1. ip is real-analytic; 2. the rank of <p equals p on an everywhere dense subset of U; 3. (f(U) is closed in V; 4. for each compact subset K C <p(U), there exists a compact subset H C U such that <p(H) = K. Then the composition subalgebra A? = {foip: f e C°°(V)} is closed in C°°(U), when this algebra carries its natural Frechet topology (convergence on compact subsets of the function and all it...

In Accelerated life testing (ALT), a log-linear relationship between life and stress is used. However instead of original parameters, transformed parameters are used for estimation which loose originality due to various assumptions. In this paper the geometric process is used for the analysis of ALT under constant stress for the Frechet Distribution. The maximum likelihood procedure is followed...

function, 51 Riemann integral, 51 adjoint bilinear form, 65 almost separably valued, 53 Ascoli Theorem, 8 Banach space reflexive, 6 separable, 2 Banach-Steinhaus Theorem, 5 Bessel’s inequality, 9 biharmonic, 61 bilinear form, 55, 58 bounded, 58 strongly positive, 58 Bochner-Pettis Theorem Theorem, 53 Bounded Inverse Theorem, 6 Calculus in W 1,p(I;X) Theorem, 54 Campanato ’63 Theorem, 86 Campana...

In this paper, we studied the long-time properties of solutions generalized Kirchhoff-type equation with strongly damped terms. Firstly, appropriate assumptions are made for nonlinear source term g (u) and Kirchhoff stress term M (s) in equation, existence uniqueness solution proved by using uniform prior estimates time Galerkin’s finite element method. Then, abounded absorption set B0k is obta...

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In this paper, the largest and the smallest observations are considered, at the time when a new record of either kind (upper or lower) occurs based on a sequence of independent random variables with identical continuous distributions. We prove that sequences of the residual or past entropy of the current records characterizes F in the family of continuous distributions. The exponential and the ...