Note: This list is limited to linguists who have worked specifically on the Altaic problem since the publication of the first volume of Ramstedt's Einführung in 1952.

Note that pure application of this method may provide only a partial ordering on the strings, since different strings can represent the same number ( as with " 2 " and " 2. 0 ", or when scientific notation is used, " 2e3 " and " 2000 ").

Treasury Notes are generally considered to be inherently less risky than real estate, since the value of the Note is guaranteed by the US Government and there is a liquid market for the purchase and sale of T-Notes.

Although siblinghood is symmetric ( if A is a sibling of B, then B is a sibling of A ) and transitive on any 3 distinct people ( if A is a sibling of B and C is a sibling of B, then A is a sibling of C, provided A is not C ( Note that " is a sibling of " is NOT a transitive relation, since A R B, and B R A implies A R A by transitivity )), it is not reflexive ( A cannot be a sibling of A ).

Note that this property is itself positive, since it is the conjunction of the ( infinitely many ) positive properties.

The Village Gate, the Village Vanguard and The Blue Note ( since 1981 ), hosted some of the biggest names in jazz on a regular basis.

Note that ƒ cannot be extended to a homomorphism of rings ( from the complex numbers to the real numbers ), since it does not preserve addition:

Note that in Europe, sophisticated diesel-engined cars have taken over about 40 % of the market since the 1990s.

( Note: Revenue collected from Karachi includes revenue from some other areas since the Large Tax Unit ( LTU ) Karachi and Regional Tax Offices ( RTOs ) Karachi, Hyderabad, Sukkur & Quetta cover the entire province of Sindh and Balochistan ).

#* Note: This fact provides a proof of the infinitude of primes distinct from Euclid's Theorem: if there were finitely many primes, with p being the largest, we reach an immediate contradiction since all primes dividing 2 < sup > p </ sup > − 1 must be larger than p .</ li >

Note that stress is not a true pressure since it is not scalar.

Note that a device designed primarily as a comparator may be better if, for instance, speed is important or a wide range of input voltages may be found, since such devices can quickly recover from full on or full off (" saturated ") states.

Note that reading properly exposed hands of other players at showdown is not a violation of this rule, since no further decisions can be made.

Note: Christian Scientists, Quakers and the Salvation Army cannot be classified as specifically opposing infant baptism, since they generally do not observe baptism in any form.

( Note: Apparently this only goes for religions that are widely practiced today, since gods and goddesses of ancient religions are obviously acceptable to the IAU.

Since we've assumed that we can infallibly identify programs for computing squares, we can determine whether t, which depends on a and i, is such a program, and that for every a and i ; thus we have obtained a program that decides whether program a halts on input i. Note that our halting-decision algorithm never executes t, but only passes its description to the squaring-identification program, which by assumption always terminates ; since the construction of the description of t can also be done in a way that always terminates, the halting-decision cannot fail to halt either.

Note that the probability of risk occurrence is difficult to estimate, since the past data on frequencies are not readily available, as mentioned above.

Note: The airlines and destinations listed are not definite since very few airlines have a dedicated pier or gates ; the piers listed below are based on regularity.

Note also that the visible bubbles in carbonated water are not the dissolved gas, but only an effervescence of carbon dioxide that has come out of solution ; the dissolved gas itself is not visible since it is dissolved on a molecular level.

Note that the earth itself has no role in this fault-clearing process since current must return to its source, not the earth as is sometimes believed ( see Kirchhoff's circuit laws ).

Note that, especially in the second sentence, all this information can seem redundant, since quantity is already indicated by the numeral " two ".

In recent years she has appeared at the Blue Note in New York as a guest performer for Janis Siegel of The Manhattan Transfer, and as part of a trio with Anthony Jackson on bass and Cliff Almond on drums in concerts at the Blue Note Tokyo since 2003.

Note that since and are both homeomorphisms, the transition map is also a homeomorphism.

Note: this article concerns the discipline of intellectual history, and not its object, the whole span of human thought since the invention of writing.

Note that the RGB color may be premultiplied, hence saving the additional multiplication before RGB in the equation above.

Note that in any font the glyph of " x " is not exactly the same as one of the multiplication sign.

( Note that the asterisk denotes convolution in this context, and not multiplication.

Note that Z, equipped with these operations of addition and multiplication, is a ring, and is in fact, the prototypical example of a ring.

Note, however, that because the quaternions are not commutative, the order of the factors in the multiplication formula becomes important — if the last factor in the multiplication formula were rather than

( Note that we no longer have the multiplication by 1 / 2, because the IMDCT normalization differs by a factor of 2 in the windowed case.

Note that this is an abuse of notation, since the codomain of the operation needs only to be a group: "− 1 " does not have a precise meaning since a multiplication is not necessarily defined on.

: ( Note that represents a sequence of digits, not multiplication )

:: Note that the notation does not denote the modular multiplication of times the modular multiplicative inverse of but rather the quotient of divided by, i. e., the largest integer value to satisfy the relation.

where is the number of ways to distribute cards between hands of two cards each .< ref name =" prod " group =" Note "> See " Capital Pi notation for multiplication " for a description of the ( capital π or pi ) symbol .</ ref > is the factorial # Double factorial | double factorial operator: ( 2n-1 )!!

Note: This sūtra can also be applied to multiplication of numbers with the same first digit and the sum of their last unit digits is 10.

Note that the multiplication is done in the opposite order from the English sentence: the matrix of " A followed by B " is BA, not AB.

Note that this decomposition requires the special case which many implementations optimize for, thereby eliminating one multiplication for each value of C.

Note that division in the system is evaluated after multiplication:

Note that all Jones vectors and matrices on this page assumes that the phase of the light wave is, which is used by Hecht.

Note that in this vector dotted with Pauli vector operation the Pauli matrices are treated in a scalar like fashion, commuting with the vector basis elements.

Note that although s and S are infinite, this works for finite matrices by only considering Stirling numbers up to some number N.

Note that the above examples show that the sum of diagonalizable matrices need not be diagonalizable.

Note that 0 and I are 2 × 2 matrices here.

Note that any element in the direct sum of two vector spaces of matrices could be represented as a direct sum of two matrices.

Note that the two-dimensional case is the only non-trivial ( e. g. one dimension ) case where the rotation matrices group is commutative, so that it does not matter the order in which multiple rotations are performed.

This is n direct sum equivalent copies V. Note that if ρ < sub > 1 </ sub > and ρ < sub > 2 </ sub > are equivalent G-irreducible representations, the respective images of the intertwining matrices would give rise to the same G × G-irreducible representation of C.

Note that the anticommutation relations for the Pauli matrices make the proof of the above defining property trivial.