in this paper, after collecting the rock samples from eight mines and one high way slope, the tests for determination of dry density, uniaxial compressive strength, tensile strength (brazilian test), elastic modulus, schmidt hammer rebound number have been done on samples. in addition, in order to calculating the mean size of rock grains, quartz content, hardness and abrasivity, a thin sections...

In this paper we introduce and study Besselian $g$-frames. We show that the kernel of associated synthesis operator for a Besselian $g$-frame is finite dimensional. We also introduce $alpha$-dual of a $g$-frame and we get some results when we use the Hilbert-Schmidt norm for the members of a $g$-frame in a finite dimensional Hilbert space.

This preprint is intended to provide a general reference for jet spaces and jet differentials, valid in maximal generality (at the level of EGA). The approach is rather concrete, using Hasse-Schmidt (divided) higher differentials. Discussion of projectivized jet spaces (as in Green and Griffiths [G-G]) is included. This paper contains a few brief notes on how to define jets using Hasse-Schmidt ...

(3) In addition to solutions for | k | ^ 9999, we have solutions, for y ^ 104 and | k | g 99999; there are 1221 for positive k and 799 for negative k. The vast majority of solutions are with y < 100 and Table 2 gives the number of solutions for various ranges of y. The fact that the number of solutions is a rapidly decreasing function of y suggests that for at least some k the solution set may ...

A Gram-Schmidt type algorithm is given for finite d-dimensional reflexive forms over division rings. The algorithm uses d/3 + O(d) ring operations. Next, that algorithm is adapted in two new directions. First a sequential algorithm is given whose complexity matches the complexity of matrix multiplication. Second, a parallel NC algorithm is given with similar complexity.

The Gram-Schmidt Process (GSP) is used to convert a non-orthogonal basis (a set of linearly independent vectors) into an orthonormal basis (a set of orthogonal, unit-length vectors). The process consists of taking each vector and then subtracting the elements in common with the previous vectors. This paper introduces an Enhanced version of the Gram-Schmidt Process (EGSP) with inverse, which is ...

Recent results, extending the Schmidt decomposition theorem to wavefunctions of pairs of identical particles, are reviewed. They are used to give a definition of reduced density operators in the case of two identical particles. Next, a method is discussed to calculate time averaged entanglement. It is applied to a pair of identical electrons in an otherwise empty band of the Hubbard model, and ...

We welcome and appreciate the comment by Braun and Schmidt on our recent correspondence about the gambler's fallacy in goalkeeper behaviour during penalty shoot-outs. Braun and Schmidt assert that the binomial is more appropriate for analysing the data than our resampling approach. Their analyses appear to assume that dive direction is binomially distributed with a probability of 0.5. In fact, ...

We prove that certain Gibbs measures on subshifts of finite type are nonsingular and ergodic for certain countable equivalence relations, including the orbit relation of the adic transformation (the same as equality after a permutation of finitely many coordinates). The relations we consider are defined by cocycles taking values in groups, including some nonabelian ones. This generalizes (half ...