Sentence examples for in wide classes from inspiring English sources

Although there exist some gaps in the proofs of Rabinowitz's Theorems 1.27, 1.40, and 1.27 has been used several times in the literature to analyze the global behavior of the component of nodal solutions emanating from u = 0 in wide classes of boundary value problems for equations and systems [1, 2, 8, 9].

Finally, we would like to mention that such side effects – narrowing the "width" of quasi-species distribution by setting mutation rate to zero affects the population dynamics at ecological time scale – can happen in wider classes of ecological systems (e.g., see van der Laan and Hogeweg (1994) Proc R Soc Lond B 259 35).

This method is efficient and powerful in solving a wide classes of nonlinear partial fractional differential equations.

The algorithm was designed to save reasonable speed and perfect quality of learning in a wide class of problems occurring in the computational molecular biology.

It is oriented at the modifications of the classical Wishart's Goodman's pdfs adapted to the ML estimates of the data CMs in a wide class of signal processing (SP) problems in systems with centrally symmetric (CS) receive channels.

In a wide class of problems that we characterize formally in the paper, these methods allow us to find generalized plans with loops for solving problem instances of unbounded sizes and also to determine the correctness and applicability of the computed generalized plans.

We refine the technique in [10] to obtain a formula for the Riesz angle in a wide class of weighted Orlicz sequence spaces.

Poisson noise also appears in a wide class of real-world applications, e.g., positron emission tomography in medical imaging [9], fluorescence microscopy [10] and radiography images [11, 12].

Our construction produces solutions, for all initial data in dense sets, of wide classes of first and second order Cauchy problems, including the Schrödinger equation, the backwards heat equation and the Laplace equation, on Lp(Rn) or Lp, I ≤ p ≤ ∞, where Ω is a region in Rn with smooth boundary.

Our Theorem 3.1 is also valid in a wide class of general Banach spaces while Theorem 1.1 is valid in Banach spaces having weakly sequentially duality mappings.

In a wide class of weighted Bergman spaces, we construct invertible non-cyclic elements.