Search results

...R}^{n\times n}</math>. Let <math>\rho(X)</math> be the [[spectral radius]] of a matrix <math>X</math>. Let <math>T_J=D^{-1}(L+U)</math> and <math>T_1=(D- ...th>a_{ii} > 0</math> for <math>i=1,\ldots,n</math>. Then, one and only one of the following mutually exclusive relations is valid: ...

...arl Gustav Jacob Jacobi|Jacobi]] (which is essentially just a special case of the [[Poisson summation formula]] in classical harmonic analysis): ...n|date=2019-07-17|title=A proof of the Landsberg-Schaar relation by finite methods|class=math.NT|eprint=1810.06172}}</ref> ...

...eorem.svg|thumb|upright=1.25|<math> \begin{align} &\text{D and E midpoints of AC and BC}\\ \Rightarrow \, &DE \parallel AB\text{ and } 2|DE|=|AB|\end{ali ...|last=French |first=Doug |title=Teaching and learning geometry: issues and methods in mathematical education |date=2004 |publisher=Continuum |isbn=978-0-8264- ...

...t. This theorem is a key tool in one of the quickest proofs of amenability of abelian groups. Let <math>S</math> be a family of continuous mappings of <math>K</math> to itself which commute and are ''affine'', meaning that <ma ...

...of [[topology|topological]] and [[algebraic topology|algebro-topological]] methods to solving problems in [[combinatorics]]. ...cepts in topology and in the early 20th century this turned into the field of [[algebraic topology]]. ...

...hrmann, O.; Hoory, S.; Shacham, O.; Strichman, O. ''Linear-time Reductions of Resolution Proofs''. Hardware and Software: Verification and Testing, p. 11 ...lause (logic)|clauses]], i.e. clauses containing only one literal. Certain proof nodes can be replaced with the nodes representing these unit clauses. ...

...heorem''' states that the [[Hadamard product (matrices)|Hadamard product]] of two [[positive definite matrices]] is also a positive definite matrix. ...and His School in Berlin | doi = 10.1112/blms/15.2.97 | journal = Bulletin of the London Mathematical Society | volume = 15 | issue = 2 | pages = 97–106 ...

{{Short description|Method of finding axes and veritces of an ellipse}} ...ate diameters|conjugated half-diameters]]. If the center and the semi axis of an ellipse are determined the ellipse can be drawn using an ellipsograph or ...

...number theory]]. It is useful for proving results about the [[normal order of an arithmetic function]].<ref name="Tenenbaum" />{{Rp|305–308}} The theorem ==Statement of the theorem== ...

| title = Methods of Mathematical Physics, Vol. I Plotting this function for different values of ''n'' reveals that as ''n'' goes to infinity, <math> L_n(t) </math> approac ...

...[Fatou's lemma]] to an equality. As such, it has been useful for the study of many [[variational problem]]s.{{sfnm|1a1=Lions|1y=1985}} ==The lemma and its proof== ...

| name = Using the Borsuk–Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry ...athematics textbook in [[topological combinatorics]]. It describes the use of results in [[topology]], and in particular the [[Borsuk–Ulam theorem]], to ...

...s one of the earliest known proofs of the Pythagorean theorem and also one of the simplest. The text in ''Zhoubi Suanjing'' accompanying the diagram has ...when this is subtracted from the square plate of area 24) the remainder is of area 25. This (process) is called "piling up the rectangles" (''chi chu''). ...

...ogy |date=1973 |volume=27 |pages=65–104 |pmid=4148886}}</ref> is a measure of how external factors such as inhibitors, pharmaceutical drugs, or boundary where in both cases <math>x</math> is the concentration of the external factor. The response coefficient measures how sensitive a path ...

In [[mathematics]], specifically in the field of [[modular representation theory]], the | title = Proceedings of the international symposium on algebraic number theory, Tokyo and Nikko, 19 ...

...shall Ash, Allan Berele, Stefan Catoiu: ''Plausible and Genuine Extensions of L’Hospital’s Rule''. In: ''Mathematics Magazine'', Vol. 85, No. 1, Februar ...or sequence <math> (a_n)</math> with <math>a_n\to a </math> and a sequence of positive real numbers <math> (p_n)</math> with <math>\frac{1}{p_1+\cdots+p_ ...

....org/stable/2238089. Accessed 15 Aug. 2022.]</ref> in 1965 in the [[Annals of Mathematical Statistics]]. == Statement of the Theorem == ...

...321 | year = 2000 | doi = 10.1023/A:1022238410461 |title=The life and work of Zbyněk Šidák (1933–1999)| hdl = 10338.dmlcz/134443 | hdl-access = free }}</ * Given ''m'' different null hypotheses and a familywise alpha level of <math>\alpha</math>, each null hypothesis is rejected that has a p-value lo ...

{{short description|The group of K-rational points of an abelian variety is a finitely-generated abelian group}} | first proof by = [[André Weil]] ...

...t=L. |date=1974-05-01 |title=Lower bounds on the maximum cross correlation of signals (Corresp.) |url=https://ieeexplore.ieee.org/document/1055219 |journ ...t2=Stephen |last3=Cochran |first3=Douglas |date=2012-05-29 |title=Geometry of the Welch Bounds |arxiv=0909.0206 }}</ref><math display="block">\frac{1}{m^ ...