What's the difference between four and quaternion?
Four
Definition:
(a.) One more than three; twice two.
(n.) The sum of four units; four units or objects.
(n.) A symbol representing four units, as 4 or iv.
(n.) Four things of the same kind, esp. four horses; as, a chariot and four.
Example Sentences:
(1) These included bringing in the A* grade, reducing the number of modules from six to four, and a greater attempt to assess the whole course at the end.
(2) Low birth weight, short stature, and mental retardation were common features in the four known patients with r(8).
(3) It was shown in experiments on four dogs by the conditioned method that the period of recovery of conditioned activity after one hour ether anaesthesia tested 7 to 7.5 days.
(4) However, four of ten young adult outer arm (relatively sun-exposed) and one of ten young adult inner arm (relatively sun-protected) fibroblasts lines increased their saturation density in response to retinoic acid.
(5) A 61-year-old man experienced four bouts of pancreatitis in 1 year.
(6) The promoters of the adenovirus 2 major late gene, the mouse beta-globin gene, the mouse immunoglobulin VH gene and the LTR of the human T-lymphotropic retrovirus type I were tested for their transcription activities in cell-free extracts of four cell lines; HeLa, CESS (Epstein-Barr virus-transformed human B cell line), MT-1 (HTLV-I-infected human T cell line without viral protein synthesis), and MT-2 (HTLV-I-infected human T cell line producing viral proteins).
(7) In each study, all subjects underwent four replications (over two days) of one of the six permutations of the three experimental conditions; each condition lasted 5 min.
(8) Four cytotoxic antibiotics, bikaverin, duclauxine, PSX-1 and vermiculine, were examined with respect to their interference with glycolysis and respiration and their possible ionophoric or cytolytic activity.
(9) The invaginations were classified into four easily recognized types: regular, chunky, filigree, and ridge (present only in axon hillock regions).
(10) During the study period four family outbreaks and seven recurrences of infection were observed.
(11) These four antigens consisted of S of MNSs blood group, Lua of Lutheran blood group, and K and Kpa of Kell-Cellano blood group.
(12) Binding data for both ligands to the enzyme yielded nonlinear Scatchard plots that analyze in terms of four negatively cooperative binding sites per enzyme tetramer.
(13) Even so, amputation of fifteen extremities and four other major excisions were required in twelve patients.
(14) Four of the 39 ticks in our colony were infected with a spirochete; presumably, Borrelia crocidurae.
(15) Four other independent LCMV-GP2(275-289) specific H-2Db-restricted CTL clones also expressed V alpha 4 and V beta 10 gene elements.
(16) The hospital whose A&E unit has been threatened with closure on safety grounds has admitted that four patients died after errors by staff in the emergency department and other areas.
(17) Maximal covalent binding of [4,5-14C]ronidazole to DNA also required four-electron reduction, consistent with previous studies of the covalent binding of this agent to immobilized sulfhydryl groups [Kedderis et al.
(18) We investigated whether these peptides also affect the sleep EEG in humans when given intravenously by comparing polysomnographically the effects of four boluses of (1) placebo, (2) 50 micrograms GHRH or (3) 50 micrograms SRIF administered at 22.00, 23.00, 24.00 and 1.00 h to 7 male controls.
(19) Since the start of this week, markets have been more cautious, with bond yields in Spain reaching their highest levels in four months on Tuesday amid concern about the scale of the austerity measures being imposed by the government and fears that the country might need a bailout.
(20) In 14 of the patients the imaging results were checked against the histological findings of a subsequent thymectomy, which revealed four thymomas and (with the exception of one normal thymus) hyperplastic changes in all the others.
Quaternion
Definition:
(n.) The number four.
(n.) A set of four parts, things, or person; four things taken collectively; a group of four words, phrases, circumstances, facts, or the like.
(n.) A word of four syllables; a quadrisyllable.
(n.) The quotient of two vectors, or of two directed right lines in space, considered as depending on four geometrical elements, and as expressible by an algebraic symbol of quadrinomial form.
(v. t.) To divide into quaternions, files, or companies.
Example Sentences:
(1) During visually guided movements, arm follows gaze, and the nine-dimensional rotatory configuration space for eye-head-arm-synergies (three degrees of freedom for each system) is reduced to a two-dimensional plane in the space of quaternion vectors.
(2) Many testable predictions made by quaternion models also turn up in models based on other mathematics.
(3) Quaternion models predict that eye position is represented on four channels in the oculomotor system: three for the vector components of eye position and one inversely related to gaze eccentricity and torsion.
(4) The four-component rotational operators called quaternions, which represent eye rotations in terms of their axes and angles, have several advantages over other representations of eye position (such as Fick coordinates): they provide easy computations, symmetry, a simple form for Listing's law, and useful three-dimensional plots of eye movements.
(5) In other words, angular eye positions in space (expressed as quaternions) were constrained to a two-dimensional surface.
(6) Findings 1 and 3 show that saccadic control signals accurately reflect the properties of three-dimensional rotations, as predicted by a new quaternion model of the saccadic system; models that approximate rotational kinematics using vectorial addition and integration do not predict these findings.
(7) Tweed and Vilis (Journal of Neurophysiology, 58, 832-849, 1987) have argued that quaternion algebra provides the most appropriate description of the rotations of the eye, and have derived a three-dimensional model of gaze control based on quaternion operations.
(8) A canonical unitary representation of the Euclidean group on the range space of the Gabor transform is constructed from mathematical properties of the Euclidean group and the quaternions.
(9) The positions of the arm in space were described by quaternion vectors, i.e., a particular position was described in terms of the axis and amplitude of a rotation from a reference position to that position.
(10) In this paper we present algorithms for computing eye position quaternions and eye angular velocity (not the derivative of position in three dimensions) from two search coils (not necessarily orthogonal) on one eye in two or three magnetic fields, and for locating primary position using quaternions.
(11) In our three-dimensional models, we represent eye position using four-component rotational operators called quaternions.