Sentence examples similar to generalized day from inspiring English sources

First, we give a characterization of generalized Day-James spaces.

Hence, the space ( R 2, ∥ ⋅ ∥ ) is a generalized Day-James space.

Every two-dimensional real normed space is isometrically isomorphic to a generalized Day-James space.

Recently, Alonso showed that every two-dimensional normed space is isometrically isomorphic to a generalized Day-James space introduced by Nilsrakoo and Saejung.

Since the space R 2 endowed with a normal norm is a generalized Day-James space by Proposition 1, we have the result of Alonso as a corollary.

Proposition 1 Let ∥ ⋅ ∥ be a norm on R 2. Then the space ( R 2, ∥ ⋅ ∥ ) is a generalized Day-James space if and only if ∥ ⋅ ∥ ∞ ≤ ∥ ⋅ ∥ ≤ ∥ ⋅ ∥ 1. Proof If ( R 2, ∥ ⋅ ∥ ) is a generalized Day-James space, then one can easily have ∥ ⋅ ∥ ∞ ≤ ∥ ⋅ ∥ ≤ ∥ ⋅ ∥ 1.

It is proved that any two-dimensional normed space is isometrically isomorphic to a generalized Day-James space ℓ ψ -ℓ φ, introduced by W. Nilsrakoo and S. Saejung.

In 2006, Nilsrakoo and Saejung [9] introduced and studied generalized Day-James spaces ℓ φ - ℓ ψ, where ℓ φ - ℓ ψ is defined for φ, ψ ∈ Ψ 2 as the space R 2 endowed with the norm ∥ ( x, y ) ∥ φ, ψ = { ∥ ( x, y ) ∥ φ, if  x y ≥ 0, ∥ ( x, y ) ∥ ψ, if  x y ≤ 0. Recently, Alonso [10] showed that every two-dimensional normed space is isometrically isomorphic to a generalized Day-James space.

Included are generalized Mantel-Haenszel tests, estimators for a common odds ratio, and generalized Breslow-Day test for the homogeneity of odds ratios across the strata. Environ Health Perspect 102(Suppl 8): 57–60 (1994).

A 10-year-old girl presented with abdominal pain, vomiting, diarrhea, fever and developed generalized edema a day after admission.

In the course of the analysis, we introduce a generalized random 2-SAT formula, which is of self interest, and show its phase transition phenomenon.