Search results

== 大挑战 (Lovász's simplified version of the Kruskal-Katona theorem)== ...

...[mass]]. However, this is a simplified version of his equation. The longer version of his equation is E²=m²c⁴+p²c< ...

...pdf slides] | [http://lamda.nju.edu.cn/yinyt/notes/random1-print.pdf print version] ...pdf slides] | [http://lamda.nju.edu.cn/yinyt/notes/random2-print.pdf print version] ...

...that the opposite number of a number, is the [[negative number|negative]] version of the [[positive]] number. This is what the opposite of 7 is or the opposi ...

An '''approximation''' is a version of a piece of [[information]] that does not describe it exactly, but is clo ...

* ''Introduction to Fluid Mechanics'' Fourth Edition, Wiley, SI Version, R.W. Fox & A.T. McDonald ...

...ansversely Vibrating Beams using four Engineering Theories|version = final version|publisher = Academic Press|date = March 22, 1999|url = http://csxe.rutgers. ...

==Time independent Version== ...

...ect, and ''v'' is the [[velocity]] of the object. An alternate but correct version of this formula is ...

...sources/the-world-factbook/graphics/ref_maps/political/pdf/world.pdf large version] (pdf, 1.8MB)]] ...

...was given. In this way, it can solve a problem by first solving a simpler version of the problem. ...

|Definition (martingale, general version)| ==Azuma's inequality -- general version== ...

...eir real name, so he used the name "Student" to hide his identity. Another version is that the brewery did not want their competitors to know that they were u ...

This is another version, which is also true. ...

Prove the following independent set version of the Turan theorem: ...

Prove the following independent set version of the Turan theorem: ...

Prove the following independent set version of the Turan theorem: ...

....php/Complexity_Zoo:N#nl NL]. In fact USTCON is complete for the symmetric version of nondeterministic log-space. That is, every problem in the class of [http ...

...Qualification authority specifically mentions this skill in document 13004 version 2, dated 17 October 2003 titled [http://www.nzqa.govt.nz/nqfdocs/units/pdf/ ...

...tz conjecture seems to be hard to prove, consider the following randomized version: ...

Usually, [[Dirichlet]] is credited with the version used in schools until the second half of the 20th century: ...[[Bourbaki]] generalized the Dirichlet definition and gave a set theoretic version of the definition as a correspondence between inputs and outputs; this was ...

...ijn graphs are defined as directed graphs, here we consider the undirected version.) ...

#:This version of the Chebyshev inequality is sometimes referred to as the <b>Chebyshev-Ca ...

|Definition (martingale, general version)| |Azuma's Inequality (general version)| ...

...valent definitions of the set cover problem. We take the '''hitting set''' version.) ...

Let's first consider the decision version of the problem. That is, given as input a graph <math>G(V,E)</math>, decide ...

...al|generalizes]] readily into higher [[dimension]]s. The three-dimensional version is called [[Pascal's pyramid]] or ''Pascal's tetrahedron''. A higher-dimens ...

We consider the non-lazy version of random walk. We observe that the random walk has the following stationar ...

A stricter version of the big O is the little-o. The difference between big O and little-o is ...

We will prove a general version of the local lemma, where the events <math>A_i</math> are not symmetric. Th This gives the symmetric version of local lemma. ...

McLaughlin also created directions for an approximate version which can be done with just [[mental calculation]]. In 1995, Dale and Chall published a new version of their formula with an upgraded word list.<ref name=Dale-Chall2>Chall J.S ...

|Definition (martingale, general version)| |Azuma's Inequality (general version)| ...

Consider the following independent set version of the Turan theorem: ...

...For any <math>\lambda<0</math>, by the same analysis as in the upper tail version, |Definition (martingale, general version)| ...

...For any <math>\lambda<0</math>, by the same analysis as in the upper tail version, |Definition (martingale, general version)| ...

...For any <math>\lambda<0</math>, by the same analysis as in the upper tail version, |Definition (martingale, general version)| ...

...For any <math>\lambda<0</math>, by the same analysis as in the upper tail version, |Definition (martingale, general version)| ...

...oordinates|cylindrical polar coordinates]] (''r'', θ, ''z''), an unbounded version of the Möbius strip can be represented by the equation: *[http://www.toroidalsnark.net/mkmb.html Knitted version] ...

|Definition (martingale, general version)| |Azuma's Inequality (general version)| ...

|Definition (martingale, general version)| |Azuma's Inequality (general version)| ...

|Definition (martingale, general version)| |Azuma's Inequality (general version)| ...

|Definition (martingale, general version)| ====Azuma's inequality -- general version==== ...

...ue to Sauer, and independently due to Shelah and Perles. A slightly weaker version is found by Vapnik and Chervonenkis, who use the framework to develop a the And the general version of the Kruskal-Katona theorem can be deduced. ...

...ue to Sauer, and independently due to Shelah and Perles. A slightly weaker version is found by Vapnik and Chervonenkis, who use the framework to develop a the And the general version of the Kruskal-Katona theorem can be deduced. ...

We consider the the optimization version of SAT, which ask for an assignment that the number of satisfied clauses is We will prove a general version of the local lemma, where the events <math>A_i</math> are not symmetric. Th ...

We consider the the optimization version of SAT, which ask for an assignment that the number of satisfied clauses is We will prove a general version of the local lemma, where the events <math>A_i</math> are not symmetric. Th ...

{{Theorem|FPRAS (equivalent simple version)| ...dent to more than one edges in <math>M</math>, i.e. a matching is an "edge-version" of independent set. ...

...valent definitions of the set cover problem. We take the '''hitting set''' version.) ...

The following is the weighted version of set cover problem: ...

In the hitting set version, the frequency should be defined for each set: for a set <math>S_i</math> i The vertex cover problem is '''NP-hard'''. Its decision version is among [https://en.wikipedia.org/wiki/Karp%27s_21_NP-complete_problems Ka ...

In the hitting set version, the frequency should be defined for each set: for a set <math>S_i</math> i The vertex cover problem is '''NP-hard'''. Its decision version is among [https://en.wikipedia.org/wiki/Karp%27s_21_NP-complete_problems Ka ...

In the hitting set version, the frequency should be defined for each set: for a set <math>S_i</math> i The vertex cover problem is '''NP-hard'''. Its decision version is among [https://en.wikipedia.org/wiki/Karp%27s_21_NP-complete_problems Ka ...

...entical parallel machines'''. It can be described as the following simpler version as a load balancing problem: {{Theorem|Minimum Makespan on Identical Parallel Machines (load balancing version)| ...

In the hitting set version, the frequency should be defined for each set: for a set <math>S_i</math> i The vertex cover problem is '''NP-hard'''. Its decision version is among [https://en.wikipedia.org/wiki/Karp%27s_21_NP-complete_problems Ka ...

...entical parallel machines'''. It can be described as the following simpler version as a load balancing problem: {{Theorem|Minimum Makespan on Identical Parallel Machines (load balancing version)| ...

In the hitting set version, the frequency should be defined for each set: for a set <math>S_i</math> i The vertex cover problem is '''NP-hard'''. Its decision version is among [https://en.wikipedia.org/wiki/Karp%27s_21_NP-complete_problems Ka ...

The following is a general asymmetric version of the local lemma. This generalization is due to Spencer. ...he dependency graph has <math>d\ge 2</math>, we can have another symmetric version of the local lemma. ...

...valent definitions of the set cover problem. We take the '''hitting set''' version.) ...

The following is the asymmetric version of the Lovász Local Lemma. This generalization is due to Spencer. This generalized version of the local lemma immediately implies the symmetric version of the lemma. Namely, <math>\Pr\left[\bigwedge_{i}\overline{A_i}\right]>0</ ...

The following is the weighted version of set cover problem: ...

We will prove a general version of the local lemma, where the events <math>A_i</math> are not symmetric. Th ...

...se is also true: we can find the optimum by making queries to the decision version. Through binary search, this can be done efficiently. ...imization problem is an '''NP-hard''' optimization problem if its decision version is '''NP-hard'''. Many interesting optimization problems are '''NP-hard'''. ...

We consider the following randomized version of the quicksort. ...

The following is the weighted version of set cover problem: ...

...unt is configured so your solutions are not publicly visible. Many popular version control systems provide free repositories to students. ...

The following is the weighted version of set cover problem: ...

...unt is configured so your solutions are not publicly visible. Many popular version control systems provide free repositories to students. ...

...valent definitions of the set cover problem. We take the '''hitting set''' version.) ...

...valent definitions of the set cover problem. We take the '''hitting set''' version.) ...

The following is the weighted version of set cover problem: ...

...T) problem], which is NP-hard. The decision version of one of the weighted version of the problem is one of the [http://en.wikipedia.org/wiki/Karp%27s_21_NP-c ...

...s hard to compute, because it is '''NP-complete'''. Actually, the weighted version of max-cut is among the [http://en.wikipedia.org/wiki/Karp's_21_NP-complete ...clauses are true. The maximum satisfiability (MAXSAT) is the optimization version of SAT, which ask for an assignment that the number of satisfied clauses is ...

...a diagram of dots (or squares), called a '''Ferrers diagram''' (the square version of Ferrers diagram is also called a '''Young diagram''', named after a stru |align=center|Ferrers diagram (''dot version'') of (5,4,2,1)|| ...

...ath>S</math>. The expansion property can be interpreted as a combinatorial version of [http://en.wikipedia.org/wiki/Isoperimetric_inequality isoperimetric ine ...

|Definition (martingale, general version)| |Azuma's Inequality (general version)| ...

...a diagram of dots (or squares), called a '''Ferrers diagram''' (the square version of Ferrers diagram is also called a '''Young diagram''', named after a stru |align=center|Ferrers diagram (''dot version'') of (5,4,2,1)|| ...

[https://arxiv.org/pdf/1709.05143.pdf Variable Version Lovász Local Lemma: Beyond Shearer's Bound]<br>[https://arxiv.org/pdf/1804. [https://arxiv.org/abs/1709.05143 Variable Version Lovász Local Lemma: Beyond Shearer's Bound] ...

...d his work in 1647, while Cavalieri published his in 1635 with a corrected version appearing in 1653. Cavalieri first used polar coordinates to solve a proble ...

We consider the the optimization version of SAT, which ask for an assignment that the number of satisfied clauses is ...

...For any <math>\lambda<0</math>, by the same analysis as in the upper tail version, ...

We consider the the optimization version of SAT, which ask for an assignment that the number of satisfied clauses is ...

The following is the weighted version of set cover problem: ...

...a diagram of dots (or squares), called a '''Ferrers diagram''' (the square version of Ferrers diagram is also called a '''Young diagram''', named after a stru |align=center|Ferrers diagram (''dot version'') of (5,4,2,1)|| ...

...a diagram of dots (or squares), called a '''Ferrers diagram''' (the square version of Ferrers diagram is also called a '''Young diagram''', named after a stru |align=center|Ferrers diagram (''dot version'') of (5,4,2,1)|| ...

...a diagram of dots (or squares), called a '''Ferrers diagram''' (the square version of Ferrers diagram is also called a '''Young diagram''', named after a stru |align=center|Ferrers diagram (''dot version'') of (5,4,2,1)|| ...

...a diagram of dots (or squares), called a '''Ferrers diagram''' (the square version of Ferrers diagram is also called a '''Young diagram''', named after a stru |align=center|Ferrers diagram (''dot version'') of (5,4,2,1)|| ...

...a diagram of dots (or squares), called a '''Ferrers diagram''' (the square version of Ferrers diagram is also called a '''Young diagram''', named after a stru |align=center|Ferrers diagram (''dot version'') of (5,4,2,1)|| ...

...a diagram of dots (or squares), called a '''Ferrers diagram''' (the square version of Ferrers diagram is also called a '''Young diagram''', named after a stru |align=center|Ferrers diagram (''dot version'') of (5,4,2,1)|| ...

...a diagram of dots (or squares), called a '''Ferrers diagram''' (the square version of Ferrers diagram is also called a '''Young diagram''', named after a stru |align=center|Ferrers diagram (''dot version'') of (5,4,2,1)|| ...

...a diagram of dots (or squares), called a '''Ferrers diagram''' (the square version of Ferrers diagram is also called a '''Young diagram''', named after a stru |align=center|Ferrers diagram (''dot version'') of (5,4,2,1)|| ...

...a that describes the spring is exactly the same as the Newtonian mechanics version except only certain energies or energy levels are allowed. Think of the ene ...

|Definition (martingale, general version)| ...

|Definition (martingale, general version)| ...

|Definition (martingale, general version)| ...

|Definition (martingale, general version)| ...

|Definition (martingale, general version)| ...

We will prove a general version of the local lemma, where the events <math>A_i</math> are not symmetric. Th This gives the symmetric version of local lemma. ...

...s hard to compute, because it is '''NP-complete'''. Actually, the weighted version of max-cut is among the [http://en.wikipedia.org/wiki/Karp's_21_NP-complete ...

...nce of 1 can be replaced by arbitrary constants, which gives a generalized version of Lipschitz condition. |Definition (Lipschitz condition, general version)| ...

:Define the '''decision version''' of the minimum cut problem as follows. For a graph <math>G</math>, <math ...