Sentence examples for trace is proved from inspiring English sources

For a locally modular JW-algebra the existence of a faithful semifinite normal trace is proved.

When the electrical signal transmitted in a unit length of the conductors or printed circuit traces, it is proved that there will be a certain time delay between terminal and signal source (called propagation delay unit, tp), which is proportional to the square root of the dielectric permittivity of the signal channel insulate material.

Therefore, the correctness of the tracking and ray tracing equations for the target-aligned heliostat is proved.

It is proved that for this functional calculus the trace formula of Helton-Howe holds.

Moreover, we combine the Birman Solomyak approach with the observation that for (fin B_{infty,1}^1({mathbb R})), the function (tmapsto f(A+t B-A))), (tin {mA+t B-A}), is continuously differentiable in the trace norm (this can be proved in the same way as Theorem 1.5.1) and the Daletskii–Krein formula holds for the derivative of this operator function.

Industry officials maintain that these substances are scrupulously controlled and are released from PVC in trace amounts that have not been proved harmful.

Using a ray tracing technique (deterministic), Rician parameters (statistical) were proved to be related to building height, street width and other terrain parameters.

In this paper, two results concerning the trace of powers of the Oriented Markov Matrix are proved.

Third hydroxylation was proved by the detection of traces of 1,2,4-trihydroxybenzene and hydroxy-p-benzoquinone (Figure 1).

It partially degrades under the heat process to form trace amounts of semicarbazide, which shows carcinogenicity and has been proved to cause tumors [ 1].

The developed program of backward tracing technique is implemented to the hydroforming process in a square and a rectangular die and has been proved to be effective.