From these equations, we can also determine expressions for other stress measures. For example, from Equation (4.145), we get that the Cauchy stress can be determined from the Helmholtz free energy by (4.235)σ(F,θ0)=1J∂Ψ^(F,θ0)∂FF⊤. For many materials, the rate of heat...
Suppose Y is related to R and S in the following nonlinear way: Y = aR^bS^c Twenty-six observations are used to obtain the following regression results: Suppose Fira estimated a model by OLS and obtained this equation: Given the following ...
There has even been work on this system to try to determine how the full wave function behaves in the limit of infinite nuclear masses [Frolov, 2003]. Perhaps the most highly accurate calculation so far on H2+ is that of Cassar and Drake [Cassar and Drake, 2004] which was made to try...
The Maker-Breaker game was introduced by Erdős and Selfridge [4], also in the 1970s. The game is played on an arbitrary hypergraph by two players named Maker and Breaker. The players alternately select an unplayed vertex of the hypergraph during the game. Maker’s aim is to occupy all ...
Can we uniquely determine f(x) and α simultaneously? Here, Zob is defined as in Problem 1.1.It is worth noting that the observations required in this work are only for a limited period (i.e., t∈(0,T)), which is in contrast to Li and Zhang [21, Theorem 1.1]. Our aim is to...
(26) and (25), we can determine h(\zeta ). Next, by substituting h(\zeta ) into Eq. (15), we can find v(\zeta ). Finally, by replacing v(\zeta ) in Eq. (6) along with Eq. (7), we can obtain the solutions of Eq. (5) when \varpi = 2, \varrho = 1, p = 2,...
First, the Good News.Firms are worth a range of values and more options exist than ever before. A few factors/drivers determine if your business is worth a premium valuation if you exit to strategic buyer or investor. But, the bad Ugly News.Every owner exits their business, but not every...
Standard energy conserving orientational force methods8,45 are used to induce migration with a driving force of 0.01 eV and 5 replicates of each simulation. Temporal subdivision methods46,47 allowed us to determine the uncertainty of the measurements. The methods used to construct, induce, and ...
(a)Determine an initial distribution vector if this year's crop is known to be poor. (b) Calculate d(2) and use it to determine the probability that the harvest will be good in two years. Show moreView chapterExplore book Read full chapter URL: https://www.sciencedirect.com/science/...
By applying the same procedure used to determine the third-order SA, the ray aberration in the object plane for the fifth-order SA was obtained as follows: (69)δui=CS5oαo5, with (70)CS5o=−1pf∫zozidz6p6h6+3p4h4h′2−3p24h2h′4+3p08h′6=−6a6pf∫−l2l2dξp6. By ...