Mathematically, corrosion rates of glasses are characterized by normalized corrosion rates of elements NR < sub > i </ sub > ( g / cm < sup > 2 </ sup >· d ) which are determined as the ratio of total amount of released species into the water M < sub > i </ sub > ( g ) to the water-contacting surface area S ( cm < sup > 2 </ sup >), time of contact t ( days ) and weight fraction content of the element in the glass f < sub > i </ sub >:

Mathematically, the process is the same as that of quantum tunneling, except with electromagnetic waves instead of quantum-mechanical wavefunctions.

Mathematically it can be explained by considering the normal modes of electromagnetic field which explicitly depend on the boundary ( or matching ) conditions on the surfaces of the interacting bodies.

Mathematically this is expressed using the virial theorem, which states that, to maintain equilibrium, the gravitational potential energy must equal twice the internal thermal energy.

Mathematically, this energy is equal to the so-called on-the-mass-shell value of the proper self-energy operator ( or proper mass operator ) in the momentum-energy representation ( more precisely, to times this value ).

Mathematically, the Willmore energy of a smooth closed surface embedded in three-dimensional Euclidean space is defined to be the integral of the square of the mean curvature minus the Gaussian curvature.

Mathematically speaking, the most apparent distinguishing feature of the energy conditions is that they are essentially restrictions on the eigenvalues and eigenvectors of the matter tensor.

Mathematically, density is defined as mass divided by volume:

Mathematically, incompressibility is expressed by saying that the density ρ of a fluid parcel does not change as it moves in the flow field, i. e.,

Let this property be represented by just one scalar variable, q, and let the volume density of this property ( the amount of q per unit volume V ) be ρ, and the all surfaces be denoted by S. Mathematically, ρ is a ratio of two infinitesimal quantities:

The fundamental requirement for incompressible flow is that the density,, is constant within an infinitesimal volume, dV, which moves at the velocity of the fluid, v. Mathematically, this constraint implies that the material derivative ( discussed below ) of the density must vanish to ensure incompressible flow.

Mathematically, we shall not distinguish the experiment of three dice tossed once from that of one die tossed three times.

Mathematically, the light received from stars as a function of star distance in a hypothetical fractal cosmos is:

Mathematically, quasicrystals have been shown to be derivable from a general method, which treats them as projections of a higher-dimensional lattice.

Mathematically, this follows from:

Mathematically, the factor of two relating physical angles to their counterparts in Stokes space derives from the use of second-order moments and correlations, and incorporates the loss of information due to absolute phase invariance.

Mathematically, the return from a short position is equivalent to that of owning ( being " long ") a negative amount of the instrument.

Mathematically gifted, he was very young when he joined Enrico Fermi's team in Rome as one of the " Via Panisperna boys ", who took their name from the street address of their laboratory.

Mathematically, the climatological annual cycle is commonly estimated from observational data or model output by taking the average of all Januaries, all Februaries, and so forth.

Mathematically talented, Lamarr also co-invented — with composer George Antheil — an early technique for spread spectrum communications and frequency hopping, necessary for wireless communication from the pre-computer age to the present day.

Mathematically the switching mixer is not much different from a multiplying mixer, just because instead of the LO sine wave term we would use the signum function.

Mathematically, the difference between artificial perspective projection ( perspective projection onto a flat surface ) and natural perspective projection ( perspective projection onto a spherical surface ) is a distortion resulting from the small-angle approximation which results from projecting onto a flat surface.

Mathematically, apart from discretization ( whole euros both for income and for tax ), the tax is a continuous, convex, piecewise linear function of income.

Mathematically, the axiom states that the probability of selecting item i from a pool of j items is given by:

Mathematically, texture filtering is a type of anti-aliasing, but it filters out high frequencies from the texture fill whereas other AA techniques generally focus on visual edges.

Mathematically a stock can be seen as an accumulation or integration of flows over time-with outflows subtracting from the stock.

Mathematically, the problem of recovering conductivity from surface measurements of current and potential is a non-linear inverse problem and is severely ill-posed.

Mathematically, the cyclomatic complexity of a structured program is defined with reference to the control flow graph of the program, a directed graph containing the basic blocks of the program, with an edge between two basic blocks if control may pass from the first to the second.

Mathematically, two Luenberger observers can be used, if is properly selected, using, for example, positive systems properties: one for the upper bound ( that ensures that converges to zero from above when, in the absence of noise and uncertainty ), and a lower bound ( that ensures that converges to zero from below ).

Mathematically, nominal numbering is a one-to-one function from a set of objects being named to the set of numerals: it is a function because each object is assigned a numeral, and it is one-to-one because different objects are assigned different numerals.

Mathematically, barrel and pincushion distortion are quadratic, meaning they increase as the square of distance from the center.

Mathematically, the URR is closely related to Kt / V, and the two quantities can be derived from another with more or less precision, depending on the amount of additional information available about a given dialysis session.

§ — Mathematically eliminated from the chase.

Mathematically, classical physics equations are ones in which Planck's constant does not appear.

In 1827, the German scientist Georg Ohm expressed his law in this famous book " Die galvanische Kette, mathematisch bearbeitet " ( The Galvanic Circuit Investigated Mathematically ) in which he gave his complete theory of electricity.

Mathematically this law is now written:

Mathematically, Hooke's law states that

Mathematically, Gauss's law takes the form of an integral equation:

Mathematically, each physical law can be expressed with respect to the coordinates given by an inertial frame of reference by a mathematical equation ( for instance, a differential equation ) which relates the various coordinates of the various objects in the spacetime.

Mathematically, the probability of finding a particle at depth x into the material is calculated by Beer-Lambert law:

Mathematically, the law is stated:

Mathematically, the relationship between a cell and its neighbors, located within an area of influence, can be defined by a coupling law, and this is what primarily determines the behavior of the processor.