“degree”的概念、定义、翻译、参考文献-科学参考

degree

Physics

1. A unit of plane angle equal to 1/360th of a complete revolution.

2. A division on a temperature scale.

3. The power to which a variable is raised. If one expression contains several variables the overall degree of the expression is the sum of the powers. For example, the expression p²q³r⁴ has a degree of 9 overall (it is a second-degree expression in p). The degree of a polynomial is the degree of the variable with the highest power, e.g. ax⁵+bx⁴+c has a degree of 5.

4. The highest power to which the derivative of the highest order is raised in a differential equation. For example, (d²y/dx²)³+dy/dx=c is a differential equation of the third degree (but second order).

Statistics

See polynomial.

Chemistry

A division on a temperature scale.

Chemical Engineering

1. A division on a temperature scale.

2. An angle equal to 1/360th of a circle.

3. The highest power of a polynomial. For example, the quadratic equation $a x^{2} + b x + c = 0$ has a degree of 2.

4. The highest power to which a derivative of a differential equation is raised. For example:
${(\frac{d^{2} y}{d x^{2}})}^{4} + {(\frac{d y}{d x})}^{3} = 0$

is a second order differential equation of the fourth degree.

Computer

1. (of a vertex of a graph) The number of edges incident with the vertex, i.e. that emanate from that vertex. In a directed graph, the indegree is the number of edges entering a vertex while the outdegree is the number leaving a vertex.
2. (of a node in a tree) The number of children of that node, i.e. the number of subtrees rooted at that node. More correctly, this is the outdegree of the node.
3. (of a tree) The maximum degree of all the nodes in the tree.
4. (of a polynomial) See polynomial.

Logic

1. With respect to a formula $φ$ , the maximum depth at which instances of a conditional connective $\to$ are nested within each other’s scope. Recursively, where $p$ is an atom, $deg (φ)$ —the degree of $φ$ —is defined so that
- • $deg (p) = 0$
- • $deg (\neg φ) = deg (φ)$
- • $deg (φ \circ ψ) = max (deg (φ), deg (ψ))$ , where $\circ$ is a non-conditional binary connective
- • $deg (φ \to ψ) = max (deg (φ), deg (ψ)) + 1$
2. With respect to a formula $φ$ in a modal logic with a necessity operator $□$ , the maximum depth at which instances of $□$ are nested within each other. The modal degree is defined recursively:
- • $deg (p) = 0$
- • $deg (\neg φ) = deg (φ)$
- • $deg (φ \circ ψ) = max (deg (φ), deg (ψ))$ , where $\circ$ is a binary connective
- • $deg (□ φ) = deg (φ) + 1$

Philosophy

The degree of a predicate is the number of terms with which it must be combined to give a well-formed sentence. If the number is one, the predicate is monadic (e.g. ‘…is a man’), if two then it is dyadic or binary (…is brother of…), and so on. In classical formal language the degree or ‘adicity’ of a predicate is fixed, but there is no theoretical bar to predicates of variable adicity (‘…cooked supper together’).

单词	degree
释义	degree Physics 1. A unit of plane angle equal to 1/360th of a complete revolution. 2. A division on a temperature scale. 3. The power to which a variable is raised. If one expression contains several variables the overall degree of the expression is the sum of the powers. For example, the expression p²q³r⁴ has a degree of 9 overall (it is a second-degree expression in p). The degree of a polynomial is the degree of the variable with the highest power, e.g. ax⁵+bx⁴+c has a degree of 5. 4. The highest power to which the derivative of the highest order is raised in a differential equation. For example, (d²y/dx²)³+dy/dx=c is a differential equation of the third degree (but second order). Statistics See polynomial. Chemistry A division on a temperature scale. Chemical Engineering 1. A division on a temperature scale. 2. An angle equal to 1/360th of a circle. 3. The highest power of a polynomial. For example, the quadratic equation $a x^{2} + b x + c = 0$ has a degree of 2. 4. The highest power to which a derivative of a differential equation is raised. For example: ${(\frac{d^{2} y}{d x^{2}})}^{4} + {(\frac{d y}{d x})}^{3} = 0$ is a second order differential equation of the fourth degree. Computer 1. (of a vertex of a graph) The number of edges incident with the vertex, i.e. that emanate from that vertex. In a directed graph, the indegree is the number of edges entering a vertex while the outdegree is the number leaving a vertex. 2. (of a node in a tree) The number of children of that node, i.e. the number of subtrees rooted at that node. More correctly, this is the outdegree of the node. 3. (of a tree) The maximum degree of all the nodes in the tree. 4. (of a polynomial) See polynomial. Logic 1. With respect to a formula $φ$ , the maximum depth at which instances of a conditional connective $\to$ are nested within each other’s scope. Recursively, where $p$ is an atom, $deg (φ)$ —the degree of $φ$ —is defined so that • $deg (p) = 0$ • $deg (\neg φ) = deg (φ)$ • $deg (φ \circ ψ) = max (deg (φ), deg (ψ))$ , where $\circ$ is a non-conditional binary connective • $deg (φ \to ψ) = max (deg (φ), deg (ψ)) + 1$ 2. With respect to a formula $φ$ in a modal logic with a necessity operator $□$ , the maximum depth at which instances of $□$ are nested within each other. The modal degree is defined recursively: • $deg (p) = 0$ • $deg (\neg φ) = deg (φ)$ • $deg (φ \circ ψ) = max (deg (φ), deg (ψ))$ , where $\circ$ is a binary connective • $deg (□ φ) = deg (φ) + 1$ Philosophy The degree of a predicate is the number of terms with which it must be combined to give a well-formed sentence. If the number is one, the predicate is monadic (e.g. ‘…is a man’), if two then it is dyadic or binary (…is brother of…), and so on. In classical formal language the degree or ‘adicity’ of a predicate is fixed, but there is no theoretical bar to predicates of variable adicity (‘…cooked supper together’).
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