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

Alternatively, representing true values as 1 and false values as 0, we may use the formula

Alternatively, for applications in which the computation of is the most costly step and both first and second derivatives must be computed, a more efficient formula for the last case is:

Alternatively, it is possible to show that any bridgeless bipartite planar graph with n vertices and m edges has by combining the Euler formula ( where f is the number of faces of a planar embedding ) with the observation that the number of faces is at most half the number of edges ( because each face has at least four edges and each edge belongs to exactly two faces ).

Alternatively, some materials with the formula MTiO < sub > 3 </ sub > crystallize in the motif known as Perovskite ( structure ), which is also the name of the mineral form of calcium titanate ( CaTiO < sub > 3 </ sub >).

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 a bottle liner can be used to enclose the formula instead of directly in the bottle.

Alternatively, it can be used as an ingredient in a formula decoction or used to make an extract ( in liquid, capsule, or powder form ).

Alternatively, a formula may be used, such as sampling the lowest closing price over a 30-day window on either side of the grant date.

Alternatively, a liquid ketogenic diet may be produced by combining Ross Carbohydrate Free soy formula with Microlipid and Polycose.

Alternatively, note that as Cayley's formula counts the number of distinct labeled trees of a complete graph K < sub > n </ sub > we need to compute any cofactor of the Laplacian matrix of K < sub > n </ sub >.

The formula states that markup as a percentage of price equals the negative of the inverse of elasticity of demand. Alternatively, the relationship can be expressed as:

Alternatively, since the radioactive decay contributes to the " physical ( i. e. radioactive )" half-life, while the metabolic elimination processes determines the " biological " half-life of the radionuclide, the two act as parallel paths for elimination of the radioactivity, and in analogy with parallel resistors, the effective half-life could also be calculated by the formula:

Alternatively, one can define as a formula having exactly the above set of models ; furthermore, one can also avoid giving a definition of and only define minimal inference as if and only if every minimal model of is also a model of.

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, a Greek derivation from " manless, without husbands " ( a-privative and a derivation of * man-also found in Slavic muzh ) has been proposed, an explanation deemed " unlikely " by Hjalmar Frisk.

Alternatively, rehabilitation robotics can be used to provide high volumes of passive or assisted movement, depending on the individual's requirements ; this form of therapy can be useful if therapists are at a premium, and has been found effective at reducing spasticity in patients suffering from stroke.

Alternatively, at least one meta analysis has found a weak protective association between dietary ALA intake and prostate cancer risk.

Alternatively, wheel cover refers to an accessory covering an external rear-mounted spare tire ( also known as a spare tire cover ) found on some off-road or survival-type vehicles.

Alternatively the list of parts included in the model, found above the four viewing areas, can be used.

Alternatively, the name may come from the Mordvinian language, meaning " bear-river ".. A similar meaning is found in the Mari language where moská denotes " bear " whereas Mari word ava implies " mother ".

Alternatively some CEGEP's offer vocational training, but it is more likely that vocational training will be found at institutions separate from the academic institutions, though they may still be called colleges.

Alternatively, there is also an output mode that generates a cross reference file, listing information about various names found in a set of language files in human-readable form.

The difference represents the duration of the visible store which was found to be approximately 100-200 ms. Alternatively, the Phenomenal Continuity and Moving Slit Technique estimated visible persistence to be 300 ms.

Alternatively G < sub >∞</ sub > is the gain found by replacing the transistor by an ideal amplifier with infinite gain-a nullor.

Alternatively spliced transcript variants encoding different isoforms have been found for this gene.

Alternatively, such a set may be found as the complement of a spanning forest of.

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, the section labeled introduction itself may be a brief section found side-by-side with abstract, foreword, etc.

Alternatively, annexins A-I and A-II bind phosphatidylserine and phosphatidylcholine units in the cell membrane, and are often found forming monolayered clusters that lack a definite shape .< ref name =" pmid11828493 ">

Alternatively, they might occur in the western Amazonas lowlands and simply have not been found yet, though this seems less likely.

Alternatively, DUNS numbers for companies that do business with the U. S. Federal government can be found by looking up the company name via advanced search at.