The asymptotes are the lines that are parallel to the hyperbola and are assumed to meet the hyperbola at infinity. The equation of asymptotes of the hyperbola are y = bx/a, and y = -bx/a. The equation of pair of asymptotes of the hyperbola is x2a2−y2b2=0x2a2−y2b2=0. ...
ceil Returns the smallest (closest to negative infinity) value that is not less than the argument and is equal to a mathematical integer. round Round to the nearest integer. Examples: round(−2.5) = −2, round(-0.1) = 0, round(0.1) = 0, round(2.5) = 3 abs Absolute value (dista...
If the pressure approaches infinity, the molar volume equals b. Therefore, the b parameter can be considered as the volume of 1 mol of hard-sphere volume and is usually called covolume. Covolume is always less than V, and (V-b) is a positive term that represents the free space between...
as the domain space), it turns out (under reasonable regularity hypotheses) that essential self-adjointness is equivalent togeodesic completenessof the manifold, which is a global ODE condition rather than a local one: one needs geodesics to continue indefinitely in order to be able to (unitaril...
Key to the two results is Theorem3.1, which asserts that in each case the kernelKmaps any vectoruin its domain radially to its multipleand further identifies the linking function Notational convention:Throughout below,X,Yare fixed real topological vector spaces;may either be given in advance, or...
{and tends to infinity as } x_1 \rightarrow 0^{+} \text { or } x_2 \rightarrow 0^{+}. \end{aligned}$$ (1.37) [well-posedness of the landau equation] taking \(s=1\) in the above, the global well-posedness of ( 1.26 ) holds true. we state this result in details for ...
The order-of-magnitude analysis presented in the preceding section indicated that the unsaturated flow theory holds true for condensing flows only when the ratio of the kinematic viscosities of the liquid and vapor approaches infinity. However, in practice this ratio is very small, e.g. equal to...
Does the equation upper a bold x equals bold b has at least one solution for every possible b?Question:Does the equation upper a bold x equals bold b has at least one solution for every possible b?System of equationFor any matrix A and any vector X and...
On the zeros of the solutions of the equation w (k - Bank, Langley - 1990 () Citation Context ...s that if m ! 2(n \Gamma 1) , then for any non-trivial solution f of the equation, its exponent of the convergence of the zero sequence (f) equals to infinity. The same result ...
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