Alternatively, the right-hand side expression can be justified by multiplying the power series on the left by 1 − x, and checking that the result is the constant power series 1, in other words that all coefficients except the one of x < sup > 0 </ sup > vanish.

Alternatively, when a self-balancing binary search tree is used, insertion and removal also take O ( log n ) time, although building trees from existing sequences of elements takes O ( n log n ) time ; this is typical where one might already have access to these data structures, such as with third-party or standard libraries.

Alternatively, a deal in which an actor takes detrimental actions possibly in reaction to an offer, without having viewed the deal as a bargain, wouldn't be viewed as a contract under the law.

Alternatively, if the track takes the flight directly overhead a beacon, the pilot can use the ADF instrument to maintain heading relative to the beacon, though " following the needle " is bad practice, especially in the presence of a strong cross wind-the pilot's actual track will spiral in towards the beacon, not what was intended.

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 dog takes and holds an object which it has no interest in.

Alternatively, it may mean that ʿElyōn, having given the other nations to his sons, now takes Israel for himself under his name of God.

Alternatively, passengers may walk around the terminal loop instead of riding AirTrain, which takes about 25 minutes by foot ; however, passengers must ride AirTrain to access the Rental Car Center.

Alternatively, high carbon FeCr produced from high grade ore found in Kazakhstan ( among other places ) is more commonly used in specialist applications such as engineering steels where a high Cr to Fe ratio and minimum levels of other elements such as sulfur, phosphorus and titanium are important and production of finished metals takes place in small electric arc furnaces compared to large scale blast furnaces.

Alternatively, it is possible to travel by river from Miri, which is about 100 km away, using a riverboat, then a chartered long boat, which in total takes around 12 hours.

Alternatively, for those familiar with power series ( or Taylor series ), one may think of a formal power series as a power series in which we ignore questions of convergence by not assuming that the variable X denotes any numerical value ( not even an unknown value ).

Alternatively, a variable capacitor is used to tune the radio instead of the coil.

Alternatively, the variable must not appear anywhere in the respective lower sequents.

Alternatively, fields of variable length may, for instance, be separated by commas ( see Comma-separated values ) when the end of each individual field must be determined by scanning for the delimiter " one byte at a time ".

Alternatively, variable B could be collapsed out entirely, alternately sampling from p ( A | C ) and p ( C | A ) and not sampling over B at all.

Alternatively, a variant scoring system determines the winner via a point system — 1 point for a knock out, 2 points for a propaganda knock out, 3 points for a retaliation knock out, a variable number of points for position depending on number of players, and finally 2 points for surviving ( with the survivor not necessarily being the points winner ).

Alternatively, specification may state that the records are of variable length, along with the maximum record length.

Alternatively, a production function can be defined as the specification of the minimum input requirements needed to produce designated quantities of output, given available technology.

Alternatively files, some data structures and reports can be defined externally, mostly eliminating the need to hand code input and output (" I / O ") specifications.

Alternatively they may set the input control to minimum at night instead of the output, which can mean there is no heat at all for the next day.

Alternatively, an optical sight can be provided and an operator can point it at the target, which is easier than having someone input it using other methods and gives the target less warning that it is being tracked.

Alternatively, if,, and are known, but is not adjustable, the voltage difference across or current flow through the meter can be used to calculate the value of, using Kirchhoff's circuit laws ( also known as Kirchhoff's rules ).

Alternatively ( and some would say properly, in the context of electrocardiography ), the word lead may refer to the tracing of the voltage difference between two of the electrodes and is what is actually produced by the ECG recorder.

Alternatively, the cell can be current clamped in whole-cell mode, keeping current constant while observing changes in membrane voltage.

Alternatively, the three-phase alternating current of the power grid can be converted in substations by rotary transformers or static inverters into the voltage and type of current required by the trains.

for x, weight in dataWeightPairs: # Alternatively " for x, weight in zip ( data, weights ):"

Alternatively, atomic orbitals refer to functions that depend on the coordinates of one electron ( i. e. orbitals ) but are used as starting points for approximating wave functions that depend on the simultaneous coordinates of all the electrons in an atom or molecule.

Alternatively, the rock picker can feel underneath rocks at low tides for abalone.

Alternatively, for a single system at a well-defined temperature, it gives the probability that the system is in the specified state.

Alternatively, there may further be requirements for maximum terms that a government can keep power before holding an election.

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, 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, for an orientable surface the formula can be given in terms of the genus of a surface, g:

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, Portsmouth and Southsea is another railway station, used for connections to Bristol ( Temple Meads ) and Cardiff.

Alternatively, the word may be derived from an Irish word for a wooden anchor.

Alternatively, they can be termed when they are designed for combat as opposed to iaitō training swords.

Alternatively, functioning may be affected by the stress of having to hide a condition in work or school etc., by adverse effects of medications or other substances, or by mismatches between illness-related variations and demands for regularity.

Alternatively, we could control the Hamiltonian of the system, and thus the time evolution operator U ( for a time independent Hamiltonian,, where is called the generator of translations in time ) up to some fixed time interval, which yields a unitary operator.

Alternatively, the maximal round trump suit can be determined in a variety of ways: for instance, by revealing the dealer's last card as in whist or by cutting the pack before dealing.

Alternatively, the children are allowed to " steal " the afikoman and demand a reward for its return.

( Alternatively, for a preorder "", a relation "<" can be defined as a < b if and only if ( a b and a ≠ b ).

Alternatively, they may have used stored yolk products for nourishment during their first few days of life, as in modern reptiles, rather than depend on parents for food.

This permits the carrying of even more propellant, enormously improving the delta-v. Alternatively, some rockets such as for rescue scenarios or racing carry relatively little propellant and payload and thus need only a lightweight structure and instead achieve high accelerations.

Alternatively, public health strategies could selectively address socioeconomic factors that have been linked to higher rates of schizophrenia in certain groups, for example in relation to immigration, ethnicity or poverty.

Alternatively, the search engine may store a copy of each item in a cache so that users can see the state of the item at the time it was indexed or for archive purposes or to make repetitive processes work more efficiently and quickly.

Alternatively, he may have proved the heliocentric theory by determining the constants of a geometric model for the heliocentric theory and by developing methods to compute planetary positions using this model, like what Nicolaus Copernicus later did in the 16th century.