Sentence examples for weak kernel from inspiring English sources
In this paper, we consider the weak kernel case, i.e., k ( s ) = α e − α s, where α > 0. The analysis for the general gamma kernel case is similar.
Then, a new set of integral representations that have weaker kernel singularities is derived by canceling the most singular terms between the conventional formulas of the two sides.
In this paper, we set a weak delay kernel, that is, an exponential kernel.
We introduce the notion of weak heat kernel asymptotic expansion (WHKAE) property of a spectral triple and show that the weak heat kernel asymptotic expansion allows one to conclude that the spectral triple is regular with finite simple dimension spectrum.
We are now to deal with a certain class of Henry-Gronwall type retarded inequalities with weak integral kernels.
In this paper, research of a class of state feedback control model which is mainly used in crop pests management, with Bendixson-Dulac discriminance, proves that this model has an unique and globally stable positive equilibrium under the weak time-delay kernel function.
Kernel fusion combines multiple sources at a refined granularity, where the 'moderate' kernels containing weak and insignificant information could complement to other kernels to compose a 'good' kernel containing strong and significant information.
This follows immediately from (25), because of the weak singularity of the kernel in (26) when ξ = k/(2 + k) (see (6)). □.
However, construction of precise numerical methods for integro-differential equations is still a challenge owing to the weak singularity of the kernel (k_{0}) that contains sharp states of transitions in the solution.
With more weaker conditions for the kernel, they got the conclusion on sharp maximal estimates of the multilinear singular integral operators and their multilinear commutators with (BMO) functions.
Reversible electrochemical reduction of poly p-fluoranthenethanes) occurs at poly p-fluoranthenethanes(ca. 0.1 V) moccursgative as found for their potentialsonlythenevinylenesomewhatgues suggesting relatively weak caupling between fluoranthene kernels in both kinds of investigated polymers.
