The last equation equals zero due to Eqs. (9) and (14). This demonstrates that \(\varvec{\psi }^{(r)}(x)\) from Eq. (39) are indeed solutions of the Dirac Eq. (36). Diffusion coefficients of the stochastic motion In Sect. “Derivation of Dirac equation”, we derived the Dirac...
If y=3 when x=10, find x when y=1.2. Assume that y varies directly as x. Find an equation of variation where y varies directly as the square of x, and where y equals 0.43 when x equals 0.1. In the equation y=10x, what represents the constant of proportiona...
An ordinary differential equation is an equation that contains ordinary derivatives of the dependent variable y with respect to the independent variable x and the dependent variable itself. For example, {eq}\displaystyle \frac{dy}...
The sum of the values of a standardized vector equals 0, that is, zTo = 0. On the other hand, the independent variables z and residuals e are orthogonal to each other, that is, $${\mathbf{z}}^{{\text{T}}} {\mathbf{e}} = {\mathbf{z}}^{{\text{T}}} {\mathbf{o}} ...
For example, you see the analysis in a minimal surface equation, but then you also realize it has connections with other geometric questions that are not just analysis. I am definitely very attracted to the idea that there are a lot of different facets in mathematics and seeing the ...
The only problem i am having is to find slope(from slope i meant if every step is assumed as points ,this will help me to shift l and r) and slope can be find by use of its previous neighbour points to find neighbour of y=f(x),we need to find length of y so for given y=[...
In fact, we know from our approximate solution in the previous example that [H+] is near 10−3 mol l−1. Since Kw equals 1.00×10-14, the second term must be near 10−11 mol l−1, which is smaller than the first term by a factor of 108. We therefore drop the term Kw/...
Once the iterates of ΦA0t are trapped in a cone field the property (40) guarantees that its exponential growth equals the exponential growth of the projection. ◻ 4.2 End of the proof of Theorem 1 We claim that: (41) Indeed, on the one hand Birkoff’s Ergodic Theorem gives for...
Many constructs in management research are latent constructs that cannot be directly observed; therefore, researchers typically measure such constructs using established scales with multiple indicators. However, established scales do not perform equally well in different populations and samples. Moreover, ...
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