What's the difference between dimension and dimensionless?

Dimension


Definition:

  • (n.) Measure in a single line, as length, breadth, height, thickness, or circumference; extension; measurement; -- usually, in the plural, measure in length and breadth, or in length, breadth, and thickness; extent; size; as, the dimensions of a room, or of a ship; the dimensions of a farm, of a kingdom.
  • (n.) Extent; reach; scope; importance; as, a project of large dimensions.
  • (n.) The degree of manifoldness of a quantity; as, time is quantity having one dimension; volume has three dimensions, relative to extension.
  • (n.) A literal factor, as numbered in characterizing a term. The term dimensions forms with the cardinal numbers a phrase equivalent to degree with the ordinal; thus, a2b2c is a term of five dimensions, or of the fifth degree.
  • (n.) The manifoldness with which the fundamental units of time, length, and mass are involved in determining the units of other physical quantities.

Example Sentences:

  • (1) There was a linear increase in the dimensions of these zones after the chewing.
  • (2) The obtained results are used to study the relation between the acoustic characteristics of these vowels and the corresponding articulatory dimensions.
  • (3) Several dimensions of the outcome of 86 schizophrenic patients were recorded 1 year after discharge from inpatient index-treatment to complete a prospective study concerning the course of illness (rehospitalization, symptoms, employment and social contacts).
  • (4) It was considered worthwhile to report this case due to the problems which arose concerning the choice of a thoracic rather than abdominal route owing to the impossibility of associating cardiomyotomy with anti-reflux plastica surgery because of the reduced dimensions of the stomach.
  • (5) However, the effect of prior jaw motion and the effect of the recording site on the EMG amplitudes and on the vertical dimension of minimum EMG activity have not been documented.
  • (6) At that time, blood pressures, systolic and diastolic left ventricular dimensions, indices of systolic function (% FS, mVcf) and exercise capacity had not changed, while cardiac output was decreased and systemic peripheral vascular resistance was significantly increased.
  • (7) Continuity of care programs, such as that developed by the Pain Service of Memorial Sloan-Kettering Cancer Center (New York), with good communication and liaison work between hospital and community, add a much needed dimension to the pain management of these patients in the home.
  • (8) Two hundred and forty root canals of extracted single-rooted teeth were prepared to the same dimension, and Dentatus posts of equal size were cemented without screwing them into the dentine.
  • (9) Its features are consistent with observed structural dimensions and the molecular periodicities related to transcription, replication and matrix attachment domains.
  • (10) The three major RNA domains, as defined by secondary structure, appear to exist as autonomous structural units in three dimensions, for the most part.
  • (11) The surface film transition is especially noted in the pressure-area curve of the surfactant and approximates in two dimensions the broad thermotropic phase transition of the bulk phase surfactant.
  • (12) A relation between ejection fraction (EF) and the echo minor dimension measurements in end diastole and end systole was formulated, which permitted estimation of the EF from the echo measurements.
  • (13) This approach permits easy preparation of input data on the dimensions of the blocks and their positions in a 3-D arrangement.
  • (14) Fifty-one severely retarded adults were taught a difficult visual discrimination in an assembly task by one of three training techniques: (a) adding and reducing large cue differences on the relevant-shape dimension; (b) adding and fading a redundant-color dimension; or (c) a combination of the two techniques.
  • (15) Acclimation to 10 degrees C or 30 degrees C resulted in large differences in the dimensions of villi.
  • (16) The women's images of health were consistent with Smith's and Laffrey's four conceptions, but the eudaemonistic category included multiple dimensions.
  • (17) On an analytical scale, electrophoretic methods in two dimensions or in capillaries are unsurpassed in resolution power.
  • (18) High-resolution computed tomograms (HRCT) reveal strikingly little variation in the dimensions of inner ear structures among people with normal hearing.
  • (19) The kidney KGA activity was compared with the urinary KGA activity, and the following properties were found to be the same: molecular dimension, pH optimum, effect of inhibitors, and ability to liberate kinins from kininogens.3.
  • (20) The dimensions of the acetabular wall were thinner in the hips that had the thirty-two-millimeter component than in those that had the twenty-two-millimeter component (p less than 0.05).

Dimensionless


Definition:

  • (a.) Without dimensions; having no appreciable or noteworthy extent.

Example Sentences:

  • (1) Using the hypothesis that the biodynamical efficiency may not be greater than the inverse age rate beta, a dimensionless number is constructed, which is given by the product of age rate beta and the theoretical lifespan T.
  • (2) Dimensionless similarity criteria were used to produce a biological clock for ceftizoxime elimination.
  • (3) The nonideality of all three colligative expressions is described by a dimensionless constant called the solute-solvent interaction parameter I.
  • (4) Assuming that the catalytic action of the enzyme obeys a Michaelis-Menten rate expression and that the deactivation of the enzyme follows a first-order decay, the present analysis employs the dimensionless, integrated form of the overall rate expression to obtain a criterion (based on the maximization of the determinant of the derivative matrix) that relates the a priori estimates of the parameters with the times at which samples should be withdrawn from the reacting mixture.
  • (5) Two criteria are used for screening: both involve the parameter [(delta rho)4] (delta rho is a dimensionless function proportional to the Fourier transform of the set of observed structure factors).
  • (6) A new calibration constant is introduced, viz., the response factor (RF, dimensionless), which is independent of the diameter of the capillary, the construction of the universal detector and the driving current used during detection.
  • (7) On the basis of the dimensionless stride length, stride frequency, pelvic rotation and trunk rotation, deficits in the gait of stroke patients could be quantified.
  • (8) Assymptotic solutions show that the volume estimates are governed by a time constant, tau, related to diffusion in the tissue, to tissue capacity, and to wall permeability, and by a dimensionless ratio, f, describing a relation of tau to vascular transport time.
  • (9) ct and cv are dimensionless quantities that increase with [4-AP] and reflect the voltage-independent and voltage-dependent component, respectively, of block.
  • (10) The dimensionless input parameters are: U, a horizontal Froude number based on forward speed and leg length; V, a vertical Froude number based on vertical landing velocity and leg length, and KLEG, a dimensionless stiffness for the leg-spring.
  • (11) This is the most important dimensionless group influencing the motion of a particle relative to the fluid.
  • (12) The quantitative assessment of the technological effectiveness of the products is done by using a single dimensionless overall index that varies from 0 to 1, this facilitating a comparative evaluation of this effectiveness.
  • (13) The estimated dimensionless carrier parameters for 2 are J*max = 0.16, Km = 0.08 mM, P*c = 2.0, and P*m = 0.25; for lisinopril, passive absorption is not significant and its absorption is nonpassive: J*max = 0.032, Km = 0.082 mM, and P*c = 0.39 (where J*max is the maximal flux, Km is the Michaelis constant, P*c is the carrier permeability, and P*m is the passive permeability).
  • (14) Proper nondimensionalization of the resulting equations leads to the identification of dimensionless parameters which combine the transport characteristics of the endothelial wall and the intravascular flow resistance.
  • (15) The governing differential equations are given in dimensionless form to make the results representative of animals of all body sizes.
  • (16) Mean systolic pressure differences, volume losses, and energy losses, as well as dimensionless pressure losses and energy loss coefficients, are calculated from the recorded pressure, volume, and flow tracings.
  • (17) The performance of hemodialyzers was expressed schematically using three dimensionless quantities.
  • (18) It requires only the introduction of two dimensionless ratios into the standard model: the ratio of the mean unbound ligand concentration actually present within the capillary or sinusoid to its equilibrium value, and the ratio of the permeability of the membrane plus associated extracellular diffusion barriers to the permeability of the membrane alone.
  • (19) The distribution of the Arden ratio (A) and another dimensionless EOG quantity (G) devised by Gliem (1971) in a sample of normal human subjects are presented.
  • (20) In this study, we use published empirical relationships, developed to identify the initial change from oscillating laminar flow to oscillating turbulent flow in tubes, to derive the limiting relationships between a dimensionless stroke volume and the Womersley number for maintenance of laminar conditions.

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