What's the difference between mathematical and numerical?

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.

Numerical


Definition:

  • (n.) Belonging to number; denoting number; consisting in numbers; expressed by numbers, and not letters; as, numerical characters; a numerical equation; a numerical statement.
  • (n.) The same in number; hence, identically the same; identical; as, the same numerical body.

Example Sentences:

  • (1) The taxonomic relationship of strains H4-14 and 25a with previously described Xanthobacter strains was studied by numerical classification.
  • (2) Glucocorticoids have numerous effects some of which are permissive; steroids are thus important not only for what they do, but also for what they permit or enable other hormones and signal molecules to do.
  • (3) There have been numerous documented cases of people being forced to seek hospital treatment after eating meat contaminated with high concentrations of clenbuterol.
  • (4) The region containing the injection stop signal (iss) has been cloned and sequenced and found to contain numerous large repeats and inverted repeats which may be part of the iss.
  • (5) Migrant voters are almost as numerous as current Ukip supporters but they are widely overlooked and risk being increasingly disaffected by mainstream politics and the fierce rhetoric around immigration caused partly by the rise of Ukip,” said Robert Ford from Manchester University, the report’s co-author.
  • (6) Numerical results for the population of England and Wales are shown.
  • (7) Transmission electron microscopy demonstrated that these blebs were devoid of organelles and microvilli; scanning electron microscopy revealed that the blebs were highly wrinkled and more numerous than were the projections observed in tissue from animals treated with testosterone alone, or in tissue from unoperated controls.
  • (8) However, each of the studies had numerous methodological flaws which biased their results against finding a relationship: either their outcome measures had questionable validity, their research designs were inappropriate, or the statistical analyses were poorly conceived.
  • (9) Further exploration of these excretory pathways will provide interesting new insights on the numerous cholestatic and hyperbilirubinemic syndromes that occur in nature.
  • (10) We present numerical methods for studying the relationship between the shape of the vocal tract and its acoustic output.
  • (11) An efficient numerical algorithm based on the cyclic coordinate search method to solve the latter is explained.
  • (12) History contains numerous examples of government secrecy breeding abuse.
  • (13) The numerical chromosome values in 53 human tumors were determined and compared with the modal DNA values as measured by flow cytometry.
  • (14) Electron microscopy revealed the presence of a hitherto unreported peculiar "pilovacuolar" inclusion in numerous mitochondria, composed of an electron dense pile or rod within a vacuole, while globular or crystalline inclusions were absent.
  • (15) There are numerous other male protagonists out there in desperate need of a sex change.
  • (16) This force will be numerically similar to the net driving Starling force in small pores, but distinctly different in large pores.
  • (17) However, when beta-xyloside-treated cultures were supplied with exogenous basement membrane, Schwann cells produced numerous myelin segments.
  • (18) Though the problems associated with Robin sequence may be numerous, especially if the primary cause of the sequence is a multiple anomaly syndrome, the most acute problems in affected newborns is upper airway obstruction.
  • (19) Moreover, the most recent combined application of the rat interstitial cell testosterone (RICT) bioassay and a novel multiple-parameter deonvolution model has allowed investigators to dissect plasma concentration profiles of bioactive LH into defined secretory bursts, which have numerically explicit amplitudes, locations in time, and durations, and are acted upon by determinable subject- and study-specific endogenous metabolic clearance rates.
  • (20) However, almost all of the numerous compounds found to inhibit ammonia oxidizers also inhibit methanotrophs, and most of the inhibitors act upon the monooxygenases.