Sentence examples for equation triangle from inspiring English sources

Here W is the solution of the following elliptic equation: triangle W+|W|^{frac{4}{N-2}}Win,quadot{n dot{H}^{1}.

For transverse electric (TE) mode we assume that (E_{z}= 0) in (7) and the longitudinal magnetic field (H_{z}) satisy the Helmholtz equation triangle H_{z} + k^{2} H_{z} = 0, (8) where △ is the Laplace operator in cylindrical coordinates, (k^{2}) is defined in (5) and H_{z} (r, varphi, z) := H_{z}(r, varphi) e^{- i beta z}.

Notes: These figures present the results of the rolling estimations of the equation (triangle e_{t+1} = alpha +beta D + gamma r^{omega }_{t+1}+delta D r^{omega }_{t+1} + epsilon _{t+1}), where D is a dummy equal to one when stock returns are below their sample average and zero otherwise.

For transverse magnetic (TM) mode we assume that (H_{z}= 0) in (7) and the longitudinal electric field (E_{z}) satisy the Helmholtz equation triangle E_{z} + k^{2} E_{z} = 0, (15) where △ is again the Laplace operator in cylindrical coordinates, (k^{2}) is defined in (5) and E_{z} (r, varphi, z) := E_{z}(r, varphi) e^{- i beta z}.

These results are typical of elliptic systems and may be explained by the Dirichlet problem for the Poisson equation triangle u=f,quad mathbf{x}in G,qquad u(mathbf{x})=0, quad mathbf{x}in partial G. Namely, if (f in L_{q}(G)), then (u in W^{2,q}(G)) and | u| _{W^{2,q}(G)} leq| f| _{L_{q}(G }quad mbox{for } q>1.

Now that you know two sides and the angle in between them, you can find the area using the equation: ' Triangle Area = (1/2) * S * S * sin(a) Triangle Area = (1/2) * S * S * sin(a) Example Y: A = (1/2) * 7 centimeter (2.8 in) * 5 centimeter (2.0 in) * sin(43) = (1/2) * 7 * 5 * 0.68 = 11.9 squared cm.

A new preoperative adjustment method achieved by resistance compensation method is proposed, and the dynamic equation of triangle mechanism is deduced.

Our study is motivated by [1], where Poláčik et al. developed a general method for obtaining universal initial and final blow-up rates for the scalar equation (u_{t}-triangle u=u^{p}) ((p>1)), based on rescaling arguments and Liouville-type theorems, combined with a key doubling property.

Mixture proportions returned by a simple model (Eq. 1, blue squares), by an enrichment-corrected model (ρ -corrected mixture equations, green triangles) and by the DeconRNASeq package [ 36 ] (red circles) on SEQC data.

Using equation (10), the triangle inequality, the following inequalities ( a + b ) p ≤ 2 p ( a p + b p ), 0 < p < 1, a, b ≥ 0, (11).

where is the eigen wave function ofE n solved from the Schrodinger equation with the triangle-shaped confined potential well and so different staten has different For ground state,n = 0, furthermore, Eq. (4) can be transformed to (5).