What's the difference between demonstration and mathematical?

Demonstration


Definition:

  • (n.) The act of demonstrating; an exhibition; proof; especially, proof beyond the possibility of doubt; indubitable evidence, to the senses or reason.
  • (n.) An expression, as of the feelings, by outward signs; a manifestation; a show.
  • (n.) The exhibition and explanation of a dissection or other anatomical preparation.
  • (n.) (Mil.) a decisive exhibition of force, or a movement indicating an attack.
  • (n.) The act of proving by the syllogistic process, or the proof itself.
  • (n.) A course of reasoning showing that a certain result is a necessary consequence of assumed premises; -- these premises being definitions, axioms, and previously established propositions.

Example Sentences:

  • (1) The Na+ ionophore, gramicidin, had a small but significant inhibitory effect on Na(+)-dependent KG uptake, demonstrating that KG uptake was not the result of an intravesicular positive Na+ diffusion potential.
  • (2) Patient plasma samples demonstrated evidence of marked complement activation, with 3-fold elevations of C3a desArg concentrations by the 8th day of therapy.
  • (3) The influence of the various concepts for the induction of lateral structure formation in lipid membranes on integral functional units like ionophores is demonstrated by analysing the single channel current fluctuations of gramicidin in bimolecular lipid membranes.
  • (4) Of the patients 73% demonstrated clinically normal sensibility test results within 23 days after operation.
  • (5) Lucy and Ed will combine coverage of hard and breaking news with a commitment to investigative journalism, which their track record so clearly demonstrates”.
  • (6) These immunocytochemical studies clearly demonstrated that cells encountered within the fibrous intimal thickening in the vein graft were inevitably smooth muscle cell in origin.
  • (7) Competition with the labelled 10B12 MAb for binding to the purified antigen was demonstrated in sera of tumor-bearing and immune rats.
  • (8) Using monoclonal antibodies directed against the plasma membrane of Madin-Darby canine kidney (MDCK) cells, we demonstrated previously that a glycoprotein with an Mr = 23,000 (gp23) had a non-polarized cell surface distribution and was observed on both the apical and basolateral membranes (Ojakian, G. K., Romain, R. E., and Herz, R. E. (1987) Am.
  • (9) These results demonstrate that increased availability of galactose, a high-affinity substrate for the enzyme, leads to increased aldose reductase messenger RNA, which suggests a role for aldose reductase in sugar metabolism in the lens.
  • (10) Intravesical BCG is clearly superior to oral BCG, and controlled studies have demonstrated that percutaneous administration is not necessary.
  • (11) We have previously shown that serotonin is present in secretory granules of frog adrenochromaffin cells; concurrently, we have demonstrated that serotonin is a potent stimulator of corticosterone and aldosterone secretion by adrenocortical cells.
  • (12) Microionophoretically applied excitatory amino acids induced firing of extracellularly recorded single units in a tissue slice preparation of the mouse cochlear nucleus, and the similarly applied antagonist 2-amino-5-phosphonovalerate (2APV) was demonstrated to be a selective N-methyl-D-aspartate (NMDA) receptor antagonist.
  • (13) The results demonstrated that K2PtCl4 was bound to a greater degree than CDDP in this system with 3-5 and 1-2 platinum atoms respectively, bound per transferrin molecule.
  • (14) These studies, in addition to demonstrating that the placenta contains TRH deamidase activity, suggest that losses of fetal TRH through the placenta are not large.
  • (15) Light microscopic studies of pancreata from mice sacrificed at this time demonstrated insulitis and beta cell necrosis.
  • (16) Western blot analysis of these mitochondria using an antibody against carnitine palmitoyltransferase II purified from beef heart demonstrates a 68-kDa protein, which under ischemic conditions apparently is decreased by 2 kDa.
  • (17) Acquired drug resistance to INH, RMP, and EMB can be demonstrated in M. kansasii, and SMX in combination with other agents chosen on the basis of MIC determinations are effective in the treatment of disease caused by RMP-resistant M. kansasii.
  • (18) In 1 of the 3, anterior capsular detachment was also demonstrated radiographically and confirmed surgically.
  • (19) This result demonstrates that branching enzyme belongs to a family of the amylolytic enzymes.
  • (20) Histological studies of nerves 2 years following irradiation demonstrated loss of axons and myelin, with a corresponding increase in endoneurial, perineurial, and epineurial connective tissue.

Mathematical


Definition:

  • (a.) Of or pertaining to mathematics; according to mathematics; hence, theoretically precise; accurate; as, mathematical geography; mathematical instruments; mathematical exactness.

Example Sentences:

  • (1) We present a mathematical model that is suitable to reconcile this apparent contradiction in the interpretation of the epidemiological data: the observed parallel time series for the spread of AIDS in groups with different risk of infection can be realized by computer simulation, if one assumes that the outbreak of full-blown AIDS only occurs if HIV and a certain infectious coagent (cofactor) CO are present.
  • (2) On the basis of mathematical models of the obtained dose-time-effect relationship, the risk of cancer occurrence due to small carcinogen doses is predicted.
  • (3) Unfortunately more than three quantitative data cannot be judged simultaneously without help of mathematical methods.
  • (4) The kinetic properties of the cell-free extracts fit mathematical models developed for in vitro systems reconstituted from purified enzymes.
  • (5) All of the multivariate data were treated with mathematic method of cluster analysis.
  • (6) Problems of calculations and predictions on more than two particles moving are known in mathematics and physics since a long time already.
  • (7) The normal anatomical position of the point of junction of the superficial cerebral veins with the superior sagittal and transverse sinuses of the rat was studied with an analytical mathematical method.
  • (8) Such measured courses may be mathematically modelled by the so-called BATEMAN function type, an expression consisting of 2 e-function terms.
  • (9) This review begins with a mathematical and qualitative description of the inverse problem in terms of epicardial potentials.
  • (10) For both cases, mathematical expressions as proposed and used by Sager are applied.
  • (11) Since the four determining coefficients may change over evolutionary time-scales, the mathematical results together with a natural selection argument proves that virulence gamma 2 attenuates.
  • (12) The selection of optimal parameters, development of valid measurement procedures, and use of mathematical modeling and descriptive statistics are necessary for quantitative studies by ultrasound of fetal organ growth.
  • (13) The mathematical model clearly predicts this decrease in concentration.
  • (14) The ability of a mathematical model to evaluate the effects of two different pain modulating procedures (partial nerve block and vibration) on acute experimental pulpal pain was studied.
  • (15) A mathematical model that abstracts the major features of the vegetative life cycle of Neurosopra crassa has been developed, and the action of selection in this model and various extensions of it is such as to maintain polymorphisms of vegetative incompatibility factors.
  • (16) Mathematical models describing the process of the patients treatment and permitting to pronosticate the blood and urine sugar level during the treatment were developed.
  • (17) I used to tease him with the suggestion he had chosen me as walking companion because I had no mathematics at all and so he was safe from prying questions, but in fact now and then he did used to tell me about what he was doing – and how clear it all seemed when he spoke!
  • (18) A mathematical treatment and an original microcalorimetric method are developed to verify an eventual competitive binding between any two substances for the same macromolecule.
  • (19) By means of the method of factor-geometric analysis using a computer DVK-3, mathematic calculations of the effectiveness of the operation were made.
  • (20) A mathematical model of cochlear processing is developed to account for the nonlinear dependence of frequency selectivity on intensity in inner hair cell and auditory nerve fiber responses.