Decision problems are problems solved by boolean functions of inputs. Polynomial time Turing machines are Turning machines with the number of required steps always bounded by some polynomial function of input size. Polynomial time decision problems (P) are decision problems that can always be solved by some polynomial time Turing machine. Nondeterministic polynomial time decision problems (NP) are decision problems that always have answers that can be verified by some polynomial time Turing machine. NP hard decision problems are decision problems such that, if any can be solved by some polynomial time Turing machine, then so can all NP decision problems. NP complete decision problems are decision problems that are both NP hard and NP decision problems. An example of an NP hard decision problem is the halting problem. An example of an NP complete decision problem is the traveling salesman problem. An example of a P decision problem is primality determination.
Determining cause and effect relationships can be hampered by noise. If an effect occurs some percentage of the time in the presence of a specific cause, then that cause and effect pair has a statistical power equal to that percentage. If an effect occurs some percentage of the time in the absence of a specific cause, then that cause and effect pair has a p value equal to that percentage. The confidence level is the percentage equal to 100 minus the p value percentage.
Civilizations are groups of people with cities, governments, writing systems, divisions of labor and food surpluses. Agriculture began around 10,000 years ago. Civilizations appeared around 7000 years ago. Some of the earliest civilizations appeared along the Tigris, Euphrates and Nile rivers.
Babylonians likely chose seven day weeks because Moon phases last about that long, many constellations have seven stars, and, they knew about seven "wanders" (Mercury, Venus, Mars, Jupiter, Saturn, Sun and Moon).
Telemetry is automatic device data transmission such as in race cars, aircraft and spacecraft.
Consider a horizontal surface of area A submersed in a fluid. Also, consider increasing the vertical coordinate by the infinitesimal dz. This will remove the pressure contribution from the weight of an infinitesimal cylinder. This infinitesimal cylinder has the weight ρgAdz where ρ is the fluid density and g is the freefall acceleration. Therefore, if dP is the infinitesimal change in pressure:
dP = -ρgdz
The ideal gas law implies:
where P is the air pressure, ρ is the air density, T is the air temperature, M is the air molar mass, and, R is the ideal gas constant. Also:
dP = -ρgdz
where g is the freefall acceleration, and, z is the vertical coordinate. Therefore:
dP / P = -gMdz / (RT)
If it is assumed that T = To + Lz for some air temperature lapse rate L, where To is the ground level air temperature, then:
P = Po (1 + Lz / To)-gM / (RL)
where Po is the ground level air pressure. This allows altitude to be approximated from the air pressure!
Tensors are geometric objects. Arrays are data structures. Note that matrices are arrays and that tensors can be represented by arrays.
