For many years a state tax on cities and towns was paid by the several municipalities to the state from the proceeds of the general property tax.

For the policy officer will know that action can almost never be secret and that in general the effectiveness of policy will be conditioned by the readiness of the country to sustain it.

For the near term, however, it must be realized that the industrial and commercial market is somewhat more sensitive to general business conditions than is the military market, and for this reason I would expect that any gain in 1961 may be somewhat smaller than those of recent years ; ;

For any pencil in a plane containing a Af-fold secant of **zg has an image regulus which meets the plane of the pencil in Af lines, namely the images of the lines of the pencil which pass through the intersection of **zg and the multiple secant, plus an additional component to account for the intersections of the images of the general lines of the pencil.

For many of these unwed mothers, the data on their family life and early childhood experiences revealed several indications and sources of their basic mistrust of their parents in particular and of the world in general.

-- For a second month in a row, Multnomah County may be short of general assistance money in its budget to handle an unusually high summer month's need, the state public welfare commission was told Friday.

For general morale reasons and to encourage the efforts of his supply officers, when food was short for combat troops he cut the rations of his headquarters staff accordingly.

For this latest addition to the Great Letters Series, under the general editorship of Louis Kronenberger, Miss Hardwick has made a selection which admirably displays the variety of James's genius, not to mention the felicities of his style.

* For the general reader.

For general computer use access technology such as screen readers, screen magnifiers and refreshable Braille displays has been widely taken up along with standalone reading aids that integrate a scanner, optical character recognition ( OCR ) software, and speech software in a single machine.

For biologists, this includes human beings, although for the general public the term " animal " means only non-human animals.

For example, in some groups, the group operation is commutative, and this can be asserted with the introduction of an additional axiom, but without this axiom we can do quite well developing ( the more general ) group theory, and we can even take its negation as an axiom for the study of non-commutative groups.

For other uses, see Alexander and Alexander ( Aetolian general )

For Hume, philosophy can be split into two general parts: natural philosophy and the philosophy of human nature ( or, as he calls it, " moral philosophy ").

For the frequent case of propositional logic, the problem is decidable but Co-NP-complete, and hence only exponential-time algorithms are believed to exist for general proof tasks.

For example, if James's will states that he is leaving $ 500, 000 to his son Sam then the money would be a general devise.

For years, it was traded privately until a ROM was made available to the general public.

For example, abstracting a leather soccer ball to the more general idea of a ball retains only the information on general ball attributes and behavior, eliminating the other characteristics of that particular ball.

For this reason, players should choose badminton shoes rather than general trainers or running shoes, because proper badminton shoes will have a very thin sole, lower a person's centre of gravity, and therefore result in fewer injuries.

For many years, the U. S. has borrowed and bought while in general, the rest of the world has lent and sold.

For several decades from the 1970s to early 2000s, the focus in designing high performance general purpose CPUs was largely on achieving high ILP through technologies such as pipelining, caches, superscalar execution, out-of-order execution, etc.

For example, the Napoleonic code expressly forbade French judges from pronouncing general principles of law.

For example, the copyright to a Mickey Mouse cartoon restricts others from making copies of the cartoon or creating derivative works based on Disney's particular anthropomorphic mouse, but does not prohibit the creation of other works about anthropomorphic mice in general, so long as they are different enough to not be judged copies of Disney's.

For many decades, consciousness as a research topic was avoided by the majority of mainstream scientists, because of a general feeling that a phenomenon defined in subjective terms could not properly be studied using objective experimental methods.

* For a semisimple module, the endomorphism ring is a von Neumann regular ring.

For example, in the work of Harish-Chandra one finds the principle that what can be done for one semisimple ( or reductive ) Lie group, should be done for all.

For G semisimple, the set of all G-integral weights is a sublattice P ( G ) ⊂ P ( g ).

Also, starting with any compact real form of a semisimple Lie algebra g its complexification as a real Lie algebra of twice the dimension splits into g and a certain solvable Lie algebra ( the Iwasawa decomposition ), and this provides a canonical bicrossproduct quantum group associated to g. For su ( 2 ) one obtains a quantum group deformation of the Euclidean group E ( 3 ) of motions in 3 dimensions.

For semisimple groups the rank is equal to the number of nodes in the associated Dynkin diagram.

For a left Artinian ring, it is known that the conditions " left primitive ", " right primitive ", " prime ", and " simple " are all equivalent, and in this case it is a semisimple ring isomorphic to a square matrix ring over a division ring.

For example, if the base ring R is semisimple, then all R-modules would automatically be semisimple.

For example the ring of integers, Z, is J-semisimple, but not artinian semisimple.

For a semisimple Lie group this is a consequence of the Cartan fixed point theorem.

For a semisimple or disconnected compact Lie group the level consists of an integer for each connected, simple component.

For Lie algebras the definition is slightly different.

: For an elementary introduction to how Lie algebras are related to particle physics, see the article Particle physics and representation theory.

For example, the Lie algebra of SU ( n ) is written as.

For any associative algebra A with multiplication, one can construct a Lie algebra L ( A ).

For example, for even n > 1, S < sup > n </ sup > is not a Lie group because it does not admit a nonvanishing vector field and so a fortiori cannot be parallelizable as a differentiable manifold.

For example, the orthogonal group O < sub > n </ sub >( R ) consists of matrices A with AA < sup > T </ sup > = 1, so the Lie algebra consists of the matrices m with ( 1 + εm )( 1 + εm )< sup > T </ sup > = 1, which is equivalent to m + m < sup > T </ sup > = 0 because ε < sup > 2 </ sup > = 0.

For example, simple Lie groups are usually classified by first classifying the corresponding Lie algebras.

For every finite dimensional matrix Lie algebra, there is a linear group ( matrix Lie group ) with this algebra as its Lie algebra.

For example, " In the Sweet By and By " became " There'll Be Pie in the Sky When You Die ( That's a Lie )".

For example, Lie algebras are non-associative rings that are especially imporant in the mathematical study of theoretical physics.

For example, the three-dimensional object physics calls angular velocity is a differential rotation, thus a vector in the Lie algebra tangent to SO ( 3 ).

* Season 2: " School Hard " ( first appearance ), " Halloween ", " Lie to Me ", " What's My Line, Part One ", " What's My Line, Part Two ", " Surprise ", " Innocence ", " Bewitched, Bothered and Bewildered ", " Passion ", " I Only Have Eyes For You ", " Becoming, Part One " ( Also in flashbacks ), " Becoming, Part Two "

: For the 1951 anti-communist propaganda film, see The Big Lie.

He is a regular guest on various BBC-broadcasted comedy panel game shows such as They Think It's All Over, Would I Lie To You ?, QI and has guest hosted Have I Got News For You.

For a matrix Lie group the Lie algebra is the tangent space of the identity I, and the commutator is simply = XY − YX ; the exponential map is the standard exponential map of matrices,

For many reductive Lie groups this has been solved ; see representation theory of SL2 ( R ) and representation theory of the Lorentz group for examples.

For an ordinary function f, the Lie derivative is just the contraction of the exterior derivative with the vector field X:

For a general differential form, the Lie derivative is likewise a contraction, taking into account the variation in X:

For a quite long time, physicists had been using Lie derivatives, without reference

( For a more elementary introduction to how the representation theory of Lie algebras are related to particle physics, see the article Particle physics and representation theory.