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Finite strain theory

In continuum mechanics, the finite strain theory—also called large strain theory, or large deformation theory—deals with deformations in which strains and/or rotations are large enough to invalidate assumptions inherent in infinitesimal strain theory. In this case, the undeformed and deformed configurations of the continuum are significantly different, requiring a clear distinction between them. This is commonly the case with elastomers, plastically deforming materials and other fluids and biological soft tissue.

Deformation gradient tensor

The deformation gradient tensor $$\mathbf F(\mathbf X,t) = F_{jK} \mathbf e_j \otimes \mathbf I_K$$ is related to both the reference and current configuration, as seen by the unit vectors $$\mathbf e_j$$ and $$\mathbf I_K\,\!$$, therefore it is a two-point tensor. Two types of deformation gradient tensor may be defined.

Due to the assumption of continuity of $$\chi(\mathbf X,t)\,\!$$, $$\mathbf F$$ has the inverse $$\mathbf H = \mathbf F^{-1}\,\!$$, where $$\mathbf H$$ is the spatial deformation gradient tensor. Then, by the implicit function theorem, the Jacobian determinant $$J(\mathbf X,t)$$ must be nonsingular, i.e. $$J(\mathbf X,t) = \det \mathbf F(\mathbf X,t) \neq 0$$

The material deformation gradient tensor $$\mathbf F(\mathbf X,t) = F_{jK} \mathbf e_j\otimes\mathbf I_K$$ is a second-order tensor that represents the gradient of the mapping function or functional relation $$\chi(\mathbf X,t)\,\!$$, which describes the motion of a continuum. The material deformation gradient tensor characterizes the local deformation at a material point with position vector $$\mathbf X\,\!$$, i.e., deformation at neighbouring points, by transforming (linear transformation) a material line element emanating from that point from the reference configuration to the current or deformed configuration, assuming continuity in the mapping function $$\chi(\mathbf X,t)\,\!$$, i.e. differentiable function of $$ \mathbf {X} $$ and time $$t\,\!$$, which implies that cracks and voids do not open or close during the deformation. Thus we have, $$ \begin{align} d\mathbf{x} &= \frac {\partial \mathbf{x}} {\partial \mathbf {X}}\,d\mathbf{X} \qquad &\text{or}& \qquad dx_j =\frac{\partial x_j}{\partial X_K}\,dX_K \\ &= \nabla \chi(\mathbf X,t) \,d\mathbf{X} \qquad &\text{or}& \qquad dx_j =F_{jK}\,dX_K \,. \\   & = \mathbf F(\mathbf X,t) \,d\mathbf{X} \end{align}$$

Relative displacement vector
Consider a particle or material point $$P$$ with position vector $$\mathbf X = X_I \mathbf I_I$$ in the undeformed configuration (Figure 2). After a displacement of the body, the new position of the particle indicated by $$p$$ in the new configuration is given by the vector position $$\mathbf{x} = x_i \mathbf e_i\,\!$$. The coordinate systems for the undeformed and deformed configuration can be superimposed for convenience.

Consider now a material point $$Q $$ neighboring $$P\,\!$$, with position vector $$\mathbf{X}+ \Delta \mathbf{X} = (X_I+\Delta X_I) \mathbf I_I\,\!$$. In the deformed configuration this particle has a new position $$q$$ given by the position vector $$\mathbf{x}+ \Delta \mathbf{x}\,\!$$. Assuming that the line segments $$\Delta X$$ and $$\Delta \mathbf x$$ joining the particles $$P$$ and $$Q$$ in both the undeformed and deformed configuration, respectively, to be very small, then we can express them as $$d\mathbf X$$ and $$d\mathbf x\,\!$$. Thus from Figure 2 we have $$\begin{align} \mathbf{x}+ d\mathbf{x}&= \mathbf{X}+d\mathbf{X}+\mathbf{u}(\mathbf{X}+d\mathbf{X}) \\ d\mathbf{x} &= \mathbf{X}-\mathbf{x}+d\mathbf{X}+ \mathbf{u}(\mathbf{X}+d\mathbf{X}) \\ &= d\mathbf{X}+\mathbf{u}(\mathbf{X}+d\mathbf{X})- \mathbf{u}(\mathbf{X}) \\ &= d\mathbf{X}+d\mathbf{u} \\ \end{align}$$

where $$\mathbf {du}$$ is the relative displacement vector, which represents the relative displacement of $$Q$$ with respect to $$P$$ in the deformed configuration.

Taylor approximation
For an infinitesimal element $$d\mathbf X\,\!$$, and assuming continuity on the displacement field, it is possible to use a Taylor series expansion around point $$P\,\!$$, neglecting higher-order terms, to approximate the components of the relative displacement vector for the neighboring particle $$Q$$ as $$\begin{align} \mathbf{u}(\mathbf{X}+d\mathbf{X})&=\mathbf{u}(\mathbf{X})+d\mathbf{u} \quad & \text{or} & \quad u_i^* = u_i+du_i \\ &\approx \mathbf{u}(\mathbf{X})+\nabla_{\mathbf X}\mathbf u\cdot d\mathbf X \quad & \text{or} & \quad u_i^* \approx u_i + \frac{\partial u_i}{\partial X_J}dX_J \,. \end{align}$$ Thus, the previous equation $$d\mathbf x = d\mathbf{X} + d\mathbf{u}$$ can be written as $$\begin{align} d\mathbf x&=d\mathbf X+d\mathbf u \\ &=d\mathbf X+\nabla_{\mathbf X}\mathbf u\cdot d\mathbf X\\ &=\left(\mathbf I + \nabla_{\mathbf X}\mathbf u\right)d\mathbf X\\ &=\mathbf F d\mathbf X \end{align}$$

Time-derivative of the deformation gradient
Calculations that involve the time-dependent deformation of a body often require a time derivative of the deformation gradient to be calculated. A geometrically consistent definition of such a derivative requires an excursion into differential geometry but we avoid those issues in this article.

The time derivative of $$\mathbf{F}$$ is $$ \dot{\mathbf{F}} = \frac{\partial \mathbf{F}}{\partial t} = \frac{\partial}{\partial t} \left[\frac{\partial \mathbf{x}(\mathbf{X}, t)}{\partial \mathbf{X}}\right] = \frac{\partial}{\partial \mathbf{X}}\left[\frac{\partial \mathbf{x}(\mathbf{X}, t)}{\partial t}\right] = \frac{\partial}{\partial \mathbf{X}}\left[\mathbf{V}(\mathbf{X}, t)\right] $$ where $$\mathbf{V}$$ is the (material) velocity. The derivative on the right hand side represents a material velocity gradient. It is common to convert that into a spatial gradient by applying the chain rule for derivatives, i.e., $$ \dot{\mathbf{F}} = \frac{\partial}{\partial \mathbf{X}}\left[\mathbf{V}(\mathbf{X}, t)\right] = \frac{\partial}{\partial \mathbf{X}}\left[\mathbf{v}(\mathbf{x}(\mathbf{X}, t),t)\right] = \left.\frac{\partial}{\partial \mathbf{x}}\left[\mathbf{v}(\mathbf{x},t)\right]\right|_{\mathbf{x} = \mathbf{x}(\mathbf{X}, t)} \cdot \frac{\partial \mathbf{x}(\mathbf{X}, t)}{\partial \mathbf{X}} = \boldsymbol{l}\cdot\mathbf{F} $$ where $$\boldsymbol{l} = (\nabla_{\mathbf{x}} \mathbf{v})^T$$ is the spatial velocity gradient and where $$\mathbf{v}(\mathbf{x},t) = \mathbf{V}(\mathbf{X},t)$$ is the spatial (Eulerian) velocity at $$\mathbf{x} = \mathbf{x}(\mathbf{X}, t)$$. If the spatial velocity gradient is constant in time, the above equation can be solved exactly to give $$ \mathbf{F} = e^{\boldsymbol{l}\, t} $$ assuming $$\mathbf{F} = \mathbf{1}$$ at $$t = 0$$. There are several methods of computing the exponential above.

Related quantities often used in continuum mechanics are the rate of deformation tensor and the spin tensor defined, respectively, as: $$ \boldsymbol{d} = \tfrac{1}{2} \left(\boldsymbol{l} + \boldsymbol{l}^T\right) \,, \boldsymbol{w} = \tfrac{1}{2} \left(\boldsymbol{l} - \boldsymbol{l}^T\right) \,. $$ The rate of deformation tensor gives the rate of stretching of line elements while the spin tensor indicates the rate of rotation or vorticity of the motion.

The material time derivative of the inverse of the deformation gradient (keeping the reference configuration fixed) is often required in analyses that involve finite strains. This derivative is $$ \frac{\partial}{\partial t} \left(\mathbf{F}^{-1}\right) = - \mathbf{F}^{-1} \cdot \dot{\mathbf{F}} \cdot \mathbf{F}^{-1} \,. $$ The above relation can be verified by taking the material time derivative of $$\mathbf{F}^{-1} \cdot d\mathbf{x} = d\mathbf{X}$$ and noting that $$\dot{\mathbf{X}} = 0$$.

Polar decomposition of the deformation gradient tensor

The deformation gradient $$\mathbf{F}\,\!$$, like any invertible second-order tensor, can be decomposed, using the polar decomposition theorem, into a product of two second-order tensors (Truesdell and Noll, 1965): an orthogonal tensor and a positive definite symmetric tensor, i.e., $$ \mathbf{F} = \mathbf{R} \mathbf{U} = \mathbf{V} \mathbf{R}$$ where the tensor $$\mathbf{R}$$ is a proper orthogonal tensor, i.e., $$\mathbf R^{-1} = \mathbf R^T$$ and $$\det \mathbf R = +1\,\!$$, representing a rotation; the tensor $$\mathbf{U}$$ is the right stretch tensor; and $$\mathbf{V}$$ the left stretch tensor. The terms right and left means that they are to the right and left of the rotation tensor $$\mathbf{R}\,\!$$, respectively. $$\mathbf{U}$$ and $$\mathbf{V}$$ are both positive definite, i.e. $$\mathbf x \cdot \mathbf U \cdot \mathbf x > 0 $$ and $$\mathbf x\cdot\mathbf V \cdot \mathbf x > 0 $$ for all non-zero $$\mathbf x \in \R^3$$, and symmetric tensors, i.e. $$\mathbf U = \mathbf U^T$$ and $$\mathbf V = \mathbf V^T\,\!$$, of second order.

This decomposition implies that the deformation of a line element $$d\mathbf X$$ in the undeformed configuration onto $$d\mathbf x$$ in the deformed configuration, i.e., $$d\mathbf x = \mathbf F \,d\mathbf X\,\!$$, may be obtained either by first stretching the element by $$\mathbf U\,\!$$, i.e. $$d\mathbf x' = \mathbf U \,d\mathbf X\,\!$$, followed by a rotation $$\mathbf R\,\!$$, i.e., $$d\mathbf x' = \mathbf R \,d\mathbf x\,\!$$; or equivalently, by applying a rigid rotation $$\mathbf R$$ first, i.e., $$d\mathbf x' = \mathbf R \, d\mathbf X\,\!$$, followed later by a stretching $$\mathbf V\,\!$$, i.e., $$d\mathbf x' = \mathbf V \, d\mathbf x$$ (See Figure 3).

Due to the orthogonality of $$\mathbf R$$ $$\mathbf V = \mathbf R \cdot \mathbf U \cdot \mathbf R^T$$ so that $$\mathbf U$$ and $$\mathbf V$$ have the same eigenvalues or principal stretches, but different eigenvectors or principal directions $$\mathbf{N}_i$$ and $$\mathbf{n}_i\,\!$$, respectively. The principal directions are related by $$\mathbf{n}_i = \mathbf{R} \mathbf{N}_i. $$

This polar decomposition, which is unique as $$\mathbf F$$ is invertible with a positive determinant, is a corollary of the singular-value decomposition.

Transformation of a surface and volume element
To transform quantities that are defined with respect to areas in a deformed configuration to those relative to areas in a reference configuration, and vice versa, we use Nanson's relation, expressed as $$ da~\mathbf{n} = J~dA ~\mathbf{F}^{-T} \cdot \mathbf{N} $$ where $$da$$ is an area of a region in the deformed configuration, $$dA$$ is the same area in the reference configuration, and $$\mathbf{n}$$ is the outward normal to the area element in the current configuration while $$\mathbf{N}$$ is the outward normal in the reference configuration, $$\mathbf{F}$$ is the deformation gradient, and $$J = \det\mathbf{F}\,\!$$.

The corresponding formula for the transformation of the volume element is $$ dv = J~dV $$

Fundamental strain tensors
A strain tensor is defined by the IUPAC as: "'A symmetric tensor that results when a deformation gradient tensor is factorized into a rotation tensor followed or preceded by a symmetric tensor'."

Since a pure rotation should not induce any strains in a deformable body, it is often convenient to use rotation-independent measures of deformation in continuum mechanics. As a rotation followed by its inverse rotation leads to no change ($$\mathbf{R}\mathbf{R}^T=\mathbf{R}^T\mathbf{R}=\mathbf{I}\,\!$$) we can exclude the rotation by multiplying the deformation gradient tensor $$\mathbf{F}$$ by its transpose.

Several rotation-independent deformation gradient tensors (or "deformation tensors", for short) are used in mechanics. In solid mechanics, the most popular of these are the right and left Cauchy–Green deformation tensors.

Cauchy strain tensor (right Cauchy–Green deformation tensor)
In 1839, George Green introduced a deformation tensor known as the right Cauchy–Green deformation tensor or Green's deformation tensor (the IUPAC recommends that this tensor be called the Cauchy strain tensor), defined as:

$$\mathbf C=\mathbf F^T\mathbf F=\mathbf U^2 \qquad \text{or} \qquad C_{IJ}=F_{kI}~F_{kJ} = \frac {\partial x_k} {\partial X_I} \frac {\partial x_k} {\partial X_J}.$$

Physically, the Cauchy–Green tensor gives us the square of local change in distances due to deformation, i.e. $$d\mathbf x^2=d\mathbf X\cdot\mathbf C \cdot d\mathbf X$$

Invariants of $$\mathbf{C}$$ are often used in the expressions for strain energy density functions. The most commonly used invariants are $$ \begin{align} I_1^C & := \text{tr}(\mathbf{C}) = C_{II} = \lambda_1^2 + \lambda_2^2 + \lambda_3^2 \\ I_2^C & := \tfrac{1}{2}\left[(\text{tr}~\mathbf{C})^2 - \text{tr}(\mathbf{C}^2) \right] = \tfrac{1}{2}\left[(C_{JJ})^2 - C_{IK}C_{KI}\right] = \lambda_1^2\lambda_2^2 + \lambda_2^2\lambda_3^2 + \lambda_3^2\lambda_1^2 \\ I_3^C & := \det(\mathbf{C}) = J^2 = \lambda_1^2\lambda_2^2\lambda_3^2. \end{align} $$ where $$J:=\det\mathbf{F}$$ is the determinant of the deformation gradient $$\mathbf{F}$$ and $$\lambda_i$$ are stretch ratios for the unit fibers that are initially oriented along the eigenvector directions of the right (reference) stretch tensor (these are not generally aligned with the three axis of the coordinate systems).

Finger strain tensor
The IUPAC recommends that the inverse of the right Cauchy–Green deformation tensor (called the Cauchy strain tensor in that document), i. e., $$\mathbf C^{-1}$$, be called the Finger strain tensor. However, that nomenclature is not universally accepted in applied mechanics.

$$\mathbf{f}=\mathbf C^{-1}=\mathbf F^{-1}\mathbf F^{-T} \qquad \text{or} \qquad f_{IJ}=\frac {\partial X_I} {\partial x_k} \frac {\partial X_J} {\partial x_k}$$

Green strain tensor (left Cauchy–Green deformation tensor)
Reversing the order of multiplication in the formula for the right Green–Cauchy deformation tensor leads to the left Cauchy–Green deformation tensor which is defined as: $$\mathbf B = \mathbf F\mathbf F^T = \mathbf V^2 \qquad \text{or} \qquad B_{ij} = \frac {\partial x_i} {\partial X_K} \frac {\partial x_j} {\partial X_K}$$

The left Cauchy–Green deformation tensor is often called the Finger deformation tensor, named after Josef Finger (1894).

The IUPAC recommends that this tensor be called the Green strain tensor.

Invariants of $$\mathbf{B}$$ are also used in the expressions for strain energy density functions. The conventional invariants are defined as $$ \begin{align} I_1 & := \text{tr}(\mathbf{B}) = B_{ii} = \lambda_1^2 + \lambda_2^2 + \lambda_3^2\\ I_2 & := \tfrac{1}{2}\left[(\text{tr}~\mathbf{B})^2 - \text{tr}(\mathbf{B}^2)\right] = \tfrac{1}{2}\left(B_{ii}^2 - B_{jk}B_{kj}\right) = \lambda_1^2\lambda_2^2 + \lambda_2^2\lambda_3^2 + \lambda_3^2\lambda_1^2 \\ I_3 & := \det\mathbf{B} = J^2 = \lambda_1^2\lambda_2^2\lambda_3^2 \end{align} $$ where $$J:=\det\mathbf{F}$$ is the determinant of the deformation gradient.

For compressible materials, a slightly different set of invariants is used: $$ (\bar{I}_1 := J^{-2/3} I_1 ~; \bar{I}_2 := J^{-4/3} I_2 ~; J\neq 1) ~. $$

Piola strain tensor (Cauchy deformation tensor)
Earlier in 1828, Augustin-Louis Cauchy introduced a deformation tensor defined as the inverse of the left Cauchy–Green deformation tensor, $$\mathbf B^{-1}\,\!$$. This tensor has also been called the Piola strain tensor by the IUPAC and the Finger tensor in the rheology and fluid dynamics literature.

$$\mathbf{c}=\mathbf B^{-1}=\mathbf F^{-T}\mathbf F^{-1} \qquad \text{or} \qquad c_{ij}=\frac {\partial X_K} {\partial x_i} \frac {\partial X_K} {\partial x_j}$$

Spectral representation
If there are three distinct principal stretches $$\lambda_i \,\!$$, the spectral decompositions of $$\mathbf{C}$$ and $$\mathbf{B}$$ is given by

$$ \mathbf{C} = \sum_{i=1}^3 \lambda_i^2 \mathbf{N}_i \otimes \mathbf{N}_i \qquad \text{and} \qquad \mathbf{B} = \sum_{i=1}^3 \lambda_i^2 \mathbf{n}_i \otimes \mathbf{n}_i$$

Furthermore,

$$ \mathbf U = \sum_{i=1}^3 \lambda_i \mathbf N_i \otimes \mathbf N_i ~; \mathbf V = \sum_{i=1}^3 \lambda_i \mathbf n_i \otimes \mathbf n_i $$ $$ \mathbf R = \sum_{i=1}^3 \mathbf n_i \otimes \mathbf N_i ~; \mathbf F = \sum_{i=1}^3 \lambda_i \mathbf n_i \otimes \mathbf N_i $$

Observe that $$ \mathbf{V} = \mathbf{R}~\mathbf{U}~\mathbf{R}^T = \sum_{i=1}^3 \lambda_i~\mathbf{R}~(\mathbf{N}_i\otimes\mathbf{N}_i)~\mathbf{R}^T = \sum_{i=1}^3 \lambda_i~(\mathbf{R}~\mathbf{N}_i)\otimes(\mathbf{R}~\mathbf{N}_i) $$ Therefore, the uniqueness of the spectral decomposition also implies that $$ \mathbf{n}_i = \mathbf{R}~\mathbf{N}_i \,\!$$. The left stretch ($$\mathbf{V}\,\!$$) is also called the spatial stretch tensor while the right stretch ($$\mathbf{U}\,\!$$) is called the material stretch tensor.

The effect of $$\mathbf{F}$$ acting on $$\mathbf{N}_i$$ is to stretch the vector by $$\lambda_i$$ and to rotate it to the new orientation $$\mathbf{n}_i\,\!$$, i.e., $$ \mathbf{F}~\mathbf{N}_i = \lambda_i~(\mathbf{R}~\mathbf{N}_i) = \lambda_i~\mathbf{n}_i $$ In a similar vein, $$ \mathbf{F}^{-T}~\mathbf{N}_i = \cfrac{1}{\lambda_i}~\mathbf{n}_i ~; \mathbf{F}^T~\mathbf{n}_i = \lambda_i~\mathbf{N}_i ~; \mathbf{F}^{-1}~\mathbf{n}_i = \cfrac{1}{\lambda_i}~\mathbf{N}_i ~. $$

Examples

 * Uniaxial extension of an incompressible material
 * This is the case where a specimen is stretched in 1-direction with a stretch ratio of $$\mathbf{\alpha=\alpha_1}\,\!$$. If the volume remains constant, the contraction in the other two directions is such that $$\mathbf{\alpha_1 \alpha_2 \alpha_3 =1}$$ or $$\mathbf{\alpha_2=\alpha_3=\alpha^{-0.5}}\,\!$$.  Then: $$\mathbf{F}=\begin{bmatrix}

\alpha & 0 & 0 \\ 0 & \alpha^{-0.5} & 0 \\ 0 & 0 & \alpha^{-0.5} \end{bmatrix}$$ $$\mathbf{B} = \mathbf{C} = \begin{bmatrix} \alpha^2 & 0 & 0 \\ 0 & \alpha^{-1} & 0 \\ 0 & 0 & \alpha^{-1} \end{bmatrix}$$
 * Simple shear
 * $$\mathbf{F}=\begin{bmatrix}

1 & \gamma & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$$ $$\mathbf{B} = \begin{bmatrix} 1+\gamma^2 & \gamma & 0 \\ \gamma & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$$ $$\mathbf{C} = \begin{bmatrix} 1 & \gamma & 0 \\ \gamma & 1+\gamma^2 & 0 \\ 0 & 0 & 1 \end{bmatrix}$$
 * Rigid body rotation
 * $$\mathbf{F} = \begin{bmatrix}

\cos \theta & \sin \theta & 0 \\ - \sin \theta & \cos \theta & 0 \\ 0 & 0 & 1 \end{bmatrix}$$ $$\mathbf{B} = \mathbf{C} = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} = \mathbf{1}$$

Derivatives of stretch
Derivatives of the stretch with respect to the right Cauchy–Green deformation tensor are used to derive the stress-strain relations of many solids, particularly hyperelastic materials. These derivatives are $$ \cfrac{\partial\lambda_i}{\partial\mathbf{C}} = \cfrac{1}{2\lambda_i}~\mathbf{N}_i\otimes\mathbf{N}_i = \cfrac{1}{2\lambda_i}~\mathbf{R}^T~(\mathbf{n}_i\otimes\mathbf{n}_i)~\mathbf{R} ~; i=1,2,3 $$ and follow from the observations that $$  \mathbf{C}:(\mathbf{N}_i\otimes\mathbf{N}_i) = \lambda_i^2 ~;~\cfrac{\partial\mathbf{C}}{\partial\mathbf{C}} = \mathsf{I}^{(s)} ~;~ \mathsf{I}^{(s)}:(\mathbf{N}_i\otimes\mathbf{N}_i)=\mathbf{N}_i\otimes\mathbf{N}_i. $$

Physical interpretation of deformation tensors
Let $$\mathbf{X} = X^i~\boldsymbol{E}_i$$ be a Cartesian coordinate system defined on the undeformed body and let $$\mathbf{x} = x^i~\boldsymbol{E}_i$$ be another system defined on the deformed body. Let a curve $$\mathbf{X}(s)$$ in the undeformed body be parametrized using $$s \in [0,1]$$. Its image in the deformed body is $$\mathbf{x}(\mathbf{X}(s))$$.

The undeformed length of the curve is given by $$ l_X = \int_0^1 \left| \cfrac{d \mathbf{X}}{d s} \right|~ds = \int_0^1 \sqrt{ \cfrac{d \mathbf{X}}{d s}\cdot\cfrac{d \mathbf{X}}{d s}}~ds = \int_0^1 \sqrt{ \cfrac{d \mathbf{X}}{d s}\cdot\boldsymbol{I} \cdot\cfrac{d \mathbf{X}}{d s} }~ds $$ After deformation, the length becomes $$ \begin{align} l_x & = \int_0^1 \left| \cfrac{d \mathbf{x}}{d s} \right|~ds = \int_0^1 \sqrt{\cfrac{d \mathbf{x}}{d s}\cdot\cfrac{d \mathbf{x}}{d s}}~ds = \int_0^1 \sqrt{ \left(\cfrac{d \mathbf{x}}{d \mathbf{X}}\cdot\cfrac{d \mathbf{X}}{d s}\right) \cdot \left(\cfrac{d \mathbf{x}}{d \mathbf{X}}\cdot\cfrac{d \mathbf{X}}{d s}\right)}~ds \\     & = \int_0^1 \sqrt{\cfrac{d \mathbf{X}}{d s}\cdot\left[ \left(\cfrac{d \mathbf{x}}{d \mathbf{X}}\right)^T\cdot \cfrac{d \mathbf{x}}{d \mathbf{X}}\right] \cdot\cfrac{d \mathbf{X}}{d s} }~ds \end{align} $$ Note that the right Cauchy–Green deformation tensor is defined as $$ \boldsymbol{C} := \boldsymbol{F}^T\cdot\boldsymbol{F} = \left(\cfrac{d \mathbf{x}}{d \mathbf{X}}\right)^T\cdot \cfrac{d \mathbf{x}}{d \mathbf{X}} $$ Hence, $$  l_x = \int_0^1 \sqrt{ \cfrac{d \mathbf{X}}{d s}\cdot\boldsymbol{C} \cdot\cfrac{d \mathbf{X}}{d s} }~ds $$ which indicates that changes in length are characterized by $$\boldsymbol{C}$$.

Finite strain tensors
The concept of strain is used to evaluate how much a given displacement differs locally from a rigid body displacement. One of such strains for large deformations is the Lagrangian finite strain tensor, also called the Green-Lagrangian strain tensor or Green–St-Venant strain tensor, defined as

$$\mathbf E=\frac{1}{2}(\mathbf C - \mathbf I)\qquad \text{or} \qquad E_{KL}=\frac{1}{2}\left( \frac{\partial x_j}{\partial X_K}\frac{\partial x_j}{\partial X_L}-\delta_{KL}\right)$$

or as a function of the displacement gradient tensor $$\mathbf E =\frac{1}{2}\left[ (\nabla_{\mathbf X}\mathbf u)^T + \nabla_{\mathbf X}\mathbf u + (\nabla_{\mathbf X}\mathbf u)^T \cdot\nabla_{\mathbf X}\mathbf u\right]$$ or $$E_{KL}=\frac{1}{2}\left(\frac{\partial u_K}{\partial X_L}+\frac{\partial u_L}{\partial X_K}+\frac{\partial u_M}{\partial X_K}\frac{\partial u_M}{\partial X_L}\right)$$

The Green-Lagrangian strain tensor is a measure of how much $$\mathbf C$$ differs from $$\mathbf I\,\!$$.

The Eulerian finite strain tensor, or Eulerian-Almansi finite strain tensor, referenced to the deformed configuration (i.e. Eulerian description) is defined as

$$\mathbf e=\frac{1}{2}(\mathbf I - \mathbf c)=\frac{1}{2}(\mathbf I - \mathbf B ^{-1}) \qquad \text{or} \qquad e_{rs} = \frac{1}{2} \left(\delta_{rs} - \frac{\partial X_M}{\partial x_r} \frac{\partial X_M}{\partial x_s}\right)$$

or as a function of the displacement gradients we have $$e_{ij} = \frac{1}{2} \left(\frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i} - \frac{\partial u_k}{\partial x_i} \frac{\partial u_k}{\partial x_j}\right)$$

Seth–Hill family of generalized strain tensors
B. R. Seth from the Indian Institute of Technology Kharagpur was the first to show that the Green and Almansi strain tensors are special cases of a more general strain measure. The idea was further expanded upon by Rodney Hill in 1968. The Seth–Hill family of strain measures (also called Doyle-Ericksen tensors) can be expressed as

$$\mathbf E_{(m)}=\frac{1}{2m}(\mathbf U^{2m}- \mathbf I) = \frac{1}{2m}\left[\mathbf{C}^{m} - \mathbf{I}\right]$$

For different values of $$m$$ we have: The second-order approximation of these tensors is $$ \mathbf{E}_{(m)} = \boldsymbol{\varepsilon} + {\tfrac 1 2}(\nabla\mathbf{u})^T\cdot\nabla\mathbf{u} - (1 - m) \boldsymbol{\varepsilon}^T\cdot\boldsymbol{\varepsilon} $$ where $$\boldsymbol{\varepsilon}$$ is the infinitesimal strain tensor.
 * Green-Lagrangian strain tensor $$\mathbf E_{(1)} = \frac{1}{2} (\mathbf U^{2}- \mathbf I) = \frac{1}{2} (\mathbf{C}-\mathbf{I})$$
 * Biot strain tensor $$ \mathbf E_{(1/2)} = (\mathbf U - \mathbf I) = \mathbf{C}^{1/2}-\mathbf{I}$$
 * Logarithmic strain, Natural strain, True strain, or Hencky strain $$\mathbf E_{(0)} = \ln \mathbf U = \frac{1}{2}\,\ln\mathbf{C}$$
 * Almansi strain $$\mathbf{E}_{(-1)} = \frac{1}{2}\left[\mathbf{I}-\mathbf{U}^{-2}\right]$$

Many other different definitions of tensors $$\mathbf{E}$$ are admissible, provided that they all satisfy the conditions that:
 * $$\mathbf{E}$$ vanishes for all rigid-body motions
 * the dependence of $$\mathbf{E}$$ on the displacement gradient tensor $$\nabla\mathbf{u}$$ is continuous, continuously differentiable and monotonic
 * it is also desired that $$\mathbf{E}$$ reduces to the infinitesimal strain tensor $$\boldsymbol{\varepsilon}$$ as the norm $$|\nabla\mathbf{u}| \to 0$$

An example is the set of tensors $$ \mathbf{E}^{(n)} = \left({\mathbf U}^n - {\mathbf U}^{-n}\right)/2n $$ which do not belong to the Seth–Hill class, but have the same 2nd-order approximation as the Seth–Hill measures at $$m=0$$ for any value of $$n$$.

Physical interpretation of the finite strain tensor
The diagonal components $$E_{KL}$$ of the Lagrangian finite strain tensor are related to the normal strain, e.g.

$$E_{11}=e_{(\mathbf I_1)}+\frac{1}{2} e_{(\mathbf I_1)}^2$$

where $$e_{(\mathbf I_1)}$$ is the normal strain or engineering strain in the direction $$\mathbf I_1\,\!$$.

The off-diagonal components $$E_{KL}$$ of the Lagrangian finite strain tensor are related to shear strain, e.g.

$$E_{12}=\frac{1}{2}\sqrt{2E_{11}+1}\sqrt{2E_{22}+1}\sin\phi_{12}$$

where $$\phi_{12}$$ is the change in the angle between two line elements that were originally perpendicular with directions $$\mathbf I_1$$ and $$\mathbf I_2\,\!$$, respectively.

Under certain circumstances, i.e. small displacements and small displacement rates, the components of the Lagrangian finite strain tensor may be approximated by the components of the infinitesimal strain tensor

Compatibility conditions
The problem of compatibility in continuum mechanics involves the determination of allowable single-valued continuous fields on bodies. These allowable conditions leave the body without unphysical gaps or overlaps after a deformation. Most such conditions apply to simply-connected bodies. Additional conditions are required for the internal boundaries of multiply connected bodies.

Compatibility of the deformation gradient
The necessary and sufficient conditions for the existence of a compatible $$\boldsymbol{F}$$ field over a simply connected body are $$ \boldsymbol{\nabla}\times\boldsymbol{F} = \boldsymbol{0} $$

Compatibility of the right Cauchy–Green deformation tensor
The necessary and sufficient conditions for the existence of a compatible $$\boldsymbol{C}$$ field over a simply connected body are $$ R^\gamma_{\alpha\beta\rho} := \frac{\partial }{\partial X^\rho}[\,_{(X)}\Gamma^\gamma_{\alpha\beta}] - \frac{\partial }{\partial X^\beta}[\,_{(X)}\Gamma^\gamma_{\alpha\rho}] + \,_{(X)}\Gamma^\gamma_{\mu\rho}\,_{(X)}\Gamma^\mu_{\alpha\beta} - \,_{(X)}\Gamma^\gamma_{\mu\beta}\,_{(X)}\Gamma^\mu_{\alpha\rho} = 0 $$ We can show these are the mixed components of the Riemann–Christoffel curvature tensor. Therefore, the necessary conditions for $$\boldsymbol{C}$$-compatibility are that the Riemann–Christoffel curvature of the deformation is zero.

Compatibility of the left Cauchy–Green deformation tensor
General sufficiency conditions for the left Cauchy–Green deformation tensor in three-dimensions were derived by Amit Acharya. Compatibility conditions for two-dimensional $$\boldsymbol{B}$$ fields were found by Janet Blume.

title: Finite strain theory


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Los Angeles High School is the oldest public high school in the Southern California Region and in the Los Angeles Unified School District. Its colors are royal blue and white and the teams are called the Romans.

Los Angeles High School is a public secondary high school, enrolling an estimated 2,000 students in grades 9–12. After operating on a year-round basis consisting of three tracks for ten years, it was restored to a traditional calendar in 2010. Los Angeles High School receives accreditation approval from the Western Association of Schools and Colleges (WASC). Concurrent enrollment programs, provided in large by the Los Angeles Unified School District and the Los Angeles Community College District, are offered with West Los Angeles College, Los Angeles Trade–Technical College, Los Angeles City College, or Santa Monica College.

Los Angeles High School is a large, urban, inner-city school located in the Mid-Wilshire District of Los Angeles. The attendance boundary consists of a contrasting spectrum of economic diversity ranging from affluent Hancock Park and Lafayette Square to the low-income, densely populated immigrant community of Koreatown. Within the school is a College Incentive Magnet Program. Forty-four percent of the student population is identified as LEP, or Limited English Proficient. Currently, 66% of the students are identified as eligible to receive supplemental instructional services and materials through the Federal Title I Program.

The magnet high school has a university preparatory secondary high school program and a "school within a school." First established as a part of student integration services in the 1970s, the Los Angeles High School Math/Science/Technology magnet prepares students with an intensive, rigorous course load in order to better prepare them for university entrance. There are 317 students enrolled in the magnet program, grades 9-12.

Typically, the senior class has approximately 50% of seniors entering into four-year universities and schools. The magnet senior class typically has 90% of its senior class entering into four-year colleges and universities.

1873, Poundcake Hill
Early buildings commissioned to house the Los Angeles High School were among the architectural jewels of the city, and were strategically placed at the summit of a hill, the easier to be pointed to with pride. One of the school's long standing mottos is "Always a hill, always a tower, always a timepiece."

Construction on Los Angeles' first public high school, (the private Loyola High School is older) began on July 19, 1872, at the former site of Central School on what was then known as Poundcake Hill, at the southeast corner of Fort Street (later Broadway), which the front of the school faced, and Temple Street, with the back of the school to New High Street (later Spring Street). The approximate coordinates are 34.05568°N, -118.24347°W. As it was on the hill, a few hundred feet from the streets below, steep wooden stairways led up to the schoolyard.

The two-story wooden structure was so big and grand, the finest school south of San Francisco at that time, with classic lines and a tower with a clock in it, that people traveled from miles around to see it. The teachers liked the wide corridors, walnut banisters, generous windows and the transoms over the doors.

The schoolhouse was completed at a cost of $20,000 in 1873. Nearby, in succession, was the Court House, the City Hall, the Jones-Lindley Market and the Post Office. The first principal was Rev. Dr. William T. Lucky (1821–1876) and the first graduating class, in 1875, consisted of seven students. In 1879, a natural science club, the Star and Crescent Society, was founded at LAHS and consisted then of the entire student body. It soon left its specific focus on science and became a de facto student government and organizational body.

1887, Sand Street
In 1887, the decision was made to move the high school building to Sand Street (later California Street, now part of the Hollywood Freeway), just to the west of North Hill Street and below the south side of Fort Moore Hill, in order for the Los Angeles County Courthouse to be built on Poundcake Hill. The contractor, Mr. Hickam, said he could do the job with scaffolding, rollers, horses and workmen. But his bid turned out to be too low. He lost a considerable amount of money because of his elaborate preparations, including the high wooden trestle which carried the building over the intersection of Temple and Fort Street. Hickam managed to get the schoolhouse halfway up Temple Street when he ran out of money and left it right in the middle of the street. It was there for a good while. They jacked it up on scaffolding high enough for the Temple Street street cars to run under it. Finally, they got it moved up to its new location on Sand Street, where LAHS students and faculty remained until the second high school was built a few years later.

The original schoolhouse remained at the Sand Street (California Street) site for many years, while in continuous use. After the high school moved out, it became a school for the lower grades. It went completely unharmed by the Long Beach earthquake in 1933, which did a lot of damage to the newer buildings in downtown. By April 1936, nearly 300 children attended school there.

1891, Fort Moore Hill
In 1890, construction began on a new red brick schoolhouse facing North Hill Street on Fort Moore Hill, between Sand Street and Bellevue Avenue (later Sunset Boulevard, now Cesar Chavez Avenue), at coordinates 34.05844°N, -118.24246°W, which was a short distance from the older wooden one then facing Sand Street below.

That same year, the Los Angeles City High School District was formed. It served students of LAHS while the Los Angeles City School District and various other elementary school districts served elementary and junior high school students.

This second location atop a hill was completed in 1891 and LAHS moved in. It was an enormous building for its time. The new high school was built on part of the site of the abandoned Fort Moore Hill Cemetery, the first Protestant cemetery in Los Angeles, which was spread over the slopes of the hill. It had become neglected, practically unattended and desecrated by grave robbing vandals. The Board of Education purchased the property from the city in 1884, and other portions of land were sold as residential lots. The city neglected to remove the remains and clear away the grave sites and some LAHS students in the 1890s thought it was "fun" to sit and eat their lunch while they leaned against a tombstone.

At a meeting regarding the improvement of the school grounds on June 4, 1896, the committee was directed to wait on the Board of Education the following Monday evening to secure the cooperation of the board in having dirt being taken from the Hill Street cut used in filling up the grounds of the high school, so that shrubbery could be grown about the building. LAHS was the only high school in Los Angeles until 1905.

The second high school, on Fort Moore Hill, eventually became a school for problem students, a lot of them truancy cases. By September 1948, when preparing for the school to be razed for the construction of the Hollywood Freeway, plans were made to transfer the students to Belmont High School, in the Echo Park area of Los Angeles. As Belmont students and parents protested the transfers, an alternative plan provided that 12 persons be assigned to the senior and junior high schools in the six attendance areas to carry out the program. The headquarters of the Board of Education was later built on the property. Most of Fort Moore Hill itself was removed in 1949 for the construction of the freeway, which opened in December 1950. Also located on what remains of the hill is the Fort Moore Pioneer Memorial, which was opened to the public in 1957.

1917, Olympic Boulevard
In 1917, the school moved to its current location on Olympic Boulevard, and Rimpau, with 1,937 students. An edifice was erected that became an international cultural landmark for the famed school. To insure a permanently beautiful vista for their contemplation, and to honor classmates who had fallen in World War I, the students purchased the land across the street for the creation of a tree-filled memorial park.

Actual student government was instituted at LAHS in the early 1900s, eliminating one of the main reasons for Star and Crescent's existence. Meanwhile, as the size of the student body increased over years, the lower grades were successively dropped from Star and Crescent until by 1935 only seniors were members. Star and Crescent probably disappeared after World War II, but it is difficult to determine the exact year since no one at the school today can say when it ended. In particular, yearbooks were published during the years of America's involvement in that war, so it seems likely it might have disappeared after the war years. In the S'42 yearbook a page was devoted to Star and Crescent with its Officers and Faculty sponsors listed. The graduating class of 1970 received their Star & Crescent pins at a special ceremony.

On July 1, 1961, the Los Angeles City High School District and the elementary school districts were merged into the Los Angeles Unified School District. For many years, The Blue and White Daily was one of the few high school newspapers to be published Tuesday through Friday mornings during the school year except for holidays and the first 11 and last 5 days of the semester. It was a 4-page paper. In 1962, "Daily" was dropped from the name and the publication became a weekly. It is currently published monthly.

Los Angeles High School is shown in the opening credits of the 1940s movie "Strike Up The Band" and the 1943 movie "Henry Aldrich Gets Glamour". The popular late 1960s and early 1970s television series Room 222 was filmed at LAHS.

1971, Olympic Boulevard
The 1917 building sustained moderate cosmetic damage, principally in the tower area, during the Sylmar earthquake in 1971. Efforts spearheaded by the Alumni Association, founded in 1876, to repair and preserve the iconic structure were opposed by certain commercial interests, who lobbied for its demolition, and finally decisively thwarted when it was gutted by a fire of mysterious origin. The replacement structure has been universally decried and finds no champions among either current or former students and faculty, or residents of the neighboring community.

The school population peaked at 10,800, but overcrowding at the school has been relieved by West Adams Preparatory High School, which opened in the 2007–2008 school year. In 2009, some territory of Los Angeles High School's attendance boundary was transferred to Fairfax High School.

In February 2012, a gunman shot at teens near the high school. Two were wounded.

Neighborhoods served by LAHS
Neighborhoods zoned to LAHS include: Brookside, Harvard Heights, Koreatown, Lafayette Square, and Little Ethiopia, and portions of Hancock Park and the Pico-Union District.

Demographics
As of 2001, 75% of the student body was Hispanic and Latino. 14% was black and 7% was Asian. Other ethnic groups made up the remainder.

Academics
As of 2001 the school has the only full-time Korean language classes in LAUSD. As of that year there were over 100 students in these classes, and 80% of them were not of Korean heritage.

Advanced Placement Program
Students are accepted into the Advanced Placement Program and individual advanced placement classes based on faculty and counselor recommendations. A student may be admitted into an AP class by request if the AP instructor has approved the request.
 * Biology
 * Calculus AB and BC
 * Chemistry
 * English Language and Composition
 * English Literature and Composition
 * Environmental Science
 * Macroeconomics
 * Microeconomics
 * Physics C: Mechanics
 * Psychology
 * Spanish Language
 * Spanish Literature
 * Statistics
 * Studio Art Drawing, 2-D, and 3-D
 * United States History
 * United States Government and Politics

English Learners and Standard English Learners Program
The focus of this program is the implementation of the LAUSD 2018 Master Plan for English Learners and Standard English Learners with fidelity, so that student achievement is realized. During 2018–2019 school year 19% of the total student enrollment are students identified as English Learners, and 23% are students classified as AEA Probable Standard English Learners. At LAHS all content teachers use ELD standards. The PLDs (proficiency level descriptors) represent English language development as a part of a continuum from native language competencies to lifelong language learning. The CA ELD Standards are organized in two main sections: Section 1 provides a foundation for an orientation to the standards; Section 2 provides detailed grade level ELD standards with the corresponding CCSS-ELA. The CA ELD Standards are not taught in isolation but are used in the context of developing meaningful, intellectual interaction. The role of the Title III Coach is to collaborate with school staff in building capacity to design and deliver professional development that utilizes and aligns standards-based content with effective classroom pedagogy to increase proficiency in the area of English language arts for all students through effective first teaching.

Notable alumni

 * Margaret Q. Adams, first female deputy sheriff in United States
 * Yda Hillis Addis, translator who mysteriously disappeared
 * Lou Almada, baseball player
 * Mel Almada, first Mexican-American in Major League Baseball
 * Jimmy Allen, NFL player, 1972–73 UCLA, 1974–77 Pittsburgh Steelers, 1978–81 Detroit Lions
 * Tod Andrews, actor
 * Jack Banta, NFL player
 * Anne Baxter, Oscar-winning actress
 * Scotty Beckett, actor
 * Pauline Betz, tennis champion
 * Fletcher Bowron, four-term mayor of Los Angeles 1938–53
 * Ray Bradbury, science-fiction author
 * Larry Brown, Dallas Cowboys, Oakland Raiders cornerback, Super Bowl XXX MVP
 * Charles Bukowski, writer, poet
 * John Cage, composer
 * John P. Cassidy, Los Angeles City Council member, 1962–67
 * Richard Chew, film editor
 * Frank Chuman, civil rights attorney and author
 * Johnnie Cochran, attorney who defended O. J. Simpson
 * Lynn "Buck" Compton, World War II veteran portrayed in Band of Brothers, Deputy DA of Los Angeles County who convicted Sirhan Sirhan
 * Gary Conway, actor
 * Lillian Copeland (1904–1964), Olympic discus champion; set world records in discus, javelin, and shot put
 * Harry Danning, 4x MLB All Star baseball player
 * Vernon Dean, NFL player
 * Mel Durslag, sportswriter
 * Aileen Eaton, boxing promoter
 * Bruce Edwards, actor
 * Mike Evans, actor
 * Robert C. Farrell (born 1936), journalist and member of the Los Angeles City Council, 1974–91
 * Louise Fazenda, actress
 * Lita Gaithers, Tony Award-nominee singer-songwriter
 * Siedah Garrett, Grammy-winning singer-songwriter
 * Marjorie Gestring, Olympian (swimming and diving)
 * John M. Goddard, led first explorations by kayak down Nile and Congo Rivers
 * Dave Gold, founder of 99 Cents Only Stores
 * Carl Greenberg, newspaperman
 * Clementina D. Griffin, educator, principal, aviator
 * Horace Hahn, actor
 * Juanita Hansen, silent film actress
 * Aiko Herzig-Yoshinaga, activist, did not graduate due to internment in Manzanar in senior year (1942) but later received her diploma in 1989
 * Dustin Hoffman, Oscar-winning actor
 * Robert Horton, actor
 * Christianne Meneses Jacobs, writer, editor and founder of Iguana Magazine (nation's only Spanish-language magazine for children)
 * Cornelius Johnson, Olympic champion (1936, track and field)
 * Willis Lamb, shared Nobel Prize for Physics in 1955 for discoveries related to superfine structure of hydrogen spectrum
 * Milt Larsen, co-founder of Magic Castle
 * Piper Laurie, 3-time Oscar-nominated actress
 * Homer Lea, general in army of Sun Yat-sen, writer of books of geopolitics
 * Gene LeBell, stuntman
 * Linda Levi, artist
 * Bessie Love, actress
 * Mike Marienthal, athlete, 1990 UCLA Sports Hall of Fame
 * Sam Match (1923–2010), tennis player
 * Ray May, NFL player, 1967–69 Pittsburgh Steelers, 1970–73 Baltimore Colts (Super Bowl), 1973–75 Denver Broncos
 * Naida McCullough, pianist, teacher
 * Bob Meusel, baseball player, New York Yankees teammate of Babe Ruth and Lou Gehrig
 * Josephine Miles, poet
 * Marvin Mitchelson, palimony attorney
 * Carmel Myers, actress
 * Jerry Nemer (1912–1980), basketball player and attorney
 * Anita Ortega, basketball player, LAPD
 * Budge Patty, tennis champion
 * Don Paul, NFL player
 * Leonard Pennario, concert pianist
 * Cal Peterson, NFL player
 * Emily Brown Portwig, Los Angeles clubwoman and pharmacist
 * Donald Prell, futurologist
 * Al Raffo, baseball player
 * Madlyn Rhue, actress
 * Charles Francis Richter, inventor of Richter Scale
 * Frederick Madison Roberts, first African American elected to California State Legislature (1919–1933)
 * Earl Scheib, auto-painting entrepreneur
 * Budd Schulberg, Oscar-winning screenwriter
 * Leonard Slatkin, music director of National Symphony Orchestra
 * Bowen Stassforth, Olympian (silver medalist in swimming)
 * Art Stoefen, basketball player
 * Lester Stoefen, tennis player
 * Louise Suski, newspaper editor
 * Miiko Taka, actress
 * George Takei, actor, known for Star Trek
 * Harry Thompson, NFL player
 * William Irwin Thompson, poet and cultural historian
 * Kathryn Doi Todd, first Asian American female judge
 * Mel Tormé, singer, songwriter and actor
 * Dick Walsh, baseball and soccer executive
 * Doodles Weaver, actor and comedian
 * Francis J. Weber, historian, author on California's mission period
 * Matt Weinstock, newspaper columnist
 * Tad Wieman, college football coach
 * Rosalind Wiener Wyman, political figure
 * Anna May Wong, actress
 * Chloé Zhao, Oscar-winning film director

Current administration

 * Marguerette Gladden, Principal
 * Mr. Michael Berger, Assistant Principal
 * Mrs. Batia Oren, Assistant Principal
 * Mr. Pacino Furioso, Assistant Principal
 * Mr. Eric Fitzpatrick, Assistant Principal

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Los Angeles High School


text:
KGA

KGA (1510 AM) is a commercial radio station in Spokane, Washington. Owned by Stephens Media Group, it broadcasts a sports radio format. KGA's studios and offices are on East 57th Avenue. Most of the programming comes from Fox Sports Radio. The station carries broadcasts of the Spokane Indians minor league baseball team, the Spokane Chiefs junior ice hockey team, and teams fielded by Gonzaga University. Going on the air in 1927, it was one of the earliest radio stations in Washington.

By day, KGA is powered at 50,000 watts non-directional, the maximum for commercial AM stations. But to reduce interference to other stations on 1510 AM, during critical hours the power is lowered to 45,000 watts. And at night, power is greatly reduced to 540 watts. The transmitter site is on East Stutler Road near U.S. Route 195 in Spangle, Washington. Programming is also heard on 99-watt FM translator K278CY at 103.5 MHz in Spokane.

Early years
KGA signed on the air on. Its original owner was Louis Wasmer. KGA's first studios were in the old Radio Center Building across the street from the Davenport Hotel. Its transmitter was on the northside of Spokane where the Lidgerwood Elementary School is now located.

In the 1930s, KGA was powered at 5,000 watts, broadcasting at 1470 kilocycles. It moved to 1510 after the North American Regional Broadcasting Agreement (NARBA) took effect in 1941. KGA was an affiliate of the NBC Blue Network, airing its dramas, comedies, variety shows, news and sports during the "Golden Age of Radio." That network later became ABC Radio. As network programming moved from radio to television in the 1950s and 60s, KGA switched to a full service, middle of the road (MOR) format, airing popular adult music, news and sports.

KGA played Top 40 hits from January 1968 until June 1969, featuring disc jockeys Shane Showtime (Gibson) and Joe Fialla. It was more successful as a country music outlet from 1969 until 1994. But by the 1990s, most people listening to country music were switching to the FM band.

Talk and Sports
KGA flipped to a news/talk format in 1994. It relied mostly on nationally syndicated talk shows from commentators such as Bill O'Reilly, Laura Ingraham and Michael Savage, along with several local programs. Former Los Angeles police detective and author Mark Fuhrman, who lives in nearby Coeur d'Alene, Idaho, hosted a local morning show on weekdays until his program was discontinued in November 2007. In April 2008, KGA's news/talk format moved to sister station 790 KJRB, with KJRB's sports format switched to KGA.

KGA has had several owners (including Gonzaga University in its early history), has changed frequency several times, and has had its studio and transmitter site relocated over the years. But it has retained the same three-letter call sign from its founding. No other station in Spokane has kept its call letters over so many decades.

Loss of Clear-Channel status
KGA was a 50,000-watt clear-channel Class A station for most of its life, and could be heard after sunset around the Pacific Northwest, plus part of Western Canada. On July 15, 2008, KGA reduced its nighttime power from 50,000 watts to 15,000 watts, surrendered its status as a Class A, downgrading to Class B, and changed its directional antenna system.. Class A stations have the widest coverage areas and best protection from interference from other stations.

All of this was done so that its then-sister station, KPIG (AM) in Piedmont, California, could increase its nighttime power from 230 watts to 2,400 watts and gain nearly a million potential listeners in the San Francisco Bay Area. KGA received a construction permit to simplify its antenna system to a single tower with non-directional operation (FCC.gov AM Station Query). It was granted a nighttime power reduction, to 540 watts, with a slight power reduction just after sunrise and just before sunset critical hours to 45,000 watts.

Sports and Hip Hop
In January 2019, after adding a new translator in Spokane on 103.5 FM, the station dropped Fox Sports Radio and flipped to urban contemporary as 103.5 The Game. While playing hip hop music and other rhythmic contemporary hits, the station retained its existing contracts to broadcast sports play-by-play. It began using the slogan "Sports and Hip Hop."

On September 30, 2019, the station was sold to Stephens Media Group after it acquired most of the properties of former owner Mapleton Communications. On March 19, 2021, the station dropped its urban format and returned to being a full-time network affiliate of Fox Sports Radio.

title: KGA


text:
Arwa bint Kurayz

Arwā bint Kurayz (أَرْوَى بِنْت كُرَيْز) was the mother of Uthman ibn Affan, a companion of the Islamic prophet Muhammad, and the third of the Rashidun or "Rightly Guided Caliphs".

Ancestry
Arwa was the daughter of Kurayz ibn Rabi'ah ibn Habib ibn Abd Shams ibn Abd Manaf, so she was of Banu Abd-Shams, a sub-clan of the tribe of Quraysh. Arwa's mother was Umm Hakim bint Abd al-Muttalib, so Arwa was a cousin of Muhammad.

Children
Arwa married Affan ibn Abi al-'As and bore him Uthman and Amina. After the death of Affan, Arwa married Uqba ibn Abu Mu'ayt, to whom she bore al-Walid, 'Ammara, Khalid, Umm Kulthum, Umm Hakim and Hind.

Biography

Arwa bint Kurayz converted to Islam and emigrated to Medina after her daughter, Umm Kulthum bint Uqba. She gave allegiance to Muhammad, and remained in Madina, until she died during the caliphate of her son, Uthman ibn Affan.

title: Arwa bint Kurayz


text:
User:Jondel/Scrapbookx/Michael Kearney

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http://www.findarticles.com/
 FindArticles > Saturday Evening Post > May-June, 1996 > Article > Print friendly

Letting Michael be Michael … a 12-year-old with 4 Guinness records - gifted child Michael Kevin Kearney - includes related information on scholarship presentation Tom Tozer "Your child will be developmentally slow," doctors told Cassidy Kearney when she was...

 * (snipped... continued at ... or  ... see also )

...The Kearneys call Michael a prodigy, rather than a genius. A genius, they say, is an individual who creates a whole new area of human endeavor or knowledge - Einstein, for example. A prodigy is a child who performs in an adult field at an adult level. "Since Michael has not yet contributed anything to the sum of human knowledge," Kevin says, "he's not a genius." Contemplating Michael's potential on one level, yet not grasping it at all, leaves one wondering just when and how his genius might manifest itself and affect all of humankind. COPYRIGHT 1996 Saturday Evening Post Society

COPYRIGHT 2004 Gale Group

title: User:Jondel/Scrapbookx/Michael Kearney


text: Category:Continuous distributions

title: Category:Continuous distributions


text:
Wikipedia:Articles for deletion/The Gak

 This page is an archive of the proposed deletion of the article below. Further comments should be made on the appropriate discussion page (such as the article's talk page or on a Votes for Undeletion nomination). No further edits should be made to this page.

The result of the debate was keep (no consensus). There are some merge votes, but they don't specify a target. Therefore, I will just call this one an outright keep. Sjakkalle (Check!)  09:00, 21 July 2005 (UTC)

The Gak
A band who only played one show and that was at a party? Sounds like a glorified jam session - clearly non-notable, despite the obvious notability of participants XmarkX 05:14, 11 July 2005 (UTC)

 * Delete as per nominator. -mysekurity 05:56, 11 July 2005 (UTC)
 * Delete. nn, an improvised band that existed for a few hours. --TheMidnighters 08:00, 11 July 2005 (UTC)
 * Delete non notable jam. JamesBurns 09:23, 11 July 2005 (UTC)
 * Keep I don't see this as a band page at all, and once again I feel I need to ask JamesBurns: what is your threshold for a notable jam? A major event with unarguable super-stars of corporate rock isn't notable? Pray, what is? Elvis returning from the dead to jam with the Statue of Liberty?!
 * This event was clearly an item for the rock-n-roll history books even if you don't like these performers (as I do not). -Harmil 12:04, 11 July 2005 (UTC)
 * That wouldnt be notable - it wouldnt be true. Everyone knows that Elvis is alive and working at my local burger franchise, so he couldnt possibly be dead. JamesBurns 06:07, 12 July 2005 (UTC)

 * Delete. Everything celebrities do is not inherently worthy of an encyclopedia article, and I just don't see the possibility of expanding this to be a real article.  The info can be added to the real bands/performers articles under "trivia."  Soundguy99 14:45, 11 July 2005 (UTC)
 * Delete per Soundguy99. Dcarrano 14:55, July 11, 2005 (UTC)
 * Merge somewhere or keep, notable incident. Kappa 15:00, 11 July 2005 (UTC)
 * Keep, absolutely a stick-on keeper james gibbon 15:01, 11 July 2005 (UTC)
 * Delete. "the gak" hetfield gets only 5 hits, including WP mirrors. The jam may be notable somewhere (probably a la Soundguy99), but this name seems to be a non-notable neologism. Niteowlneils 15:30, 11 July 2005 (UTC)
 * Delete. Only one show?  --Carnildo 20:05, 11 July 2005 (UTC)
 * Keep. Extremely notable band members. Pburka 23:23, 11 July 2005 (UTC)
 * Merge one night that doesn't need it's own article. --Etacar11 00:46, 12 July 2005 (UTC)
 * Delete, fails WP:MUSIC. Radiant_ >|< 13:38, July 12, 2005 (UTC)
 * Delete no evidence for continued existance of this band. Yes, members are notable, but this doesn't make everything they do automatically notable.  Friday 14:09, 12 July 2005 (UTC)
 * Keep Easily passes WP:MUSIC]. Since we cannot merge and redirect to each notable member, it should be kept as small article.  A small article such as this can be mentioned in each participant's page.  This is an example of where a "perfect article" in Wikipedia would necessarily be very small.  Unfocused 15:41, 12 July 2005 (UTC)
 * Delete or Merge somewhere. Despite the notability of the participants, event doesn't warrant its own article. carmeld1 00:02, 14 July 2005 (UTC)
 * Keep per WP:MUSIC.  Grue  19:10, 14 July 2005 (UTC)
 * The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in an undeletion request). No further edits should be made to this page.

title: Wikipedia:Articles for deletion/The Gak


text:
Daniel Fuchs

Daniel Fuchs (June 25, 1909 – July 26, 1993) was an American screenwriter, fiction writer, and essayist.

Biography
Daniel Fuchs was born to a Jewish family on the Lower East Side, Manhattan, but his family moved to Williamsburg, Brooklyn while Fuchs was an infant. He wrote three early novels, published by the Vanguard Press — Summer in Williamsburg (1934), Homage to Blenholt (1936), and Low Company (1937). The earlier two of these depicted Jewish life in Williamsburg; the last focused on various ethnic types in Brighton Beach. A single-volume edition of these was published by Basic Books in 1965 under the title "Three Novels." Subsequent one-volume editions include The Brooklyn Novels,  with an introduction by the novelist Jonathan Lethem, published in 2006 by Black Sparrow Books, an imprint of David R. Godine, Publisher.

Homage to Blenholt concerns a well-meaning tenement schlemiel who hopes to escape poverty via various inventions and get-rich quick schemes. Fuchs also wrote short stories and personal essays, mainly for The New Yorker. When he was 26, he moved to Los Angeles, California to work on films.

Fuchs wrote the screenplay for the crime noir Criss Cross (1949). He also penned the psychodrama Panic in the Streets (1950), which was directed by Elia Kazan. In 1995, Criss Cross was remade as The Underneath by director Steven Soderbergh, with credit given to Fuchs. Love Me or Leave Me, a biopic about the torch singer Ruth Etting, which won Fuchs an Oscar for Best Story in 1955, featured a performance by James Cagney in the role of a Chicago hoodlum and Doris Day as the beleaguered songstress.

Fuchs' Hollywood novel, West of the Rockies, was published in 1971, and in 1979 appeared a collection of mostly earlier-written short stories, "The Apathetic Bookie Joint." The Golden West: Hollywood Stories, a collection of Fuchs's fiction and essays about Hollywood, was published in 2005 by Black Sparrow Books.

Fuchs died in Los Angeles.

Critique
Irving Howe wrote of Fuchs for Commentary Magazine in 1948 that "he showed such a rich gift for fictional portraiture of Jewish life in the American city that, given sustained work and growth of mind, he might have written its still-uncreated comedie humaine. After reading Fuchs' work one wonders: What was the source of his talent and the cause of his silence, and, perhaps more important, what was the relationship between his talent and his silence?"

John Updike said, "Nobody else writes like Daniel Fuchs. I think of him as a natural—a poet who never had to strain after a poetic effect, a magician who made magic look almost too easy."

Books
Fuchs published with the Viking Press via the Maxim Lieber Literary Agency; Elizabeth Nowell (who later became Thomas Wolfe's exclusive agent) handled him.
 * Summer in Williamsburg (1934)
 * Homage to Blenholt (1936)
 * Low Company (1937)
 * Three Novels (1965): omnibus of earlier novels

Scripts

 * The Hard Way (1943)
 * Between Two Worlds (1944)
 * The Gangster (1947), based on his own novel Low Company
 * Hollow Triumph (1948)
 * Criss Cross (1949)
 * Panic in the Streets (1950)
 * Storm Warning (1951)
 * The Human Jungle (1954)
 * Love Me Or Leave Me (1955)
 * Jeanne Eagels (1957)
 * Interlude (1957)

Awards

 * 1980: National Jewish Book Award for The Apathetic Bookie Joint

title: Daniel Fuchs


text:
Talk:Tung Ping Chau

Untitled
Ping Chau and Tung Ping Chau are poles apart! The former one is just north of Discovery Bay. -- Jerry Crimson Mann 05:15, 11 July 2005 (UTC)

 * hee~ just find a clue in the Chinese wikipedia. :-D -- Jerry Crimson Mann 05:17, 11 July 2005 (UTC)

Most people in Hong Kong call it "Tung Ping Chau" now. In English, "Peng Chau" adpated a different spelling (and hence pronunciation), but in Chinese, most of the time people refer it as "Tung Ping Chau"; "Ping Chau" is seldom used. --Hello World! 03:00, 27 July 2005 (UTC)

Regarding History section: Ping Chau is now deserted and has a checkered history. Guns and opium were once smuggled from here, and during the Cultural Revolution many mainlanders swam through shark-infested waters in hopes of reaching Ping Chau and the freedom of Hong Kong.

Reference? There are no waters around HK that are "shark-infested". — Preceding unsigned comment added by Kevinarpe (talk • contribs) 08:59, 3 August 2011 (UTC)

Tung Ping Chau Public Pier
The article Tung Ping Chau Public Pier was turned into a redirect to this article. You can view the redirect's history for the history of the redirected article. Olivier (talk) 12:57, 8 September 2014 (UTC)

Dung Chow Ping??
A search for "Dung Chow Ping" leads to this article.

Last I looked, this referred to a person, not to an island. — Preceding unsigned comment added by 70.89.176.249 (talk) 20:10, 30 January 2019 (UTC)

title: Talk:Tung Ping Chau


text: Category:Discrete distributions

title: Category:Discrete distributions


text: File:Richardpryorevolution.jpg

title: File:Richardpryorevolution.jpg


text:
Barney's Hide & Seek Game

Barney's Hide & Seek Game is a video game that was released on June 1, 1993, by Sega of America for the Sega Mega Drive/Genesis.

This game was released exclusively in the North and South American markets. It was based on the children's television series Barney & Friends. Educational concepts taught in the game include counting, matching, and problem solving. There is a self-play feature that guides the player to the objective without input from the player.

The voice of Barney was recorded by Bob West, who also did it on the television show. There are more than one hundred words and two hundred phrases spoken by Barney the Dinosaur.

Gameplay

In this game, the objective is to move Barney around four themed levels and locate five children and five presents that are hiding throughout the level. Should the player find all the children and presents in different levels, they would be rewarded with a "special surprise". During the surprise, the purple balloon pop and confetti and streamers fall from above onto excited children, as well as Barney and Baby Bop. Players are unable to lose in the game, even if they did not retrieve all the objects and find all the missing children in the level.

When nowhere near an object to interact with, Barney can blow kisses in the air complete with flying heart symbols. Locating a child results in giving him or her a hug. Barney can fly on balloons, float on clouds, and jump on nearby platforms. The inability for Barney to die is indicated by his refusal to fall off floating platforms; instead there is a safety lecture handed out by Barney so kids can learn to be careful like him. Cloud jumping is only possible when the traffic light is showing a green signal.

Favorite things are always mentioned by name by Barney when the player helps him discover them. Most of the lines for the game were recorded with the nouns and verbs being fractured, resulting in one-second pauses between non-crucial words and words crucial to gameplay.

Reception
The game received mixed reviews based on its very simplistic gameplay. Brett Alan Weiss of AllGame gave it a rating of 4/5, stating that the game was "perfectly suited" for its target audience. On the other hand Vince Thornburg of Sega-16 stated that the game "did its purpose of being a simple game for kids, and that’s about it."

Speedrunning interest
The game received attention from the speedrunning community due to its unique self-playing feature. The game will beat itself even if given no input by the player, but random elements cause playthroughs to take different amounts of time despite the lack of player interaction. This prompted the creation of a speedrunning category called "Any% No Controller", in which players do not touch the controller, and instead wait for the game to play itself to completion. Inconsistencies in the hardware seem to make it so the world record of 9 minutes and 9 seconds (as of January 2020) can only be achieved via a physical console, and not on an emulator.

title: Barney's Hide & Seek Game


text:
Talk:Victorian morality

Comment from 2005
I've removed the cleanup tag that I put here earlier as the article has greatly improved thanks to the edits of Theo and others. -- Sundar \talk \contribs 05:17, July 11, 2005 (UTC)

low tolerance of crime
In what way?

The Victorian era saw the rise of the penitentiary. Thus, capital punishment (which was tradionally applied for stealing things like handkerchiefs, etc.) was no longer used.

(It's funny that who ever wrote that in the article was trying to "warm up" to the idea of Victorian morality, but included an incorrect description of it - thus expressing their own conservative desires, not those of the Victoria era). —Preceding unsigned comment added by 60.240.69.86 (talk) 05:48, 7 December 2008 (UTC)

victorian ideas on morality and social class
I just added a sentence to the paragraph on Victoria and Albert regarding sexual behavior: My point does not contradict the paragraph. It shows that both Victoria and Albert were personally affected by the open sexual escapades done by those around them.

I referred to the Prince Consort's broken childhood home due to sexual scandals and his loss of his mother shortly thereafter. This is public info one can see in various sources including Cecil Woodham's and Lady Longford's books on Queen Victoria.

Victorianezine 15:42, 23 October 2007 (UTC)Victorianezine

What's this leg thing???
Victorian prudery sometimes went so far as to deem it improper to say "leg" in mixed company (the preferred euphemism if such must be mentioned was "limb")

A little confusing to me, if there's something I'm missing, just go out and say it.

Because your not sexually oprest enouft.It means this kind of leg ;-) --81.245.58.149 19:45, 6 August 2006 (UTC)

I get the impression a lot of that was limited to the "genteel" middle class in North America - the table leg thing is supposed to originate in a malicious rumour about the Americans started by the British? Livlivliv 00:25, 3 January 2007 (UTC)

cromwell was no republican
he was a dictator! England was a republic in name only RomanYankee(24.75.194.50 17:18, 23 August 2006 (UTC))

Article is still a mess, IMHO
Look at the Victorian fashion article for what I think is a slightly better take on things. Among other things, it demolishes the piano leg canard.

I studied anthropology, though I never finished my degree, and I did a fair bit of historical work. It's just plain wrong to claim that there was some unified "morality" in 19th century England. People then believed different things, did different things, and argued vociferously. The article seems to be about later stereotypes of Victorian morality, courtesy of Lytton Strachey and the like (again, see the Victorian fashion article). It's useful to discuss the stereotypes, but it's even more necessary to point out how much "Victorians" differed on various topics. Zora 00:35, 3 January 2007 (UTC)

Victorian attitudes to criminality (copied from WP:RD/H)
Crime, as we understand it today, might be said to be the creation of the Victorian age. Literacy had created the demand for a popular press; and the press fed on the public's taste for crime, particularly in its more lurid forms. Let's take one one case where Victorian perceptions shaped, and continue to shape, how one particular case has been projected and understood: namely the Whitechapel Murders of 1888. Here we are in the realm of Jack the Ripper. He was a 'gentleman', was he not, one who may even have come all the way down to the slums from the palaces of royalty? Well, in fact, we know virtually nothing about the Ripper, because he was never caught. But the journalists of the day were quite happy to fulfill the popular prejudice, no doubt stimulated by the publication two years previously of Robert Louis Stevenson's The Strange Case of Dr. Jekyll and Mr. Hyde, that the Ripper was a 'toff', who got his 'pleasures' slumming in London's seedy east end.

The next big concern was over the nature of criminality itself. Most law-breakers, of course, were from the urban poor, the seedbed of the new 'criminal classes'. An explanation was required, beyond mere poverty of course, and was readily supplied by the likes of Edwin Chadwick, the Poor Law reformer, who believed criminality was the response of the idle and the feckless, tempted by easy returns as an alternative to honest labour. Temperance reformers placed the blame on alcohol, just as reformers in education blamed ignorance and lack of opportunity. For the evangelists, it was all due to the abandonment of the standards set by religion. With the growth of popular forms of Social Darwinsim hereditary became a factor; and by the end of the century the notion of the habitual criminal, tainted by birth and background, was gaining ascendency over the notions of morality and idelness. From this management and control became the dominant elements of law-enforcement; and so it remains today. Clio the Muse 03:14, 11 July 2007 (UTC)

Naked Portriat Is Inapporite im removing it
It is not appportite for this site removeing it now —Preceding unsigned comment added by Bvernon199 (talk • contribs) 21:10, 29 June 2009 (UTC)

Crisis of Faith
The "Crisis of Faith" would hit religion and the citizens' Faith like a brick. The Crisis of Faith was brought about in 1859 with Charles Darwin's work On the Origin of Species; his theory was (in the basic form) that the Natural World had become what it was through gradual change over eons.[14] He told that natural selection and survival of the fittest was the reason man had survived so long.[15] His theory of evolution based on empirical evidence would call into question Christian beliefs, and the Victorian Values.[16] People's lives became totally uprooted and there was a need to find a new system to base their values and morality on.[17] Unable to completely lose Faith they combined both their Religious beliefs with individual Duty -- [18] duty to one's God, fellow man, social class, neighbour, to the poor and the ill.[19]

What "Crisis of Faith"? Is it a book? You keep capitalizing it like it is a book. In fact, you seem to be capitalizing things all willy nilly.

--68.44.13.238 (talk) 13:03, 8 January 2010 (UTC) Quba Osman

There were many different reasons for unbelief in the nineteenth century (such as eighteenth-century French arguments like Voltaire's, or the philosophy of Hume), and Darwin's theory was not uncritically accepted (the main problem was that he and his nineteenth-century adherents knew nothing of dominant and recessive genes, and couldn't gainsay the counterargument that mutations would disappear in the gene pool of a large population). This encyclopedia page depends too much on that single book by S. B. 4.154.253.213 (talk) 01:09, 21 January 2010 (UTC)

This article is one of history, and this section, as far as the evidence and citations provided goes, seems to be mostly a hopeful projection of what the author assumes was the impact of Darwinism and the supposed universal psychological process of the population being "unable to completely lose their faith". Largely citing one and only one book, this appears more misinformation by someone eager to work his worldview into his historical narrative than objective history. Apart from actual demographic data as to the supposed social impact of the time, this section is nonsense. — Preceding unsigned comment added by Empiric (talk • contribs) 14:04, 2 April 2013 (UTC)

"Prostitution and child labor"
Boy! This is sloppy. " . . . [T]he outward appearance of dignity and restraint together with the prevalence of social phenomena such as prostitution and child labour." What other society in previous history did *not* have prostitution and child labour?

While I'm griping, there appears to be only one -- perhaps two -- books sited for this article/opinion piece. If there were more, I might be readier to believe its credibility. Pittsburgh Poet (talk) 23:16, 16 May 2010 (UTC)

Sexually transmitted diseases were an important element of the Victorian sexual prudery. Note the "free love" movement screeched to a halt when AIDS was introduced. Also, the proliferation and plight of orphans, especially out of wedlock waifs, is not mentioned in articles about "Victorian sexual morality." These issues are interesting and important in the history of sexual morals and habits. It was abt 1860s -1870s that the transmissibility of STDs was discovered. — Preceding unsigned comment added by 206.169.89.135 (talk) 03:19, 22 December 2021 (UTC)

Religious morality - single source
There is only a single source in use for Religious morality. I note that, from what I know of the subject, it wasn't evolution that the Victorians made a fuss about (except for the real fundamentalist types); it was natural selection and the element of chance. Allens (talk) 22:43, 31 October 2011 (UTC)

Dubious sources
I've noticed that 90% of the citations in this article are from 'Bayley, S (2008). Victorian Values: An Introduction. Montreal: Dawson College.' However, I can find nothing about this book anywhere - except for a reference from a year 2000 college course, run by a Susan Bayley at Dawson College, to a 'Manual of readings prepared by the instructor'. Suggest that these citations be removed and replaced by something more appropriate. — Preceding unsigned comment added by 86.7.200.178 (talk) 00:32, 25 February 2012 (UTC)
 * Agreed--and the sections citing Bayley do not actually deal with morality. so I deleted them. Rjensen (talk) 21:36, 25 May 2018 (UTC)

Prudery
My great-grandmother reckoned that in Victorian times a naked teapot spout was considered to be so suggestive that special covers were knitted to cover the spout.AT Kunene (talk) 15:16, 4 March 2012 (UTC)

Needs rewrite
In my opinion the entire Religious Morality section is in need of a rewrite. I feel that it's poorly-written and has too many clichés.

69.127.82.225 (talk) 05:32, 14 October 2013 (UTC)

Lacking racial referents; Class
While not limited to English Victorians, the 19th century was ambiguous on race: individual people "of color" could be noble, admirable, etc. but only the white race could be counted on generally, for morality.

The same could be said for "class": only nobility could be "counted on." Disadvantaged people were suspect, though there were individual exceptions. Student7 (talk) 01:10, 2 September 2014 (UTC)

Body functions
Descriptions of body functions were taboo in writing and often verbally, as well. Difficult to tell from general primary sources exactly when the conversion from privies to indoor toilets took place, for example. What sort of "rest stop" arrangements are made for women on stage coaches, for example? Totally missing from literature. At dances at people's homes where many people needed to use facilities? Forget it! Student7 (talk) 01:49, 2 September 2014 (UTC)

Confusion
The text mixes 1) what the morality of the times was with 2) what modern people think it was and 3) what the literature of the times reveals. These need to be clearly delineated. Student7 (talk) 16:39, 2 September 2014 (UTC)

title: Talk:Victorian morality


text:
User:Thakingkobra

I am ThaKingKobra and I am using the same name as my Xbox Live Gamertag, which I use for Halo 2. I also love to play San Andreas on my Xbox.

title: User:Thakingkobra


text:
User talk:Th3darkforce

Welcome!
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title: User talk:Th3darkforce


text:
Talk:Poultry

Who came First egg or chicken
? 2C0F:F0F8:639:1404:313F:7A46:C4C4:E037 (talk) 19:44, 23 October 2023 (UTC)
 * Yes.  Philroc  (talk) 19:46, 23 October 2023 (UTC)

title: Talk:Poultry


text: File:Olive-extravirgin.jpg

title: File:Olive-extravirgin.jpg


text:
Iron Savior

Iron Savior is a German power metal band that was formed in Hamburg in 1996. Following a period of several years working behind the scenes in music production, multi-instrumentalist and producer/engineer Piet Sielck joined with former Helloween bandmate Kai Hansen and then-drummer for Blind Guardian, Thomen Stauch in a new project that would blend power metal with a high-concept science fiction story. The band's debut album Iron Savior introduced the story that would be told over the course of multiple albums, featuring a self-aware space vessel called the Iron Savior and its relationship to the mythical lost civilization of Atlantis.

Critics have compared Iron Savior's sound and musical approach to classic heavy metal bands like Judas Priest, Iron Maiden, and Queensrÿche. Kai Hansen's presence in the band brought to the Iron Savior albums on which he appeared a style heavily influenced by Gamma Ray and Helloween.

Since its inception, Iron Savior has released twelve studio albums, two EPs, three singles and one live album.

Despite numerous lineup changes, Piet has continued to direct the band and is currently the only remaining founding member.

Current band members

 * Piet Sielck – lead vocals, guitar (1996–present), bass (1996)
 * Jan-Sören Eckert – bass, vocals (1997–2003, 2011–present)
 * Joachim "Piesel" Küstner – guitar, backing vocals (2000–present)
 * Patrick Klose – drums (2017–present)

Former band members

 * Kai Hansen – guitar, vocals (1996–2001)
 * Thomen Stauch – drums (1996–1998)
 * Andreas Kück – keyboards, backing vocals (1998–2003)
 * Dan Zimmermann – drums (1998–1999)
 * Thomas Nack – drums (1999–2017; touring member: 1997–1998)
 * Yenz Leonhardt – bass, backing vocals (2003–2011)

Albums

 * Iron Savior (1997)
 * Unification (1999)
 * Dark Assault (2001)
 * Condition Red (2002)
 * Battering Ram (2004)
 * Megatropolis (2007) (re-recorded in 2015 as Megatropolis 2.0)
 * The Landing (2011)
 * Rise of the Hero (2014)
 * Titancraft (2016)
 * Reforged – Riding on Fire (2017)
 * Kill or Get Killed (2019)
 * Skycrest (2020)
 * Reforged – Ironbound (2022)
 * Firestar (2023)

Extended plays

 * Coming Home (1998)
 * Interlude (1999)
 * I've Been to Hell (2000)
 * Curse of the Machinery (2023)

Singles

 * Titans of Our Time (2002)
 * Time Will Tell (2004)
 * In the Realm of Heavy Metal (2023)
 * Firestar (2023)
 * Through the Fires of Hell (2023)

Live albums

 * Live at the Final Frontier (2015)

title: Iron Savior


text:
Talk:John Oliver (British Columbia politician)

Untitled
Was John Oliver Highschool in Vancouver named after him too?

Yes. http://www.vancouverhistory.ca/whoswho_O.htm

Apple (symbolism)
This former Premier of the province of British Columbia recognized the symbolism of the apple - he was always eating from a basket of them on the floor of the Legislative Assembly. My authority on this is the History of BC Politics course led by Norman Ruff. Unfortunately, I can't find adequate independent support of this.


text:
Polo Urías

Leopoldo "Polo" Urías Ramírez (born November 15, 1954) is a Mexican singer. He specializes in regional Mexican music; specifically the norteño-sax genre. He is the leader of the band Polo Urías y su Máquina Norteña.

Early life
Urías was born on November 15, 1954, in Ojinaga, Chihuahua, Mexico. He recalls that when he was very young, he would often sing while plowing in the fields with his mules.

Musical career
Polo's professional career started in 1975 as founding member of the band Los Jilgueros del Arroyo along with his brothers, Israel, Alberto, Jesús, and Raúl. Polo served as the bassist. Then in 1985, he joined Los Rieleros del Norte as the band's primary vocalist and bassist. He was also a songwriter. His tenure with said band ended in 1994. One year later, he formed the band Polo Urías y su Máquina Norteña, being the group's lead vocalist and director, as well as occasional songwriter; positions he holds to this day.

Although he resides in El Paso, Texas, the city of Ojinaga has officially honored him for his contributions. He also has impacted the city of Odessa, Texas; leading the former mayor, Larry Melton, to honor him with the key to the city and marking every November 15 as "Polo Urías Day".

Today, Polo Urías y su Máquina Norteña are popular in several regions of México and the United States.

Personal life
Urías has eleven siblings. His sons Aarón and Izaiah have been his band's accordionist and bajo sexto player, respectively for several years. His nephews Adolfo and Rubén are the leaders of their own norteño-sax bands; Adolfo Urías y su Lobo Norteño and Rubén Urías y sus Aliados de Ojinaga.

In 2007, Polo bought a tour bus valued at over $250,000 after his original bus was burned. He and his band had just finished a concert in Utah and were on their way to another gig in Colorado, when near Española, New Mexico, the bus' rear engine caught fire. All members of the band, including Polo, were asleep at the time of the incident, but managed to escape unharmed thanks to a motorist who flagged down the bus driver, José Luis Ávila. In a matter of minutes, the entire bus became engulfed in flames.

In August 2020, Urías suffered from a severe case of COVID-19 and spent several days in intensive care at an El Paso, Texas, hospital. In early 2021, he suffered from a second bout of COVID-19. At the same time, one of his brothers, Jesús Urías, passed away.

With Los Rieleros del Norte

 * Corazón Cerrado (1985)
 * El Regalito (1986)
 * Nací Cantando (1987)
 * Copa Sin Vino (1988)
 * Ya Para Que (1988)
 * La Golosa (1989)
 * ...En Gira Internacional (1989)
 * Castillo de Ilusión (1990)
 * Me Lo Contaron Ayer (1991)
 * A Toda Máquina (1991)
 * Volando Alto (1992)
 * Pecado de Amor (1992)
 * Vías por Conocer (1993)
 * Peor que Nada (1994)

As Polo Urías y su Máquina Norteña

 * Sigue La Aventura (1995)
 * Incontenible (1996)
 * El Campeon de Campeones (1996)
 * A Todo Vapor (1997)
 * El Número Uno (1998)
 * ¿A Que Te Supo? (1998)
 * Mi Historia (2000)
 * De Chihuahua Para Ti (2001)
 * Sin Frenos (2002)
 * Para Mi Raza (2003)
 * En La Cumbre (2004)
 * Que Barbaros (2005)
 * En Vivo - 30 Aniversario (2005)
 * Y... Sigue La Máquina Dando (2006)
 * A Paso Firme (2008)
 * Sigo Siendo El Maestro (2009)
 * Grandes Recuerdos de Cantina (2011)
 * La Madre de Todas las Máquinas (2013)
 * Clásicas de Ayer y Siempre (2014)
 * Así de Plano (2021)
 * Dos Amigos 4 Historias (2024) (EP featuring Milo Meléndez, another former vocalist of Los Rieleros del Norte)

title: Polo Urías


text:
SO10

SO10 was the former designation of the London's Metropolitan Police's Covert Operations Group.

History
The group's origins can be traced back to 1960, with the formation of what was known as the Criminal Investigation Branch, which later evolved and was merged into SO10 and the Public Order Unit. The group's original name referred to its Specialist Operations designation prior to restructuring of the Metropolitan Police, which saw it re- designated to the Specialist Crime Directorate as SCD10, though it is still colloquially referred to as SO10.

Role
The group's role is to provide specially trained officers and resources for cases requiring covert policing and evidence gathering. It had responsibility for all undercover policing in London, particularly focusing on surveillance and relying on support from armed officers and specialist surveillance photography. Some of their most notable work is that in counter-terrorism operations, the most high profile of which led to the shooting of Brazilian Jean Charles de Menezes who was mistakenly identified as a suspected suicide bomber on July 22, 2005.

title: SO10


text:
Esquivel

Esquivel is a surname of Basque origin as well as a place name.

Origin
The last name Esquivel (or Esquibel) has its origins in the village of Esquivel, located in the ayuntamiento of Mendoza, Álava, in Euskadi.

Meaning
Usually surnames were originated in the Basque Country as name of houses, being families known by the name of the house they inhabited once. Esquivel was originally spelled Ezkibel and evolved from the Basque words Ezki, which means lime tree, and Gibel, which means behind. Therefore, Esquivel means the house behind the lime trees.

Argentina

 * Adolfo Pérez Esquivel, Nobel Peace Prize recipient
 * George Esquivel, shoe designer and craftsman
 * Laura Natalia Esquivel, teen actress and singer

Costa Rica

 * Aniceto Esquivel Sáenz, former President of Costa Rica
 * Ascensión Esquivel Ibarra, Nicaraguan-born former of Costa Rica
 * Juan Bautista Esquivel, soccer player
 * Natalia Esquivel, composer and author

Mexico

 * Carlos Esquivel, Mexican footballer
 * Juan García Esquivel, Mexican band leader, pianist and composer
 * Laura Esquivel, Mexican author
 * Yasmín Esquivel Mossa (born 1963), minister of the Supreme Court of Justice

Perú

 * Rodrigo de Esquivel, conquistador (conqueror) and encomendero in Cuzco, 16th century
 * Diego de Esquivel, first Marquis of San Lorenzo del Valleumbroso, Cuzco, 1687.

Spain

 * Emilio Morote Esquivel, novelist
 * Juan de Esquivel, explorer, first governor of Jamaica
 * Juan Esquivel Barahona, composer
 * Miguel de Álava y Esquivel, General and statesman

Other

 * Celso Esquivel, Paraguayan soccer player
 * Julia Esquivel, Guatemalan writer and human rights activist
 * Manuel Esquivel, former Belizean Prime Minister
 * Rafael Esquivel, former Venezuelan Football Federation directive

title: Esquivel