Sentence examples for defined in the sense of from inspiring English sources

The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative.

The integral in (2) is defined in the sense of Hadamard finite-part integral for (m>1).

Recently, Agrawal [10] presented an eigenfunction expansion approach for a class of distributed system whose dynamics is defined in the sense of Caputo.

Our result of Section 3 will guarantee that there is a solution y of inequality (4) close to the measured output x and closeness is defined in the sense of generalized Ulam-Hyers-Rassias stability.

That is, some functional in terms of a norm of the solution defined in the sense of Theorem 2.1 satisfies a differential inequality that necessarily implies that such norm blows up in finite time.

In this paper, we establish a finite difference scheme for a class of time fractional parabolic equations with variable coefficient, where the time fractional derivative is defined in the sense of the Caputo derivative.

Here the optimality is defined in the sense that the variance of the important weights is minimized.

The PHR augmented Lagrangian of (16) is well defined, in the sense that it ensures the typical properties of ordinary Lagrangians of convex functions, i.e., the zero duality gap property and the applicability of a saddle point theorem.

Mental health problems were defined in the broadest sense of the word, from minor mental health problems to severe psychopathology.

Physicians were defined in the general sense of having completed a requisite six-year medical school programme plus a one-year internship, rather than possessing specialist qualifications, and this definition is used throughout this manuscript.

We propose here an analytical framework that reduces to the WHO fixed-weight methodology as a special case, but that allows varying degrees of freedom for weights to be defined that – in the sense of Melyn and Moesen – implicitly take into account individual country circumstances.