pentad

Definitions

  • WordNet 3.6
    • n pentad the cardinal number that is the sum of four and one
    • ***
Webster's Revised Unabridged Dictionary
    • n Pentad (Chem) Any element, atom, or radical, having a valence of five, or which can be combined with, substituted for, or compared with, five atoms of hydrogen or other monad; as, nitrogen is a pentad in the ammonium compounds.
    • Pentad Any grouping of five things.
    • a Pentad (Chem) Having the valence of a pentad.
    • ***
Century Dictionary and Cyclopedia
    • n pentad The number five, in the abstract: a set of five things considered together: as, the Pythagorean pentad: correlated with monad, dyad, triad, tetrad, etc.
    • n pentad Specifically A period of five consecutive years.
    • n pentad In chem., an element one atom of which will combine with five univalent atoms or radicals; a pentavalent element.
    • n pentad A period of five days, introduced by Dove for use in climatological study. The pentads begin January 1–5, and continue in groups of five days each throughout the ordinary year. The twelfth pentad, from February 25-March 1, may be increased by one day, namely, February 29th, without disturbing the calendar dates of the subsequent pentads.
    • ***
Chambers's Twentieth Century Dictionary
    • n Pentad pen′tad the number five, a group of five things: a mean of temperature, &c., taken every five days.
    • ***

Etymology

Webster's Revised Unabridged Dictionary
Gr. penta`s penta`dos, a body of five, fr. pe`nte five

Usage

In literature:

Five, or the pentad, is everything; it stops the power of poisons, and is dreaded by evil spirits.
"Three Thousand Years of Mental Healing" by George Barton Cutten
***

In science:

There four similar pentads exist : I call one of them (the pentad β ) the light pentad, and three (ζ , η , θ) - the chromatic pentads.
Zero
First summand of this equation contains elements of the light pentad, only.
Zero
The mass members with elements of the light pentad ( M0 and M4 ) conform to neutrino and its’ lepton states .
Zero
And six mass members with elements of chromatic pentads conform to three pairs (up and down) of chromatic states (red, green, blue).
Zero
Thus, only all five elements of a Clifford pentad provide an entire set of speed components and, for completeness, yet two ”space” coordinates x4 and x5 should be added to our three x1 , x2 , x3 .
Zero
Clearly, this notion can be generalized for the sixteen possible tetrads, for the thirty-two possible pentads, etc.
A Mathematical Random Number Generator (MRNG)
Considering the above, for random binary strings of various lengths, one can calculate – from a theoretical perspective – the most probable numbers for the different dyads, triads, tetrads, pentads and the transitions that will be present in them.
A Mathematical Random Number Generator (MRNG)
Hence of only all five elements of the Clifford pentad lends the entire kit of the velocity components and, for the completeness, yet two ”space” coordinates x5 and x4 should be added to our three x, y , z .
A Piece of the Lepton Theory from a Probability
The Clifford pentads of the 4X4 complex matrices define the current vectors of the particles.
The lepton, quark and hadron currents
The Clifford pentads sextet contains single light pentad and three chromatic pentads.
The lepton, quark and hadron currents
The Cartesian frame rotations confound the chromatic pentads.
The lepton, quark and hadron currents
Three diagonal members (β 1 , β 2 , β 3 ) of the Clifford pentad define the 3dimensional space ℜ, in which ux , uy , uz are located.
The lepton, quark and hadron currents
Each chromatic pentad with 3 diagonal matrices and with 2 antidiogonal matrices, like the light pentad, defines single 2-dimensional space, in which the weak isospin interaction acts, and defines single 3-dimensional space for the moving the physics ob jects.
The lepton, quark and hadron currents
That is the red pentad and the green pentad are confounded on the angle 2 · φ3 in their space under the Cartesian frame rotation about Z-axis on this angle.
The lepton, quark and hadron currents
For all the Cartesian frame rotations - the chromatic pentads are confounded, but the hadron monad behaves like the vector.
The lepton, quark and hadron currents
***