There, at a distance of from the LM, Young and Duke sampled material from the vicinity of Flag Crater, which scientists believed penetrated through the upper regolith layer to the underlying Cayley Formation.

" The next stop, station six, was a blocky crater, where the astronauts believed they could sample the Cayley Formation as evidenced by the firmer soil found there.

Sir George Cayley is credited as the first person to identify the four aerodynamic forces of flight — weight, lift, drag, and thrust — and the relationships between them.

Cayley also looked to nature for aerodynamic shapes with low drag.

Sir George Cayley ( 1773 – 1857 ) also used a whirling arm to measure the drag and lift of various airfoils.

Over the next five decades Cayley worked on and off on the problem, during which he formulated most of basic aerodynamic theory, introducing such ideas as lift and drag.

At Descartes, the Cayley and Descartes formations were the primary areas of interest in that scientists suspected, based on telescopic and orbital imagery, that the terrain found there was formed by magma more viscous than that which formed the lunar maria.

The Cayley formation's age was approximated to be approximately that of Mare Imbrium based on the local frequency of impact craters.

Later, in Medieval England, campanology provided examples of what is now known as Hamiltonian cycles in certain Cayley graphs on permutations.

More than one century after Euler's paper on the bridges of Königsberg and while Listing introduced topology, Cayley was led by the study of particular analytical forms arising from differential calculus to study a particular class of graphs, the trees.

Cayley linked his results on trees with the contemporary studies of chemical composition.

All hypercomplex number systems based on the Cayley – Dickson construction from sedenions on contain zero divisors.

Seat belts were invented by George Cayley in the early 19th century, though Edward J. Claghorn of New York, was granted the first patent (, on February 10, 1885 for a safety belt ).

The Cayley graph for the free group on two generators.

Cayley, from Brompton-by-Sawdon, near Scarborough in Yorkshire, inherited Brompton Hall and its estates on the death of his father, the 5th baronet.

In group theory, Cayley's theorem, named in honor of Arthur Cayley, states that every group G is isomorphic to a subgroup of the symmetric group acting on G. This can be understood as an example of the group action of G on the elements of G.

Another method based on the Cayley – Hamilton theorem finds an identity using the matrices ' characteristic polynomial, producing a more effective equation for A < sup > k </ sup > in which a scalar is raised to the required power, rather than an entire matrix.

Airmen like Otto Lilienthal, who introduced cambered airfoils in 1891, used gliders to analyze aerodynamic forces. The Wright brothers were interested in Lilianthal's work and read several of his publications. They also found inspiration in Octave Chanute, an airman and the author of Progress in Flying Machines ( 1894 ). It was the preliminary work of Cayley, Lilienthal, Chanute, and other early aerospace engineers that brought about the first powered sustained flight at Kitty Hawk, North Carolina on December 17, 1903, by the Wright brothers.

While this provides a valid proof ( for matrices over the complex numbers ), the argument is not very satisfactory, since the identities represented by the theorem do not in any way depend on the nature of the matrix ( diagonalizable or not ), nor on the kind of entries allowed ( for matrices with real entries the diagonizable ones do not form a dense set, and it seems strange one would have to consider complex matrices to see that the Cayley – Hamilton theorem holds for them ).

The Cayley – Dickson construction can be carried on ad infinitum, at each step producing a power-associative algebra whose dimension is double that of the algebra of the preceding step.

( 1935 ), Neville Cayley writes that it has " a pleasant call resembling sweet pretty little creature, frequently uttered during the day or night, especially on moonlight nights ".

* More generally, the conjugation involution in any Cayley – Dickson algebra such as the complex numbers, quaternions and octonions, if a blind eye is turned on the nonassociativity of the latter.

He called it the " transcendent angle ," and it went by various names until 1862 when Arthur Cayley suggested it be given its current name as a tribute to Gudermann's work in the 1830s on the theory of special functions.

Arthur Cayley was born in Richmond, London, England, on 16 August 1821.

To this journal, at the age of twenty, Cayley contributed three papers, on subjects which had been suggested by reading the Mécanique analytique of Lagrange and some of the works of Laplace.

In 1799 Sir George Cayley set forth the concept of the modern airplane as a fixed-wing flying machine with separate systems for lift, propulsion, and control.

In 1799, Sir George Cayley set forth the concept of the modern aeroplane as a fixed-wing flying machine with separate systems for lift, propulsion, and control.

Cayley was building and flying models of fixed-wing aircraft as early as 1803, and he built a successful passenger-carrying glider in 1853.

In 1799 Sir George Cayley set forth the concept of the modern airplane as a fixed-wing flying machine with separate systems for lift, propulsion, and control.

Later Cayley turned his research to building a full-scale version of his design, first flying it unmanned in 1849, and in 1853 his coachman made a short flight at Brompton, near Scarborough in Yorkshire.

Bienvenu., and was known by Sir George Cayley, but it was the first used of twisted rubber to power a flying model.

Now if A admits a basis of eigenvectors, in other words if A is diagonalizable, then the Cayley – Hamilton theorem must hold for A, since two matrices that give the same values when applied to each element of a basis must be equal.

Thus one can see that the Cayley – Hamilton theorem must be true.

After selecting the landing site for Apollo 16, sampling the Descartes and Cayley formations, two geologic units of the lunar highlands, were determined by mission planners to be the primary sampling interests of the mission.

( In other words: For two elements a and b, b can be found in row a and in column a of the quasigroup's Cayley table.

For a general n × n invertible matrix A, i. e., one with nonzero determinant, A < sup >− 1 </ sup > can thus be written as an ( n − 1 )- th order polynomial expression in A: As indicated, the Cayley – Hamilton theorem amounts to the identity

In fact, this expression, ½ (( trA )< sup > 2 </ sup >− tr ( A < sup > 2 </ sup >)), always gives the coefficient c < sub > n − 2 </ sub > of λ < sup > n − 2 </ sup > in the characteristic polynomial of any n × n matrix ; so, for a 3 × 3 matrix A, the statement of the Cayley – Hamilton theorem can also be written as

The left hand side can be worked out to an n × n matrix whose entries are ( enormous ) polynomial expressions in the set of entries of A, so the Cayley – Hamilton theorem states that each of these expressions are equivalent to 0.

None of these computations can show however why the Cayley – Hamilton theorem should be valid for matrices of all possible sizes n, so a uniform proof for all n is needed.

There is a great variety of such proofs of the Cayley – Hamilton theorem, of which several will be given here.

A necessary and sufficient condition for A to be self-adjoint is that its Cayley transform W ( A ) be unitary.

The Cayley table of the group D < sub > 4 </ sub > can be derived from the group presentation

In his place, Brigadier General Cayley, formerly the commander of the 39th Brigade, would be elevated to command of the division.

It can be thought of as a generalisation of the complex numbers, by e. g. the Cayley – Dickson construction, and generates rotations in a similar way by multiplication.

If the degree is 4 or less, or the graph is also edge-transitive, or the graph is a minimal Cayley graph, then the vertex-connectivity will also be equal to d.

Flannery did not make any claims that the Cayley – Purser algorithm would replace RSA, knowing that any new cryptographic system would need to stand the test of time before it could be acknowledged as a secure system.

The short answer is nobody really knows for sure .... So just in case I sometimes do a quick check of the old hot-spots when I get off the Peak Chair .." Recent seismic imaging from Geological Survey of Canada employees supported lithoprobe studies in the region of Mount Cayley in which scientists found a large reflector interpreted to be a pool of molten rock roughly below the surface.

This can also be interpreted ( in algebraic topology ) as the universal cover of the Cayley graph, which is not in general simply connected.

These engines may be based on a number of thermodynamic cycles encompassing both open cycle devices such as those of Sir George Cayley and John Ericsson and the closed cycle engine of Robert Stirling.

In 2010 another new exhibition called “ Pioneers of Aviation ”, and funded by the Heritage Lottery Fund, is to be opened featuring the lives and achievements of Sir George Cayley, Sir Barnes Wallis, Robert Blackburn, Nevil Shute and Amy Johnson.