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If the chain complex depends on the object X in a covariant manner ( meaning that any morphism X → Y induces a morphism from the chain complex of X to the chain complex of Y ), then the H < sub > n </ sub > are covariant functors from the category that X belongs to into the category of abelian groups ( or modules ).
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If and chain
If Af leads to an address Af that is equal to the address computed from Af, even though Af does not match Af, the chain of information cells is extended from Af by storing the address of the next available cell in the Y-region, Af, in Af.
If, however, there are no shares left when the chain is founded, then the founding player does not receive the free share.
If there is a tile in 5F, then placing either tile 4F or 5G would result in founding a new hotel chain.
If a tile is placed between two hotel chains of the same size, the individual player who places the tile decides which hotel chain remains on the board and which is acquired.
If two players tie for minority, they will share the minority shareholder bonus. Suppose Festival is the chain being acquired.
If a player holds onto his stock, he runs the risk that the acquired chain may not reemerge before the game ends.
If placing a tile causes three or four chains to merge, then the merger steps are handled between the largest and second-largest chain, then with the third-largest chain, and finally with the smallest chain.
If a is a point in R < sup > n </ sup >, then the higher dimensional chain rule says that:
If the density of the chain is variable then the analysis above can be adapted to produce equations for the curve given the density, or given the curve to find the density.
If a reaction results in a small energy release making way for more energy releases in an expanding chain, then the system will typically collapse explosively until much or all of the stored energy has been released.
If there is another functional group at a carbon, it may be named with the Greek letter, e. g., the gamma-amine in gamma-aminobutanoic acid is on the third carbon of the carbon chain attached to the carboxylic acid group.
If the network is one-dimensional, and the chain of nodes is connected to form a circular loop, the resulting topology is known as a ring.
If a partially ordered set does not contain any infinite descending chains, it is called well-founded or, in some case, Artinian ; it is then said to satisfy the descending chain condition.
If the chain of events leading up to the person having something meets this criterion, they are entitled to it: that they possess it is just, and what anyone else does or doesn't have or need is irrelevant.
If enough nuclear fuel is assembled in one place, or if the escaping neutrons are sufficiently contained, then these freshly emitted neutrons outnumber the neutrons that escape from the assembly, and a sustained nuclear chain reaction will take place.
If the blocks are deselected ( usually by dragging away from them, or tapping another block chain or a single block ), the highlight is removed.
If too many of these neutrons are absorbed by other uranium-235 nuclei, a nuclear chain reaction occurs that results in a burst of heat or ( in special circumstances ) an explosion.
That means, define E ≤ F if E is an initial segment of F and the ordering of the members in E is the same as their ordering in F. If E is a chain in A, then the union of the sets in E can be ordered in a way that makes it a continuation of any set in E ; this ordering is a well ordering, and therefore, an upper bound of E in A.
If a jet aircraft is at full throttle but is tied to a very strong tree with a very strong chain, then the jet engine produces no propulsive power.
If pyramid scheme chain letters are sent through email it may constitute wire fraud.
If the amino acids that are in the chain are changed, the shape of the histone sphere might be modified.
If the engine must be operated in any orientation ( for example a chain saw ), a float chamber cannot work.
If is too small the chain will mix slowly ( i. e., the acceptance rate will be high but successive samples will move around the space slowly and the chain will converge only slowly to ).
If and complex
If we are discussing differentiable complex-valued functions, then Af and V are complex vector spaces, and Af may be any complex numbers.
If X is a Banach space and K is the underlying field ( either the real or the complex numbers ), then K is itself a Banach space ( using the absolute value as norm ) and we can define the continuous dual space as X ′ = B ( X, K ), the space of continuous linear maps into K.
If A is a self-adjoint operator, then is always a real number ( not complex ).
If more than one eigenvalue is negative, then the stationary point is a more complex one, and is usually of little interest.
If X is Cauchy distributed with median μ and scale parameter γ, then the complex variable
If a simply stable system response neither decays nor grows over time, and has no oscillations, it is marginally stable: in this case the system transfer function has non-repeated poles at complex plane origin ( i. e. their real and complex component is zero in the continuous time case ).
If the weight of the cable and supporting wires are not negligible then the analysis is more complex.
If a stitch in a finished crocheted item breaks, the stitches above and below remain intact, and because of the complex looping of each stitch, the stitches on either side are unlikely to come loose unless heavily stressed.
If we look for solutions that have the form, where C is a constant, we discover the relationship, and thus must be one of the complex numbers or.
If < math > c ^ 2 < 4km </ math > there are two complex conjugate roots a ± ib, and the solution ( with the above boundary conditions ) will look like this:
If anything, the research has shown the situation is even more complex than initially imagined, and we believe not enough is known to structure the classification of psychiatric disorders according to etiology.
If the obstructing object provides multiple, closely spaced openings, a complex pattern of varying intensity can result.
If the ether is part of a more complex molecule, it is described as an alkoxy substituent, so-OCH < sub > 3 </ sub > would be considered a " methoxy -" group.
If the cell is synthesizing DNA each pore complex needs to transport about 100 histone molecules per minute.
If the cell is growing rapidly, each complex also needs to transport about 6 newly assembled large and small ribosomal subunits per minute from the nucleus to the cytosol, where they are used to synthesize proteins.
If it is unaffected, then it is a simple partial seizure ; otherwise it is a complex partial ( psychomotor ) seizure.
If ƒ is complex differentiable at every point z < sub > 0 </ sub > in an open set U, we say that ƒ is holomorphic on U. We say that ƒ is holomorphic at the point z < sub > 0 </ sub > if it is holomorphic on some neighborhood of z < sub > 0 </ sub >.
If a complex function = is holomorphic, then u and v have first partial derivatives with respect to x and y, and satisfy the Cauchy – Riemann equations:
If the coordinates are chosen badly, the laws of motion may be more complex than necessary.
In The Origin of Species, he wrote, " If it could be demonstrated that any complex organ existed, which could not possibly have been formed by numerous, successive, slight modifications, my theory would absolutely break down.
If ( i ) or ( j ) have side effects or introduce run time errors, the subtle differences between ( l ) and ( l ') can be complex.
If, however, the set of allowed candidates is expanded to the complex numbers, every non-constant polynomial has at least one root ; this is the fundamental theorem of algebra.
* If R denotes the ring CY of polynomials in two variables with complex coefficients, then the ideal generated by the polynomial Y < sup > 2 </ sup > − X < sup > 3 </ sup > − X − 1 is a prime ideal ( see elliptic curve ).
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