The phrase "and continuous up to" is correct and usable in written English.
It can be used to indicate that something extends or remains in effect until a certain point or limit.
Example: "The project timeline is set for six months and continuous up to the final review date."
Alternatives: "and ongoing until" or "and extends to".
end{aligned}In the half-line case and under suitable conditions on the potential, the (modified) perturbation determinant (D zeta )) (Sect. 2) is simply given by (D zeta )=omega (zeta )) and is analytic in (zeta ) for (mathfrak {I}zeta >0) and continuous up to (mathfrak {I}zeta =0) except possibly at (zeta =0).
Since (lambda=2sqrt{q}cos z) maps (P_{0}) to the domain (Lambda :={mathbb{C}}backslash[-2sqrt{q},2sqrt{q}]), the function (E lambda):={E t,lambda)}_{tin q^{{mathbb{N}}}}) is analytic in Λ, and continuous up to the interval ([-2sqrt{q},2sqrt {q}]), under the condition (1.3).
In the present study we aimed to investigate the acute and continuous (up to 14 days of treatment) effect of growth hormone substitution on blood pressure regulation.
The aim of the study was to evaluate the acute and continuous (up to 14 days of treatment) effect of growth hormone (GH) on blood pressure (BP) regulation and to investigate the interplay between GH, nitric oxide (NO) and BP.
Therefore, (N^) and (N^) are analytic in (mathbb{C} _= { lambda:lambdainmathbb{C},operatorname{Im}lambda >0 } ) and (mathbb{C}_= { lambda:lambdainmathbb {C},operatorname{Im}lambda<0 } ), respectively, and are continuous up to the real axis.
In Theorem 1.3, it is not necessary to assume that and are continuous up to.
Since (u_{n}) is bounded and g is continuous, up to subsequence, there is (t_{0}geq0) such that gbigl(|u_{n}|^{p}bigr to gbigl(t_{0}^{p} bigr geqalpha_{0}quad text{as } ntoinfty, and so lim_{ntoinfty} int_{Omega}|nabla u_{n}|^{p-2}nabla u_{n}nabla u_{n}-u),dx=0.
The solution is continuous irrespective of the time segment (step) and the derivatives are continuous up to orderN-1 whereNis the order of the series expansion.
The behavior of such gapless surface states that exist on the topologically non-trivial side is continuous, up to and at the gap closing.
It follows from (3.6) and (3.14) that the function (N^) is analytic in (mathbb{C}_), and all of its derivatives are continuous up to the real axis.
It follows from (2.2) and (2.3) that the function f is analytic in C +, continuous up to the real axis and f ( z + 4 π ) = f ( z ).
