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In the forthcoming sections, we describe the methods used to design the nanoscale field probe and to fabricate its first prototype.
In the forthcoming sections, the uniqueness theorem is first utilized to establish the true distribution of the internal forces at collapse.
Further, most frequently used engineered metal nanoparticles are discussed in the forthcoming sections.
This section contains important concepts which will be used in the forthcoming sections.
The mathematical treatment of the proposed structural system is presented in the forthcoming sections.
Section 2 contains some basic notations on Malliavin calculus that will be used in the forthcoming sections.
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We shall elaborate the derivation of the IM method in the forthcoming section.
In the forthcoming section, we give the Euler functional of BVP (1.1) and some basic lemmas.
In this preliminary section, for the reader's convenience, we collect some basic results that will be used in the forthcoming section.
In the forthcoming section, we present lower and upper bounds on Randic index of connected graphs and trees in terms of modified Zagreb indices given in (4).
The Banach spaces introduced in the next Section 2.1 (resp. Section 2.2) will be crucial in the construction of analytic solutions of a convolution problem investigated in the forthcoming Section 4.2 (resp. Section 4.4).
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