Section 2 summarizes the results of the prevous work [7,8,9] used in the present article. Section 3 contains the general derivation of the linear tensor equation for one component that is equivalent to the Dirac equation. Formulations of the linear tensor equation in terms of antisymmetric sec...
B_s\\pi B s π– B\\barK B K ¯ interactions in finite volume and X(5568) The recent observation of X ( 5568 ) by the D0 Collaboration has aroused a lot of interest both theoretically and experimentally. In the present work, we rst point out that X ( 5568 ) and D s 0 ( ...
Note that in the previous work [16], the first author studied similar questions for the non-fractional regime, namely γ=1 and a non-local source term. Here, one needs to deal with the non-local fractional Laplacian operator which gives serious complications. In particular, there is no ...
If we let the radius of the surface enclosing the volume go to infinity, the surface integral term must vanish. This is because φ1 goes to zero as 1r2 or faster, ∇φ1 goes to zero as 1r2 or faster, and the surface area goes to infinity as r2. We now have (1.47)Σi=1N∮...
Moran’s index is an important spatial statistical measure used to determine the presence or absence of spatial autocorrelation, thereby determining the selection orientation of spatial statistical methods. However, Moran’s index is chiefly a statistica
(mg/L), S is the amount of solute sorbed (mg/kg), q is the rate of flow (mL/min), ρ soil bulk density (g/cm3), θ is volumetric water content (cm3/cm3) and VT is the volume of the stirred-flow vessel (mL) and Cin and Cout are the inflow and outflow concentrations, ...
The number of degrees of freedom of a function is bounded by the product of its spatial uncertainty and its frequency uncertainty (or more generally, by the volume of the phase space uncertainty). In particular, there are not enough degrees of freedom for a non-trivial function to be simulat...
the same law. In order to avoid technicalities related to infinite volume issues, we restrict (1.2) to thed-dimensional torus\({\mathbb {T}}^d_{\varepsilon }\)of side-length\(2\pi /\varepsilon \). Here,\(\varepsilon \)is the “scale” parameter which will later be sent to 0....
This reduces the expression to a first-order one, therefore, (15)vdvdx=−gR2x2,∫vdv=∫−gR2x2dx,v2=gR2x2+C, where C is an arbitrary constant. It can be understood from the equation that v decreases as x increases, so if v is not sufficiently large, then eventually it will go...
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