Sentence examples for theory q from inspiring English sources

At the base one has the very weak theory Q and one climbs upward by adding "closure principles".

As a response to the Bezboruah and Sheperdson result, Pudlák gives (1996) an intensionally correct consistency statement for Robinson's theory Q, which Q fails to prove.

This form of pluralism is difficult to articulate since, for example, assuming that Q is consistent the theory Q + ¬Con(Q) is consistent.

For rod-shaped particles, the exponents do not initially follow Rayleigh scattering theory (q = 2) because the rods are simulated with a complex refractive index (absorption) and with a length significantly longer than the wavelength of light, where Rayleigh theory fails.

(1.2) In [6], the Kantorovich type of the Szász-Mirakjan operators was defined as K_{n}(f,x =ne^{-nx}sum _{k=0}^{infty}frac{(nx)^{k}}{k!} int_{frac{k}{n}}^{frac{k+1}{n}}f(t),x =ne^{-nx}sume f is a continuous nondecreasing function on ([0,infty)). In the field of approximation theory, q-calculus plays an important role.

Therefore, it follows from (2.28) and the classical result of the Lebesgue theory that q ( t ) is the classical derivative of D α ( u ( t ) ) a.e. on [ 0, T ] which means that (i) in Definition 2.9 is verified.

Recently, the Nevanlinna theory involving q-difference has been developed to study q-difference equations and q-difference polynomials.

In this paper, using the theory of q-fractional calculus, we deal with the q-Mittag-Leffler stability of q-fractional differential systems, and based on it, we analyze the direct Lyapunov method of q-fractional differential systems.

In this paper, we propose the q-Mittag-Leffler stability and the q-fractional Lyapunov direct method with a hope to enrich the knowledge of the theory of q-fractional calculus.

The basic theory of q-symmetric quantum calculus needs to be explored.

The basic theory of q-symmetric quantum calculus operators need be explored.