What's the difference between infinitesimal and trace?

Infinitesimal


Definition:

  • (a.) Infinitely or indefinitely small; less than any assignable quantity or value; very small.
  • (n.) An infinitely small quantity; that which is less than any assignable quantity.

Example Sentences:

  • (1) The first 2 ms of these transients were described by a linear model in which the fibre is regarded as a rod composed of infinitesimally small, identical segments containing a mass, one undamped elastic element and in the case of relaxed fibres two damped elastic elements in series, or in the case of activated fibres three such elastic elements in series.
  • (2) These equations can be solved easily by stepwise numerical integration involving sucessive infinitesimal rotations (SIR).
  • (3) The present day IBV might be progeny from a unique pool of primordial genome via mutation and host-induced variation, or even persistence of primordial virus as an infinitesimal portion of the population.
  • (4) Examples of current input considered are (1) an infinitesimally brief (Dirac delta function) pulse and (2) a step pulse.
  • (5) Pickup, now 71, recalls the "horrible, infinitesimal detail of how accurate you had to be, partly because you didn't want stones bouncing off the pram into the audience".
  • (6) The chances of Keeler being installed in Downing Street were infinitesimal.
  • (7) For infinitesimal steps the eigen-functions of the diffusion operator are known analytically, while for random motion of arbitrary step size they are determined by diagonalizing the transition matrix appropriate for the step model used.
  • (8) The two principal plasminogen activators (PA) and the two PA-inhibitors are present in infinitesimal concentrations in blood (pM to microM range) and in tissues.
  • (9) Experimental spectra are compared with computer simulations of spectra carried out for isotropic Brownian (limit of infinitesimal step size) and free diffusion (arbitrary step size) models.
  • (10) The infinitesimal change in entropy of a system (dS) is calculated by measuring how much heat has entered a closed system (δQ) divided by the common temperature (T) at the point where the heat transfer took place.
  • (11) However, incidence data indicate the chance of disclosing tumors, non-inflammatory cysts or other serious bone disease in the asymptomatic patient by screening jaw films is infinitesimal.
  • (12) Statistical analysis permitted empirical evaluation of creep of the cellular membrane within the range of infinitesimal stress.
  • (13) "The chances of each of us coming into existence are infinitesimally small," he argues, "and even though we shall all die some day, we should count ourselves fantastically lucky to get our decades in the sun."
  • (14) Of course, fear of risk is actually the bestselling tool of all: it is the basis of the entire insurance industry, whose profit base is predicated on the fact that fear is a very real emotion selling the product, but the statistical probability of anything actually happening, well, that is infinitesimal.
  • (15) The armed seizure of the Crimean parliament, the cynical insistence that Russian troops were not operating in Crimea when they clearly were, and the breakneck speed and flagrant violations involved in organising the Crimean referendum at short notice have been hidden behind a thread of plausible deniability stretched infinitesimally thin – and a knowing smirk on Putin's face.
  • (16) It is shown that the behavior of these waves may be explained, to a large extent, by considering the effect of the continuous stream of infinitesimal reflections that is set up whenever any wave travels in a region of vessel where the local impedance, (that is, the ratio of elastic wavespeed to tube area) is not constant.
  • (17) These changes could not be attributed to the effects of inbreeding or of selection in an infinitesimal model and suggested that some change in variance due to change in gene frequency had occurred during the course of the experiment.
  • (18) Ten healthy subjects received two treatments: a single 1 g oral dose of nalidixic acid (NA) followed 1 h later by either an infinitesimal dilution of the drug (NA 7CH) or by succussed water which served as placebo.
  • (19) The finite deformation theory describes the large strain behavior of cartilage observed in one-dimensional confined compression experiments at equilibrium, and it reduces to the linear biphasic theory under infinitesimal strain and slow strain rate conditions.
  • (20) Watson jokes that he has worked out that his Luton Town has an infinitesimally small chance of making it to the Premier League in time for matches to be aired on BT Vision before the end of the three-year deal in 2016.

Trace


Definition:

  • (n.) One of two straps, chains, or ropes of a harness, extending from the collar or breastplate to a whiffletree attached to a vehicle or thing to be drawn; a tug.
  • (v. t.) A mark left by anything passing; a track; a path; a course; a footprint; a vestige; as, the trace of a carriage or sled; the trace of a deer; a sinuous trace.
  • (v. t.) A very small quantity of an element or compound in a given substance, especially when so small that the amount is not quantitatively determined in an analysis; -- hence, in stating an analysis, often contracted to tr.
  • (v. t.) A mark, impression, or visible appearance of anything left when the thing itself no longer exists; remains; token; vestige.
  • (v. t.) The intersection of a plane of projection, or an original plane, with a coordinate plane.
  • (v. t.) The ground plan of a work or works.
  • (v. t.) To mark out; to draw or delineate with marks; especially, to copy, as a drawing or engraving, by following the lines and marking them on a sheet superimposed, through which they appear; as, to trace a figure or an outline; a traced drawing.
  • (v. t.) To follow by some mark that has been left by a person or thing which has preceded; to follow by footsteps, tracks, or tokens.
  • (v. t.) Hence, to follow the trace or track of.
  • (v. t.) To copy; to imitate.
  • (v. t.) To walk over; to pass through; to traverse.
  • (v. i.) To walk; to go; to travel.

Example Sentences:

  • (1) Glyceryl p-aminobenzoate and amyl p-dimethyl-aminobenzoate were labeled on 1 and 3 sunscreens, respectively, but glyceryl p-aminobenzoate was not found in any of them and only traces of amyl p-dimethylaminobenzoate were found in 1 sunscreen.
  • (2) Throughout the entire cultivation cytidyl derivatives occurred in trace quantities.
  • (3) persisted and was more abnormal in 23% of the cases including specific tracings in 37%.
  • (4) Traces of the sulphoxide of butylmercapturic acid have been found in rat urine but not in rabbit urine.
  • (5) No 7 beta-hydroxysteroid dehydrogenase activity and only a trace of 7 alpha-hydroxysteroid dehydrogenase activity could be demonstrated when bile acid was deleted from the growth medium.
  • (6) Silicon, a relatively unknown trace element in nutritional research, has been uniquely localized in active calcification sites in young bone.
  • (7) Although various micronutrients (vitamins and trace elements) have also been found to have either a positive or negative association, findings were more clear-cut for the different food items contributing the micronutrients than for the specific micronutrients themselves.
  • (8) Methods used in tracing and improving cooperation of subjects are described.
  • (9) Her black persona unravelled this week when Ruthanne and Larry Dolezal, a couple named on her Montana birth certificate as her biological parents, told Spokane’s KREM 2 News that her ancestry was German and Czech, with traces of Native American.
  • (10) they are shown to inhibit in vitro the release of iron from acidified host cell cytosol, consisting mostly of hemoglobin, a process that could provide this trace element to the parasite.
  • (11) Thus, the carotid pulse tracing provides an accurate reproduction of the morphology of the pressure tracing recorded from the ascending aorta, and when calibrated by peripheral blood pressure measurement, it can be used to calculate LV pressure throughout ejection.
  • (12) Mutant C grew anaerobically in the light, whereas mutant G1 was light sensitive and produced only trace amounts of bacteriochlorophyll a (0.6 mumole per ml of protein).
  • (13) The effect was shown to be due to caldesmon and not to a trace contaminant by its full reversibility after addition of a monospecific caldesmon antibody.
  • (14) Of 15 organochlorine compounds analyzed, trace amounts mainly of p,p-DDE and polychlorinated biphenyls (PCBs) were detected, but could not be quantitated.
  • (15) Fifty physiologically characterized units were injected with horseradish peroxidase (HRP) or Lucifer yellow CH (LY) and their processes were traced to the crista.
  • (16) Polysomnography has revealed that this drug has several interesting qualities that benzodiazepines do not possess: stages 3-4 increase, stage 2 is unchanged or slightly reduced and no abnormal changes are detected on the EEG tracing.
  • (17) We find that the labelled cell has a myelinated axon, but that the axon loses its myelin within 50 microns of the soma and has not yet been traced further.
  • (18) He is likely to propose increased funding of plant disease experts, the stepping up of surveillance at ports of entry and a Europe-wide "plant passport" system to trace the origins of all plants coming into Britain.
  • (19) In addition, the postulated personality for PD may predispose to hard work, perspiration, and increased exposure to putative trace elements in the water supply.
  • (20) The voltage trace is then analysed with a piece of transparent paper, on which lines corresponding to solutions of the diffusion equation convert the time axis of the voltage trace into a concentration axis.