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The mechanically-based approach to non-local elastic continuum, will be captured through variational calculus, based on the assumptions that non-adjacent elements of the solid may exchange central body forces, monotonically decreasing with their interdistance, depending on the relative displacement, and on the volume products.
The Piccola calculus is a process calculus, based on the asynchronous π-calculus, extended with explicit namespaces.
We first establish the soundness and the completeness of the labelled tableau calculus based on the soundness and completeness results of its constituent logics.
The main purpose of this paper is to construct the H∞ functional calculus based on the notion of S-spectrum for both quaternionic operators and for n-tuples of noncommuting operators.
A calculus based on the operator (D_{beta}) and its inverse is established.
In this paper, we present new results of the calculus based on the Hahn difference operator.
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In Section 3, we establish mean value theorems in the calculus based on this operator.
Also, some new results of the calculus based on this operator like a mean value theorem were obtained.
The aim of this paper is to introduce new concepts of Hahn's difference operator, the (q_{k},omega_{k} -Hahn difference operator,omega_{k} -Hahn calculus basedifferenceoperator and to construct thestablishted integral.
However, it turned out to be difficult to establish a sound constraint calculus based on these relations.
A calculus based on this operator and its inverse was established.
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