Sentence examples for basic properties for the from inspiring English sources

Table 2 shows the basic properties for the numerical analysis.

Remark 2.1 The following basic properties for the Banach space E and for the normalized duality mapping J can be found in Cioranescu [23].

Remark 1.1 The following basic properties for the Banach space X and for the normalized duality mapping J can be found in Cioranescu [1].

In this section, we state some basic properties for the generalized Apostol-Euler polynomials E n [ m − 1, α ] ( x ; λ ) defined by (1.8).

To do this, we consider some of the basic properties for the integral operator corresponding to problem (P λ ) in the setting of weighted Sobolev spaces.

In this paper, we extend the results of the above classes to the classes HST ( ϕ, χ, k, α ) and HST ¯ ( ϕ, χ, k, α ), we also obtain some basic properties for the class HST ¯ ( ϕ, χ, k, α ).

The basic properties for fast system (6), including the existence of infection-free equilibrium (B_{0}), infected equilibrium (B^) (when (E=0)) and infected equilibrium (B_{1}) (when (E>0)), the positivity and ultimate boundedness of the solutions with positive initial values, are established.

The following basic properties for Banach space E and for the normalized duality mapping J can be found in Cioranescu [1].

The basic properties for modification to be implemented in the non-separable structure shown in Fig. 8a, b have different lifting procedures but are equivalent as shown in Eqs.

One of the basic properties for harmonic self-mappings of ({mathbb {D}}) is the Heinz inequality [4].

In order to prove the main theorems, we need the following lemma which includes the basic properties for stochastic domination.