Consider an open connected 4-dimensional
manifold M the closure of which is compact.
In the 4-dimensional
space-time, though the geodesic length does not equal the area of the minimal surface, it has been shown that both the geodesic length and area of the minimal surface, which are dual to the two point correlation function and entanglement entropy respectively, are nonlocal probes and have the same effect as they are used to probe the thermalization behavior and phase transition process [23-40].
Moreover, we see that homogeneous 3-spaces with 4-dimensional
isometry group pose bundle-like metrics and their classes of congruence are completely determined, up to topology, for a pair of constants: the curvature of the base surface c, and the bundle curvature [tau].
By moving to N-Flight Planning, Royal Jordanian is fully expecting industry leading flight planning response time, improvements with robust 4-dimensional
(4D) calculations that will result in an estimated 2% fuel savings, 20% improvement to staff production, along with greater aircraft utilization.
There are [2.sup.8] = 256 responses possible to the eight questions and since each of the suits in the diagram does double duty, the diagram really represents a 4-dimensional
cube with 16 nodes.
The Regional Ocean Modeling System (ROMS) 4-dimensional
variational data assimilations systems, Part I--System overview and formulation.
In circa 1954 Synge  published a study on the idea of 3-waves propagating in the 4-dimensional
First of all, we consider 4-dimensional
traffic of a mobile cellular network: two newly originated traffic types and corresponding two handoff traffic types.
Recently, deriving lung ventilation distribution from 4-dimensional
Computed Tomography (4DCT) using deformable image registration (DIR) has been developed [3-5].
It has turned out that the 6-mode extension of the Lorenz model (1) recently suggested as a more appropriate minimal model of the two-dimensional RBC  could also be treated in terms of G-models, namely, as a 4-dimensional
Table 2 shows the process of dividing the 4-dimensional
input data into two 2-dimensional datasets [div.sub.1] and [div.sub.2] using UB-Basic algorithm, and Figure 3 shows the result of [div.sub.1] and [div.sub.2].
The illustration of trends body of (22) requires a 4-dimensional
This time, the assumption on matching size is replaced with a requirement of even distribution of its edges among 4-dimensional
I also studied Bradford Skow's critique in his 2015 volume, Objective Becoming, which explores the possibility of a "robust" rather than "anemic" understanding of the "passage of time" (his adjectives) within alternative post-Einsteinian models that undo the separation of temporal from spatial dimensions, producing the useful concept of 4-dimensional
Tchizawa, "On a local model for finding 4-dimensional
duck solutions," in Selected Topics in Mathematical Methods and Computational Techniques in Electrical Engineering, pp.