Any real-valued differentiable function, H, on a symplectic manifold can serve as an energy function or Hamiltonian.

Any smooth real-valued function H on a symplectic manifold can be used to define a Hamiltonian system.

Any Hamiltonian cycle can be converted to a Hamiltonian path by removing one of its edges, but a Hamiltonian path can be extended to Hamiltonian cycle only if its endpoints are adjacent.

Any smooth function on a symplectic manifold gives rise, by definition, to a Hamiltonian vector field and the set of all such form a subalgebra of the Lie Algebra of symplectic vector fields.

Any tournament on a finite number of vertices contains a Hamiltonian path, i. e., directed path on all vertices ( Rédei 1934 ).

Any conserved quantum number is a symmetry of the Hamiltonian of the system ( see Noether's theorem ).

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.

Any directed graph generates a small category: the objects are the vertices of the graph, and the morphisms are the paths in the graph ( augmented with loops as needed ) where composition of morphisms is concatenation of paths.

Any nonplanar graph has as minors either the complete graph, or the complete bipartite graph, but the Petersen graph has both as minors.

Any undirected graph may be made into a DAG by choosing a total order for its vertices and orienting every edge from the earlier endpoint in the order to the later endpoint.

Any directed graph may be made into a DAG by removing a feedback vertex set or a feedback arc set.

Any square matrix can be viewed as the adjacency matrix of a weighted directed graph, with representing the weight of the arc from vertex i to vertex j.

Any of these equations can be plotted on a graph.

Any linear code can be represented as a graph, where there are two sets of nodes-a set representing the transmitted bits and another set representing the constraints that the transmitted bits have to satisfy.

Any graph is homomorphically equivalent to a unique core.

A graph coloring is an assignment of one of k colors to a graph G so that the endpoints of each edge have different colors, for some number k. Any coloring corresponds to a homomorphism from G to a complete graph K < sub > k </ sub >: the vertices of K < sub > k </ sub > correspond to the colors of G, and f maps each vertex of G with color c to the vertex of K < sub > k </ sub > that corresponds to c. This is a valid homomorphism because the endpoints of each edge of G are mapped to distinct vertices of K < sub > k </ sub >, and every two distinct vertices of K < sub > k </ sub > are connected by an edge, so every edge in G is mapped to an adjacent pair of vertices in K < sub > k </ sub >.

Any induced subgraph of a comparability graph is itself a comparability graph, formed from the restriction of the partial order to a subset of its elements.

Any finite graph has a finite ( though perhaps exponential ) number of distinct simple cycles, and if the graph is embedded into three-dimensional space then each of these cycles forms a simple closed curve.

Any closed curve within the plane bounds a disk below the plane that does not pass through any other graph feature, and any closed curve through the apex bounds a disk above the plane that does not pass through any other graph feature.

Any Bayesian network or Markov random field can be represented as a factor graph.

* ' Class 4-Heavy Rigid Vehicle ' - Any rigid vehicle of any weight, any Combination vehicle which consists of a heavy vehicle and a light trailer, or any vehicle of Class 1 or 2 ( but not 3 ).

The first, Any Day Now ( 1968 ), consists exclusively of Dylan covers.

Any electromagnetic radiation consists of an electric field component E and a magnetic field component H. In the far-field, the relationship between the electric field component E and the magnetic component H is that characteristic of any freely propagating wave, where ( in units where c = 1 ) E is equal to H at any point in space.

Any University of North Texas student is welcome to work at the station, but most of the staff consists of those majoring in Radio, Television, and Film or Journalism.

Any model of this theory consists of disjoint copies of the full integers in addition to the natural numbers, since once one generates a submodel from 0 all remaining points admit both predecessors and successors indefinitely.

Any questions as to membership or disqualification are determined by a tribunal convened in secret that consists of a Supreme Court judge appointed by the Chief Justice and two members appointed by the Council.

Any service west of King of Prussia would require new construction and the purchasing of extra push-pull consists hauled by hybrid locomotives.

Any codex of Bede's Easter cycle is normally found together with a codex of his " De Temporum Ratione ".

Any small perturbation from the closed trajectory would cause the system to return to the limit cycle, making the system stick to the limit cycle.

Any more time, and the body enters into its usual sleep cycle.

Any formal SEWS process must incorporate blindspots analysis as part of its cycle.

Any of the aforementioned fuels can be made with plutonium and other actinides as part of a closed nuclear fuel cycle.

Any other point of intersection between C and Af will be called a tangent point.

Most of the C code being written nowadays is based on ANSI C. Any program written only in standard C and without any hardware dependent assumptions is virtually guaranteed to compile correctly on any platform with a conforming C implementation.

The blitter's block copying mode takes zero to three data sources in memory, called A, B and C, performs a programmable boolean function on the data sources and writes the result to a destination area, D. Any of these four areas can overlap.

* Any ghost ship, in the sense of a vessel found drifting without a crew, for example the Event Horizon from the film of that name, and the Rama from Arthur C. Clarke's Rendezvous with Rama.

Any increase or decrease in % C from 5 % increases the pore size, as pore size with respect to % C is a parabolic function with vertex as 5 % C.

* Any two objects X and Y of C have a product X × Y in C.

* Any two objects Y and Z of C have an exponential Z < sup > Y </ sup > in C.

Any prospect for further mining of the lead-zinc resource would now require significant investment to bring in mining equipment, and it would need to come entirely by road unless a B. C .- Alaska railway is built or the White Pass route is reopened to freight traffic to Whitehorse.

Any SCBA conforming to this standard will have been verified to reliably operate and protect the user from-30 ° C to + 60 ° C under a wide range of severe simulated operational conditions.

Gates 20-28 are swing gates between Concourse B and C. Any US bound flight is treated as a " C " Gate, whereas any Canadian-bound / International-bound flight is treated as a " B " Gate.

* Red rectangle with a black letter " C ", grounding symbol & CSA symbol-Soles that are electrically conductive ( Any industrial environment where low-lower electrical charges can be a hazard for workers or equipment )

Many programmers have been influenced by the writings of Arthur C. Clarke, who said, " Any sufficiently advanced technology is indistinguishable from magic.

Among software engineers, Greenspun is known for his Tenth Rule of Programming: " Any sufficiently complicated C or Fortran program contains an ad hoc, informally-specified, bug-ridden, slow implementation of half of Common Lisp.

) compete for Challenge ( best ) Dog and Challenge Bitch ; the individuals who will challenge each other for the accolade Best of Breed ( except dogs that are entered in " The import Register " or " Any Variety Not Separately Classified " classes, in these classes the dogs compete for " best import " or " best A. V. N. S. C .").