Combining the two kinds of fields into a single algebra requires the introduction of a Z < sub > 2 </ sub >- grading under which the bosons are the even elements and the fermions are the odd elements.

Combining this fact with the fact that every member of one of these equivalence classes belongs to one of the sets S < sub > i </ sub >, this gives a many-to-one relation from states of A to equivalence classes, implying that the number of equivalence classes is finite and at most n.

Combining the terms with the same value of m < sub > 1 </ sub > + m < sub > 2 </ sub > + ... + m < sub > n </ sub > = k and noticing that m < sub > j </ sub > has to be zero for j > n − k + 1 leads to a somewhat simpler formula expressed in terms of Bell polynomials B < sub > n, k </ sub >( x < sub > 1 </ sub >,..., x < sub > n − k + 1 </ sub >):

Combining these expressions with the far-field expression for E < sub > θ </ sub > for a short dipole gives

Combining this result with Ohm's law for R < sub > E </ sub >, V < sub > e </ sub > can be eliminated, to find :< ref group =" nb "> Notice that as A < sub > v </ sub > → ∞, V < sub > e </ sub > → 0 and I < sub > b </ sub > → I < sub > X </ sub >.</ ref >

Combining this with the equation for the polarization, and taking only linear terms and those in χ < sup >( 3 )</ sup >| E < sub > ω </ sub >|< sup > 3 </ sup >:

Combining with Newton's second law for the hanging masses, and solving for T < sub > 1 </ sub >, T < sub > 2 </ sub >, and a, we get:

Combining the functional equation and the fact that Γ ( s ) is zero at all integers less than or equal to zero yields that ζ < sub > K </ sub >( s ) vanishes at all negative even integers.

< li > Combining these calculated values to be able to deduce quickly whether, for each group of digits, that group is going to propagate a carry that comes in from the right .</ li ></ ol >

Combining structural and horticultural elements was not unfamiliar to the Commission ’ s architects.

The first attempt to produce such database was the FAU Aibo Emotion Corpus for CEICES ( Combining Efforts for Improving Automatic Classification of Emotional User States ), which was developed based on a realistic context of children ( age 10-13 ) playing with Sony ’ s Aibo robot-pet.

Combining a market segmentation strategy with a product differentiation strategy was seen as an effective way of matching a firm ’ s product strategy ( supply side ) to the characteristics of your target market segments ( demand side ).

Combining in-depth understanding of Eurasia ’ s history with expertise on politics, economics and energy, the Center provides distinctive research and advice to governments and businesses worldwide.

Combining these two constructions yields a pushforward operation, along an invertible linear map, for tensors of any rank ( r, s ).

Combining scientific theory and applied technology, UCM ’ s College of Science and Technology has a unique focus that sets the university apart from other comprehensive institutions.

Combining these two possible differences between the operator and the average firm in the economy, the operator ’ s retail prices ( revenue ) should change at the rate of inflation, minus ( conversely, plus ) the extent to which its input prices inflate less than ( conversely, greater than ) the rate of inflation, and minus ( conversely, plus ) the extent to which the operator ’ s productivity is expected to improve at a rate that is greater than ( conversely, less than ) the average firm in the economy.

Combining historical fantasy, martial arts, and science-fiction, Tong ’ s film follows archaeologist Jack ( Jackie Chan ) and scientist William ( Tony Leung Ka-Fai ) on their adventures in investigating the veracity of a myth involving immortality, levitation, and a Korean princess-turned-concubine for Emperor Qin towards the end of the Qin Dynasty.

Combining small town values with progressive policies, he took the Tories through three successive electoral victories winning majority governments in 1951, 1955 and 1959.

Combining the above, a map τ is said to be a measure-preserving transformation of X, if it is a map from X to itself, it is Σ-measurable, and is measure-preserving.

Combining and averaging information from various internet sites, langpop. com claims that in 2008 the 10 most cited programming languages are ( in alphabetical order ): C, C ++, C #, Java, JavaScript, Perl, PHP, Python, Ruby, and SQL.

Combining these data suggests that Senegal was first populated from the north and east in several waves of migration, the last being that of the Wolof, the Fulani and the Serer.

Combining these forces with the undead armies he could raise, the final victory of Balor seemed imminent ; the Leveler would finally succeed in scouring all life from the face of the earth.

Combining with Aeolians from Thebes they founded Myus.

Combining the materialist principle with Millisian epistemology evades the principle difficulty with classical empiricism — that all knowledge comes from the senses.

* Sensor fusion: Combining information from different sensors for use on board the vehicle

The staff at Variety magazine wrote, " Combining dramatic content of four Eugene O ' Neill one-act plays, John Ford pilots adventures of a tramp steamer from the West Indies to an American port, and then across the Atlantic with cargo of high explosives.

Combining the Pentium II Deschutes core in a flip-chip package with a 512 KB full speed L2 cache chip from the Pentium II Xeon into a Socket 8-compatible module resulted in a 300 or 333 MHz processor that could run on a 60 or 66 MHz front side bus.

Combining data from nDNA c-myc exon 3, RAG-1 and myoglobin intron 2 sequences with that of mtDNA cytochrome b ( Ericson & Johansson 2003 ) supports their scenario as does a restudy using the myoglobin intron 2 and cytochrome b sequences of a wider ( though not denser ) range of taxa ( Alström et al.

Combining elements from several of Doyle's stories, he mainly utilized the plots " A Scandal in Bohemia " and " The Final Problem ".

Combining these methods with the reciprocal measurements from above leads to the formulas for the resistances being

Combining these two viewpoints resulted in Guild socialism, a political philosophy he began to argue for from about 1910.

Combining the results from a survey of pregnant women prior to their due date in correlation with the health of their children and an ex vivo rat model, the study found that pregnant women who had been exposed to mild analgesics had a higher prevalence of baby boys born with congenital cryptorchidism.

Combining a production-based V8 engine from the V8 and V8 Vantage models, the engine was refined by Aston Martin Tickford in order to handle the increased output.

Combining in new ways the idea of Performance art, radical and new Choreography, sound from avant-garde composers, and dancers in collaboration with several New York School Visual artists.

Combining this with an earlier conversation about Culla's eyesight, Demwa concludes that Culla can project laser light from his eyes: he has been faking the anthropomorphic ghosts.

Combining earnings from both passenger and military rates, Guthrie ensured that the line's infrastructure at the close of the war was superior to what it had been before the war started.

Combining these forces with the undead armies he could raise, the final victory of Balor seemed imminent ; the Leveler would finally succeed in scouring all life from the face of the earth.

Combining two colored lights from different parts of the spectrum may produce a third color that appears like a light from another part of the spectrum, even though dissimilar wavelengths are involved.

Combining this with a removal of dialogue from speech balloons to captions at the bottom of the panel afforded Raymond the space to create detailed and atmospheric backgrounds.

Combining two or more thermodynamic cycles results in improved overall efficiency, reducing fuel costs.

" Combining the root * mei with the " tool suffix "-tra-" that which ..." ( also found in man-tra -, " that which causes to think "), then literally means " that which binds ," and thus " covenant, treaty, agreement, promise, oath " etc.

Combining these corrections with estimates of successive murder probabilities by affluent non-smokers, Mathematics Professor Ray Hill found that the probability of Clark's guilt could be as low as 10 % ( based solely on the fact of two unexplained child deaths, and before any other evidence was considered ).

Combining these results, the magnetic field is found using the integral form of Ampère's law with an arbitrary choice of contour provided the displacement current density term is added to the conduction current density ( the Ampère-Maxwell equation ):

Combining formalised strength events found in Highland Games, with elements of powerlifting and weightlifting, along with an eclectic selection of events involving the lifting of rocks, refrigerators, pulling vehicles ( trains, lorries, planes etc.

Combining that with the over two dozen scholarly articles or studies found within the various CI bibliographic entries, it is clear that no shortage of study has gone into better classifying, understanding and addressing CI ethics.

Combining their data, they found the most likely planet mass to be 1. 5 times the mass of Jupiter.

Combining the side-scrolling gameplay of a beat ' em up with some aspects found in a role-playing video game, Shadow over Mystara has many game mechanics not commonly found in arcade games.