In some neighborhood in the f-plane of any ordinary point of the graph, the function f is a single-valued, continuous function.

Banach's fixed point theorem is also applied in proving the existence of solutions of ordinary differential equations, and is used in one proof of the inverse function theorem.

In its mathematical form it is analogous to the description of a physical wave, but its " crests " and " troughs " indicate levels of probability for the occurrence of certain phenomena ( e. g., a spark of light at a certain point on a detector screen ) that can be observed in the macro world of ordinary human experience.

Various reasons have been suggested for the resistance to the Celsius system in the U. S., including the larger size of each degree Celsius ( resulting in the need for decimals where integer Fahrenheit degrees were adequate for much non-technical work ), the lower zero point in the Fahrenheit system ( which reduces the number of negative signs when measurements such as weather data were averaged ), and the more intuitive alignment of its 0-100 scale to the ordinary range of outdoor temperatures seen in most of the U. S. ( e. g., 0 ° F

By the 18th century, however, Geneva had come under the influence of Catholic France, which cultivated the city elite, who tended to be at odds with the ordinary townsfolk – to the point that an abortive revolution took place in 1782.

At the point when money velocity and prices rapidly accelerate in a vicious circle, hyperinflation is out of control, because ordinary policy mechanisms, such as increasing reserve requirements, raising interest rates, or cutting government spending will be ineffective and be responded to by shifting away from the rapidly devalued money and towards other means of exchange.

* Node ( autonomous system ), behaviour for an ordinary differential equation near a critical point

Often this point was made by referring to " ordinary English ," since the school of philosophy that most vigorously promoted this meta-philosophy was Oxford.

An ordinary polygon is unbounded because the sequence closes back in itself in a loop or circuit, while an apeirogon ( infinite polygon ) is unbounded because it goes on for ever so you can never reach any bounding end point.

In the ordinary Euclidean plane, two lines typically intersect in a single point, but there are some pairs of lines ( namely, parallel lines ) that do not intersect.

Some of these experiments resulted in what was seemingly a new form of water with a higher boiling point, lower freezing point, and much higher viscosity than ordinary water, about that of a syrup.

The laws of thermodynamics predicted that, since polywater had a higher boiling point than ordinary water, it meant that it was more stable, and the whole column of ordinary water should have turned spontaneously into polywater, instead of just part of it.

One suggested starting point is ordinary quantum field theories which, after all, are successful in describing the other three basic fundamental forces in the context of the standard model of elementary particle physics.

One attempt to overcome these limitations is to replace ordinary quantum field theory, which is based on the classical concept of a point particle, with a quantum theory of one-dimensional extended objects: string theory.

For water, however, this is not true because the melting point of ordinary ice decreases as a function of pressure, as shown by the dotted green line in the phase diagram.

For example, the triple point at 251 K (− 22 ° C ) and 210 MPa ( 2070 atm ) corresponds to the conditions for the coexistence of ice Ih ( ordinary ice ), ice III and liquid water, all at equilibrium.

Such a vector field serves to define a generalized ordinary differential equation on a manifold: a solution to such a differential equation is a differentiable curve on the manifold whose derivative at any point is equal to the tangent vector attached to that point by the vector field.

An " echoppe " point can be made from an ordinary tempered steel etching needle, by grinding the point back on a carborundum stone, at a 45 – 60 degree angle.

Instead of describing a process which can only evolve in one way ( as in the case, for example, of solutions of an ordinary differential equation ), in a stochastic or random process there is some indeterminacy: even if the initial condition ( or starting point ) is known, there are several ( often infinitely many ) directions in which the process may evolve.

An ordinary hot bath or shower will do the same.

Ironic, is it not, that after completing years of costly scientific training he will receive a cut in pay from what he is receiving as an ordinary unskilled laborer??

The number of ordinary values of the function f{t} at T will be called its multiplicity at T.

According to Price, the dream world will not follow the laws of physics just as ordinary dreams do not.

The interpretation of an n-ary morphism as an ordinary morphisms whose domain is some sort of product of the domains of the original n-ary morphism will work in a monoidal category.

These false Christs will perform great signs and are no ordinary people " For they are spirits of demons, performing signs, which go out to the kings of the earth and of the whole world, to gather them to the battle of that great day of God Almighty.

:: If patients fail to experience the healing power of Christian Science, and think they can be benefited by certain ordinary physical methods of medical treatment, then the Mind-physician should give up such cases, and leave invalids free to resort to whatever other systems they fancy will afford relief.

We say that the mutation is recessive because the organism will exhibit the wild type phenotype ( ordinary trait ) unless both chromosomes of a pair have the mutation ( homozygous mutation ).

In ordinary prose, the script chosen will usually be hiragana.

One reason for such a threat is that, unlike the typical sword and sorcery adventurer, the hero is seldom bored stiff by ordinary life and therefore will not abandon it quickly and on any excuse.

Essentially, ordinary humans — those who have faith but do not possess the special knowledge — will not attain salvation.

* I will prove to you that this wonderful teacher, this woman-hater, is not satisfied with ordinary enjoyments during the night.

However, near a refractive boundary ( say a nucleus within the cytoplasm ), the difference between the ordinary and the extraordinary beam will generate a relief in the image.

This is not the only way probabilistic statements are used in ordinary human language: when people say that " it will probably rain ", they typically do not mean that the outcome of rain versus not-rain is a random factor that the odds currently favor ; instead, such statements are perhaps better understood as qualifying their expectation of rain with a degree of confidence.

Thus the spinor rotation γ ( ψ ) = γψ ( ordinary quaternionic multiplication ) will rotate the spinor ψ through an angle one-half the measure of the angle of the corresponding vector rotation.

However, if a third medium with a higher refractive index than the low-index second medium is placed within less than several wavelengths distance from the interface between the first medium and the second medium, the evanescent wave will be different from the one under " ordinary conditions " and it will pass energy across the second into the third medium.

In the atmosphere at ordinary temperatures, therefore, gaseous water ( known as water vapor ) will condense to liquid if its partial pressure is increased sufficiently.

* Astrophysicists studying the universe confirm its age at 13. 7 billion years, discover that it will most likely expand forever without limit, and conclude that only 4 % of the universe's contents are ordinary matter ( the other 96 % being still-mysterious dark matter, dark energy, and dark flow ).

Rousseau's striking phrase that man must " be forced to be free " should be understood this way: since the indivisible and inalienable popular sovereignty decides what is good for the whole, then if an individual lapses back into his ordinary egoism and disobeys the leadership, he will be forced to listen to what they decided as a member of the collectivity ( i. e. as citizens ).

For example, if a telecommunications service provider decides to offer different qualities of voice connection, then a premium voice connection will require a better connection quality compared to an ordinary voice connection.

These secondary clocks appear to run like an ordinary plug-in electric clock and run on their own synchronous electric motor and will maintain correct time unless there is an interruption in electric service, depending on the master clock only for the periodic synchronizing impulse.

From two to three pounds of seed are sown upon the acre ( 2 to 3 kg / hectare ), though the smallest of these quantities will give many more plants in ordinary seasons than are necessary ; but as the seed is not an expensive article the greater part of farmers incline to sow thick, which both provides against the danger of part of the seed perishing, and gives the young plants an advantage at the outset.