Sentence examples for element of the integral from inspiring English sources

To establish formula (1.5.1), we can represent the divided difference (mathfrak {D}f) as an element of the integral projective tensor product begin{aligned} (mathfrak {D}f)(s_1,s_2)=int varphi _x(s_1)psi _x(s_2),dsigma (x), end{aligned}where (sigma ) is a (sigma )-finite measure and begin{aligned} int Vert varphi _xVert _{L^infty }Vert psi _xVert _{L^infty },dsigma (x)

Put begin{aligned} u_kmathop limits ^{mathrm {def}}Rleft( int gamma _k,dE_3right) fquad hbox {and}quad v_jmathop limits ^{mathrm {def}}T^*left( int overline{alpha _j},dE_1right) g. end{aligned} (3.2.6)We consider the vectors (v_j) and (u_k) as elements of the direct integral (3.2.4), i.e., vector functions on ({mathscr {X}}_2).

The experimental and FE simulation results of the flexible element and the integral flexible structure indicate that the presented mechanical model is capable of capturing the linear behavior.

However, the triangle is the fundamental element of an integral in our triangular integral theory.

The 36 activities that make up the conceptual model are the minimum requirements for the functioning of the systems of human activities that considers cyber security and cyber defense, as an element of the security, defense and integral development of the Nation.

The stiffness of the Maxwell model's element is expressed in terms of the integral operator with the exponential kernel of relaxation and thus the relationship for the contact force takes the integral form with a function of relaxation.

The theory is based on the assumption that each element of integration in the Kirchhoff integral is a patch of a circular cylinder perpendicular to the plane of incidence.

It may not be her showiest or fullest performance, nor the most exquisite ("Guys and Dolls"), but it's perfectly integrated into the texture of the movie and an integral element of the methods of its director, Otto Preminger.

Bowie first physically encountered Yamamoto's work at Boston 151, the Fulham Road shop where he bought the platform-soled red patent leather boots which became one of the integral elements of the second-phase Ziggy look (arguably, as the promotion for his follow-up album Aladdin Sane kicked in).

Another benefit of the proposed method is the fact that neither polynomial expansions nor interpolations of the integral elements is needed and the resulting solution for the distribution functions is only endowed by the error of the second virial approximation.

They also believe that the commitment to civilian safety is one of the integral elements of Sri Lankan success.