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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.
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Alternatively and entropy
Alternatively, one can apply the thermodynamic identity for differential entropy:
Alternatively and can
Alternatively, if characters ' attribute ranks are close, the weaker character can try to change the relevant attribute by changing the nature of the conflict.
Alternatively, the rock picker can feel underneath rocks at low tides for abalone.
Alternatively they can be organized by whether the raw stock is of natural, or synthetic origin, or by their starting physical phase.
Alternatively, if the boards are pre-dealt, " curtain cards " may be supplied which have each hand printed on them, so that each player can check at the beginning of the deal that he has the right cards.
Alternatively SCSI Enclosure Services can be used.
Alternatively, she can seek a surgical solution.
Alternatively, there may further be requirements for maximum terms that a government can keep power before holding an election.
Alternatively, rasterization can be done in a more complicated manner by first rendering the vertices of a face and then rendering the pixels of that face as a blending of the vertex colors.
Alternatively, diagnosis and strain identification can be made using polymerase chain reaction ( PCR ).
Alternatively, the business can be sold as a going concern with the net proceeds of the sale distributed to creditors ratably in accordance with statutory priorities.
Alternatively, the coordinates of a point p can also be taken as the ( signed ) distances from p to the three planes defined by the three axes.
Alternatively, dualism can mean the tendency of humans to perceive and understand the world as being divided into two overarching categories.
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, a single hostname may correspond to many IP addresses: this can facilitate fault tolerance and load distribution, and also allows a site to move physical locations seamlessly.
Alternatively, and especially in connection with the relational model of database management, the relation between attributes drawn from a specified set of domains can be seen as being primary.
Alternatively, the method can be used to value the company based on the value of total invested capital.
Alternatively, they can be fitted with tom heads and tuned as shallow concert toms.
Alternatively, two figures are congruent if one can be moved on top of the other so that it matches up with it exactly.
Alternatively, the image can be photographically recorded by exposing a photographic film or plate directly to the electron beam, or a high-resolution phosphor may be coupled by means of a lens optical system or a fibre optic light-guide to the sensor of a CCD ( charge-coupled device ) camera.
Alternatively, for an orientable surface the formula can be given in terms of the genus of a surface, g:
Alternatively, gdbserver can be used to remotely debug the program without needing to change it in any way.
Alternatively, they can be termed when they are designed for combat as opposed to iaitō training swords.
Alternatively, microscopes can be classed on whether they analyse the sample via a scanning point ( confocal optical microscopes, scanning electron microscopes and scanning probe microscopes ) or analyse the sample all at once ( wide field optical microscope and transmission electron microscopes ).
Alternatively, it can be thought of as maximizing the minimum gain ( maximin ).
Alternatively and be
Alternatively, civilian vehicles may be modified into improvised armored cars in ad-hoc fashion.
Alternatively, a unique position on the board on which a game piece may be located while in play.
Alternatively, a binary function may be interpreted as simply a function from X × Y to Z.
Alternatively, a coin may be tossed, with the winners choosing whether to serve or receive first, or choosing which end of the court to occupy, and their opponents making the leftover the remaining choice.
" Alternatively, they might be folded to make small cheap books or " chapbooks " which often drew on ballad stories.
Alternatively, the game may be played with ring-shaped pieces with a central hole.
Alternatively, computer programs may be executed with the aid of an interpreter, or may be embedded directly into hardware.
Alternatively, if Bishop Cellach was appointed by Giric, it may be that the gathering was intended to heal a rift between king and church.
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, they may be joined as clusters to form क ् नय knaya, कन ् य kanya, or क ् न ् य knya.
Alternatively and defined
Alternatively, anomalous perturbation is defined as an interaction with matter without the use of all known physical mechanisms.
Alternatively, NP can be defined using deterministic Turing machines as verifiers.
( Alternatively, for a preorder "", a relation "<" can be defined as a < b if and only if ( a b and a ≠ b ).
Alternatively, if M is a linear subspace then ; apply this inequality to the subspace defined by the ( orthogonal ) complement of the image of BC in the image of B, whose dimension is ; its image under A has dimension
Alternatively, a contravariant vector is defined to be a tangent vector, and the rules for transforming a contravariant vector follow from the chain rule.
Alternatively, the magnetic field can be defined in terms of the torque it produces on a magnetic dipole ( see magnetic torque on permanent magnets below ).
Alternatively, it can be defined as the region where the average temperature for the warmest month ( July ) is below ; the northernmost tree line roughly follows the isotherm at the boundary of this region.
Alternatively, an integer sequence may be defined by a property which members of the sequence possess and other integers do not possess.
Alternatively, nanowires can be defined as structures that have a thickness or diameter constrained to tens of nanometers or less and an unconstrained length.
Alternatively, ZPP can be defined as the class of problems for which a probabilistic Turing machine exists with these properties:
Alternatively defined, the number of people living in an approximately 40-mile radius of the city is approximately 300, 000.
Alternatively, it might be seen as a case of poorly defined property rights, as with, for example, pollution of bodies of water that may belong to no-one ( either figuratively, in the case of publicly owned, or literally, in some countries and / or legal traditions ).
Alternatively, it can be defined in terms of the Euler characteristic χ, via the relationship χ = 2 − 2g for closed surfaces, where g is the genus.
Alternatively, it can be defined for a closed surface in terms of the Euler characteristic χ, via the relationship χ = 2 − k, where k is the non-orientable genus.
Alternatively, it may be defined as the maximum time for which the magnitude change of channel is correlated to its previous value.
Alternatively, John Howell defined twelve groups: the Evergreen, Alpina, Macropetala, Montana, Rockery, Early Large-Flowered, Late Large-Flowered, Herbaceous, Viticella, Texensis, Orientalis, and Late Mixed groups.
Alternatively, linear independence can be directly defined as follows: a set of vectors is linearly independent if and only if the only representations of the zero vector as linear combinations of its elements are trivial solutions, i. e., whenever a < sub > 1 </ sub >, a < sub > 2 </ sub >, ..., a < sub > n </ sub > are scalars such that
Alternatively, the name " Fermi level " can be used as the name of a quantity ( ζ or μ ) that has a well-defined numerical value because it is defined as measured relative to a specified energy reference zero.
Alternatively, in cases where x is defined only for n ≥ 0, the single-sided or unilateral Z-transform is defined as
In other words X is if it is defined by a formula allowed to ask questions about membership in Y. Alternatively one can view the sets as those sets that can be built starting with sets recursive in Y and alternatively projecting and taking the complements of these sets up to n times.
Alternatively, the product may be defined through equations.
* Alternatively, the Lie derivative can be defined as
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