Sentence examples for an arbitrary field from inspiring English sources

But, with the creation of an abstract theory of fields, it was natural to want a theory of varieties defined by equations with coefficients in an arbitrary field.

Definition 8.2 Let K be an arbitrary field.

Let G be a finite group and K an arbitrary field.

Let (X, d) be a locally finite extended metric space as in Sect. 2 and (mathbb {K}) an arbitrary field.

The one given in [11] is purely algebraic, whereas the one proposed in [6] reduces the case of an arbitrary field to that of.

However, the argument utilized in the case is rather important as it inspired our proof for the case in [7] and therefore laid the foundation of the general result for an arbitrary field.

BP can be performed over any arbitrary field.

This paper presents a method for re-parameterization based on an arbitrary scalar field named the relaxation field.

A wafer shape modulation chuck that can address arbitrary field locations and sizes on a wafer with a novel actuation scheme that minimizes the number of actuators while increasing imprinting speed and reducing process defects significantly is presented.

They characterize the average linear network coding throughput for the combination network with min-cut 2 over an arbitrary finite field, and provide a network code, which is completely specified by the field size and achieves the average coding throughput for the combination network.

end{aligned} (2.28 where (zeta ) is an arbitrary spinor field.