Sentence examples for 1 solves from inspiring English sources

(1) solves (1.4) if and only if exists with if and only if with for.

We split u on S R = S R ( y 0 ) as u = u 1 + u 2 so that u 1 solves the problem (2.4).

Given a potential f ∈ H 1 2 on the boundary the induced potential u ∈ H 1 solves the Dirichlet problem ∇ · ( γ ∇ u ) = 0 in Ω, u | ∂ Ω = f.

Theorem 1 solves a theoretical question raised in connection with the application of Dirichlet-Sch type inequality, obtained by Huang (see [1]), which has been already applied to obtain multiplicity results for boundary value problems in several recent papers.

A point x ∗ ∈ H 1 solves SFP (1) if and only if x ∗ is a fixed point of the operator (3): P C ( I − γ A ∗ ( I − P Q ) A ).

Given the n × 1 vector of consumer demand, y, and A, the n × n matrix whose columns describe the intermediate input requirements per unit of output, the familiar quantity model, mathbf{x}=mathbf{Ax}+mathbf{y} mathrm{or} mathbf{x}={left(mathbf{I}hbox mathbf{A}right)}^{-1}mathbf{y}, (1)solves for the outputs of goods and services, the n × 1 vector x.

Step 1: Solve the recursive Eqs.

Algorithm 1: Solving -HS problem using -nets.

Step 1 Solve the feeder-line flow for the system.

"We don't think Chapter 9 solves the problem," he said.

(b) If α γ>1 and A>A c then there exists three interior steady states with land holdings (x L (A), x H (A)), (1,1), and (x H (A), x L (A)), where x L (A)=2−x H (A)∈ 0,1) solves Δ x, A =0.