ProphetesAI is thinking...
characterize
MindMap
Loading...
Sources
characterize
characterize, v. (ˈkærəktəraɪz) Also 7 car-. [ad. med.L. charactērizāre, ad. Gr. χαρακτηρίζειν to designate by a characteristic mark, f. χαρακτήρ character; cf. F. caractériser.] † 1. trans. To engrave, imprint, impress; to inscribe, write; to define in form or outline; also fig.; = character v. 1. ...
Oxford English Dictionary
prophetes.ai
characterize
characterizecharacterise, / ˈkærəktəraɪz; `kærɪktəˌraɪz/ v1 [Cn.n/a] ~ sb/sth as sth describe or portray the character of sb/sth as sth 将某人[某事物]的特点描述成或刻画成某事物 The novelist characterizes his heroine as capricious and passionate. 这位小说家把女主人公刻画成反覆无常而又多情的人.2 [Tn esp passive 尤用於被动语态]be typical of (sb/sth);...
牛津英汉双解词典
prophetes.ai
2.4: Early Experiments to Characterize the Atom
The neutron, however, was not discovered until 1932, when James Chadwick (1891-1974, a student of Rutherford; Nobel Prize in Physics, 1935) discovered it. As a result of Rutherford's work, it became clear that an α particle contains two protons and neutrons, and is therefore the nucleus of a helium atom.
chem.libretexts.org
Characterize an analytic function with restriction of its growth Characterize all analytic functions $f(x)$ in $|z|<1$ such that $|f(z)|\leq|\sin(1/z)|$ for all points in punctured disk. I think we should change the ...
**Hint:** Take the sequence $\\{z_n\\}=\left\\{\frac{1}{n\pi}\right\\}$ and use **Identity theorem**. What is $f(z_n)$ ?
prophetes.ai
Characterize continuous functions $f : X → Y$ for which $f^{− 1} ( \{ a\} )$ is open Let X and Y be topological spaces and f : X → Y be a continuous function. Prove that for every a ∈ Y the set $f^{−1}$({a}) is a clos...
If $Y$ is $T_1$, then all sets $\\{a\\}$ for $a \in Y$ are closed subsets, so $f^{-1}[\\{a\\}]$ is closed as the inverse image of a closed set under a continuous function. If there is some $a_0 \in Y$ such that $f^{-1}[\\{a_0\\}]$ is non-empty and open, and if $X$ is connected, then $f^{-1}[\\{a_0\\...
prophetes.ai
Characterize the set of functions $g:\mathbb{C}\setminus\{0\}\to\mathbb{C}$ with the given property > Characterize the set of holomorphic functions $g:\mathbb{C}\setminus\\{0\\}\to\mathbb{C}$ that are bounded away fro...
Let $f(z)=\frac{1}{z}$. Then consider functions $h=f \circ g$. Then $|h(z)|<|z|^{\frac{7}{3}}$ Then, $h(z)$ is similar to a quadratic polynomial. This in turn characterises $g(z)$.
prophetes.ai
Characterize all analytic functions satisfyinf the given condition > Characterize all analytic functions $f(z)$ in $|z|<1$ such that $|f(z)|\le |\sin(1/z)|$ , for all $0<|z|<1$. I can't understand from where I will s...
First prove that a non-constant analytic function can have at most finitely many zeros in a bounded, compact set. Proof idea: if it's bounded and compact, and has infinitely many zeros, there must be an accumulation point, so the function must be identically zero. Now notice that $z_i=1/(n\pi)$ is s...
prophetes.ai
Characterize those non-empty graphs with the property that every two distinct maximal independent set of vertices are disjoint > > An independent set of vertices in a graph $G$ is **maximal independent** if $S$ is not...
HINT: Suppose that maximal independent sets of vertices of $G=\langle V,E\rangle$ are pairwise disjoint. Define a relation $\sim$ on $V$ by $u\sim v$ iff $\\{u,v\\}$ is independent. * Show that $\sim$ is an equivalence relation on $V$. * Show that for all $u,v\in V$, $uv$ is an edge of $G$ iff $u\no...
prophetes.ai
Characterization of a subfield $K \varsubsetneq \mathbb {C}$ and $x\in \mathbb{R}$ > Characterize $x \in \mathbb R$ such that there exist a subfield $K \varsubsetneq \mathbb C$ such that $K(x) = \mathbb C$. -All subf...
Denote by $E$ the set of $x \in \mathbb{R}$ satisfying your conditions. * If $x \in \mathbb{R}$ is transcendental over $\mathbb{Q}$ or algebraic not totally real, then $x \in E$. > Take $y=i \pi$ if $x$ is transcendental or $y \notin \mathbb{R}$ conjugate to $x$ if $x$ is algebraic not totally real....
prophetes.ai
Characterize Powersets among CPOs Powersets can be seen as complete atomic boolean algebras. > Is it possible to characterize **complete atomic boolean algebras** (CABA) among **complete partial orders** (CPO)? For ...
As indicated in this nlab page, > Powersets are precisely atomic CPOs. The definition of atom and atomic is a bit different from the one expected by lattice theorists. Traslating from mine terminology to theirs, _atomic_ means that **there is a join-dense subset of completely join-irreducible elemen...
prophetes.ai
Characterize the novel “Lord of the Rings”
The novel “Lord of the Rings” is a classic epic fantasy story set in a distant land of elves, dwarves, men, and hobbits. It is a story of courage, friendship, and self-sacrifice, as the characters must protect their world from the forces of darkness. The novel is full of thrilling action, magical cr...
prophetes.ai
Characterize pseudometrizable topologies. Are there interesting characterizations of topologies that admit a pseudometric?
Suppose that $d$ is a pseudometric generating the topology of $X$, and for $x,y\in X$ let $x\sim y$ iff $d(x,y)=0$. Then $X/\\!\sim$ is metrizable by $\bar{d}\big([x],[y]\big)=d(x,y)$, where $[x]$ is the $\sim$-class of $x$. In effect we’ve simply collapsed the topologically indistinguishable points...
prophetes.ai
Characterize finite dimensional algebras without nilpotent elements > Characterize all finite dimensional algebras (may not be commutative) over a field $K$ without nilpotent elements. My condition: Let $A$ be any al...
Suppose that $A$ is a finite dimensional associative algebra with $1$ which has no nilpotent elements. The Jacobson radical $J(A)$ of $A$ is then zero, because $J(A)$ is a nilpotent ideal of $A$, so its elements are themselves nilpotent. This implies that $A$ is a semisimple algebra and Wedderburn's...
prophetes.ai
Is there a non abelian group that characterize a one dimensional lattice structure? Of all groups that characterize a one dimensional lattice structure (symmetry operations including translation, $C_2$, mirror plane, ...
The isometries of the real line are of the forms $t_a(x)=a+x$ and $r_a(x)=a-x$. We have $$t_a\circ t_b = t_{a+b}\\\ t_a\circ r_b = r_{b+a}\\\ r_a\circ t_b = r_{a-b}\\\ r_a\circ r_b = t_{a-b}$$ Also, $t_0$ is the identity. They are not commutative: $$r_0\circ t_1(x)=-(1+x)\neq 1-x= t_1\circ r_0(x).$$...
prophetes.ai
Characterize cokernel pair in Set In the category of sets ( **Set** ), can we characterize the cokernel pair of a function $f : A\rightarrow B$?
Let $s, t:B\rightarrow C$ be the cokernel pair. $C$ is the coproduct $B + B$, but with the image of $f$ identified (glued together), in other words: $$C = \mathrm{im} f + (B - \mathrm{im} f) + (B - \mathrm{im} f)$$ The two morphism $s, t$ are simply the left and right coprojections into $C$. To see ...
prophetes.ai