Learn more about Stack Overflow the company, and our products. A function is well defined only if we specify the domain and the codomain, and iff to any element in the domain correspons only one element in the codomain. About. As an approximate solution one takes then a generalized solution, a so-called quasi-solution (see [Iv]). Sep 16, 2017 at 19:24. where $\epsilon(\delta) \rightarrow 0$ as $\delta \rightarrow 0$? I see "dots" in Analysis so often that I feel it could be made formal. Department of Math and Computer Science, Creighton University, Omaha, NE. Thus, the task of finding approximate solutions of \ref{eq1} that are stable under small changes of the right-hand side reduces to: a) finding a regularizing operator; and b) determining the regularization parameter $\alpha$ from additional information on the problem, for example, the size of the error with which the right-hand side $u$ is given. Is there a solutiuon to add special characters from software and how to do it, Minimising the environmental effects of my dyson brain. Topology is a relatively new branch of mathematics; most of the research in topology has been done since 1900. My code is GPL licensed, can I issue a license to have my code be distributed in a specific MIT licensed project? The idea of conditional well-posedness was also found by B.L. [V.I. How to handle a hobby that makes income in US. In mathematics, a well-defined expressionor unambiguous expressionis an expressionwhose definition assigns it a unique interpretation or value. - Henry Swanson Feb 1, 2016 at 9:08 After stating this kind of definition we have to be sure that there exist an object with such properties and that the object is unique (or unique up to some isomorphism, see tensor product, free group, product topology). Only if $g,h$ fulfil these conditions the above construction will actually define a function $f\colon A\to B$.
ill-defined - Wiktionary adjective. Proceedings of the 31st SIGCSE Technical Symposium on Computer Science Education, SIGCSE Bulletin 32(1), 202-206. A variant of this method in Hilbert scales has been developed in [Na] with parameter choice rules given in [Ne]. The words at the top of the list are the ones most associated with ill defined, and as you go down the relatedness becomes more slight. Can I tell police to wait and call a lawyer when served with a search warrant? The formal mathematics problem makes the excuse that mathematics is dry, difficult, and unattractive, and some students assume that mathematics is not related to human activity. How can we prove that the supernatural or paranormal doesn't exist? As IFS can represents the incomplete/ ill-defined information in a more specific manner than FST, therefore, IFS become more popular among the researchers in uncertainty modeling problems.
Ill-defined - crossword puzzle clues & answers - Dan Word There are two different types of problems: ill-defined and well-defined; different approaches are used for each. Approximate solutions of badly-conditioned systems can also be found by the regularization method with $\Omega[z] = \norm{z}^2$ (see [TiAr]). Frequently, instead of $f[z]$ one takes its $\delta$-approximation $f_\delta[z]$ relative to $\Omega[z]$, that is, a functional such that for every $z \in F_1$, Definition. This set is unique, by the Axiom of Extensionality, and is the set of the natural numbers, which we represent by $\mathbb{N}$.
Ill-Defined -- from Wolfram MathWorld Tip Two: Make a statement about your issue. Groetsch, "The theory of Tikhonov regularization for Fredholm equations of the first kind", Pitman (1984), C.W. Ill-defined. The function $\phi(\alpha)$ is monotone and semi-continuous for every $\alpha > 0$. The best answers are voted up and rise to the top, Not the answer you're looking for? \end{align}. This paper describes a specific ill-defined problem that was successfully used as an assignment in a recent CS1 course. (2000). Under certain conditions (for example, when it is known that $\rho_U(u_\delta,u_T) \leq \delta$ and $A$ is a linear operator) such a function exists and can be found from the relation $\rho_U(Az_\alpha,u_\delta) = \delta$. $$0=\emptyset,\ 1=0^+,\ 2=1^+,\ \cdots$$ This poses the problem of finding the regularization parameter $\alpha$ as a function of $\delta$, $\alpha = \alpha(\delta)$, such that the operator $R_2(u,\alpha(\delta))$ determining the element $z_\alpha = R_2(u_\delta,\alpha(\delta)) $ is regularizing for \ref{eq1}. You missed the opportunity to title this question 'Is "well defined" well defined? There's an episode of "Two and a Half Men" that illustrates a poorly defined problem perfectly. For the interpretation of the results it is necessary to determine $z$ from $u$, that is, to solve the equation 'Well defined' isn't used solely in math. is not well-defined because $$(d\omega)(X_0,\dots,X_{k})=\sum_i(-1)^iX_i(\omega(X_0,\dots \hat X_i\dots X_{k}))+\sum_{i
Ill-Posed -- from Wolfram MathWorld General Topology or Point Set Topology. Next, suppose that not only the right-hand side of \ref{eq1} but also the operator $A$ is given approximately, so that instead of the exact initial data $(A,u_T)$ one has $(A_h,u_\delta)$, where $$ In this case, Monsieur Poirot can't reasonably restrict the number of suspects before he does a bit of legwork. The ACM Digital Library is published by the Association for Computing Machinery. Tikhonov, "On stability of inverse problems", A.N. Can archive.org's Wayback Machine ignore some query terms? This is said to be a regularized solution of \ref{eq1}. &\implies x \equiv y \pmod 8\\ Deconvolution is ill-posed and will usually not have a unique solution even in the absence of noise. Suppose that $Z$ is a normed space. vegan) just to try it, does this inconvenience the caterers and staff? Well-defined: a problem having a clear-cut solution; can be solved by an algorithm - E.g., crossword puzzle or 3x = 2 (solve for x) Ill-defined: a problem usually having multiple possible solutions; cannot be solved by an algorithm - E.g., writing a hit song or building a career Herb Simon trained in political science; also . A Dictionary of Psychology , Subjects: If $A$ is a linear operator, $Z$ a Hilbert space and $\Omega[z]$ a strictly-convex functional (for example, quadratic), then the element $z_{\alpha_\delta}$ is unique and $\phi(\alpha)$ is a single-valued function. The main goal of the present study was to explore the role of sleep in the process of ill-defined problem solving. PS: I know the usual definition of $\omega_0$ as the minimal infinite ordinal. This is important. There is a distinction between structured, semi-structured, and unstructured problems. ILL DEFINED Synonyms: 405 Synonyms & Antonyms for ILL - Thesaurus.com 1: meant to do harm or evil. Origin of ill-defined First recorded in 1865-70 Words nearby ill-defined ill-boding, ill-bred, ill-conceived, ill-conditioned, ill-considered, ill-defined, ill-disguised, ill-disposed, Ille, Ille-et-Vilaine, illegal These include, for example, problems of optimal control, in which the function to be optimized (the object function) depends only on the phase variables. quotations ( mathematics) Defined in an inconsistent way. . (hint : not even I know), The thing is mathematics is a formal, rigourous thing, and we try to make everything as precise as we can. &\implies 3x \equiv 3y \pmod{12}\\ Semi structured problems are defined as problems that are less routine in life. As a normal solution of a corresponding degenerate system one can take a solution $z$ of minimal norm $\norm{z}$. The answer to both questions is no; the usage of dots is simply for notational purposes; that is, you cannot use dots to define the set of natural numbers, but rather to represent that set after you have proved it exists, and it is clear to the reader what are the elements omitted by the dots. In principle, they should give the precise definition, and the reason they don't is simply that they know that they could, if asked to do so, give a precise definition. Numerical methods for solving ill-posed problems. How to show that an expression of a finite type must be one of the finitely many possible values? Furthermore, Atanassov and Gargov introduced the notion of Interval-valued intuitionistic fuzzy sets (IVIFSs) extending the concept IFS, in which, the . It only takes a minute to sign up. In the second type of problems one has to find elements $z$ on which the minimum of $f[z]$ is attained. | Meaning, pronunciation, translations and examples Identify those arcade games from a 1983 Brazilian music video. When one says that something is well-defined one simply means that the definition of that something actually defines something. \rho_U(A\tilde{z},Az_T) \leq \delta In other words, we will say that a set $A$ is inductive if: For each $a\in A,\;a\cup\{a\}$ is also an element of $A$. Many problems in the design of optimal systems or constructions fall in this class. About an argument in Famine, Affluence and Morality. The regularization method is closely connected with the construction of splines (cf. A minimizing sequence $\set{z_n}$ of $f[z]$ is called regularizing if there is a compact set $\hat{Z}$ in $Z$ containing $\set{z_n}$. Therefore this definition is well-defined, i.e., does not depend on a particular choice of circle. I have encountered this term "well defined" in many places in maths like well-defined set, well-defined function, well-defined group, etc. Let $\tilde{u}$ be this approximate value. www.springer.com For convenience, I copy parts of the question here: For a set $A$, we define $A^+:=A\cup\{A\}$. What sort of strategies would a medieval military use against a fantasy giant? Should Computer Scientists Experiment More? The use of ill-defined problems for developing problem-solving and empirical skills in CS1, All Holdings within the ACM Digital Library. Proceedings of the 34th Midwest Instruction and Computing Symposium, University of Northern Iowa, April, 2001. (eds.) ensures that for the inductive set $A$, there exists a set whose elements are those elements $x$ of $A$ that have the property $P(x)$, or in other words, $\{x\in A|\;P(x)\}$ is a set. an ill-defined mission Dictionary Entries Near ill-defined ill-deedie ill-defined ill-disposed See More Nearby Entries Cite this Entry Style "Ill-defined." Developing Empirical Skills in an Introductory Computer Science Course. L. Colin, "Mathematics of profile inversion", D.L. In the first class one has to find a minimal (or maximal) value of the functional. This page was last edited on 25 April 2012, at 00:23. Equivalence of the original variational problem with that of finding the minimum of $M^\alpha[z,u_\delta]$ holds, for example, for linear operators $A$. We call $y \in \mathbb{R}$ the. Journal of Physics: Conference Series PAPER OPEN - Institute of Physics il . Let me give a simple example that I used last week in my lecture to pre-service teachers. In some cases an approximate solution of \ref{eq1} can be found by the selection method. A well-defined problem, according to Oxford Reference, is a problem where the initial state or starting position, allowable operations, and goal state are all clearly specified. As $\delta \rightarrow 0$, $z_\delta$ tends to $z_T$. Learner-Centered Assessment on College Campuses. Identify the issues. Can these dots be implemented in the formal language of the theory of ZF? \norm{\bar{z} - z_0}_Z = \inf_{z \in Z} \norm{z - z_0}_Z . that can be expressed in the formal language of the theory by the formula: $$\forall y(y\text{ is inductive}\rightarrow x\in y)$$, $$\forall y(\varnothing\in y\wedge\forall z(z\in y\rightarrow z\cup\{z\}\in y)\rightarrow x\in y)$$. Copyright HarperCollins Publishers As a result, what is an undefined problem? This can be done by using stabilizing functionals $\Omega[z]$. If the construction was well-defined on its own, what would be the point of AoI? Some simple and well-defined problems are known as well-structured problems, and they have a set number of possible solutions; solutions are either 100% correct or completely incorrect. Identify the issues. What are the contexts in which we can talk about well definedness and what does it mean in each context? See also Ambiguous, Ill-Posed , Well-Defined Explore with Wolfram|Alpha More things to try: partial differential equations 4x+3=19 conjugate: 1+3i+4j+3k, 1+-1i-j+3k Cite this as: Weisstein, Eric W. "Ill-Defined." p\in \omega\ s.t\ m+p=n$, Using Replacement to prove transitive closure is a set without recursion. For a number of applied problems leading to \ref{eq1} a typical situation is that the set $Z$ of possible solutions is not compact, the operator $A^{-1}$ is not continuous on $AZ$, and changes of the right-hand side of \ref{eq1} connected with the approximate character can cause the solution to go out of $AZ$.