Mathematically, this corresponds to the fact that spherical coordinates do not define a coordinate chart on the sphere at zenith and nadir.

Mathematically, we write: " 40: 60 " = " 2: 3 " ( dividing both quantities by 20 ).

Mathematically, the ( real valued ) amplitude of one wave component is represented by a scalar wave function u that depends on both space and time:

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

Mathematically speaking, both in a standard and a TD approach, we would try to optimize some cost function, related to the error in our predictions of the expectation of some random variable, E. However, while in the standard approach we in some sense assume E = z ( the actual observed value ), in the TD approach we use a model.

: Mathematically speaking, charge transfer in semiconductor devices is due both to conduction driven by the electric field ( drift ) and by diffusion.

Such omissions were criticized by such groups as Mathematically Correct, and some states and districts have since abandoned this experiment, though it remains widely used.

It was here that he began his work with intellectually gifted youth, creating in 1971 the Study of Mathematically Precocious Youth ( SMPY ), which would eventually lead to a revolution in how gifted children were to be identified and treated within the education system.

However, in what newspapers such as the Wall Street Journal later call the " math wars ", organizations such as Mathematically Correct complain that some elementary texts based on the standards, including Mathland, have almost entirely abandoned any instruction of traditional arithmetic in favor of cutting, coloring, pasting, and writing.

Mathematically, this says that the state vector is confined to one of the two eigenspaces of P, and is not allowed to range over the entire Hilbert space.

Mathematically, this condition is also approached exponentially ; in theory it takes infinite time, but in practice it is over, for all intents and purposes, in a much shorter period.

Mathematically, a Yang – Mills instanton is a self-dual or anti-self-dual connection in a principal bundle over a four-dimensional Riemannian manifold that plays the role of physical space-time in non-abelian gauge theory.

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

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

Mathematically, this means the coefficient for the projection of onto.

Mathematically, this means that for a causal linear system to be stable all of the poles of its transfer function must have negative-real values, i. e. the real part of all the poles are less than zero.

Mathematically, the catenary curve is the graph of the hyperbolic cosine function.

Mathematically, the conjecture states that, for generic initial data, the maximal Cauchy development possesses a complete future null infinity.

Mathematically, the conjecture states that the maximal Cauchy development of generic compact or asymptotically flat initial data is locally inextendible as a regular Lorentzian manifold.

Mathematically speaking, magnetic fields and electric fields are convertible with relative motion as a 2nd-order tensor or bivector.

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, the unification is accomplished under an SU ( 2 ) × U ( 1 ) gauge group.

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.,

Mathematically, this is because in reversible processes, the change in entropy of the cold reservoir is the negative of that of the hot reservoir ( i. e., ), keeping the overall change of entropy zero.

Mathematically, a sequence of coin flips ( fair or not ) is an example of a Bernoulli process, and its entropy is given by the binary entropy function.

Mathematically, this is expressed by saying that the curl of the flow field is everywhere equal to zero.

Mathematically, the potential of the ion cores can be treated by various models, the simplest being the nearly free electron model.

Mathematically this invariance can be ensured in one of two ways: by treating the four-vectors as Euclidean vectors and multiplying time by the square root of ; or by keeping time a real quantity and embedding the vectors in a Minkowski space.

Mathematically, a neuron's network function is defined as a composition of other functions, which can further be defined as a composition of other functions.

Mathematically, the formula above entails that all incomes are at least the lower bound x < sub > m </ sub >, which is positive.

Mathematically, this correspondendence is supported by the second term, on the r. h. s.

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

The decision allowed Florida Secretary of State Katherine Harris's previous certification of George W. Bush as the winner of Florida's 25 electoral votes to stand.

Florida's 25 electoral votes gave Bush, the Republican candidate, 271 electoral votes, enough to defeat Al Gore.

Florida's 25 electoral votes gave Bush, the Republican candidate, 271 electoral votes, defeating Gore, who ended up with 266 electoral votes ( with one D. C. elector abstaining ).

South Florida's ascension into the top 25 from entry into I-A / FCS is the fastest in NCAA history, surpassing Boise State's rise by a mere seven weeks.

Dyer was elected the 32nd mayor of Orlando on February 25, 2003, in a special election after the previous mayor, Glenda Hood, was appointed Florida's Secretary of State.

There was a disagreement over who won Florida's 25 electoral votes, the recount that happened there, and the uncommon event that the winner got fewer popular votes than the loser.

Still around from the previous version are the Top 25 toughest places to play ( The University of Florida's Ben Hill Griffin Stadium, or " The Swamp ", remains # 1 in 06 ), a still-revamped Dynasty Mode ( with a new In-Season Recruiting feature ), all-time and historic teams, Create-a-School, and much more.

Florida's votes gave Bush, the Republican candidate, 271 electoral votes, one more than the required 270 electoral votes to win the Electoral College and defeat Democratic candidate Al Gore, who received 266 electoral votes ( a District of Columbia elector abstained ).

The decision allowed Harris's previous certification of Bush as the winner of Florida's electoral votes to stand.

After an intense recount process, Bush officially won Florida's electoral votes and as a result, the entire presidential election.

In 1964, Republican Barry Goldwater carried the district by such a large margin that it nearly pushed Florida's electoral votes into the Republican column.