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2 × 5 × 5 = 2 × 5 2 . {\displaystyle {\begin{aligned}50&=2\times 5\times 5\\&=2\times 5^{2}.\end{aligned}}} The terms in the product are called prime...

\\\end{aligned}}} Approximate conversions (rounded to some arbitrary number of digits, except when denoted by "≡") are shown in the following table. Conversion...

In mathematics, the pentagram map is a discrete dynamical system on the moduli space of polygons in the projective plane. The pentagram map takes a given...

= 0   ,     d 3 w ^ n d x 3 = 0 at     x = L . {\displaystyle {\begin{aligned}&{\hat {w}}_{n}=0~,~~{\frac {d{\hat {w}}_{n}}{dx}}=0\quad {\text{at}}~~x=0\\&{\frac...

{\begin{aligned}G'(\omega ,T)&=G'\left(a_{\rm {T}}\,\omega ,T_{0}\right)\\G''(\omega ,T)&=G''\left(a_{\rm {T}}\,\omega ,T_{0}\right).\end{aligned}}} A decrease...

{\displaystyle {\begin{aligned}P_{0}(n)&=P_{d}(0)=1,\\P_{d}(n)&=P_{d}(n-1)+P_{d-1}(n)\\&=\sum _{i=0}^{n}P_{d-1}(i)=\sum _{i=0}^{d}P_{i}(n-1).\end{aligned}}} The symmetry...

L 2 = C j j i i {\displaystyle {\begin{aligned}L_{1}&=C_{\,\,\,ij}^{ij}\\L_{2}&=C_{\,\,\,jj}^{ii}\end{aligned}}} and the quadratic invariants are { L...

complex variables. They show up in many topics, including Abelian varieties, moduli spaces, quadratic forms, and solitons. Theta functions are parametrized...

) ] ε z z = 1 E [ σ z z − ν ( σ x x + σ y y ) ] {\displaystyle {\begin{aligned}\varepsilon _{xx}&={\frac {1}{E}}\left[\sigma _{xx}-\nu \left(\sigma _{yy}+\sigma...

of metabolic or biochemical activity in the body can be more precisely aligned or correlated with anatomic imaging obtained by CT scanning. PET-CT gives...

}{E}}\sigma _{2}\,,\end{aligned}}} and ε 1 ‴ = − ν E σ 3 , ε 2 ‴ = − ν E σ 3 , ε 3 ‴ = 1 E σ 3 . {\displaystyle {\begin{aligned}\varepsilon _{1}'''&=-{\frac...

u ( 0 ) + u ( 1 ) + X ) = ρ 0 ∂ 2 u ( 1 ) ∂ t 2 {\displaystyle {\begin{aligned}\rho _{0}{\ddot {{\boldsymbol {x}}'}}&=\rho _{0}{\frac {\partial ^{2}}{\partial...

− 2 b 1 + b 2 {\displaystyle {\begin{aligned}\chi &=h^{0,0}-h^{0,1}+h^{0,2}\\c_{2}&=2-2b_{1}+b_{2}\end{aligned}}} we arrive at: 10 + 12 h 0 , 2 = 8 h...

along the grain (axial direction), because most cellulose fibrils are aligned that way. It is usually least stiff in the radial direction (between the...

degrees Baum e ´ for density lesser than water {\displaystyle {\begin{aligned}\mathrm {degrees\ Baum{\acute {e}}} &={\begin{cases}\displaystyle 145\left(1-{\frac...

^{2}(2\theta )\\\end{aligned}}} where θ {\displaystyle {\begin{aligned}\theta \end{aligned}}} is the angle between the axis of symmetry...

producing cold spots and hot spots on the cosmic microwave background aligned with vast supervoids and superclusters. This so-called late-time Integrated...

S2CID 6234826. Mathar, Richard J. (2010). "Table of Dirichlet L-series and prime zeta modulo functions for small moduli". arXiv:1008.2547 [math.NT]. Weisstein...

mod 11 ) . {\displaystyle {\begin{aligned}p(7k+5)&\equiv 0{\pmod {7}},\\p(11k+6)&\equiv 0{\pmod {11}}.\end{aligned}}} The first one comes from Ramanujan's...

x+C}{2x^{2}}}.\end{aligned}}} Again, the bound on n may be decreased by loosening the parameter. For example, pn < n B2(log n; 0) for n ≥ 3468. The table compares...