Sentence examples for fundamental vector from inspiring English sources

Consequently, it induces a Killing vector field Z∗, called the fundamental vector field on M, given by Z q ∗ = d dt | 0 ( τ ( exp ( tZ ) ) ( q ) ), q ∈ M. Open image in new window.

This numerical technique is based on the use of time evolution equations for fundamental vector and tensor quantities defined on the front and represents a new and convenient way to couple the advantages of the Eulerian description given by a Level-Set function ϕ to the use of Lagrangian massless particles.

In the sequel it is assumed that the so-called principal BVP L x = f, r x = α (14) is uniquely solvable for any f ∈ B, α ∈ R n. Recall that in such a case we have the representation [[8]] (Theorem 1.16, p.11) x = X α + G f (15) to the solution of (2.10) with X called the fundamental vector and G called the Green operator.

To rule out a vector size effect on the reduction in electrotransformation efficiency (pSY6catP is 8,498 bp, whereas pMTL85141 is 2,963 bp), we also attempted to transform pHT3, a 7,377 bp vector with the same fundamental vector components as pMTL85141ermB, in addition to a heterologous lacZ gene from Thermoanaerobacterium thermosulfurogenes EM1 [ 49] (Table  2).

Let (mathbf{e}^{mathbf{j}}), (j=1,ldots,n), be the fundamental vectors of (mathbb{R}^{n}).

(iv) Finally, the national identity approach allows understanding the fundamental vectors that structure a country's approach to immigration regardless of the political system in place.

The contrast factor parameters are evaluated in terms of the fundamental Burgers vector types in hexagonal crystals.

Despite their differences, generalized linear systems have two fundamental operations: vector addition ⊕ and scalar multiplication ⊗, which are defined by using the generating function as follows: xoplus y=phi^{-1}left[phi(x)+phi y)right] (12).

An in depth understanding of mosquito breeding biology and factors regulating population sizes is fundamental for vector population control.

In this evaluation, we thus concentrate on these two fundamental attack vectors: The Database administrator (DBA) possesses administrator privileges on the database itself, including the ability to change logging routines and user rights, as well as read access to the underlying file system.

It is well known that VEP includes fundamental mathematical problems like vector optimization, vector variational inequality, and vector complementarity problem.