Part 2 of this course on modeling with partial differential equations (PDEs), we will have a closer look at using the Coefficient Form PDE and General Form PDE interfaces to model with general diffusion-type equations, such as Poisson's equation, the Laplace equation, and the heat equation. ...
termed as “cell deconvolution” within the context of cell biology. The estimation of cell type-specific gene expression is a well established and challenging problem in the field. Prior work includes but is not limited to TAPE [5], bMIND [6], BayesPrism [7], and...
The mathematical expressions for the expectations referred to in Equation (31) lack precision and can be located in Cohen’s work [26], where he computed the asymptotic variance–covariance matrices for various sample types. Therefore, we rely on the estimated asymptotic variance–covariance matrix ...
1. A computer implemented method of automatically solving simultaneous parameterized equations of context qualified types for solution elements comprising: 1) other context qualified types implied by equation parameters, 2) code instances of said context qualified types and 3) type difference transformations...
equation-environment: \begin{equation} a = b + c \end{equation} a=b+c (1) In case one does not want to have an equation number, the *-version is used: \begin{equation*} a = b + c \end{equation*} a=b+c All other possibilities of typesetting simple equations have disadvantages:...
To simplify the calculation, the inclusion is assumed to be an inert spherical solid with a constant density of 3900 kg/m3, and its size will not change even if a collision happens; the motion of inclusions does not influence the macroscopic flow pattern. Considering the chaotic effect of ...
It is a powerful and versatile equation editor designed to simplify the process of inclusion of mathematical notations in desktop and web applications.Is it safe?Yes, this app is developed by a reputable software team from Wiris.AlternativesMicrosoft Equation Editor –A competent built-in equation ...
13. Here we study a different mean-field equation, simplify the proofs and weaken non-physical initial conditions. The simplification is due to the introduction of the infinite Wasserstein distance. The results are obtained for L1 u2229 Lu221e vorticities without any sign assumption, in the ...
in the dynamic character of the machining process52. During the machining process, the degrees of freedom with wide amplitudes of modal mass distribution are referred to as weak machine components53. For the free vibration of the machine tool structures, we have the following dynamic equation: ...
13. Here we study a different mean-field equation, simplify the proofs and weaken non-physical initial conditions. The simplification is due to the introduction of the infinite Wasserstein distance. The results are obtained for L1 ∩ L∞ vorticities without any sign assumption, in the periodic ...