The value distribution is similar to floating-point, but the value-to-representation curve, i. e. the graph of the logarithm function, is smooth ( except at 0 ).

" Restricted QCC " refers to the first two moments of the probability distribution and is true even when the wave packets diffract, while " detailed QCC " requires smooth potentials which vary over scales much larger than the wavelength, which is what Bohr considered.

which, when c is scaled appropriately and the P distribution is smooth enough to think of the system in a continuum limit becomes:

The integral of any smooth, positive, " bump-shaped " function will be sigmoidal, thus the cumulative distribution functions for many common probability distributions are sigmoidal.

, most cosmologists favor the cold dark matter theory as a description of how the Universe went from a smooth initial state at early times ( as shown by the cosmic microwave background radiation ) to the lumpy distribution of galaxies and their clusters we see today — the large-scale structure of the Universe.

If K ( x ) has an isolated singularity at the origin, but is an otherwise " nice " function, then the principal value distribution is defined on compactly supported smooth functions by

The epithet of the genus was derived from Greek lisso, smooth, and delphis ; the specific epithet, borealis, indicates the northern distribution.

The " relaxation " of stars is the process deflecting the individual trajectories of stars from the one they would have if the distribution of matter was perfectly smooth.

The second are Coulombic repulsion terms between electrons in a mean-field theory description ; a net repulsion energy for each electron in the system, which is calculated by treating all of the other electrons within the molecule as a smooth distribution of negative charge.

If D is a smooth tangent distribution on M, then the annihilator of D, I ( D ) consists of all forms α ∈ Ω ( M ) such that

An initial smooth distribution of matter will eventually collapse and cause a hierarchy of structures, such as clusters of galaxies, stellar groups, stars and planets.

When the measure μ is associated to a mass distribution on a sufficiently smooth hypersurface S ( a Lyapunov surface of Hölder class C < sup > 1, α </ sup >) that divides R < sup > d </ sup > into two regions D < sub >+</ sub > and D < sub >−</ sub >, then the Newtonian potential of μ is referred to as a simple layer potential.

A sub-Riemannian manifold is a triple, where is a differentiable manifold, is a completely non-integrable " horizontal " distribution and is a smooth section of positive-definite quadratic forms on.

Pseudo-differential operators are pseudo-local, which means informally that when applied to a distribution they do not create a singularity at points where the distribution was already smooth.

The parameters of the low-dimensional probability distribution, the smooth map and the noise are all learned from the training data using the expectation-maximization ( EM ) algorithm.

Sands and gravels that possess a wide range of particle sizes with a smooth distribution of particle sizes are called well graded soils.

" David George Kendall had previously argued that pacing would have created a greater difference in measurements between sites, he concluded after investigation for the Royal Academy, that " The hypothesis of a smooth, non-quantal distribution of circle diameters ( for Scottish, English and Welsh true circles ) is thus rejected at the 1 % level.

In mathematics, mollifiers ( also known as approximations to the identity ) are smooth functions with special properties, used in distribution theory to create sequences of smooth functions approximating nonsmooth ( generalized ) functions, via convolution.

In connection with foliation theory, a subbundle of the tangent bundle of a smooth manifold may be called a distribution ( of tangent vectors ).

Additionally, for large molecular weight particles, sedimentation is not always smooth.

The molecular mechanism seems to be mediated by oxygen-sensitive potassium ion channels in the cell membrane of pulmonary smooth muscle.

In gas phase spectroscopy, the fine structure afforded by these factors can be discerned, but in solution-state spectroscopy, the differences in molecular micro environments further broaden the structure to give smooth bands.

The smooth muscle of the myometrium is basically very similar in molecular structure to smooth muscle in other sites of the body, with myosin and actin being the predominant proteins expressed.

Removal of Ca < sup > 2 +</ sup > after contraction induces relaxation of the smooth muscle, and restores the molecular structure of the sarcoplasmic reticulum to avail for the next contractile stimulus.

The primary benefits over rifled barrels is reduced barrel wear, longer ranges that can be achieved ( due to the reduced loss of energy to friction and gas escaping around the projectile via the rifling ) and larger explosive cores for a given caliber artillery due to less metal needing to be used to form the case of the projectile because of less force applied to the shell from the non-rifled sides of the barrel of smooth bore guns.

A shotgun usually retains its ancestor's smooth bore, and while originally designed to fire a packet of relatively small shot pellets, is also capable of firing larger slugs, or specialty ( often " less lethal ") rounds such as bean bags, tear gas or breaching rounds.

A Tesla turbine consists of a set of smooth disks, with nozzles applying a moving gas to the edge of the disk.

Steps to reattach the retina may include vitrectomy to clear the inner jelly, scleral buckling to create a support for the reattached retina, membranectomy to remove scar tissue, injection of dense liquids to smooth the retina into place, photocoagulation to bond the retina back against the wall of the eye, and injection of a gas or silicone oil to secure the retina in place as it heals.

Besides his smooth and deep voice, Cornelius was best known for the catchphrase that he used to close the show: "... and you can bet your last money, it's all gonna be a stone gas, honey!

Farmers can use weather derivatives to hedge against poor harvests caused by drought or frost ; theme parks may want to insure against rainy weekends during peak summer seasons ; and gas and power companies may use heating degree days ( HDD ) or cooling degree days ( CDD ) contracts to smooth earnings.

They have a smooth shell over a large body chamber, which is divided into subchambers filled with an inert gas ( similar to the composition of atmospheric air, but with more nitrogen and less oxygen ) making the animal neutrally buoyant in the water.

The pipes may be either corrugated / slotted to enhance heat transfer and provide condensate drainage or smooth / solid to prevent gas / liquid transfer.

* with a smooth or twisted surface: very compact surface ; vesicles ( gas bubbles ) are rare.

The long crankshaft tends to exhibit torsional vibration modes under high power, while side-valve flathead engines inhibit smooth intake and exhaust gas flow, limiting power.

This will crosslink the polymer and allows the coating, which will be porous due to the evolution of gas during the deposition process, to flow out and become smooth and continuous.

If clay is slightly out of shape, square straight sides with guide sticks or rulers pressed against opposite sides, or smooth round pieces with damp fingers.

If the background of design is too smooth, or you wish to create a wood-grained effect, it may be added at this time with a dull tool such as the handle of a fine paintbrush.

When the cloth is smooth, apply another coat of resin, spreading it with a paint roller.

One of these is the `` dissolve '', which makes possible a visually smooth transition from scene to scene.

Salamanders lack claws, have a scale-free skin, either smooth or covered with tubercles, and a tail that is usually flattened from side to side and often finned.

A hand on the anchor line may telegraph a series of jerks and jolts, indicating the anchor is dragging, or a smooth tension indicative of digging in.

The smooth muscle of the great arteries and the population of cells that form the aorticopulmonary septum that separates the aorta and pulmonary artery is derived from cardiac neural crest.

This contribution of the neural crest to the great artery smooth muscle is unusual as most smooth muscle is derived from mesoderm.

In fact the smooth muscle within the abdominal aorta is derived from mesoderm, and the coronary arteries, which arise just above the semilunar valves, possess smooth muscle of mesodermal origin.

The fundamental unit of the aorta is the elastic lamella, which consists of smooth muscle and elastic matrix.

Aortic pressure is highest at the aorta and becomes less pulsatile and lower pressure as blood vessels divide into arteries, arterioles, and capillaries such that flow is slow and smooth for gases and nutrient exchange.

It is noted for its smooth bark, white flowers, and hard wood.

" After a string quartet ," Martin explains, " I do not think there is a satisfactory sound for strings until one has at least three players on each line ... as a rule two stringed instruments together create a slight " beat " which does not give a smooth sound.

These paints are good for watercolor techniques, airbrush application, or when smooth coverage is desired.

If a circular building is aerodynamically smooth, and cooler than the ground, it can be passively cooled by the " dome effect.

Whether hand laid or built in a mould, FRP boats usually have an outer coating of gelcoat which is a thin solid colored layer of polyester resin that adds no structural strength, but does create a smooth surface which can be buffed to a high shine and also acts as a protective layer against sunlight.

The mouthfeel is smooth, with low to moderate carbonation and no astringency.

Mouthfeel is full and smooth, with significant alcohol, although this should not be hot or sharp.

The smooth coat is marked with 10 – 15 vertical white-yellow stripes, spread along the back from the base of the neck to the rump.