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It may be used to prove Nicomachus's theorem that the sum of the first cubes equals the square of the sum of the first positive integers. [2] Summation by parts is frequently used to prove Abel's theorem and Dirichlet's test.
The default ordering is in ascending order, to reverse the order, the OrderByDescending operator is to be used. ThenBy and ThenByDescending specifies subsequent ordering of the elements. The function to extract the key value from the object is specified by the user as a delegate. Reverse The Reverse operator reverses a collection. GroupBy
The colon comes from a general Scala syntax mechanism whereby the apparent infix operator is invoked as a method on the left operand with the right operand passed as an argument, or vice versa if the operator's last character is a colon, here applied symmetrically. Scala also features the tree-like folds using the method list.fold(z)(op). [11]
Cubes (OLAP server) is another lightweight open-source toolkit implementation of OLAP functionality in the Python programming language with built-in ROLAP. ClickHouse is a fairly new column-oriented DBMS focusing on fast processing and response times. DuckDB [32] is an in-process SQL OLAP [33] database management system.
One can think that the Karhunen–Loève transform adapts to the process in order to produce the best possible basis for its expansion. In the case of a centered stochastic process {X t} t ∈ [a, b] (centered means E[X t] = 0 for all t ∈ [a, b]) satisfying a technical continuity condition, X admits a decomposition
U.S. consumers who were “tricked” into purchases they didn't want from Fortnite maker Epic Games are now starting to receive refund checks, the Federal Trade Commission said this week. Back in ...
The WNBA and the league's players union met in person Wednesday to discuss a new collective bargaining agreement. “Today’s meeting included preliminary conversations and constructive dialogue ...
[230] [231] Some authors regard a point process and stochastic process as two different objects such that a point process is a random object that arises from or is associated with a stochastic process, [232] [233] though it has been remarked that the difference between point processes and stochastic processes is not clear.