A Bose – Einstein condensate ( BEC ) is a state of matter of a dilute gas of weakly interacting bosons confined in an external potential and cooled to temperatures very near to absolute zero.

At very low temperatures in the vicinity of absolute zero, matter exhibits many unusual properties, including superconductivity, superfluidity, and Bose – Einstein condensation.

The civilian population of the city dropped to near zero during the eight-years Iran – Iraq War. As of the 1986 census due to the war the population dropped to only 6 people.

A Bose – Einstein condensate ( BEC ) is a state of matter of a dilute gas of bosons cooled to temperatures very near absolute zero ( or ).

In light of the physical interpretation, a vector field with constant zero divergence is called incompressible or solenoidal – in this case, no net flow can occur across any closed surface.

Cyan is zero magnitude, green – yellow – red and blue – pink – red are increasing strengths in opposing directions.

Maxwell's equations take the form of an electromagnetic wave in an area that is very far away from any charges or currents ( free space ) – that is, where and are zero.

The Rankine temperature scale was created to use degree intervals the same size as those of the Fahrenheit scale, such that a temperature difference of one degree Rankine ( 1 R ) is equal to a difference of 1 ° F, except that absolute zero is 0 R – the same way that the Kelvin temperature scale matches the Celsius scale, except that absolute zero is 0 K. The Fahrenheit scale uses ( in the same manner as the later Celsius scale ) the symbol ° to denote a point on the temperature scale and the letter F to indicate the use of the Fahrenheit scale ( e. g. " Gallium melts at 85. 5763 ° F "), as well as to denote a difference between temperatures or an uncertainty in temperature ( e. g. " The output of the heat exchanger experiences an increase of 72 ° F " and " Our standard uncertainty is ± 5 ° F ").

With this additional condition — the covariant divergence of the energy – momentum tensor, and hence of whatever is on the other side of the equation, is zero — the simplest set of equations are what are called Einstein's ( field ) equations:

It uses sixteen distinct symbols, most often the symbols 0 – 9 to represent values zero to nine, and A, B, C, D, E, F ( or alternatively a – f ) to represent values ten to fifteen.

Note that the dipole – dipole interaction between two atoms is usually zero, because atoms rarely carry a permanent dipole.

The exponential map and the Lie algebra determine the local group structure of every connected Lie group, because of the Baker – Campbell – Hausdorff formula: there exists a neighborhood U of the zero element of, such that for u, v in U we have

As long as the second stagnation point is at its initial location on the upper surface of the wing, the circulation around the airfoil is zero and, in accordance with the Kutta – Joukowski theorem, there is no lift.

* 1858 – Modified Julian Day zero.

Gerbert learned of Hindu – Arabic digits and applied this knowledge to the abacus, but according to Charles Seife without the numeral of zero.

On the other hand, by the Riemann – Lebesgue lemma, the weak limit exists and is zero.

In game theory and economic theory, a zero – sum game is a mathematical representation of a situation in which a participant's gain ( or loss ) of utility is exactly balanced by the losses ( or gains ) of the utility of the other participant ( s ).

Thus cutting a cake, where taking a larger piece reduces the amount of cake available for others, is a zero – sum game if all participants value each unit of cake equally ( see marginal utility ).

In contrast, non-zero – sum describes a situation in which the interacting parties ' aggregate gains and losses are either less than or more than zero.

The mean is the only single number for which the residuals defined this way sum to zero.

According to the theorem, it is possible to expand the power ( x + y )< sup > n </ sup > into a sum involving terms of the form ax < sup > b </ sup > y < sup > c </ sup >, where the exponents b and c are nonnegative integers with, and the coefficient a of each term is a specific positive integer depending on n and b. When an exponent is zero, the corresponding power is usually omitted from the term.

The slope of the surface adjusts to make all three forces sum to zero.

To quote Anthony and Brackett: Moreover, because the element of water does not move, the sum of all three forces must be zero.

To sum to zero, the force of the water must point oppositely to the sum of the centrifugal and gravity forces, which means the surface of the water must adjust so its normal points in this direction.

An example of an NP-complete problem is the subset sum problem: given a finite set of integers is there a non-empty subset which sums to zero?

To give a proof of a " yes " instance, one must specify a non-empty subset which does sum to zero.

" To give a proof of a " no " instance one must specify a non-empty subset which does sum to zero, which is easily verified.

Since the chain is at rest the sum of these forces must be zero.

When waves are added together, their sum is determined by the relative phases as well as the amplitudes of the individual waves so that the summed amplitude of the waves can have any value between zero and the sum of the individual amplitudes.

* Kirchhoff's voltage law: The directed sum of the electrical potential differences around a loop must be zero.

Otherwise the sum would again be zero due to the antisymmetry, thus representing a physically impossible state.

* ( the sum of zero items, i. e., the summation of the empty set )

The mercantilist idea that all trade was a zero sum game, in which each side was trying to best the other in a ruthless competition, was integrated into the works of Thomas Hobbes.

Equivalent technical statements are that the sum total magnetic flux through any Gaussian surface is zero, or that the magnetic field is a solenoidal vector field.

An example of a non-multiplicative function is the arithmetic function r < sub > 2 </ sub >( n )-the number of representations of n as a sum of squares of two integers, positive, negative, or zero, where in counting the number of ways, reversal of order is allowed.

A polynomial is either zero or can be written as the sum of a finite number of non-zero terms.

Thus each polynomial is actually equal to the sum of the terms used in its formal expression, if such a term a < sub > i </ sub > X < sup > i </ sup > is interpreted as a polynomial that has zero coefficients at all powers of X other than X < sup > i </ sup >.

In equilibrium, the forces on the moving block must sum to zero.

The first and last terms on the right hand side are diagonal elements and are zero, and the whole sum is equal to zero.

In order to maintain the steady-state propulsion of the system without either accelerating or decelerating the system, the sum of all the external forces on the system, averaged over the cycle, must be zero.

For example, the sum of the empty set is NULL, meaning zero, the average of the empty set is NULL, meaning undefined, and NULL appearing in the result of a LEFT JOIN can mean " no value because there is no matching row in the right-hand operand ".