first moment of area in the x and y directions are respectively given by: Sx=Ay¯=∑i=1nyidAi=∫AydA{\displaystyle S_{x}=A{\bar {y}}=\sum _{i=1}^{n}{y_{i}\,dA_{i}}=\int...

rotation, dAy=[10dϕ010−dϕ01].{\displaystyle dA_{\mathbf {y} }={\begin{bmatrix}1&0&d\phi \\0&1&0\\-d\phi &0&1\end{bmatrix}}.} Compare the products dAx dAy to dAydAx...

denominator have absolute values not greater than the square root of the modulus. More precisely, for every pair of integers (a, m) with m > 1, given two...

small-scale shear modulus in any direction, not to any rigidity or stiffness properties such as its bulk modulus or Young's modulus. Stiffness is often...

2 + b 2 . {\displaystyle x={\frac {b(bx_{0}-ay_{0})-ac}{a^{2}+b^{2}}}{\text{ and }}y={\frac {a(-bx_{0}+ay_{0})-bc}{a^{2}+b^{2}}}.} Horizontal and vertical...

using Young's modulus of elasticity, the ratio of stress to strain along an axis, in Pascals. Thus, a material with a high Young's modulus is very rigid...

f has a unique global minimum on Rn. A uniformly convex function, with modulus ϕ {\displaystyle \phi } , is a function f {\displaystyle f} that, for all...

the Kronecker delta, K is the bulk modulus (or incompressibility), and μ {\displaystyle \mu } is the shear modulus (or rigidity), two elastic moduli....

⟩  for all  x , y ∈ R n . {\displaystyle \langle Ax,y\rangle =-\langle x,Ay\rangle \quad {\text{ for all }}x,y\in \mathbb {R} ^{n}.} This is also equivalent...

glutamate, it may greatly augment the efflux of dopamine. Tsvetkov, PO; Roman, AY; Baksheeva, VE; Nazipova, AA; Shevelyova, MP; Vladimirov, VI; Buyanova, MF;...