A system of concepts,
such as the equations of thermodynamics, is a complex theoretical and experimental structure to which many individuals contributed.
Mathematical models,
such as the equations for the growth of a population of insects, are used to make quantitative predictions of particular variables.
Unfortunately, today's rather immature (and still somewhat numerically challenged) first - year science student needs to be led more gently and slowly into the intricacies of topics
such as the equations of stellar interiors, spherical trigonometry and introductory cosmology.
The latest PISA report, Equations and Inequalities, notes that exposure to «pure mathematics,»
such as equations and functions, builds conceptual knowledge necessary to solve complex problems.
Not exact matches
It was a smart move, because it let Apple take advantage of growing interest in disintermediation — the removal of traditional middlemen,
such as retailers, from the buying and selling
equation.
With the rise of self - driving cars and apps
such as Hailo, it's perhaps only a matter of time before humans are taken entirely out of the
equation.
But maybe the rise of companies
such as CGI Group Inc. and Shopify Inc. will change the
equation?
Now take humans out of the
equation and parachute in a purely natural factor,
such as a predator.
The superstructure of the Absolute or of a personal God may have been relinquished, but the idealization of the human
equation, consonant with
such a superstructure, was
as decisive
as ever.
Those
equations...
such as the ones for the Law of Gravity, are empirical derivations expressed in mathematical form.
Later in chapter five, statements about variables and numbers,
such as algebraic
equations, are called algebraic forms, which Whitehead does not define because «the conception of form is so general that it is difficult to characterize it in abstract terms» (TM 45).
The very notion of a «field»,
such as the Higgs field, is a mathematical and physical model describing the interrelationship of matter at the subatomic level, what Holloway would have called an «equational» relationship since in this vision (that espoused by Faith movement) the cosmos is a vast, ordered
equation.
In ancient hebrew the word morning is yom, which is always used to represent the mathematical
equation for 24 hours when accompanied by a number,
such as «and there was morning and evening, the fourth day».
This means that the future can be regarded, on
such an hypothesis,
as a value implicit and potential in a cosmic
equation, a value yet to be educed, a value the eduction of which involves a universalrearrangement of the more generalised value, just
as the eduction of a new value in an
equation is a value relationship in a total relativity of values.
Fact - a theory or
equation is only
as good
as it's assumptions, and the fact is C - 14 dating has some flawed starting out assumptions
such as assuming no carbon has been added or subtracted to the environment since the beginning of the planet.
The implications of expressing the thesis
as such an
equation are (1) if the viewed action is not at all salient for the person (i.e., = 0) the action will not affect the viewer's behavior («act»); (2) the chance that a particular viewed action will affect a person's behavior will decrease to the extent that they have other alternatives in their «repertoire»; and (3) if the individual is not aroused to act he will not exhibit the viewed behavior, no matter how salient it is.
For this «scholar» to propose
such an interpretation is
as intelligent
as a chemist who choses to only examine part of a balanced
equation because if he considers the whole
equation... it might tell him something he does nt want to know or may prove him to be wrong for his «conclusions»....
In 1955 he published a series of papers on topics
such as the integration of systems of differential
equations, harmonic analysis, and rational iteration.
Considerations
such as time spent with the child and the income of the mother are factored into a complex
equation and can slightly reduce or increase the award.
Snodgrass, Feghouli and Fletcher would also come into the
equation if they remain with us, together with the young players
such as Rice, Burke, Cullen, Quina and Martinez and perhaps others, if they are given a chance.
So I totally understand that the super delegates include those
such as the president, vice president, senators, past presidents, etc., but I was wondering if there was an exact mathematical
equation...
Cutting local authorities out of the
equation will end any meaningful local planning to target funding to the children who need more help
such as those with special needs.
Gov. Andrew Cuomo, naturally, stands the most to lose in
such an
equation as he pushes a post-budget agenda that he'll need the powerful speaker to sign off on.
«We want to look at how an individual person responds to an individual drug by deriving and using sophisticated mathematical models,
such as differential
equations.»
The researchers created a statistical analysis framework of differential
equations that they expect will help doctors and pharmacists, by simulating
such variables
as protein - protein and protein - DNA interactions a drug has in a patient.
It allows particles,
such as electrons or photons of light, the equivalent of an interest - free loan: they may borrow energy from empty space and use it to make mass, according to Einstein's famous
equation E = mc2.
Climate modelers do not include effects on land - based ice in these regions because they can not reduce them to
equations,
such as x amount of extra heat equals y amount of melting.
For much of the past century, they have evaluated disease outbreaks with a comparatively simple set of
equations that divide people into a few categories —
such as susceptible, contagious, and immune — and that assume perfect mixing, meaning that everybody in the affected region is in contact with everyone else.
But epidemiologists are increasingly turning to agent - based models to include factors that the
equations ignore,
such as geography, transportation networks, family structure, and behavior change — all of which can strongly affect how disease spreads.
The point of
such models is to avoid describing human affairs from the top down with fixed
equations,
as is traditionally done in
such fields
as economics and epidemiology.
Many previous models also assume independence between climate models, whereas this paper accounts for commonalities shared by various models —
such as physical
equations or fluid dynamics — and correlates between data sets.
In situations where consumers must average ratio information,
such as comparing the fuel efficiency of two cars using the ratio miles per gallon, they often flub the numbers by incorrectly assuming the mathematic
equation to find miles per gallon would be to average the sum of the mileage of both cars and then divide by two, instead of using a more complex
equation needed to accurately compare ratios.
«Among
such structures, one of the more interesting is similar to structures found in nature, and is referred to
as a «moth - eye» pattern: tiny nanopillars which can «beat» the Fresnel
equations at certain wavelengths and angles.»
The wave
equation can be modified to deal with more complex, messy phenomena,
such as earthquakes.
The discrepancy has consequences for
equations such as those that describe the motion of particles or the propagation of waves.
This is how some fractal mathematical objects,
such as the Mandelbrot set — a set of complex numbers for which a particular iterated
equation does not approach infinity — are generated.
The
equations utilised to solve the problem are based on the physicists» basic knowledge,
such as the definition of an event horizon and the so - called equivalence principle, which is part of the foundation of Einstein's theory of gravity.
The panel recognizes the value of several new features in the guideline,
such as specific risk
equations for African - Americans,
equations to calculate both 10 - year and 30 - year lifetime risk, inclusion of stroke
as an adverse cardiovascular event, and emphasis on shared decision - making.
Perhaps most importantly, the approach used can be applied to other physical phenomena that are described by wave
equations,
such as acoustics.
They are plugged into
equations to estimate total emissions from industrial activities,
such as the burning of coal in boilers.
For example, the classical
equations used to predict the performance of
such materials have indicated that the logarithm of the reaction rate should vary linearly
as voltage is increased — but experiments have shown a nonlinear response, with the uptake of lithium flattening out at high voltage.
Researchers work out these
equations by measuring the objects at various points in time and then developing a formula that links all of those points together,
such as filling in a video from a set of snapshots.
It provides a potentially minimal framework in which it is possible to solve the Einstein
equations, which in turn could be a critical step toward the proof of major conjectures,
such as Penrose's cosmic censorship conjectures.
Designing radio technology into computing systems requires the use of mathematical
equations and scientific methods to solve real - world problems that affect our customers
such as radio frequency interference or battery life due to transmission of energy.
We know from very precise supernova observations that the universe is accelerating, but at the same time we rely on coarse approximations to Einstein's
equations which may introduce serious side - effects,
such as the need for dark energy, in the models designed to fit the observational data.»
The regular patterns that form in a moving fluid,
such as whirlpools or ocean waves, are mathematical consequences of these
equations, and in this sense the
equations explain the patterns.
Erwin's
equation requires figures
such as how many tree species are in the world, what proportion of bugs are beetles, and what proportion of beetles eat plants.
But in all
such known
equations, either two integers have a common factor,
as in the first example, or one of the exponents is 2,
as in the second.
With hindsight, it turns out that his mathematical description of the way space - time is warped by matter matches
equations developed by 19th - century mathematicians
such as Bernhard Riemann to des - cribe alternatives to the Eucli - dean geometry of flat planes («Pay attention, Albert Einstein!»
«Induced seismicity complicates the seismic hazard
equation,» said Gail Atkinson, professor of earth sciences at Western University in Ontario Canada, whose research details how a new source of seismicity,
such as an injection disposal well, can fundamentally alter the potential seismic hazard in an area.