फ़िल्टर-युक्त इसके अंग्रेजी अर्थ का उदाहरण

Thukpa (Nepali: थुक्पा) – boiled noodles, filtered and mixed with vegetables and/or various meat items.

From the mid-1980s, the drive to encourage the use of Pinyin filtered down to place names, resulting in some amendments.

From Egypt the rumour could have filtered to Athens through the Athenian general Chabrias who was then serving with Hakor as a military adviser.

Exciting news filtered in throughout the summer of 2009.

Wellington, Shropshire In mathematics, a filtered algebra is a generalization of the notion of a graded algebra.

A filtered algebra over the field k is an algebra (A,\cdot) over k that has an increasing sequence \{0\} \subseteq F_0 \subseteq F_1 \subseteq \cdots \subseteq F_i \subseteq \cdots \subseteq A of subspaces of A such that.

In general there is the following construction that produces a graded algebra out of a filtered algebra.

If A is a filtered algebra then the associated graded algebra \mathcal{G}(A) is defined as follows: .

An example of a filtered algebra is the Clifford algebra \operatorname{Cliff}(V,q) of a vector space V endowed with a quadratic form q.

The symmetric algebra on the dual of an affine space is a filtered algebra of polynomials; on a vector space, one instead obtains a graded algebra.

The universal enveloping algebra of a Lie algebra \mathfrak{g} is also naturally filtered.

Scalar differential operators on a manifold M form a filtered algebra where the filtration is given by the degree of differential operators.

The group algebra of a group with a length function is a filtered algebra.