Sentence examples for concerning the traces from inspiring English sources

The paper proves two theorems concerning the traces of Oriented Markov Matrices of vertex maps on graphs.

First, we state some basic results concerning the trace of the Oriented Markov Matrix.

The goal of the next two sections is to prove results concerning the trace of M f).

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

The remaining part of the schema captures the information concerning the simulated traces and time.

Using the convergence results from [JL2] concerning the regularized heat trace on finite volume hyperbolic Riemann surfaces, we shall prove the following results.

Subsequent improvements in histological staining methods allowed for new discoveries concerning the distribution of trace metals throughout tissues.

If τ ( 1 ) = 1, that is to say, we consider the von Neumann algebra ℳ to be equipped with normal faithful finite unital trace, then we can also get the following noncommutative analog of the variational inequality and we refer the readers to Theorem 2.5 of [3] for more details of the Carlen-Lieb theorems concerning the concavity of certain trace functions.

No significant differences can be traced concerning the thyroid function between different clinical subtypes of depression nor there is any correlation between specific clinical symptoms and thyroid indices.

Concerning the other STS, either trace activity (PtTPS5, PtTPS7, and PtTPS9) or no activity (PtTPS8, PtTPS14) was observed with GPP (data not shown).

These quarries are an excellent opportunity for observation and research concerning the "landscape archives" and preserve traces of man's activity, representing a real cultural heritage.