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If a closed string splits and its two parts later reconnect, its worldsheet will look like a single pipe splitting to two and then reconnecting, which also looks like a torus connected to two pipes ( one representing the ingoing string, and the other — the outgoing one ).
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If and closed
If it will simply delay the debates until the qualifications are closed next spring, and then carry all the candidates on a tour of debates, it can provide a service to the state.
If F is algebraically closed and p ( x ) is an irreducible polynomial of F, then it has some root a and therefore p ( x ) is a multiple of x − a.
If a cerebral AVM is detected before a stroke occurs, usually the arteries feeding blood into the nidus can be closed off to avert the danger.
If the holes are closed, the gas will only mix with ambient air at the point of combustion, that is, only after it has exited the tube at the top.
If it falls on a Saturday, any businesses normally closed that day will generally dedicate the following Monday as a day off.
If is any unit vector, the projection of the curl of F onto is defined to be the limiting value of a closed line integral in a plane orthogonal to as the path used in the integral becomes infinitesimally close to the point, divided by the area enclosed.
If the glass is cooled quickly in the absence of a strong light source by putting ice on the glass or placing it in the freezer with the door almost closed, it turns backwards ( i. e. the silver sides trail ).
If X is a topological space and M is a complete metric space, then the set C < sub > b </ sub >( X, M ) consisting of all continuous bounded functions ƒ from X to M is a closed subspace of B ( X, M ) and hence also complete.
* If V is a normed vector space with linear subspace U ( not necessarily closed ) and if is continuous and linear, then there exists an extension of φ which is also continuous and linear and which has the same norm as φ ( see Banach space for a discussion of the norm of a linear map ).
* If V is a normed vector space with linear subspace U ( not necessarily closed ) and if z is an element of V not in the closure of U, then there exists a continuous linear map with ψ ( x ) = 0 for all x in U, ψ ( z ) = 1, and || ψ || = 1 / dist ( z, U ).
The awards ceremony is traditionally closed with the words: " If you didn't win a prize — and especially if you did — better luck next year!
# If V is a set of strings then V * is defined as the smallest superset of V that contains λ ( the empty string ) and is closed under the string concatenation operation.
If John closed the door, it can also be interpreted as the door was closed by John.
# If G is any group acting smoothly on the manifold M, then it acts on the vector fields, and the vector space of vector fields fixed by the group is closed under the Lie bracket and therefore also forms a Lie algebra.
# If A is an open or closed subset of R < sup > n </ sup > ( or even Borel set, see metric space ), then A is Lebesgue measurable.
# If A is a Lebesgue measurable set, then it is " approximately open " and " approximately closed " in the sense of Lebesgue measure ( see the regularity theorem for Lebesgue measure ).
If N is a closed normal subgroup of a profinite group G, then the factor group G / N is profinite ; the topology arising from the profiniteness agrees with the quotient topology.
If the set of contacts was closed when the relay was de-energized, then the movement opens the contacts and breaks the connection, and vice versa if the contacts were open.
* From the above property, one can deduce the following: If X is a separable space having an uncountable closed discrete subspace, then X cannot be normal.
# Σ is closed under complementation: If A is in Σ, then so is its complement,
If the embalmer is unable to do so, or if the family requests otherwise, the funeral home can perform a closed casket service.
If the convex hull of X is a closed set ( as happens, for instance, if X is a finite set or more generally a compact set ), then it is the intersection of all closed half-spaces containing X.
If and string
If, for example, a string sounds the note C when plucked, a string twice as long will sound the same note an octave lower.
If P is a program which outputs a string x, then P is a description of x.
If M is a Turing Machine which, on input w, outputs string x, then the concatenated string < M > w is a description of x.
If the possibility of adding the empty string to a language is added to the strings recognized by the noncontracting grammars ( which can never include the empty string ) then the languages in these two definitions are identical.
( If one string runs out of letters to compare, then it is deemed to come first ; for example, " cart " comes before " carthorse ".
If the radix point is omitted then it is implicitly assumed to lie at the right ( least significant ) end of the string ( that is, the number is an integer ).
If the open string is in tune, but sharp or flat when frets are pressed, the bridge saddle position can be adjusted with a screwdriver or hex key to remedy the problem.
If the spheres only appear to rotate ( that is, we are watching stationary spheres from a rotating frame ), the zero tension in the string is accounted for by observing that the centripetal force is supplied by the centrifugal and Coriolis forces in combination, so no tension is needed.
# If V is a set of symbols or characters then V * is the set of all strings over symbols in V, including the empty string.
If you measure the three qubits, you will observe a three-bit string.
If each mass point has the mass, the tension of the string is, the separation between the mass points is and are the offset of these points from their equilibrium points ( i. e. their position on a straight line between the two attachment points of the string ) the vertical component of the force towards point is
If the string is approximated with 100 discrete mass points one gets the 100 coupled second order differential equations (), () and () or equivalently 200 coupled first order differential equations.
If the original string had several substrings that occurred often, then the transformed string will have several places where a single character is repeated multiple times in a row.
If a simple pendulum is suspended from the cusp of an inverted cycloid, such that the " string " is constrained between the adjacent arcs of the cycloid, and the pendulum's length is equal to that of half the arc length of the cycloid ( i. e. twice the diameter of the generating circle ), the bob of the pendulum also traces a cycloid path.
* If lead-acid batteries are used, all cells in the formerly good parallel strings will begin to sulfate due to the inability for them to be fully recharged, resulting in the storage capacity of these cells being permanently damaged, even if the damaged cell in the one degraded string is eventually discovered and replaced with a new one.
* Joel Spolsky ( for Apps Hungarian ): " If you read Simonyi's paper closely, what he was getting at was the same kind of naming convention as I used in my example above where we decided that meant " unsafe string " and meant " safe string.
If and splits
If the facts are related, this would be a unique case of a tradition that endured for more than a thousand years and that actually pre-dates most of the major splits in the Germanic language family.
If n is even, it splits again into two irreducible representations called the half-spin representations.
* If a wave is too big for the depth of water, it splits into two, one big and one small.
If there exists no hyperplane that can split the " yes " and " no " examples, the Soft Margin method will choose a hyperplane that splits the examples as cleanly as possible, while still maximizing the distance to the nearest cleanly split examples.
If one splits space into a number of simple cells, and if two objects can be shown not to be in the same cell, then they need not be checked for intersection.
If it is compact, then the 2 geometries can be distinguished by whether or not π < sub > 1 </ sub >( M ) has a finite index subgroup that splits as a semidirect product of the normal cyclic subgroup and something else.
If quipus are to be conserved close to their place of origin, local camelid or wool fibres in natural colors can be obtained and used to mend breaks and splits in the cords.
If each level of the factorization splits every polynomial into an O ( 1 ) ( constant-bounded ) number of smaller polynomials, each with an O ( 1 ) number of nonzero coefficients, then the modulo operations for that level take O ( N ) time ; since there will be a logarithmic number of levels, the overall complexity is O ( N log N ).
If the vector space is over a field K, then a basis on which the matrix has the required form exists if and only if all eigenvalues of M lie in K, or equivalently if the characteristic polynomial of the operator splits into linear factors over K. This condition is always satisfied if K is the field of complex numbers.
If there is a maximal torus which splits ( i. e. is isomorphic to a product of multiplicative groups ), one calls the linear group split as well.
If the object A in the above short exact sequence is injective, then the sequence splits.
If she cannot find enough food for the group, it splits into smaller groups that forage separately.
If plaintiff splits a claim in the course of a suit for special or justifiable reasons for doing so, a judgment in that action may not have the usual consequence of extinguishing the entire claim.
If the player goes diagonally with the puck, the goalie splits off from going straight back and then goes diagonal either way.
If the dorsal scapular artery comes off the transverse cervical artery, the parent transverse cervical artery splits, the dorsal scapular artery passes medially, while the transverse cervical artery passes laterally.
If the kernel N is a complete group then the extension splits: G is isomorphic to the direct product N × G '.
If a stock ever reaches $ 2. 00 it splits.
* If a flow on a manifold splits the tangent bundle into three invariant subbundles, with one subbundle that is exponentially contracting, and one that is exponentially expanding, and a third, non-expanding, non-contracting one-dimensional sub-bundle ( spanned by the flow direction ), then the flow is called an Anosov flow.
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