'Alternative form of Hamiltonization.'的English词汇
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adj
- (physics, quantum mechanics, of a process) Involving the slow change of the Hamiltonian of a system from its initial value to a final value.
- (physics, thermodynamics, of a process) Without gain or loss of heat (and thus with no change in entropy, in the quasistatic approximation).
- occurring without loss or gain of heat
noun
adj
- (mathematics, graph theory, of a graph) Containing a Hamiltonian cycle.
- Of, relating to, or in the literary style of Edmond Hamilton (1904–1977), American science fiction writer.
- Of or relating to any city named Hamilton.
- Relating to Sir William Hamilton, 9th Baronet (1788–1856), Scottish metaphysician.
- (historical, chiefly US, of certain fiscal policies) Advocated by American politician Alexander Hamilton (1755–1804).
- Relating to James Hamilton (1769–1831), or his method of teaching languages without grammar, by a literal interlinear word-for-word translation.
- (mathematics) Of, attributed to or inspired by the Irish mathematician, astronomer and physicist William Rowan Hamilton (1805–1865).
- (mathematics, graph theory, of a cycle/path) That visits each vertex exactly once.
noun
- (physics, quantum mechanics) The observable, denoted H, that corresponds to the total energy of the system.
- (physics, Hamiltonian mechanics) A function (of time), denoted H, that corresponds to the total energy of the system.
- A native or inhabitant of any city named Hamilton.
- (historical, chiefly US) A member of the faction of the US government in the George Washington administration led by Alexander Hamilton.
noun
- (physics, analytical dynamics) A formula for converting a Lagrangian function to a Hamiltonian function (or vice versa).
- (mathematics) Given a function f(x,y,z,...) which is concave up with respect to x (i.e., its second derivative with respect to x is greater than zero), an involutive procedure for replacing x with another variable, say p=∂f/∂x thus yielding another function, say F=F(p,y,z,...). This new function contains all of the information of the original f encoded, as it were, within it so that ∂F/∂p=x and applying a similar transformation to F yields the original f. The formula is: F(p,y,z,...)=p·x(p)-f(x(p),y,z,...) where x must be expressed as a function of p. (Note: The concave upwardness means that ∂f/∂x is monotonically increasing, which means that p as a function of x is invertible, so x should be expressible as a function of p.)
- (thermodynamics) A relation between internal energy (expressed in terms of volume and entropy) and enthalpy (replacing volume with pressure), or between internal energy and Helmholtz free energy (replacing entropy with temperature), or between enthalpy and Gibbs free energy (replacing entropy with temperature), or between internal energy and Gibbs free energy (replacing volume with pressure and entropy with temperature), or between Helmholtz free energy and Gibbs free energy (replacing volume with pressure).
noun
- (category theory) a colimit
- (algebra) A set of equivalence classes which partition the disjoint union of the members of a direct system; each equivalence class being a sort of “drainage basin” of the mappings (of the morphisms) of the direct system, if these are analogically considered as “rivers”. (If i<k,j<k in the indexing poset, then there exist f_ik:A_i→A_k and f_jk:A_j→A_k. If a_i∈A_i,a_j∈A_j such that f_ik(a_i)=f_jk(a_j) then a_i∼a_j. If k = j then f_jj(a_j)=a_j,f_ij(a_i)=a_j.)
noun
- (physics, analytical dynamics) A formula for converting a Lagrangian function to a Hamiltonian function (or vice versa).
- (mathematics) Given a function f(x,y,z,...) which is concave up with respect to x (i.e., its second derivative with respect to x is greater than zero), an involutive procedure for replacing x with another variable, say p=∂f/∂x thus yielding another function, say F=F(p,y,z,...). This new function contains all of the information of the original f encoded, as it were, within it so that ∂F/∂p=x and applying a similar transformation to F yields the original f. The formula is: F(p,y,z,...)=p·x(p)-f(x(p),y,z,...) where x must be expressed as a function of p. (Note: The concave upwardness means that ∂f/∂x is monotonically increasing, which means that p as a function of x is invertible, so x should be expressible as a function of p.)
- (thermodynamics) A relation between internal energy (expressed in terms of volume and entropy) and enthalpy (replacing volume with pressure), or between internal energy and Helmholtz free energy (replacing entropy with temperature), or between enthalpy and Gibbs free energy (replacing entropy with temperature), or between internal energy and Gibbs free energy (replacing volume with pressure and entropy with temperature), or between Helmholtz free energy and Gibbs free energy (replacing volume with pressure).
noun
- (category theory) a colimit
- (algebra) A set of equivalence classes which partition the disjoint union of the members of a direct system; each equivalence class being a sort of “drainage basin” of the mappings (of the morphisms) of the direct system, if these are analogically considered as “rivers”. (If i<k,j<k in the indexing poset, then there exist f_ik:A_i→A_k and f_jk:A_j→A_k. If a_i∈A_i,a_j∈A_j such that f_ik(a_i)=f_jk(a_j) then a_i∼a_j. If k = j then f_jj(a_j)=a_j,f_ij(a_i)=a_j.)
adj
- (physics, quantum mechanics, of a process) Involving the slow change of the Hamiltonian of a system from its initial value to a final value.
- (physics, thermodynamics, of a process) Without gain or loss of heat (and thus with no change in entropy, in the quasistatic approximation).
- occurring without loss or gain of heat
noun
adj
- (mathematics, graph theory, of a graph) Containing a Hamiltonian cycle.
- Of, relating to, or in the literary style of Edmond Hamilton (1904–1977), American science fiction writer.
- Of or relating to any city named Hamilton.
- Relating to Sir William Hamilton, 9th Baronet (1788–1856), Scottish metaphysician.
- (historical, chiefly US, of certain fiscal policies) Advocated by American politician Alexander Hamilton (1755–1804).
- Relating to James Hamilton (1769–1831), or his method of teaching languages without grammar, by a literal interlinear word-for-word translation.
- (mathematics) Of, attributed to or inspired by the Irish mathematician, astronomer and physicist William Rowan Hamilton (1805–1865).
- (mathematics, graph theory, of a cycle/path) That visits each vertex exactly once.
noun
- (physics, quantum mechanics) The observable, denoted H, that corresponds to the total energy of the system.
- (physics, Hamiltonian mechanics) A function (of time), denoted H, that corresponds to the total energy of the system.
- A native or inhabitant of any city named Hamilton.
- (historical, chiefly US) A member of the faction of the US government in the George Washington administration led by Alexander Hamilton.