It is easily seen that Af divides G.

The angle generated by the platform servo **yf multiplied by G is the effective acceleration acting on the accelerometer.

Although there are seven other types of annual awards presented by the Academy ( the Irving G. Thalberg Memorial Award, the Jean Hersholt Humanitarian Award, the Gordon E. Sawyer Award, the Scientific and Engineering Award, the Technical Achievement Award, the John A. Bonner Medal of Commendation, and the Student Academy Award ) plus two awards that are not presented annually ( the Special Achievement Award in the form of an Oscar statuette and the Honorary Award that may or may not be in the form of an Oscar statuette ), the best known one is the Academy Award of Merit more popularly known as the Oscar statuette.

Here G is countable while S is uncountable.

For every group G there is a natural group homomorphism G → Aut ( G ) whose image is the group Inn ( G ) of inner automorphisms and whose kernel is the center of G. Thus, if G has trivial center it can be embedded into its own automorphism group.

For each element a of a group G, conjugation by a is the operation φ < sub > a </ sub >: G → G given by ( or a < sup >− 1 </ sup > ga ; usage varies ).

Rather the form of the argument is generalized to considering configurations, which are connected subgraphs of G with the degree of each vertex ( in G ) specified.

If the graph G is connected, then the rank of the free group is equal to 1 − χ ( G ): one minus the Euler characteristic of G.

: G < sub > con </ sub > for the connected component of the identity

: G < sub > sol </ sub > for the largest connected normal solvable subgroup

: G < sub > nil </ sub > for the largest connected normal nilpotent subgroup

: G < sub > con </ sub >/ G < sub > sol </ sub > is a central extension of a product of simple connected Lie groups.

If we require that the Lie group be simply connected, then the global structure is determined by its Lie algebra: for every finite dimensional Lie algebra over F there is a simply connected Lie group G with as Lie algebra, unique up to isomorphism.

Because R is the Lie algebra of the simply connected Lie group R, this induces a Lie group homomorphism c: R → G so that

Although the MOSFET is a four-terminal device with source ( S ), gate ( G ), drain ( D ), and body ( B ) terminals, the body ( or substrate ) of the MOSFET often is connected to the source terminal, making it a three-terminal device like other field-effect transistors.

* G is connected and has no cycles.

* G is connected, but is not connected if any single edge is removed from G.

* Any two vertices in G can be connected by a unique simple path.

* G is connected and has n − 1 edges.

* Every connected graph G admits a spanning tree, which is a tree that contains every vertex of G and whose edges are edges of G.

* Hansard, George Agar ( 1841 ) The Book of Archery: being the complete history and practice of the art, ancient and modern ... London: H. G. Bohn

In complete analogy, one can define a right group action of G on X as a function X × G → X by the two axioms:

A less complete edition was edited by G. Saintsbury ( London, 1894 ).

Wallace addressed Roerich as " Dear Guru ", signed his name as " G " for Galahad — a name Roerich assigned Wallace in his religion — and showed his complete adherence to Roerich's doctrines.

If C is a complete category, then, by the above existence theorem for limits, a functor G: C → D is continuous if and only if it preserves ( small ) products and equalizers.

* If G lifts all small limits and D is complete, then C is also complete and G is continuous.

G. C. Wynne wrote that the British had eventually reached Passchendaele Ridge and captured Flandern I ; beyond them was Flandern II and Flandern III which was nearly complete.

Meanwhile, Charles L. Webster & Co. issued a " fourth edition, revised, corrected, and complete " with the text of Sherman ’ s second edition, a new chapter prepared under the auspices of the Sherman family bringing the general ’ s life from his retirement to his death and funeral, and an appreciation by politician James G. Blaine ( who was related to Sherman's wife ).

If C is a complete category, then the functors with left adjoints can be characterized by the adjoint functor theorem of Peter J. Freyd: G has a left adjoint if and only if it is continuous and a certain smallness condition is satisfied: for every object Y of D there exists a family of morphisms

This allowed G / 16 and the support battalion to escape complete destruction in their advance up the beach.

When G is complete, absolute convergence implies unconditional convergence.

* Corpus Hermeticum along with the complete text of G. R. S.

In the words of historian G. R. Elton, " from that moment his autocratic system was complete ".

Then you type the first component, which is also ' Y ' for the 点 stroke, then a ' G ' for the 横 stroke ， and since you now already have three strokes, you type the last stroke, which also happens to be a 捺, arriving at the keycode ' YYGY ' for the complete character.

As 1891 came to a close, Whitman prepared a final edition of Leaves of Grass, writing to a friend upon its completion, " L. of G. at last complete — after 33 y ' rs of hackling at it, all times & moods of my life, fair weather & foul, all parts of the land, and peace & war, young & old ".

The BBC now commissioned him to complete the 1928 " The Childermass ," to be broadcast in a dramatisation by D. G. Bridson on the " Third Programme " and published as " The Human Age.

* Great speeches of Col. R. G. Ingersoll ; complete ( Chicago: Rhodes & McClure, 1895 )

His life, with a complete list of his writings, which amounted to 287, Leben und Charakter des Kirchenraths J. G. Walch, was published anonymously by his son CWF Walch ( Jena, 1777 ).

The operator A below can be seen to have a compact inverse, meaning that the corresponding differential equation A f = g is solved by some integral, therefore compact, operator G. The compact symmetric operator G then has a countable family of eigenvectors which are complete in.

The sets X and Y are called the domain ( or the set of departure ) and codomain ( or the set of destination ), respectively, of the relation, and G is called its graph.

The questions range from counting ( e. g., the number of graphs on n vertices with k edges ) to structural ( e. g., which graphs contain Hamiltonian cycles ) to algebraic questions ( e. g., given a graph G and two numbers x and y, does the Tutte polynomial T < sub > G </ sub >( x, y ) have a combinatorial interpretation ?).

Call this graph G. G cannot have a vertex of degree 3 or less, because if d ( v ) ≤ 3, we can remove v from G, four-color the smaller graph, then add back v and extend the four-coloring to it by choosing a color different from its neighbors.

For example, the case described in degree 4 vertex situation is the configuration consisting of a single vertex labelled as having degree 4 in G. As above, it suffices to demonstrate that if the configuration is removed and the remaining graph four-colored, then the coloring can be modified in such a way that when the configuration is re-added, the four-coloring can be extended to it as well.

In graph theory, an isomorphism between two graphs G and H is a bijective map f from the vertices of G to the vertices of H that preserves the " edge structure " in the sense that there is an edge from vertex u to vertex v in G if and only if there is an edge from ƒ ( u ) to ƒ ( v ) in H. See graph isomorphism.

* How many graph colorings using k colors are there for a particular graph G?

Namely, any free group G may be realized as the fundamental group of a graph X.

The main theorem on covering spaces tells us that every subgroup H of G is the fundamental group of some covering space Y of X ; but every such Y is again a graph.

Any collection of objects and morphisms defines a ( possibly large ) directed graph G. If we let J be the free category generated by G, there is a universal diagram F: J → C whose image contains G. The limit ( or colimit ) of this diagram is the same as the limit ( or colimit ) of the original collection of objects and morphisms.