Sentence examples for define the restricted from inspiring English sources

Let σ s ( N ) = ∑ d | N d s, and let us define the restricted divisor function σ s, r ( N ; m ) = ∑ d | N d ≡ r mod m d s.

where π p ˆ : L 2 → S denotes the orthogonal projection from L 2 onto S. We define the restricted stochastic weak form of (34) by ( ∂ ∂ t x ˜ ( t, w ), Ψ ( w ) ) = ( f ˜ ( x ˜ ( t, w ), w ), Ψ ( w ) ) (35). for all Ψ ∈ S. Equation (35) can be written as a system of ordinary differential equations (ODEs) for the coefficients { q ˜ i } i ≤ p ˆ : d d t q ˜ i ( t ) = ( f ˜, Ψ i ) for  i ≤ p ˆ. (36).

A concise nomenclature defining the restricted rotational phenomena about the newly created C s-triazine)–N(exoC s-triazineial double boN exocyclics axes of (partialstereomerism, is usedouble

Flood flow zones (FFZ), high value agricultural land and retention ponds are defined as the restricted areas in Dhaka metropolitan development plan (DMDP) (shown in Fig. 4).

Of course, these results are by no means right because the boundary condition between the Rf core/IPDU intermediate-layer region and the PEG water phase does not satisfy that defined for the restricted diffusion.

Generally, the ruffles, prints and romantic detailing that so define the hippy-dippy aesthetic are restricted to just those summer months, and are packed away at the end of the heady days and hot nights.

In the discounted MDPs, Abbad and Daoui (2003) define and construct by induction the restricted MDP pk corresponding to each SCC C pk in level L p, as follows.

A particular control structure design will define (restrict) the future operability degree for the plant under study.

The requirement of two colors to define genotype restricts the number of SNP sites that can be genotyped in multiplexed fashion in single-tube format given the limit on the number of fluorophores than can be simultaneously monitored in today's fluorimeters.

Instead, they propose the following rule: that should introduce relative clauses that define and restrict the preceding noun.

We define f' restricted to G to equal f and let f'(Ee+1) = PEe+1- E k Pf (E k ).