Sentence examples for equation is left from inspiring English sources

Using cylindrical polar coordinates, the governing partial differential equation is left { textstylebegin{array}{l} frac{partial w}{partial t}=(nu+alphafrac{partial}{partial t} ) ( frac{partial^{2}}{partial r^{2}}{partial{r}frac{partial }{partial r} ) w r,t -Nw,t -Nwt)=w a,td t>0, w(r,0)=W,quad 0leq r< a,end{array}displayst>0e right.

(3.1) whose equivalent Itó equation is left { textstylebegin{array}{l} du=v, dt, dv=-A^{2}u, dt-A^{2}v, dt-bu^, dt-f u), dt-f u), dt+qu(x,tau)=u_{0}(x), qquadWu xt}(x,tau)=u_{1}(x), quad xinOmega, end{array}displaystyle right.

So, the observation equation is: left(begin{array}{c}hfill {operatorname{s}}_khfill hfill {theta}_khfill end{array}right)=left(begin{array}{c}hfill sqrt{x_k^2+{y}_k^2}hfill hfill { tan}^{-1}left(frac{y_k}{x_k}right)hfill end{array}right)+{operatorname{v}}_k (43).

Another helpful saying that tells you what to do with each part of the equation is: "Leave Me (the first fraction), Change Me (the division symbol), Turn Me Over (the second fraction).".

One of the most classical diffusive logistic equations is left { textstylebegin{array}{l@{quad}l} u_{t}-Delta u=lambda u 1-K x u^{pp} ) & mbox{in } Omega, u=0 & mbox{on } partialOmega, end{array}displaystyle right.

Extensions to the case of more general of integral equations are left for future studies.

Extensions to the case of more general systems of integral equations are left for future studies.

Denoting the threshold level as (V_{L}), the state-dependent impulsive differential equations are left { textstylebegin{array}l} left.

The MMA patient equations were left kidney length (cm) = 0.033 * height (cm) + 4.0, and right kidney length (cm) = 0.037 * height + 3.0 (p < 0.001 for β coefficients).

The control group equations were: left kidney length (cm) = 0.051 * height (cm) + 1.8, and right kidney length (cm) = 0.050 * height (cm) + 1.8.

Since these equations are left reducing variants of the otherwise well known recursions of PMcomp[ 34], one computes all entries in D in O (n 2 m 2 ) time and O (nm ) space by applying the evaluation strategy of LocARNA, which takes advantage of filtering base pairs by probability pmin.