Sentence examples for corresponding cones from inspiring English sources

Let V be a Cartesian product of a finite number of simple Euclidean Jordan algebras ( V j, ∘ ) with dimensions n j and ranks r j for j = 1, …, N, that is, V = V 1 × ⋯ × V N with its cone of squares K = K 1 × ⋯ × K N, where K j are the corresponding cones of squares of V j for j = 1, …, N. The dimension of V is n = ∑ j = 1 N n j and the rank is r = ∑ j = 1 N r j.

The absorption spectra of the corresponding cones R, each coded by a single opsin gene with two alleles, were assumed to exhibit a normal distribution (Fig. 5a) for simplicity (standard deviation of the distribution was set at 24), although the exact shape of absorption spectra of visual pigments has a shoulder.

It is well known that if the cone is normal then the corresponding cone metric associates a metric.

For EJA (mathcal{J}), the corresponding cone of squares (mathcal{K}:={x^{2}:xinmathcal{J}}) is indeed a symmetric cone.

For any EJA V, the corresponding cone of squares K ( V ) : = { x 2 : x ∈ V } (12). is indeed a symmetric cone (cf. Theorem III.2.1 in [40]).

Recently many authors proved fixed point theorems for multivalued mappings on complete cone metric spaces assuming that the corresponding cone is regular or normal (see [13 20]).

Fixed point theorems of contractive mappings in cone b-metric spaces without the assumption of the normality of a corresponding cone are proved by Huang and Xu in [27].

Lemma 1.3 Let ( X, d ) be a cone metric space with corresponding cone P. If x ∈ P and { x n } and { a n } are sequences in X and A, respectively, then: (a) If θ ⪯ x ≪ c for all c ∈ int P, then x = θ.

If the coefficient occurring in the boundary conditions takes a negative value, then the existence of a positive solution for a BVP with ϕ-Laplacian operator is less considered because it is sometimes difficult to construct a corresponding cone for applying the fixed point theorem.

In the model here, the task of the ideal observer is to predict the reflectance of a previously unseen surface ('scene') given only the corresponding cone response functions ('image') and a finite set of previous observations ('experience'experience

These developmental comparisons confirmed previous results, which showed agreement between gene expression and the presence of corresponding cone types in adults (see [ 60] and Carleton et al. unpublished).