Sentence examples for singular functional from inspiring English sources

Recently, in [1 4], Erbe, Kong, Jiang, Wang, and Weng considered the following singular functional differential equations: (1.1).

Sharp sufficient conditions for the solvability of the Cauchy problem for linear singular functional differential equations are obtained.

In the Volterra case, the Cauchy problem is considered in [20 22] for some classes of nonlinear singular functional differential equations.

The Mikhlin-Manevich asymptotic methodology is used for solving the singular functional equation describing the non-similar modes and approximate, analytical expressions are derived.

We use these results to prove the strong existence of the solutions of stochastic differential equations with singular (functional) drifts and also to prove the non-existence of strong solutions of some stochastic differential equations.

Any linear functional (fin(l_{Phi,p})^) can be uniquely expressed as (f=v+s), where v is belongs to the Köthe dual of (l_{Phi}) and s is a singular functional on (l_{Phi}), that is, for any (xin h_{Phi}) the equality (s(x)=0) holds.

Defining signatures as specific patterns derived from singular functional or cellular entities, signatures of highly purified leucocyte cell types [ 43] and precisely defined cellular stimulation (for example, stimulation by Toll-like receptor 2 in synovial fibroblasts [ 18]) contribute to the establishment of such a systematic data collection for referencing.

Recall that where consists of all singular functionals, see Aliprantis and Border [20].