If Franklin was an authentic genius, then Alexander Hamilton, with his exceptional precocity, consuming energy, and high ambition, was a political prodigy.

The Prince's perceptions were quick and his energy monstrous, but these qualities were sapped by an Oriental lethargy and a policy of letting nothing interfere with personal passions.

One's daily work becomes sacred, since it is performed in the field of influence of the moral law, dealing as it does with people as well as with matter and energy.

When carving he was charged with spontaneous energy ; ;

The accuracy of measuring the total electrical energy entering an exploding wire during a few microseconds was verified when two independent types of comparison with the heat energy produced had an uncertainty of less than 2 percent.

Sonar can be used to measure the thickness of the heart by placing small crystal transducers at opposite sides of the heart or blood vessel and exciting one with some pulsed ultrasonic energy.

It is sufficiently small compared with the surface temperature of the anode holder, to make the energy flux radiated from the environment toward the anode holder negligible within the accuracy of the present measurements.

The minimum total potential energy is found by taking the derivative with respect to H and equating to zero.

The concept of the strain energy as a Gibbs function difference Af and exerting a force normal to the shearing face is compatible with the information obtained from optical birefringence studies of fluids undergoing shear.

The child with high anxiety may first direct his anxiety-released energy toward achievement, but because his distress severely reduces the abilities of discrimination and memorization of complex symbols, the child may fail in his initial attempts to master the problem.

The individual with high anxiety in the structured classroom may approach the learning task with the same increased energy and lowered powers of discrimination.

The simplest division, and the one most frequently used ( with subdivisions ) in gas and electric rate cases, is a threefold division of the total operating and capital costs into `` customer costs '', `` energy '' or `` volumetric costs '', and `` demand '' or `` capacity '' costs.

Nickel-iron meteorites with sufficient kinetic energy to produce large terrestrial explosion craters may nevertheless melt only small quantities of material.

He contends this idea doesn't conflict with experiments on which the principle of conservation of matter and energy is based because some slight error must be assumed in such experiments.

Then she continued with energy, `` I myself did not see her until a week after she had run off to find the father.

Pure altruism consists of sacrificing something for someone other than the self ( e. g. sacrificing time, energy or possessions ) with no expectation of any compensation or benefits, either direct, or indirect ( e. g., receiving recognition for the act of giving ).

Surface water temperatures, which vary with latitude, current systems, and season and reflect the latitudinal distribution of solar energy, range from below.

A Bohr model of the hydrogen atom, showing an electron jumping between fixed orbits and emitting a photon of energy with a specific frequency

soil pollution from toxic chemicals such as DDT ; energy blockade, the result of conflict with Azerbaijan, has led to deforestation when citizens scavenged for firewood ; pollution of Hrazdan ( Razdan ) and Araks Rivers ; the draining of Sevana Lich ( Lake Sevan ), a result of its use as a source for hydropower, threatens drinking water supplies ; restart of Metsamor nuclear power plant without adequate ( IAEA-recommended ) safety and backup systems

The vast majority of energy is produced with imported fuel, including gas and nuclear fuel ( for its one nuclear power plant ) from Russia ; the main domestic energy source is hydroelectric.

Economic ties with Russia remain close, especially in the energy sector.

The Russian experimenters claim that only a small fraction of the impulse from the sensors is caused by the incident momentum with the remainder being momentum of ejected material from the sensor.

The threshold mass is derived from the momentum threshold with the assumption of a mean impact velocity of Af in the U.S. work and Af in the U.S.S.R. work.

The simple names s orbital, p orbital, d orbital and f orbital refer to orbitals with angular momentum quantum number l = 0, 1, 2 and 3 respectively.

However, the idea that electrons might revolve around a compact nucleus with definite angular momentum was convincingly argued at least 19 years earlier by Niels Bohr, and the Japanese physicist Hantaro Nagaoka published an orbit-based hypothesis for electronic behavior as early as 1904.

Shortly after, in 1913, Rutherford's postdoctoral student Niels Bohr proposed a new model of the atom, wherein electrons orbited the nucleus with classical periods, but were only permitted to have discrete values of angular momentum, quantized in units h / 2π.

In our current understanding of physics, the Bohr model is called a semi-classical model because of its quantization of angular momentum, not primarily because of its relationship with electron wavelength, which appeared in hindsight a dozen years after the Bohr model was proposed.

If denotes the quantum state of a particle ( n ) with momentum p, spin J whose component in the z-direction is σ, then one has

For the case of an object that is small compared with the radial distance to its axis of rotation, such as a tin can swinging from a long string or a planet orbiting in a circle around the Sun, the angular momentum can be expressed as its linear momentum,, crossed by its position from the origin, r. Thus, the angular momentum L of a particle with respect to some point of origin is

For an object with a fixed mass that is rotating about a fixed symmetry axis, the angular momentum is expressed as the product of the moment of inertia of the object and its angular velocity vector:

The angular momentum of a particle or rigid body in rectilinear motion ( pure translation ) is a vector with constant magnitude and direction.

so that the total angular momentum with respect to the center is

If the net force on some body is directed always toward some fixed point, the center, then there is no torque on the body with respect to the center, and so the angular momentum of the body about the center is constant.

Constant angular momentum is extremely useful when dealing with the orbits of planets and satellites, and also when analyzing the Bohr model of the atom.

Under this formalism, angular momentum is the 2-form Noether charge associated with rotational invariance ( As a result, angular momentum is not conserved for general curved spacetimes, unless it happens to be asymptotically rotationally invariant ).

) Conservation of angular momentum applies to J, but not to L or S ; for example, the spin – orbit interaction allows angular momentum to transfer back and forth between L and S, with the total remaining constant.

For a rigorous definition of basis with a continuous set of indices and consequently for a rigorous definition of position and momentum basis see.

The most general stationary black hole solution known is the Kerr – Newman metric, which describes a black hole with both charge and angular momentum.

If Af are the projections associated with the primary decomposition of T, then each Af is a polynomial in T, and accordingly if a linear operator U commutes with T then U commutes with each of the Af, i.e., each subspace Af is invariant under U.

Then in 2 we show that any line involution with the properties that ( A ) It has no complex of invariant lines, and ( B ) Its singular lines form a complex consisting exclusively of the lines which meet a twisted curve, is necessarily of the type discussed in 1.

The preceding observations make it clear that there exist line involutions of all orders greater than 1 with no complex of invariant lines and with a complex of singular lines consisting exclusively of the lines which meet a twisted curve Aj.

Hilbert obtained his doctorate in 1885, with a dissertation, written under Ferdinand von Lindemann, titled Über invariante Eigenschaften spezieller binärer Formen, insbesondere der Kugelfunktionen (" On the invariant properties of special binary forms, in particular the spherical harmonic functions ").

For example, if u < sub > 1 </ sub > is an eigenvector of A, with a real eigenvalue smaller than one, then the straight lines given by the points along α u < sub > 1 </ sub >, with α ∈ R, is an invariant curve of the map.

Some authors use " compatible with ~" or just " respects ~" instead of " invariant under ~".

Some authors use " compatible with " or just " respects " instead of " invariant under ".

:"[...] Every invariant and co-variant thus becomes expressible by a graph precisely identical with a Kekuléan diagram or chemicograph.

If a spatial extra dimension is of radius R, the invariant mass of such standing waves would be M < sub > n </ sub > = nh / Rc with n an integer, h being Planck's constant and c the speed of light.

This identifies the tangent space T < sub > e </ sub > at the identity with the space of left invariant vector fields, and therefore makes the tangent space at the identity into a Lie algebra, called the Lie algebra of G, usually denoted by a Fraktur Thus the Lie bracket on is given explicitly by = < sub > e </ sub >.

This leads to the same Lie algebra, because the inverse map on G can be used to identify left invariant vector fields with right invariant vector fields, and acts as − 1 on the tangent space T < sub > e </ sub >.

In this way he demonstrated that the laws of physics remained invariant as they had with the Galilean transformation, but that light was now invariant as well.

All unaccelerated observers agree on the amount of invariant mass in closed systems at all times, and although different observers may not agree with each other on how much relativistic mass is present in any such system, all agree that the amount does not change over time.

Newton's second law, with mass fixed, is not invariant under a Lorentz transformation.

It is interesting to note that this diversification of histone function is restricted to H2A and H3, with H2B and H4 being mostly invariant.

For example, the notion of gauge invariance forms the basis of the well-known Mattis spin glasses, which are systems with the usual spin degrees of freedom for i = 1 ,..., N, with the special fixed " random " couplings Here the ε < sub > i </ sub > and ε < sub > k </ sub > quantities can independently and " randomly " take the values ± 1, which corresponds to a most-simple gauge transformation This means that thermodynamic expectation values of measurable quantities, e. g. of the energy are invariant.

) is the group of all isometries under which the object is invariant with composition as the operation.