subset

Examples of subset in the following topics:

• Total Number of Subsets

  • The total number of subsets is the number of sets with 0 elements, 1 element, 2 elements, etc.
  • The number of subsets containing $k$ elements is represented by ($n^k$).
  • The total number of subsets of a set with $n$ elements is $2^n$.
  • For example, how many subsets are in the set: $\left \{ P, Q, R, S, T, U \right \}$ ?
  • It has 6 elements, therefore, $2^n=2^6=64$ subsets.

• Shape

  • In geometry, two subsets of a Euclidean space have the same shape if one can be transformed to the other by a combination of translations, rotations (together also called rigid transformations), and uniform scalings.
  • Having the same shape is an equivalence relation, and accordingly a precise mathematical definition of the notion of shape can be given as being an equivalence class of subsets of a Euclidean space having the same shape.
  • Shapes of physical objects are equal if the subsets of space these objects occupy satisfy the definition above.

• Regulatory T Cells

  • Regulatory T cells are a subset of T cells which modulate the immune system and keep immune reactions in check.
  • An additional regulatory T cell subset, induced regulatory T cells, are also needed for tolerance and suppression.
  • Though iTreg and nTreg cells share a similar function iTreg cells have recently been shown to be an essential non-redundant regulatory subset that supplements nTreg cells, in part by expanding TCR diversity within regulatory responses.

• Spaces Associated with a linear system Ax = y

  • The span of the columns is a subset of $\mathbf{R}^{n}$ and the span of the rows is a subset of $\mathbf{R}^{m}$ .

• Random Samples

  • Sampling is concerned with the selection of a subset of individuals from within a statistical population to estimate characteristics of the whole population .
  • A simple random sample is a subset of individuals chosen from a larger set (a population).
  • Each individual is chosen randomly and entirely by chance, such that each individual has the same probability of being chosen at any stage during the sampling process and each subset of $k$ individuals has the same probability of being chosen for the sample as any other subset of $k$ individuals.
  • MIME types of a random sample of supplementary materials from the Open Access subset in PubMed Central as of October 23, 2012.

• Impact of Dividend Policy on Clientele

  • Of those who prefer dividends over capital gains, there are further subsets of clientele; for example, investors might prefer a stock that pays a high dividend, while another subset might look for a balance between dividend payout and reinvestment in the company.
  • After all, clientele can just choose to sell off their holdings if they dislike a firm's policy change, and the firm may simultaneously attract a new subset of clientele who like the policy change.

• Vector Fields

  • A vector field is an assignment of a vector to each point in a subset of Euclidean space.
  • In vector calculus, a vector field is an assignment of a vector to each point in a subset of Euclidean space.

• Introduction to The Four Fundamental Spaces

  • The technical definition of a subspace is that it is a subset closed under addition and scalar multiplication:
  • A subspace of a vector space is a nonempty subset $S$ that satisfies

• Optimization

  • One subset is the engineering optimization, and another recent and growing subset of this field is multidisciplinary design optimization, which, while useful in many problems, has in particular been applied to aerospace engineering problems.

• Cancer and Post-Transcriptional Control

  • It appears that the subset of miRNAs expressed in breast cancer cells is quite different from the subset expressed in lung cancer cells or even from normal breast cells.