At each point x [member of] L, let us denote the time-like region of past as TPL(x), time-like region of future as TFL(x) and the 4-dimensional
ball of radius t as B(x, t).
In , the author has probed the shock wave geometry with mutual information in the 4-dimensional
plane symmetric Reissner-Nordstrom AdS black branes.
As it has been said previously, besides these spaces (whose group of isometries has dimension 6) the class of homogeneous three-space with 4-dimensional
group of isometries provides also nice examples of Killing submersions with both K and [tau] being constant.
Lorenz et al., "Pulmonary ventilation imaging based on 4-dimensional
computed tomography: Comparison with pulmonary function tests and SPECT ventilation images," International Journal of Radiation Oncology Biology Physics, vol.
Figure 4 shows an example of building the UB-Layer with the 4-dimensional
Equation (23) is 4-dimensional
map of the tendency of the flutter speed for various plates' dimensions.
Consequently, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in Steps 4 and 5 are matchings in 4-dimensional
subcubes K([Q.sup.0]) and K([Q.sup.1]), respectively, of sizes not exceeding 8/2 = 4.
So I have borrowed at least one useful concept from the philosophers: the 4-dimensional
block universe model of spacetime, which fruitfully complicates the texture of historicist approaches by recognizing each point's indivisible combination of distinct matter, time, and space.
Tchizawa, "On relative stability in 4-dimensional
duck solution," Journal of Mathematics and System Science, no.
Let ([bar.M], [bar.g], [PHI], V) be a 4-dimensional
The same applies to the simulations for 4-dimensional
geometry: the numerically obtained value u [approximately equal to] 3.3 [+ or -] 0.1 is slightly more than the expected value of u = 2[pi]/[pi]-1, but less than u = 4, which corresponds to the isotropic four-dimensional geometry.