of their tour. Mineo performs with drummer Scotty Rollins and brother Johnny Mineo. Some of his musical influences include Stevie Wonder, Van Morrison, Tom Waits & Frank Zappa.

Discography

References

Category:American male singers
Category:Living people
Category:1986 births
Category:21st-century American singers
Category:21st-century male singers


Museo Ferruccio Lamborghini

Museo Ferruccio Lamborghini is an Italian museum in Argelato, a few kilometers from the center of Bologna, Emilia-Romagna, focused on the life and work of Ferruccio Lamborghini, the founder of the Lamborghini sports car marque.

It has recently been relocated from its first Ferrarese site (Dosso di S. Agostino) to a new site located in a former Lamborghini factory in Argelato.

In 1995, the first Ferruccio Lamborghini Museum was inaugurated next to the Lamborghini Calor plant, nestled in the Ferrara countryside birthplace of Ferruccio Lamborghini.
After 19 years and thousands of visitors from all over the world, his son, Antonio (Tonino) Lamborghini, with the entrepreneurial spirit and avant-garde character that distinguishes his every project, decided to bring the Museum closer to the city of Bologna and to give more emphasis to the history of his father, genius of mechanics and Cavaliere del Lavoro, dedicating him a new exhibition space.

It collects all the industrial productions of the Doctor of Engineering (Hon. Causa) Lamborghini, from the first Carioca tractor which started his company in 1947, to the  sports cars of the 1950s, 1960s, and 1970s.  Ferruccio Lamborghini's  personal collection in the museum includes the Miura SV,  the Fiat Barchetta Sport, modified to participate in the 1948 Mille Miglia competition, the  Countach, the Jarama models, the Urraco and the Espada.

See also
Museo Lamborghini

External links
 Official website

Category:Automobile museums in Italy
Category:Lamborghini
Category:Museums in Emilia-Romagna
Category:Buildings and structures in the Metropolitan City of Bologna


601st Quartermaster Company

The 601st Quartermaster Company is an Aerial Delivery Support Company of the United States Army based in Aviano, Italy. It is a subordinate unit of the 173rd Support Battalion (United States). The members are  primarily Parachute Riggers who are responsible for the packing, storage, maintenance and issuing of both personnel and heavy drop aerial delivery support.

Organization
The 601st Quartermaster Company serves to support the 173rd Infantry Brigade Combat Team (Airborne). The Company currently consists of over 100 soldiers in two Platoons and a Headquarters Section.

601st Quartermaster Company
Pack Platoon
Heavy Drop Platoon
Headquarters Section
Issue and Receiving Section
Maintenance Section

History
The 601st Quartermaster Aerial Supply Company was activated on 10 December 1951 at Fort Campbell, Kentucky and formed from personnel of the 11th Airborne Division. The first Unit Commander was Captain Edward G. Stanford. During this time, there were three types of Aerial Delivery companies; Aerial Supply, Parachute Maintenance, and Air Equipment Repair. The 601st Quartermaster Aerial Supply Company's mission was to train and execute heavy airdrop missions and conduct re-supply operations from airdrop platforms or containers, by lashing them to the inside of the aircraft and properly ejecting them over the drop zone. This type of unit was designed to provide continued air supply to troops cut off from ground re-supply. The 601st supported re-supply operations during the Korean War. With the war in Korea, "logistic by parachute" became an established part of supporting combat operations. The poor weather, lack of road and rail networks and the brutal terrain created huge obstacles to ground resupply missions. Korea marked the first large scale use of aerial resupply, heavy drop and the standardization of airdrop procedures and units. During this war the C-54, C-119 and the C-47 cargo planes were used for air drops supported by the 601st.

Upon the deactivation of the 11th Airborne Division in 1958, the 601st Quartermaster Aerial Supply Company ceased support operations until 6 October 2016, as it re-activates to support the 173rd Airborne Brigade Combat Team. The 601st Quartermaster Company was reactivated on October 6, 2016 at an activation ceremony held on Aviano Air Base.  The activation ceremony was held at Aviano Air Base and was officiated by then-Battalion Commander of the 173rd Brigade Support Battalion (Airborne). The Unit previously supported the 173rd Airborne Brigade Combat Team (Airborne) as the Aerial Delivery Support Platoon as part of HHC, 173rd Brigade Support Battalion (Airborne).

Support Operations
The 601st Quartermaster Company's history of logistical support operations dates back to aerial delivery support during the Korean War.

The 601st Quartermaster Company provides aerial delivery support as the Brigade is the U.S. Army's Contingency Response Force in Europe, providing rapid forces to the United States European, Africa and Central Commands areas of responsibilities. Forward-based in Italy and Germany, the Brigade routinely trains alongside NATO allies and partners to build interoperability and strengthen the Alliance.

The 601st Quartermaster Company supports airborne operations all across Europe in multiple capacities through personnel parachutes and equipment/ platform drops. The 601st Parachute Riggers have provided premier aerial delivery support throughout Europe while simultaneously making history as the first brigade to successfully airdrop a M777 howitzer from a Heavy Airlift Wing C-17 for the first time in Europe.

The 601st Gryphons support airborne operations throughout the European Theatre in various countries. Notably, the 601st Quartermaster Company supported airborne operations and provided aerial delivery support during Operation Atlantic Resolve in Latvia.

The 601st Quartermaster Company made international headlines when 3 vehicle platforms were airdropped during an airborne operation in April 2016. Numerous platforms were being dropped in support of Saber Junction 16 when 3 of the vehicle platforms fell to the ground in what has been concluded as tampered with and compromised equipment. After the conclusion of over a year long investigation, the soldier charged in connection with the spectacular destruction last year of three Humvees that slipped free from their parachutes during a drop and plummeted to earth was a Germany-based Soldier from the Brigade. The incident has been deemed not due to any actions from parachute riggers but due to compromised platforms and equipment from Sergeant John Skipper. The investigation also led to the reprimand of one the Soldier who recorded a video and is heard laughing in the video that went viral internationally following the incident on 11 April 2016.

References

External links
The Official Homepage of the 173rd Brigade Support Battalion (Airborne)
The Official Facebook Page
173rd Infantry Brigade Combat Team (Airborne) Official Website
173rd Airborne Brigade Association Website

Category:United States Army


Ahmad Ajab

Ahmad Ajab (; born 13 May 1984) is a Kuwaiti footballer. After starting playing for Al-Sahel he moved to Al-Qadisia in July 2007.

Career
After moving to his new club, he was quickly crowned as the top scorer in 2007 Kuwaiti Premier League and was called up for the national team where he scored a hat-trick on his debut against Lebanon, he came from the bench after 50 minutes gone and the scoreline was 2–0 to Lebanon it finished with his hat-trick 2-3. He is currently in some fierce competition to be the World top scorer and Asia's Best Player of the Year. He helped his team to reach the second round of the AFC champions league.

International goals
Scores and results list Kuwait's goal tally first.

External links

Category:1984 births
Category:Living people
Category:Kuwaiti footballers
Category:Kuwait international footballers
Category:Qadsia SC players
Category:2011 AFC Asian Cup players
Category:Al-Shabab FC (Riyadh) players
Category:Sportspeople from Kuwait City
Category:Saudi Professional League players

Category:Association football forwards


Skujene Parish

Skujene parish () is an administrative territorial entity of Amata Municipality, Latvia. It was an administrative unit of Cēsis District. The administrative center is Skujene.

Towns, villages and settlements of Skujene parish
 Ģērķēni
 Kosa
 Māļi
 Pērkoņi
 Sērmūkši
 Skujene
 Vecskujene

See also
 Sērmūkši Manor

External links

Category:Parishes of Latvia
Category:Amata Municipality


Boryspil-Aeroport railway station

Boryspil Airport railway station serves Terminal D at Boryspil International Airport. It is served by Kyiv Boryspil Express trains direct to central Kyiv.

Services
The station has services running directly to Kyiv and Darnytsia provided by Boryspil Express, normally running every hour.

The station was opened on 30 November 2018 upon the completion of the Kyiv Boryspil Express Rail Link linking Boryspil Airport with direct non-stop services to Kyiv. Boryspil Airport is a dead-end passenger station, terminus for 19 km - Boryspil Airport line (which is a branch from Darnytsia to Hrebinka).

Since 2018, the station has been served by Southwestern Railways, part of the Ukrainian Railways. Adjoins the terminal directly. Journey time one way is 30–40 minutes.

Ticket price is UAH 80 and can be purchased at self-service terminals. Passengers can also buy tickets on the trains using contactless cards.

See also
Ukrzaliznytsia

References

External links

Category:Southwestern Railways stations
Category:Railway stations in Kiev
Category:Railway stations opened in 2018
Category:Airport railway stations


Glycine transaminase

In enzymology, a glycine transaminase () is an enzyme that catalyzes the chemical reaction

glycine + 2-oxoglutarate  glyoxylate + L-glutamate

Thus, the two substrates of this enzyme are glycine and 2-oxoglutarate, whereas its two products are glyoxylate and L-glutamate.

This enzyme belongs to the family of transferases, specifically the transaminases, which transfer nitrogenous groups.  The systematic name of this enzyme class is glycine:2-oxoglutarate aminotransferase. Other names in common use include glutamic-glyoxylic transaminase, glycine aminotransferase, glyoxylate-glutamic transaminase, L-glutamate:glyoxylate aminotransferase, and glyoxylate-glutamate aminotransferase.  This enzyme participates in glycine, serine and threonine metabolism.  It employs one cofactor, pyridoxal phosphate.

References

Category:EC 2.6.1
Category:Pyridoxal phosphate enzymes
Category:Enzymes of unknown structure


Winter (Jon Foreman EP)

Winter is the second EP released by Jon Foreman, frontman of the San Diego rock band Switchfoot. The EP was released on Tuesday, January 15, 2008, as either a digital download or as a physical copy packaged with the Fall EP in a double-disc set.

Sound
Stylistically, this EP reflects a more experimental side to Foreman's songwriting. Whereas the Fall EP displayed a more straightforward approach musically, experimentation on Winter is much more evident. "White as Snow" toys with a slightly eastern influenced sound, while "In Love" carries a very oriental, and near-mantric feel—both new concepts in Foreman's music.  The feel of the album is indeed much more 'wintry', reflecting the dead of wintertime.

Commercial performance
The Fall & Winter CD combo debuted on the Billboard Top Heatseeker's chart at No. 24.

In popculture
"Behind Your Eyes" appeared in an episode of the TV Show, One Tree Hill

Track listing

References

Category:2008 EPs
Category:Jon Foreman albums


Multiseat

Multiseat may refer to:
 Multiseat constituency, in voting systems
 Multiseat configuration or "multiterminal", single computer which supports multiple independent users at the same time


Arizona Game and Fish Department

The Arizona Game and Fish Department is a state agency of Arizona, headquartered in Phoenix. The agency is tasked with conserving, enhancing, and restoring Arizona's diverse wildlife resources and habitats through aggressive protection and management programs. It also provides wildlife resources and watercraft and off-highway vehicle recreation.

Wildlife conservation
The Arizona Game and Fish Department has developed a "Comprehensive Wildlife Conservation Strategy" (CWCS)—a 10-year vision for managing Arizona’s fish, wildlife and natural habitats, input and partnerships with various agency cooperators, sportsman and recreational groups, conservation organizations, special interest groups, Native American tribes, county and municipal governments, and the general public.

Watchable wildlife
Arizona is home to more than 900 animal species and 50 million public acres of natural land. The Arizona Wildlife Viewing Program strives to manage wildlife while providing for the responsible recreational use of the resource. Much of the support for the program comes from the Heritage Fund, a fund started in 1990 by Arizona voters to further conservation efforts in the state. Funding comes from Arizona Lottery ticket sales.

Media
The Arizona Game and Fish Department produces Arizona Wildlife Views magazine and television show.

See also

 List of law enforcement agencies in Arizona
 Game Warden
 Ben Avery Shooting Facility
 List of State Fish and Wildlife Management Agencies in the U.S.

References

External links
 Arizona Game and Fish Department

Category:State agencies of Arizona
Category:State wildlife and natural resource agencies of the United States


Mistress Nell

Mistress Nell is a 1915 American silent historical adventure film starring Mary Pickford. It is yet another story about Nell Gwyn taken from a Broadway play Mistress Nell that was very successful for stage actress Henrietta Crosman from 1900 to 1902. This production was produced by Adolph Zukor's production company Famous Players Film Company and released through Paramount Pictures. The film is extant.

A surviving print is held by Museum of Modern Art.

Cast
Mary Pickford as Nell Gwyn
Owen Moore as King Charles II
Arthur Hoops as Duke of Buckingham
Ruby Hoffman as Louise, Duchess of Portsmouth
Amelia Rose as Orange Moll
Mr. Henry as Nobleman
Mr. Rouse as Nobleman
Mr. Bosch as Nobleman
Henry S. Koser as Nobleman
J. Albert Hall
Nathaniel Sack

unbilled
Hayward Mack (unknown role)

References

External links

Category:1915 films
Category:American films based on plays
Category:American silent feature films
Category:American films
Category:Films directed by James Kirkwood Sr.
Category:1910s historical adventure films
Category:American adventure films
Category:American black-and-white films
Category:Films set in London
Category:Films set in the 17th century
Category:American historical films
Category:Paramount Pictures films