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- For larger system, consisting of ''N'' objects, this procedure can be generalized to provide a total many-body interaction energy: ...erived from quantum chemical calculations using finite atom-centered basis functions, [[basis set superposition error]]s can also contribute some degree of arti ...2 KB (353 words) - 02:32, 8 August 2023
- ...e journal |last1=Al-Nimr |first1=M. A. |last2=Alkam |first2=M. K. |title=A generalized thermal boundary condition |journal=Heat and Mass Transfer |date=19 Septemb ...rst3=A. |last4=Litkouhi |first4=Bahman |title=Heat Conduction Using Greens Functions |date=16 July 2010 |doi=10.1201/9781439895214|isbn=9781439813546}}</ref><re ...15 KB (2,080 words) - 21:18, 9 November 2023
- He showed that for any such functions the sum of the Shannon entropies is non-negative, ...|pmid=16592223 |pmc=432369 }}</ref> and in the same year interpreted as a generalized quantum mechanical uncertainty principle by [[:pl:Iwo Białynicki-Birula|Bia ...14 KB (1,990 words) - 04:41, 22 January 2024
- Because ''F'' is a thermodynamic [[Functions of state|function of state]], this [[fundamental thermodynamic relation|rel ...> are the external variables, and the <math>X_i</math> the corresponding [[generalized forces]]. ...22 KB (3,807 words) - 01:50, 14 October 2023
- ...ipation theorem]], where generalized [[Electrical impedance|impedance]] or generalized [[Electric susceptibility|susceptibility]] is used to characterize the medi == Generalized forms == ...21 KB (3,134 words) - 16:31, 8 February 2024
- Stokes' theorem is a special case of the [[generalized Stokes theorem]].<ref name="DTPO">{{cite book |first=Lawrence |last=Conlon ...short alternative proof of Stokes' theorem is given, as a corollary of the generalized Stokes' theorem. ...28 KB (4,385 words) - 15:30, 26 January 2024
- ==Cardinal functions== ...formation about the system. The fundamental equations for the two cardinal functions can in principle be interconverted by solving, for example, {{math|''U'' {{ ...32 KB (4,996 words) - 06:34, 12 February 2024
- '''Characteristic modes (CM)''' form a set of functions which, under specific boundary conditions, diagonalizes operator relating [ ...me="Garbacz1" /><ref name="Garbacz2" /> The theory has, subsequently, been generalized by [[Roger F. Harrington|Harrington]] and Mautz for antennas.<ref name="Har ...30 KB (3,965 words) - 11:49, 19 November 2023
- ...ction]]s. Linear differential equations can then be recast in the form of "functions" {{math|''F''(p)}} of the operator p acting on the unknown function equalin |title=Operational Calculus and Generalized Functions ...16 KB (2,144 words) - 02:41, 8 March 2024
- {{see also|Generalized forces|Curvilinear coordinates|Generalized coordinates|Frenet-Serret formulas}} ...his last term originates in the Lagrangian formulation for mechanics using generalized coordinates. See {{cite book |author=Francis Begnaud Hildebrand |title=Meth ...74 KB (11,570 words) - 04:52, 9 January 2024
- ...work by pushing on it). In 1850, the German physicist [[Rudolf Clausius]] generalized this picture to include the concept of the [[environment (systems)|surround ...eory]]. In 1945 he introduced ''models, principles, and laws that apply to generalized systems or their subclasses, irrespective of their particular kind, the nat ...22 KB (3,037 words) - 16:45, 27 February 2024
- {{Short description|Generalized function whose value is zero everywhere except at zero}} ...known as the '''unit impulse''',{{sfn|atis|2013|loc=unit impulse}} is a [[generalized function]] on the [[real numbers]], whose value is zero everywhere except a ...93 KB (14,126 words) - 02:03, 25 January 2024
- ...gnetic field]] <math> \mathbf{H}_1\, ,</math> where all three are periodic functions of time with [[angular frequency]] {{mvar|ω}}, and in particular they have In practical problems, there are another more generalized forms of Lorentz and other reciprocity relations, in which, in addition to ...41 KB (6,004 words) - 20:15, 29 February 2024
- ...the wave function <math>\psi = R \exp(i S / \hbar)</math> with real-valued functions <math>R</math> and <math>S</math>, where <math>R</math> is the amplitude ([ ...nction that is a [[Superposition principle|superposition]] of several wave functions of approximately disjoint [[support (mathematics)|support]] will factorize ...57 KB (8,332 words) - 14:42, 25 October 2023
- ...'''}} [[Parallel (geometry)|parallel]] to the surface must be [[Continuous functions|continuous]] (no jump in value at the surface). This equation can be generalized to include [[ellipsoid]]s having principal axes in x, y, and z directions s ...15 KB (2,188 words) - 07:18, 24 November 2023
- ...nvenient to take a continuous random field to have a [[Schwartz space]] of functions as its index set, in which case the continuous random field is a [[Distribu ...a continuous random field well enough as a [[linear map]] from a space of functions into the [[real number]]s. ...33 KB (4,918 words) - 04:26, 12 February 2024
- ===Two terminal component transfer functions=== ...or the three passive components found in electrical networks, the transfer functions are; ...39 KB (6,231 words) - 10:05, 29 November 2023
- The integral may be expressed in terms of known transcendental functions for all ellipsoidal shapes, including the symmetrical and degenerate ones.< ...icients. A less laborious way of achieving the same result is by using the generalized [[binomial theorem]].<ref name="AEM">{{cite book |first=C. R. Jr. |last=Wyl ...20 KB (3,012 words) - 06:59, 2 September 2023
- ...q_j</math> for ''i ≠ j'' are called ''Coriolis forces''. The third type is functions of <math>\boldsymbol{q}</math> only and are called ''gravitational forces'' ...44 KB (6,768 words) - 04:08, 2 March 2024
- ...epresentation in a rather more direct way than using imaginary exponential functions. Kennelly followed the graphical representation of impedance (showing resi [[File:Impedance symbol comparison.svg|thumb|right|165px|Generalized impedances in a circuit can be drawn with the same symbol as a resistor (US ...32 KB (4,972 words) - 19:19, 17 January 2024