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In the case of a CATB aqueous solution with a lower concentration, owing to the deficiency of surfactants, only a certain partial of the oil phases could form well-defined spherical emulsions, resulting in the formation of some shuttle-like nanostructures together with some irregular nanostructures.
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A fuzzy observer gain and a fuzzy residual gain in each observer are designed such that the residual is sensitive to a certain partial group of faults and robust against disturbance.
Fixed point theorems in nonlinear analysis have become indispensable tools in a vast area of the analysis ranging from proving the existence of solutions of certain partial differential equations to nonlinear optimization and related fields (see, for instance, [1]).
In the general case, when there are two or more audio sources present in the analyzed signal, a certain partial can be part of one of the sources, it can be shared by two or more sources, or it can be part of none of them (i.e., inharmonic or noisy partials).
Our results can generalize some known results and be used more effectively to study the qualitative properties of the solutions of certain partial differential and integral equations.
The class is given in terms of solvability of a certain partial differential equation.
Recently, conservation laws have been used to find exact solutions of certain partial differential equations [35], [36].
The inequalities given here can be used as handy tools to study the properties of certain partial dynamic equations on time scales.
In this section, we will apply our result to discuss the boundedness of certain partial integral equation with weakly singular kernel.
Therefore, an improper handling of certain partial failures can easily lead to accidents and severe chain reactions, and thus may cause large-scale/extensive blackout eventually.
The purpose of this paper is to generalize some integral inequalities in two independent variables with delay which can be used as handy tools in the study of certain partial differential equations and integral equations with delay.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com