“…In conclusion we mention that a two-dimensional analogue of similar studies was provided in works [7][8][9]. R.R.…”
Section: Introductionmentioning
confidence: 61%
“…Thus, we have constructed leading terms u 0 (x), u 1 (x), u 2 (x) (up to an additive constant (14) and (9). The construction of complete asymptotic expansions (14) and (9) and their rigorous justification will be provided in the next two sections.…”
Section: It Yields the Asymptotics At Infinity Of Functionsmentioning
confidence: 99%
“…Proof. We denote by u N (x, ε) and v ± N (x, ε) partial sums of series (14), (9), respectively, up to the powers ε N . Statements 3) and 6) of Theorem 1 imply the following differentiable identity…”
Section: Justification Of Constructed Asymptotics For Solution To Boumentioning
We construct and justify rigorously the complete asymptotic expansion for the electric resistance of a three-dimensional resistance connected by two small contacts of arbitrary shape. We obtain explicit formulae for the first two terms in the asymptotics generalizing the classical Holm formula of one-term asymptotics for two small round contacts of same radius.
“…In conclusion we mention that a two-dimensional analogue of similar studies was provided in works [7][8][9]. R.R.…”
Section: Introductionmentioning
confidence: 61%
“…Thus, we have constructed leading terms u 0 (x), u 1 (x), u 2 (x) (up to an additive constant (14) and (9). The construction of complete asymptotic expansions (14) and (9) and their rigorous justification will be provided in the next two sections.…”
Section: It Yields the Asymptotics At Infinity Of Functionsmentioning
confidence: 99%
“…Proof. We denote by u N (x, ε) and v ± N (x, ε) partial sums of series (14), (9), respectively, up to the powers ε N . Statements 3) and 6) of Theorem 1 imply the following differentiable identity…”
Section: Justification Of Constructed Asymptotics For Solution To Boumentioning
We construct and justify rigorously the complete asymptotic expansion for the electric resistance of a three-dimensional resistance connected by two small contacts of arbitrary shape. We obtain explicit formulae for the first two terms in the asymptotics generalizing the classical Holm formula of one-term asymptotics for two small round contacts of same radius.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.