What's the difference between dimension and tensor?

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).

Tensor


Definition:

  • (n.) A muscle that stretches a part, or renders it tense.
  • (n.) The ratio of one vector to another in length, no regard being had to the direction of the two vectors; -- so called because considered as a stretching factor in changing one vector into another. See Versor.

Example Sentences:

  • (1) However, we do point the way to further use of tensor analysis in the study of neural control of movement.
  • (2) We studied eustachian tube lengths and vectors of the tensor veli palatini muscle in 25 unilateral specimens from adult human cadavers.
  • (3) As an alternative to tensor theory, we modeled the vertical VOR as a three-layered neural network programmed using the back-propagation learning algorithm.
  • (4) The tensor palati muscle is divisible into four functional units: (1) anterior part, vertical fibers; (2) middle part, oblique fibers; (3) posterior part, horizontal fibers; and (4) posterior-most part, osseous origin.
  • (5) The 31P dipolar NMR powder spectrum of a typical stabilized ylid, (C6H5)3(31)P-13CHC(O)OCH2CH3, is analyzed in order to obtain the orientation of the 31P chemical shift tensor with respect to the 31P-13C alpha dipolar vector.
  • (6) Click evoked electromyographic (EMG) recordings were made from the contralateral tensor tympani muscle of anaesthetised mice.
  • (7) Ciliated and secretory cells were concentrated around the Eustachian tube orifice; additionally, ciliated cells were seen in two distinct bands extending posteriorly below the cochlea in the hypotympanum and above the cochlea toward the tensor tympani muscle.
  • (8) It is the purpose of this study to attempt a correlation of function, by electromyographic means, of the tensor tympani and tensor veli palatini muscles in humans.
  • (9) The latter signals experience little pseudocontact shifts which allow a rough orientation of the magnetic susceptibility tensor in the molecular frame.
  • (10) The hyperfine coupling tensor is nearly axially symmetric, with principal values (in gauss) of A(1) = 6.5, A(2) = 6.7, A(3) = 33.0.
  • (11) Perceived orientation was found to be dependent on the eigenvectors of the object's inertia tensor, computed about the point of rotation in the wrist, rather than on its spatial orientation.
  • (12) The Qzz axis of the nuclear quadrupole interaction tensor for the proximal imidazole nitrogen in MbOH was found to be aligned near gz (gmax) in MbOH, suggesting that gz is near the heme normal.
  • (13) Treatment of oxidized enzyme with CO causes the g-tensor of the paramagnetic center to change from rhombic to axial symmetry.
  • (14) The large difference in their midpoint potentials (0 and -400 mV, respectively, in the soluble enzyme) permits the acquisition of individual electron paramagnetic resonance spectra characterized by nearly identical rhombic g tensors (gz = 2.025, gy = 1.93, gx = 1.905).
  • (15) The observed paramagnetic relaxation rates are analysed in terms of the Solomon-Bloembergen theory, with the g-tensor value of 2 based on the consideration of the protein tertiary structure.
  • (16) Some peculiar experimental results such as the axial electron paramagnetic resonance spectra of adrenal ferredoxin and Pseudomonas putida ferredoxin and the electric field gradient tensor of P. putida ferredoxin are explained without assuming properties drastically different from those of the other ferredoxins, as had been suggested in the literature.
  • (17) In the pelvic region three major compartments (gluteus medius-minimus compartment, gluteus maximus compartment, and iliopsoas compartment) can be distinguished from the smaller compartment of the tensor fasciae latae muscle.
  • (18) For each Raman band in the 300-1800 cm-1 range, relative scattering intensities, Ibb and Icc, which correspond to the bb and cc components of the Raman tensor of the crystal, have been determined.
  • (19) Typical spindles were found in palatoglossus and tensor veli palatini with a greater number in the latter.
  • (20) Applications of this method, including the simplification of the measurement of the principal values of the 13C chemical shift tensor under slow MAS conditions, are described.

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