According to Noether's theorem, if the action ( the integral over time of its Lagrangian ) of a physical system is invariant under rotation, then angular momentum is conserved.

According to Noether's theorem, translational symmetry of a physical system is equivalent to the momentum conservation law.

According to Cauchy's functional equation theorem, the logarithm is the only continuous transformation that transforms real multiplication to addition.

According to (), the first historical mention of the statement of this theorem appears in ().

According to Birkhoff's theorem, it is the only vacuum solution that is spherically symmetric.

According to the theorem, it is possible to expand the power ( x + y )< sup > n </ sup > into a sum involving terms of the form ax < sup > b </ sup > y < sup > c </ sup >, where the exponents b and c are nonnegative integers with, and the coefficient a of each term is a specific positive integer depending on n and b. When an exponent is zero, the corresponding power is usually omitted from the term.

According to the theorem, it is possible to expand any power of x + y into a sum of the form

According to the theorem, within every sufficiently powerful logical system ( such as Principia ), there exists a statement G that essentially reads, " The statement G cannot be proved.

* According to a theorem of Nikolay Nikolov and Dan Segal, in any topologically finitely-generated profinite group ( that is, a profinite group that has a dense finitely-generated subgroup ) the subgroups of finite index are open.

According to the spin-statistics theorem, particles with integer spin occupy symmetric quantum states, and particles with half-integer spin occupy antisymmetric states ; furthermore, only integer or half-integer values of spin are allowed by the principles of quantum mechanics.

According to Rice's theorem, if there is at least one computable function in a particular class C of computable functions and another computable function not in C then the problem of deciding whether a particular program computes a function in C is undecidable.

According to the Rouché – Capelli theorem, the system is inconsistent if the rank of the augmented matrix is greater than the rank of the coefficient matrix.

According to the optical Raychaudhuri's theorem, this requires a violation of the averaged null energy condition.

According to the theorem, the reconstructed signal will match the original signal provided that the original signal contains no frequencies at or above this limit.

According to the Nyquist theorem, error-free detection of the line code requires a channel bandwidth of at least the Nyquist rate, which is half the line code pulse rate.

According to Shannon's source coding theorem, the optimal code length for a symbol is − log < sub > b </ sub > P, where b is the number of symbols used to make output codes and P is the probability of the input symbol.

According to the CPT theorem of particle physics, antihydrogen atoms should have many of the characteristics regular hydrogen atoms have ; i. e., they should have the same mass, magnetic moment, and transition frequencies ( see atomic spectroscopy ) between their atomic quantum states.

According to Liouville's theorem, any bounded complex analytic function defined on the whole complex plane is constant.

According to Allen Weiss, in Mirrors of Infinity, this optical effect is a result of the use of the tenth theorem of Euclid ’ s Optics which asserts that “ the most distant parts of planes situated below the eye appear to be the most elevated .” In Fouquet ’ s time, interested parties could cross the canal in a boat, but walking around the canal provides a view of the woods that mark what is no longer the garden and shows the distortion of the grottos previously seen as sculptural.

According to the virial theorem, the gravitational binding energy of a star is about two times its internal thermal energy.

According to the correspondence principle and Ehrenfest's theorem as a system becomes larger or more massive ( action >> Planck's constant ) the classical dynamics tends to emerge, with some exceptions, such as superfluidity.

According to the Kutta – Joukowski theorem, lift is the product of circulation, airspeed, and air density.

According to the Shannon – Hartley theorem, the channel capacity of a properly-encoded signal is proportional to the bandwidth of the channel and the logarithm of the signal-to-noise ratio ( SNR ) ( assuming the noise is additive white Gaussian noise ).

According to Ptolemy's second theorem,

According to the inverse function theorem, the matrix inverse of the Jacobian matrix of an invertible function is the Jacobian matrix of the inverse function.

According to one leading historian of statistics, he may have been the earliest discoverer of Bayes theorem.

According to David Steel, curator of European art at the North Carolina Museum of Art, Erin Jones " brought that museum into the modern era ," employing " a top-notch curator, John Nolan ," and following " best practices in conservation and restoration.

According to the LTTE's then head of police, the force was to be assigned to tasks such as rehabilitation, construction, forest conservation and agriculture, but would also be used to battle the Sri Lankan military if the need arose.

According to the authors, the " next industrial revolution " depends on the espousal of four central strategies: " the conservation of resources through more effective manufacturing processes, the reuse of materials as found in natural systems, a change in values from quantity to quality, and investing in natural capital, or restoring and sustaining natural resources ".

According to the authors, the " next industrial revolution " depends on the espousal of four central strategies: " the conservation of resources through more effective manufacturing processes, the reuse of materials as found in natural systems, a change in values from quantity to quality, and investing in natural capital, or restoring and sustaining natural resources.

According to general relativity, the conservation laws of linear momentum, energy and angular momentum are only exactly true globally when expressed in terms of sum of the stress – energy tensor ( non-gravitational stress – energy ) and Landau – Lifshitz stress – energy – momentum pseudotensor ( gravitational stress – energy ).

According to its Environmental Mission Statement, Bowdoin College " shall seek to encourage conservation, recycling, and other sustainable practices in its daily decision making processes, and shall take into account, in the operations of the College, all appropriate economic, environmental, and social concerns.

According to an article published in the Physiological Transactions of the Royal Society called “ The role of conservation agriculture and sustainable agriculture ” crop rotation can be used best as a “ disease control ” against other preferred crops ( Hobbs et al.

According to Marx's labor theory of value, human labor is the only source of net new economic value, but is also indispensable for the conservation and transfer of economic value ( maintenance and redistribution of capital assets ).

According to the Fund, a long-term conservation plan was conceived, which includes further repairs, documentation, and archaeological research.

According to the principle of the conservation of Energy, energy, cannot be created or destroyed ; it can only be converted from one type to another.

According to the CityTownInfo web site, MUM has more degree programs than 86 % of colleges of similar sizes, and more degrees in conservation and resource management than 93 % of all other colleges.

According to the conservation group SOS Lynx, if the Iberian lynx died out, it would be the first feline species to become extinct since prehistoric times.

According to a letter from Davis to Gaston Maspero, some of the objects found in KV55 were still in place in January 1908, and their study and attempts at conservation were still ongoing at this later date .< ref > Reeves, C. N., < cite > Valley of the Kings </ cite >, ( Keegan Paul, 1990 ), p

According to the marine conservation biologist Callum Roberts, four criteria apply when choosing seafood:

According to the laws governing fluid dynamics, a fluid's velocity must increase as it passes through a constriction to satisfy the principle of continuity, while its pressure must decrease to satisfy the principle of conservation of mechanical energy.

According to aquarium founder Bernard Marcus, the aquarium's conservation and environmental mission is just as important as its status as an attraction.

According to the orbital energy conservation equation ( also referred to as vis-viva equation ), it does not vary with time:

According to his 1972 publication Preservation he worked on setting-up the " Four Towns Report " and played an important role in establishing the foundations of conservation policy through the Town and Country Planning Act 1968 and his 1970 Kennet Report.

According to the Royal Commission on Environmental Pollution, BPEO " emphasises the protection and conservation of the environment across land, air and water.

According to the deal, Professor Jonathan West of Australia's Innovation Research Centre will, by the end of 2011, independently assess areas currently considered to be of high conservation value.

According to the Fund, the soft sandstone structure had weathered severely, and prior conservation efforts, which did not fully address all the building ’ s problems, as well as substantial biological growth, had compounded the deterioration.