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Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a differential operator, to be contrasted with the approach given by a principal connection on the frame bundle – see affine connection.
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Alternatively and covariant
Alternatively, if we are using a torsion-free connection ( e. g. the Levi Civita connection ), then the partial derivative can be replaced with the covariant derivative.
Alternatively, a solution to the field equations is local if the underlying equations are either Lorentz invariant or, more generally, generally covariant or locally Lorentz invariant.
Alternatively and derivative
( Alternatively, Lucien Gubbay suggests the name Medina could also have been a derivative from the Aramaic word Medinta, which the Jewish inhabitants could have used for the city.
* Alternatively, the Lie derivative can be defined as
Alternatively, the symmetry can be written as an algebraic statement involving the differential operator D < sub > i </ sub > which takes the partial derivative with respect to x < sub > i </ sub >:
Alternatively, the first derivative of the asset's price function with respect to the interest rate, is matched with the liabilities.
Alternatively, the operator can be generalized to operate on differential forms using the divergence and exterior derivative.
Alternatively and is
Alternatively, anomalous perturbation is defined as an interaction with matter without the use of all known physical mechanisms.
Alternatively they can be organized by whether the raw stock is of natural, or synthetic origin, or by their starting physical phase.
Alternatively, the line is divided into three four-syllable sections by two caesuras.
Alternatively, for a single system at a well-defined temperature, it gives the probability that the system is in the specified state.
Alternatively, liquid chalk is sometimes used.
Alternatively a therm is used representing 100, 000 or 10 < sup > 5 </ sup > Btu, and a quad as 10 < sup > 15 </ sup > Btu.
Alternatively, these experiments provide an operational definition of what is meant by " absolute rotation ", and do not pretend to address the question of " rotation relative to what?
Alternatively, a manager of managers is often referred to as a " senior manager ' or as an " associate vice president ", depending upon levels of management, and industry type.
Alternatively, if a line is constructed perpendicularly between Alpha Centauri and Beta Centauri, the point where the above mentioned line and this line intersect marks the Southern Celestial Pole.
Alternatively, if using more than one or two techniques for every experiment is infeasible, some of the benefits of consilience may still be obtained if it is well-established that these techniques usually give the same result.
Alternatively, it is identified with the " tree of paradise " of medieval mystery plays that were given on 24 December, the commemoration and name day of Adam and Eve in various countries.
Alternatively, if positive pressures are required, standard glassware can not be used, energy must be used for pressurization and there is a higher chance of side reactions occurring in the distillation, such as decomposition, due to the higher temperatures required to effect boiling.
Alternatively, the more reflux that is provided for a given desired separation, the fewer the number of theoretical plates required.
Alternatively, each computer may have its own user with individual needs, and the purpose of the distributed system is to coordinate the use of shared resources or provide communication services to the users.
Alternatively entropy can be defined from a classical thermodynamics viewpoint, in which the molecular interactions are not considered and instead the system is viewed from perspective of the gross motion of very large masses of molecules and the behavior of individual molecules is averaged and obscured.
( Alternatively, Esperanto may be written with English-like digraphs in h rather than with diacritics, but this is seldom seen outside email.
Alternatively, it is possible to express an even-length real-input DFT as a complex DFT of half the length ( whose real and imaginary parts are the even / odd elements of the original real data ), followed by O ( N ) post-processing operations.
Alternatively, the liquid may flow through the filter by the force exerted by a pump, a method commonly used in industry when a reduced filtration time is important.
Alternatively, in Fenichel's words, " the superego is reprojected onto external objects for the purpose of getting rid of guilt feelings ... using external objects as " witnesses " in the fight against the superego.
Alternatively, additional information is necessary to complete the find, such as a padlock combination to access the cache.
Alternatively, the word " gematria " is generally held to derive from Greek geōmetriā, " geometry ", which was used as a translation of gēmaṭriyā, though some scholars believe it to derive from Greek grammateia, rather ; it's possible that both words had an influence on the formation of the Hebrew word.
Alternatively, it may refer only to what is common to the grammars of all, or of the vast majority of English speakers ( such as subject – verb – object word order in simple declarative sentences ).
* Elevation is the angular height of an object above the horizon, Alternatively zenith distance, being equal to 90 degrees minus elevation.
Alternatively and way
Alternatively, similar to the way primary colors combine, primary emotions could blend to form the full spectrum of human emotional experience.
Alternatively, gdbserver can be used to remotely debug the program without needing to change it in any way.
Alternatively, Prakrit can be taken to mean " derived from an original ," which means evolved in natural way.
Alternatively, it has been suggested that the arrangement has a magical origin, a way to trap evil spirits.
Alternatively, technological unemployment might refer to the way in which steady increases in labour productivity mean that fewer workers are needed to produce the same level of output every year.
Alternatively, if we want to have reasonable discussion we may be practically forced to accept Occam's razor in the same way we are simply forced to accept the laws of thought and inductive reasoning ( given the problem of induction ).
Alternatively, an intermediary may wish to make a profit by acquiring financial assets and repackaging them in a way more attractive to investors.
Alternatively, democratically run communities can agree to deal with these costs and benefits in an amicable way.
Alternatively, Scots is sometimes treated as a distinct Germanic language, in the way Norwegian is closely linked to, yet distinct from, Danish.
Alternatively there is an emerging class of software which can localize an application without altering the underlying code in any way Modern development systems and operating systems include sophisticated libraries for international support of these types.
Alternatively these paintings may be of a Masonic motivation as in the 18th century it was believed that the Crusader Military orders, such as The Poor Knights of the Temple of Solomon ( Knights Templar ) and the Knights of St John ( Hospitallers ), were in some way inexplicably linked.
Alternatively, some membrane proteins penetrate all the way through the bilayer and serve to relay individual signal events from the outside to the inside of the cell.
Alternatively, the rocks here could contain a component from the lunar mantle if the basin excavated all the way through the crust.
Alternatively, some canoes proceeded by way of the upper St. Lawrence River and the lakes, passing by Detroit on the way to Michilimackinac or Green Bay.
Alternatively, it could reflect the dramatic way the island was conquered, producing the strongest sexual asymmetry in the archipelago.
Alternatively, when a rotation is specified by a vector, and it is necessary to understand the way in which the rotation occurs, the right-hand grip rule is applicable.
Alternatively, as Herbert A. Simon suggested, something is simple or complex depending on the way we choose to describe it.
Alternatively Person 2 can redefine X in way that instead concludes all things are not X.
Alternatively, we could make the level structure quasi-random in the following way:
Alternatively a machine ( which may be a workstation or a network server ) with screen, keyboard, and mouse can be set up to boot and run the VNC server as a service or daemon, then the screen, keyboard, and mouse can be removed and the machine stored in an out-of-the way location.
Alternatively walk to the top of the steep pedestrian path leading north from the station entrance, cross Barnet Hill and turn left down Barnet Hill ( allow at least five minutes to reach this stop either way ):
Alternatively ' Cripplegate ' could be from the Anglo-Saxon term crepel, meaning a covered way or underground passage.
Alternatively, when this method fails for six months or longer, a more aggressive approach may be undertaken using suppositories and enemas in a carefully programmed way to overcome the reflexive holding response and to allow the proper voiding reflex to take over.
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