This amounts to an addition operation on the circle, which in turn generalizes to addition operations on many-dimensional tori.
This requires representing the order parameter as a scalar field on many-dimensional space ψ (z → ), the perturbations (Eqs. (5) and (6) ) being modified accordingly as sin (k r → z → + ϕ r ). 3. Canonical state sampling.
This requires representing the order parameter as a scalar field on many-dimensional space ψ (z → ), the perturbations (Eqs. (5) and (6)) being modified accordingly as sin (k r → z → + ϕ r ).
Before the description of The Personality Inventory for DSM-5 (PID-5), there were many dimensional models of personality; some focused more on the characterization of normal personalities, whereas others were based on a dimensional reorganization of the diagnostic criteria for personality disorders.
They were proposing that this universe is just one of many three-dimensional bubbles (called branes) floating inside a four-dimensional hyperspace.
In principle, multi-dimensionalists may even accept that there is no fixed number or limit on how many one-dimensional lists of categories there may be, though each such list may purport to provide a unique, correct, exhaustive categorization of entities considered in the chosen respect.
Holography is an optical process that stores not only three-dimensional images like the ones placed on many credit cards for security purposes, but the 1's and 0's of digital data as well.
Thermal performance of windows depends on many parameters, such as dimensional characteristics and material properties of the components.
Often he seemed to be playing three-dimensional chess: on many planes, weighing many options, shifting friends and foes.
The exact effect of certain helper nucleotides on the strength of the signal of certain capture probes depends on many factors, including probably the three-dimensional structure of the target molecule.
Although many aspects of his thought remain the subject of scholarly debate, Xenophanes was clearly a multi-dimensional thinker who left his mark on many aspects of later Greek thought.
