Sentence examples for with first kind from inspiring English sources

In the past, several approaches have been sought for solving fourth order BVPs with first kind boundary conditions.

Let (varphi(cdot)= varphi_{1}(cdot),varphi_{2}(cdot), ldots,varphi_{n}(cdot))) be a piecewise continuous function with first kind discontinuities at the points of a fixed sequence ({t_{k}}).

(ii) (x, y) T satisfies model (1) for t ≥ 0, and x(s) = ϕ(s), y(s) = φ(s) for s ∈ (-∞, 0].  . (x, y) T is piecewise continuous with first kind discontinuity at the points t k, k ∈ K.

On one hand, equations of type (1.1) with boundary conditions of the second kind are transformable to coupled second order equations [6 12], such type of a reduction is not possible with first kind boundary conditions.

Definition 1 A function (x, y) T : → Rn+mis said to be the special solution of system (1) with initial conditions x ( s ) = ϕ ( s ), y ( s ) = φ ( s ) s ∈ ( - ∞, 0 ], if the following two conditions are satisfied (i) (x, y) T is piecewise continuous with first kind discontinuity at the points t k, k ∈ K.

Apart from these, a quartic non-polynomial spline approach has been proposed by researchers for the solution of the fourth [13] and sixth order [14] ODEs with second kind boundary conditions.

It is well known that ([9]) the function G t,s)=-frac{1}{2B}Q bigl[ e^{- ( t+s ) B}+e^{- ( 2T-t-s ) B}+e^{- vert t-s vert B}+e^{- ( 2T- vert t-s vert ) B} bigr] (4) is the Green function for the following elliptic problem with second kind boundary conditions: textstylebegin{cases} -v_{tt}(t)+Av(t)=f(t),quad 0< t< T, v_{t}(0)=varphi,quadquad v_{t}(T =xi.

Patients with luminal A cancer had good prognoses while those with luminal B did not, suggesting that perhaps patients with the first kind of tumor might do well with just hormonal therapy to block estrogen from spurring their cancers while those with the second kind might do better with chemotherapy in addition to hormonal therapy.

In the early years of such loans monthly payments are super-low because, with the first kind, the difference is added to your principal; with the second, you put off paying down the principal until later.

Tribes with the first kind of deal are inclined to grow cautiously, because slot machines that remain idle lose money.

If GPS interferes with the first kind of "getting lost", an entire flotilla of digital forces conspires to sink the second.