These states are labeled by a set of quantum numbers summarized in the term symbol and usually associated with particular electron configurations, i. e., by occupation schemes of atomic orbitals ( e. g., 1s < sup > 2 </ sup > 2s < sup > 2 </ sup > 2p < sup > 6 </ sup > for the ground state of neon -- term symbol: < sup > 1 </ sup > S < sub > 0 </ sub >).

However, this was the temperature of one particular degree of freedom a quantum property called nuclear spin not the overall average thermodynamic temperature for all possible degrees in freedom.

In particular, these include the laws of quantum mechanics, electromagnetism and statistical mechanics.

In particular the application of quantum mechanics to chemistry is called quantum chemistry.

It means that a particular approximation is rigorously defined on first principles ( quantum theory ) and then solved within an error margin that is qualitatively known beforehand.

The energy bands each correspond to a large number of discrete quantum states of the electrons, and most of the states with low energy ( closer to the nucleus ) are occupied, up to a particular band called the valence band.

In particular the application of quantum mechanics to chemistry is called quantum chemistry.

This experimental fact is highly reproducible, and the mathematics of quantum mechanics ( see below ) allows us to predict the exact probability of an electron striking the screen at any particular point.

In 1964, John Bell showed that the predictions of quantum mechanics in the EPR thought experiment are significantly different from the predictions of a particular class of hidden variable theories ( the local hidden variable theories ).

In particular, in the quantum theory a smeared supertube is present that cuts the spacetime in such a way that, although in the full spacetime a closed timelike curve passed through every point, no complete curves exist on the interior region bounded by the tube.

In contrast to bosons, only one fermion can occupy a particular quantum state at any given time.

In a few materials, a much stronger interaction between spins arises because the change in the direction of the spin leads to a change in electrostatic repulsion between neighboring electrons, due to a particular quantum mechanical effect called the exchange interaction.

Gravitons are postulated because of the great success of quantum field theory ( in particular, the Standard Model ) at modeling the behavior of all other known forces of nature as being mediated by elementary particles: electromagnetism by the photon, the strong interaction by the gluons, and the weak interaction by the W and Z bosons.

In scientific research, the behavior of the two fluid phases of helium-4 ( helium I and helium II ), is important to researchers studying quantum mechanics ( in particular the property of superfluidity ) and to those looking at the phenomena, such as superconductivity, that temperatures near absolute zero produce in matter.

In principle all kinds of magnetism originate ( similar to Superconductivity ) from specific quantum-mechanical phenomena ( e. g. Mathematical formulation of quantum mechanics, in particular the chapters on spin and on the Pauli principle ).

Just as he argues that there is no particular reason why particular macroscopic physical features in the brain should give rise to consciousness, he also thinks that there is no particular reason why a particular quantum feature, such as the electromagnetic field in the brain, should give rise to consciousness, either.

The phenomenology of quantum physics arose roughly between 1895 and 1915, and for the 10 to 15 years before the emergence of quantum theory ( around 1925 ) physicists continued to think of quantum theory within the confines of what is now called classical physics, and in particular within the same mathematical structures.

The Armed Forces Epidemiological Board agreed to submit each month a report for one of its 12 commissions, so that each commission will report once a year on some phase of its work calculated to be of particular interest and value to medical officers of the Armed Forces.

Most studies have been based only on bipolar I, however, and treatment during the acute phase can be a particular challenge.

It is possible to obtain a qualitative understanding of many diffraction phenomena by considering how the relative phases of the individual secondary wave sources vary, and in particular, the conditions in which the phase difference equals half a cycle in which case waves will cancel one another out.

The filter response can also be completely characterized in the frequency domain by its transfer function, which is the Fourier transform of the impulse response h. Typical filter design goals are to realize a particular frequency response, that is, the magnitude of the transfer function ; the importance of the phase of the transfer function varies according to the application, inasmuch as the shape of a waveform can be distorted to a greater or lesser extent in the process of achieving a desired ( amplitude ) response in the frequency domain.

Empires represented only a particular phase in the ever-changing relationship of Europe with the rest of the world: analogies with industrial systems or investment in real estate were simply misleading.

This method allows for the characterization of the particular phase, as the different phases are defined by their particular order, which must be observed.

In particular, a sharp drop of the order parameter to 0 is observed when the system undergoes a phase transition from an LC phase into the isotropic phase.

:* Phase transformation kinetics, for the kinetics of phase transformations ( with particular emphasis on solid-solid phase transitions )

This number of bits comprises the symbol that is represented by the particular phase, frequency or amplitude.

MSK and GMSK are particular cases of continuous phase modulation.

Indeed, MSK is a particular case of the sub-family of CPM known as continuous-phase frequency-shift keying ( CPFSK ) which is defined by a rectangular frequency pulse ( i. e. a linearly increasing phase pulse ) of one symbol-time duration ( total response signaling ).

Dufour bladelets are up to three centimeters in length, finely shaped with a curved profile whose retouches are semi-abrupt and which characterize a particular phase of the Aurignacian period.

In terms of modeling, describing, or understanding the behavior of a particular system, it may be efficacious to treat the interfacial region as a separate phase.

Applying higher pressure of the order of hundreds or thousands of kilobars induces a series of phase transformations, in particular with a tetragonal phase appearing at about 900 kbar.

In particular, if a complex harmonic signal with a sinusoidal component with amplitude, angular frequency and phase

That is, it may become clear in the implementation phase that a particular area of program functionality is extraordinarily difficult to implement.

This period of Viking raids on the coasts of Ireland has been named the longphort phase after these particular types of settlements.

Renaissance Venice had a phase of particular interest in depictions of the Ottoman Empire in painting and prints.

Each pattern of bits forms the symbol that is represented by the particular phase.

Capacitance is the enemy of square-wave data transmission ( in particular, it slows down edge transitions ), and this is a much more important factor for baseband digital data transmission than power handling or attenuation.

All the characteristic temperatures associated to phases transformation, glass transitions and melting points, occurring during a sinterisation cycle of a particular ceramics formulation ( i. e., tails and frits ) can be easily obtained by observing the expansion-temperature curves during optical dilatometer thermal analysis.

As mentioned in the introduction, the methods of renormalization have been applied to Statistical Physics, namely to the problems of the critical behaviour near second-order phase transitions, in particular at fictitious spatial dimensions just below the number of 4, where the above-mentioned methods could even be sharpened ( i. e., instead of " renormalizability " one gets " super-renormalizability "), which allowed extrapolation to the real spatial dimensionality for phase transitions, 3.

Many further results may be obtained, such as Fermi's golden rule, which relates the rate of transitions between quantum states to the density of states at particular energies, and the Dyson series, obtained by applying the iterative method to the time evolution operator, which is one of the starting points for the method of Feynman diagrams.

The durability and lifetime of dynamically loaded, welded steel structures are determined often by the welds, particular by the weld transitions.

Schmitt triggers can also be shown with inverting hysteresis curves and may be followed by logic gate | bubble s. The documentation for the particular Schmitt trigger being used must be consulted to determine whether the device is non-inverting ( i. e., where positive output transitions are caused by positive-going inputs ) or inverting ( i. e., where positive output transitions are caused by negative-going inputs ).

In the automata formulation, the Krohn – Rhodes theorem for finite automata states that given a finite automaton A with states Q and input set I, output alphabet U, then one can expand the states to Q ' such that the new automaton A ' embeds into a cascade of " simple ", irreducible automata: In particular, A is emulated by a feed-forward cascade of ( 1 ) automata whose transitions semigroups are finite simple groups and ( 2 ) automata which are banks of flip-flops running in parallel.

) The particular pattern of energy levels ( and, hence, of transitions in the rotational spectrum ) for a molecule is determined by its symmetry.

Current regeneration patterns may indicate which tree species will replace tanoak in diseased areas ; such transitions will be of particular importance in forest types that were relatively poor in tree species diversity even before the introduction of SOD ( e. g. redwood forest ).

Determination of the cosmic abundance of elements has a history dating back to early spectroscopic measurements of light from astronomical objects and the identification of emission and absorption lines which corresponded to particular electronic transitions in chemical elements identified on Earth.

One particular application is to critical phenomena ( phase transitions of the second order ) in systems with local interactions.

In mathematics and its applications, particularly to phase transitions in matter, a Stefan problem ( also Stefan task ) is a particular kind of boundary value problem for a partial differential equation ( PDE ), adapted to the case in which a phase boundary can move with time.

From a particular model follow a set of selection rules that determine which transitions are allowed and which are not.

As the corpus grows, and particular transitions are reinforced, they will increase in value, reaching a local maximum.

Some authorities refuse to order characters at all, suggesting that it biases an analysis to require evolutionary transitions to follow a particular path.

Contrary to popular belief, the algorithm does not explicitly assign particular character states to nodes ( branch junctions ) on a tree: the least number of steps can involve multiple, equally costly assignments and distributions of evolutionary transitions.

The main benefits to PEM coatings are the ability to conformably coat objects ( that is, the technique is not limited to coating flat objects ), the environmental benefits of using water-based processes, reasonable costs, and the utilization of the particular chemical properties of the film for further modification, such as the synthesis of metal or semiconductor nanoparticles, or porosity phase transitions to create anti-reflective coatings, optical shutters, and superhydrophobic coatings.

As opposed to IR spectroscopy, where a transition can only be seen when that particular vibration causes a net change in dipole moment of the molecule, in Raman only transitions where the polarizability of the molecule changes can be observed.

A basic requirement for such an implementation is that the energy levels are not uniformly spaced, so that photons of a particular frequency which cause transition between the 0 and 1 levels do not cause transitions from the first level to the higher levels as well.

In contrast to GSSAs, GSSPs are based on important events and transitions within a particular stratigraphic section.