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- '''Convergence proof techniques''' are canonical patterns of mathematical proofs that [[limit of a sequence ...necessary conditions and generalizations to more abstract settings. Proof techniques for the convergence of [[Series (mathematics)|series]], a particular type o ...11 KB (1,767 words) - 15:24, 4 September 2024
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- ...ques for Minimizing Resolution Proof".<ref name=Cotton>Cotton, Scott. "Two Techniques for Minimizing Resolution Proofs". 13th International Conference on Theory ...ion of these two proofs (by an additional resolution step) may result in a proof smaller than the original. ...3 KB (587 words) - 01:13, 16 July 2017
- {{Short description|Proof strategy for showing a collection of statements are pairwise equivalent.}} ...uss|lit=Proof by ring-inference}}) is a mathematical [[Proof (mathematics)|proof]] technique where the equivalence of several statements can be proven witho ...3 KB (421 words) - 22:53, 12 November 2024
- ...lver]]s, [[SMT solver|SMT-solvers]], [[first-order theorem provers]] and [[proof assistant]]s. ...elements of ''C'', the resolvent nodes are resolution inferences, and the proof has a node with conclusion <math>\kappa</math>.<ref name="Compression of Pr ...6 KB (909 words) - 00:22, 13 February 2024
- ...nd sufficient conditions on the reconstruction of sparse signals using the techniques of [[Relaxation (approximation)|<math>\ell_1</math>-relaxation]]. The term ...em. Note that this relaxation is convex and hence amenable to the standard techniques of [[linear programming]] - a computationally desirable feature. Naturally ...4 KB (673 words) - 07:21, 17 December 2023
- '''Convergence proof techniques''' are canonical patterns of mathematical proofs that [[limit of a sequence ...necessary conditions and generalizations to more abstract settings. Proof techniques for the convergence of [[Series (mathematics)|series]], a particular type o ...11 KB (1,767 words) - 15:24, 4 September 2024
- ...method for estimating the total<ref>William G. Cochran (1977), ''Sampling Techniques'', 3rd Edition, Wiley. {{ISBN|0-471-16240-X}}</ref> and mean of a [[pseudo- ...variance of <math>\hat{\mu}_{HT}</math> is not straightforward. Resampling techniques such as the bootstrap or the jackknife can be applied to gain consistent es ...5 KB (772 words) - 16:08, 21 January 2025
- ...ate finds important use in the study of patterns and [[machine learning]] techniques.<ref name="ESL">{{cite book|last1=Hastie|first1=Trevor|title=The Elements o == Proof of Minimality == ...5 KB (735 words) - 06:37, 12 January 2025
- ==Proof for ''k'' = 1== ...o <math>k=1</math>, is by far the most commonly used in applications. Its proof proceeds in two steps, each of which depends on a more basic mathematical i ...7 KB (1,150 words) - 21:25, 18 February 2023
- ...ity is important for assessing the performance of different classification techniques. A classifier is said to be [[Consistency (statistics)|consistent]] if the Proof that the Bayes classifier is optimal and [[Bayes error rate]] is minimal pr ...7 KB (1,090 words) - 20:45, 28 October 2024
- ===Proof=== ...vtxt|Grunsky|1932}} originally proved these inequalities based on extremal techniques of [[Ludwig Bieberbach]]. Subsequent proofs, outlined in {{harvtxt|Goluzin| ...6 KB (926 words) - 12:35, 10 June 2020
- |title=Techniques of Problem Solving ...there are no equichordal curves with excentricities > 0.33. The proof is mildly computer-assisted. ...7 KB (1,034 words) - 21:31, 20 December 2023
- ...ementing AIXItl as its initial sub-program, and self-modify after it finds proof that another algorithm for its search code will be better.<ref name="ultima ==Instructions used by proof techniques== ...10 KB (1,531 words) - 23:14, 12 June 2024
- ...criptstyle g^{x_i}</math> together with a [[zero-knowledge proof]] for the proof of the knowledge of the exponent <math>\scriptstyle x_i</math>. Such proofs ...may be realized by using Cramer, Gennaro, and Schoenmakers' zero-knowledge proof technique.<ref>{{Cite book|last1=Cramer|first1=Ronald|last2=Gennaro|first2= ...6 KB (930 words) - 21:23, 21 February 2025
- ...t published in 1983.<ref name="Wie83" /> A formal proof of security, using techniques from [[semidefinite programming]], was given in 2013.<ref name="MVW13">{{ci ...fact that a quantum state cannot be copied is ultimately guaranteed by its proof by the [[no-cloning theorem]], which underlies the security of this system. ...4 KB (560 words) - 00:49, 21 March 2024
- Kostochka stated that his techniques extend to <math>k\le 33</math>, but a proof of this has not been published.<ref name="ProofsFromTHEBOOK"/> ...ding proofs for many statements previously made by Kotzig without written proof.<ref name="Bondy"/> ...9 KB (1,432 words) - 23:50, 27 February 2025
- ...y measure <math>\mu\boxplus\nu</math> explicitly by using complex-analytic techniques and the R-transform of the measures <math>\mu</math> and <math>\nu</math>. ...measure <math>\mu\boxplus_c\nu</math> explicitly by using complex-analytic techniques and the rectangular R-transform with ratio <math>c</math> of the measures < ...8 KB (1,158 words) - 08:09, 21 June 2023
- | name = Proofs That Really Count: the Art of Combinatorial Proof ...n count the same type of mathematical objects, or by finding a [[bijective proof|one-to-one correspondence]] between the different types of object that they ...9 KB (1,235 words) - 08:42, 18 February 2025
- ...s such as algebraic geometry to solve combinatorics problems. While a few techniques that follow the framework of the polynomial method, such as Alon's [[Restri As an example, we outline Dvir's proof of the [[Kakeya set#Kakeya sets in vector spaces over finite fields|Finite ...9 KB (1,433 words) - 06:20, 22 January 2024
- ...ice versa; the norm residue isomorphism theorem makes it possible to apply techniques applicable to the object on one side of the isomorphism to the object on th ===History of the proof=== ...17 KB (2,436 words) - 15:55, 23 June 2024
- ...ensics has identified the data theft, follow up using traditional forensic techniques is required.<ref name="Digital_Forensics_Magazine"/> ...as only providing evidence and indications of data theft, and not concrete proof. Indeed, it requires a practitioner to "think like Sherlock, not Aristotle ...8 KB (1,082 words) - 16:57, 26 January 2023