How to Prove that you Reached the Pole

How to prove that a preconditioner cannot be superlinear

In the general case of multilevel Toeplitz matrices, we recently proved that any multilevel circulant preconditioner is not superlinear (a cluster it may provide cannot be proper). The proof was based on the concept of quasi-equimodular matrices, although this concept does not apply, for example, to the sine-transform matrices. In this paper, with a new concept of partially equimodular matrices...

How to Prove That a Committed Number Is Prime

The problem of proving a number is of a given arithmetic format with some prime elements, is raised in RSA undeniable signature, group signature and many other cryptographic protocols. So far, there have been several studies in literature on this topic. However, except the scheme of Camenisch and Michels, other works are only limited to some special forms of arithmetic format with prime element...

How to Prove That a Preconditioner Cannot Be Superlinear

In the general case of multilevel Toeplitz matrices, we recently proved that any multilevel circulant preconditioner is not superlinear (a cluster it may provide cannot be proper). The proof was based on the concept of quasi-equimodular matrices, although this concept does not apply, for example, to the sine-transform matrices. In this paper, with a new concept of partially equimodular matrices...

How To Prove Theorems Formally

3 How to Prove Important

In this paper, we show that a variety of important philosophical claims that Saul Kripke has advanced in his work are either provable in, or validated by, the theory of abstract objects (hereafteròbject theory'). 1 We'll investigate both metaphysical claims and claims concerning language which appear in Kripke's work. To establish that one of Kripke's metaphysical claims is provable in object t...