Hall Property Research Articles

Temperature‐Dependent Electronic Transport in Non‐Bulk‐Resistance‐Variation Nitrogen‐Doped Cr2Ge2Te6 Phase‐Change Material

The electronic transport mechanism of the nitrogen‐doped Cr2Ge2Te6 (NCrGT) phase‐change material (PCM) is studied, showing almost zero resistivity variation upon phase transition. A similar low‐temperature variable‐range hopping (VRH) behavior in both the amorphous and crystalline phases of the NCrGT PCM is observed by measuring the temperature‐dependent resistivity. At high temperatures above 300 K, the conduction mechanism in the amorphous NCrGT is thermally activated band conduction, while the carrier transport in the crystalline NCrGT is still driven by VRH. Moreover, Hall property measurements reveal a thermally activated carrier in the amorphous NCrGT and mobility‐driven hopping conduction in the crystalline NCrGT at a high temperature range from 300 to 400 K. The conduction mechanism difference between the amorphous and crystalline NCrGT/tungsten (W) contacts is further investigated by measuring the temperature‐dependent I–V characteristics. The conduction in the amorphous NCrGT/W contact is dominated by thermionic‐field emission, while the transport mechanism through the crystalline NCrGT/W interface is controlled by the defect‐assisted tunneling current. Such noticeable conduction mechanism variation results in a large contact resistance contrast in a memory cell.

Formations of finite groups with the M. Hall property

The first examples of formations which are arboreous (and therefore Hall) but not freely indexed (and therefore not locally extensible) are found. Likewise, the first examples of solvable formations which are freely indexed and arboreous (and therefore Hall) but not locally extensible are constructed. Some open questions are also mentioned.

Digital watermarking using Hall property image decomposition method

Most of the existing singular value decomposition-based digital watermarking methods are not robust to geometric rotation, which change the pixels’ locations without maintaining the corresponding changes to the pixel’s intensity values of entire image and yield high computational cost. To answer this, we propose a digital image watermarking algorithm using the Hall property. In the proposed method, a digital watermark image is factorized into lower-triangular, upper-triangular, and permutation matrices. The permutation matrix is used as the valid key matrix for authentication of the rightful ownership of the watermark image. The product of the lower and upper triangular matrices is processed with a few iterations of the Arnold transformation to obtain the scrambled data. The scrambled data are embedded into particular sub-bands of a cover image using Wavelet transform. Our experiments show that the proposed algorithm is highly reliable and computationally efficient compared with state-of-the-art methods that are based on singular value decomposition.

Orbital engineering of two-dimensional materials with hydrogenation: A realization of giant gap and strongly correlated topological insulators

Orbital interaction plays an important role in topological insulators. Using first-principles calculations, we demonstrate that hydrogenation can change two-dimensional (2D) trivial insulator/semimetal-like Pb, Mo, and W to a ${Z}_{2}$ topological insulator with giant gaps by filtering unwanted orbitals such as the ${p}_{z}$ orbital in Pb, and the ${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ in Mo and W. For PbH, the large intrinsic spin-orbit coupling (SOC) confined in the in-plane orbitals ${p}_{x,y}$ results in a bulk gap of 1.07 eV. For the case of MoH and WH, hydrogenation results in a novel $s{d}^{4}$ hybridization with a Dirac cone formed by the out-of-plane orbital ${d}_{yz/xz}$ orbitals. Furthermore, due to the electron-electron interaction and the strong SOC in the $4d$ and $5d$ elements, the bulk band gap is significantly enhanced with a value of 1.28 eV for MoH and 0.30 eV for WH. The strong correlation effect also induces several topological phase transitions in WH like the Dirac semimetal and Mott insulating phase, while MoH remains a topological insulator even with large correlation effect. We propose that these new strongly correlated 2D materials can be realized experimentally by using substrate such as the boron nitride sheet, which can exhibit various novel properties such as the Dirac semimetal phase with large spin-orbit energy splitting as well as the quantum spin Hall property.

Finite groups whose maximal subgroups have the hall property

We study the structure of finite groups whosemaximal subgroups have the Hall property. We prove that such a group G has at most one non-Abelian composition factor, the solvable radical S(G) admits a Sylow series, the action of G on sections of this series is irreducible, the series is invariant with respect to this action, and the quotient group G/S(G) is either trivial or isomorphic to PSL2(7), PSL2(11), or PSL5(2). As a corollary, we show that every maximal subgroup of G is complemented.

Symbolic and Exact Structure Prediction for Sparse Gaussian Elimination with Partial Pivoting

In this paper we consider two structure prediction problems of interest in Gaussian elimination with partial pivoting of sparse matrices. First, we consider the problem of determining the nonzero structure of the factors L and U during the factorization. We present an exact prediction of the structure that identifies some numeric cancellations appearing during Gaussian elimination. The numeric cancellations are related to submatrices of the input matrix A that are structurally singular, that is, singular due to the arrangements of their nonzeros, and independent of their numerical values. Second, we consider the problem of estimating upper bounds for the structure of L and U prior to the numerical factorization. We present tight exact bounds for the nonzero structure of L and U of Gaussian elimination with partial pivoting $PA = LU$ under the assumption that the matrix A satisfies a combinatorial property, namely, the Hall property, and that the nonzero values in A are algebraically independent of each other. This complements existing work showing that a structure called the row merge graph represents a tight bound for the nonzero structure of L and U under a stronger combinatorial assumption, namely, the strong Hall property. We also show that the row merge graph represents a tight symbolic bound for matrices satisfying only the Hall property.

Finite π-solvable groups whose maximal subgroups have the Hall property

Properties of an arbitrary finite π-solvable group whose maximal subgroups are Hall subgroups are established.

On the row merge tree for sparse LU factorization with partial pivoting

We consider the problem of structure prediction for sparse LU factorization with partial pivoting. In this context, it is well known that the column elimination tree plays an important role for matrices satisfying an irreducibility condition, called the strong Hall property.

Varieties of finite supersolvable groups with the M. Hall property

The varieties in the title are shown to be precisely the product varieties Gp*Ab(d) for some prime p and some positive integer d dividing p−1. Here Gp denotes the variety of all finite p-groups and Ab(d) the variety of all finite Abelian groups of exponent dividing d. It turns out that these are exactly those varieties H of supersolvable groups for which all finitely generated free pro-H groups are freely indexed in the sense of Lubotzky and van den Dries. Several alternative characterizations of these varieties are presented. Some applications to formal language theory and finite monoid theory are also given. Among these is the determination of all supersolvable solutions H to the equations PH = J*H and J*H = JOpen image in new windowH which is, to the present date, the most complete solution to a problem raised by Pin. Another consequence of our results is that for each such variety H the monoid variety PH = J*H = JOpen image in new windowH has decidable membership.

Exact Prediction of QR Fill-In by Row-Merge Trees

Row-merge trees for forming the QR factorization of a sparse matrix A are closely related to elimination trees for the Cholesky factorization of AT A. Row-merge trees predict the exact fill-in (assuming no numerical cancellation) provided A satisfies the strong Hall property, but overestimate the fill-in in general. However, here a fast and simple postprocessing step for row-merge trees is presented that predicts the exact fill-in for sparse QR factorization using Householder reflectors for general matrices.

Global Astrometric Solutions with Sparse Matrix Techniques

AbstractModern astrometric techniques lead to large, linear systems solved by the precepts of least-squares. These systems are usually sparse, and one should take advantage of the sparsity to facilitate their solution. As long as the matrix A of the equations of condition possesses the weak Hall property, characteristic of linear systems derived from astrometric reductions, it is possible to find a sparse Cholesky factor. Before the equations of condition are accumulated, by use of the fast Givens transformation, a symbolic factorization of A using Tewarson’s length of intersection technique determines the ordering of the columns of A that result in low fill-in. The non-null elements are stored in a sparse, dynamic data structure by use of dynamic hashing. Numerical experimentation shows that this competes well with alternatives such as nested dissection, and large, but sparse, linear systems with several thousand unknowns can be solved in a reasonable amount of time, even on personal computers.

The strong Hall property and symmetric chain orders

Let G=( X, Y; E) be a bipartite graph with | X|⩾| Y|. For A⊆ X, write φ( A)=| A|−| N( A)| and for a⩽| X|, define φ(a)= max{φ(A) | A⊆X, |A|=a} . The graph G is said to have the strong Hall property if φ( a)+ φ( b)⩽| X|−| Y| for all nonnegative integers a and b with a+ b⩽| X|. We shall prove that any unimodal and self-dual poset with the strong Hall property is a symmetric chain order. This result will also be used to show that the inversion poset S 5 is a symmetric chain order.

Patterns that preserve sparsity in orthogonal factorization

An m × n zero-nonzero pattern A with the Hall property allows a full rank matrix A ϵ A with a QR factorization. The union of patterns occurring in Q over all such A is denoted by Q . By further restricting A to have the strong Hall property, a Hasse diagram that is a forest is used to characterize patterns A that yield Q = A , thus preserving the sparsity of A . For fixed n, the sparsest n × n such patterns are characterized by a binary rooted tree.

Hall Effect in Fe–Cr–Co Alloy Thin Films

This paper presents the Hall effect and microstructure of Fe–XCr–10Co, Fe–XCr–Co (weight ratio WFe/WCo=1), and Fe–60Cr–XCo alloy films. After deposition by ion beam sputtering (IBS), the Hall voltage (VH) and Hall coefficient (RH) values of the as-deposited films were found to be small. After heat treatment, phase separation into α1 (ferromagnetic phase) and α2 (paramagnetic phase) was observed and verified by high resolution transmission electron microscope (HRTEM). By aging the Fe–60Cr–15Co films at 550° C for 80 min, we found the maximum Hall resistivity (ρH) and Hall voltage (VH) values which are 30 µ Ω· cm and 1.2 mV, respectively (measured at 77 K and 14 kOe). The extraordinary Hall coefficient (RS) is about 0.408 cm3/C. The Hall coefficient is positive for both as-deposited and annealed films. The alloy composition and heat treatment condition which influence film's microstructure obviously affect the Hall property.

Ordering Givens Rotations for Sparse $QR$ Factorization

The $QR$ factorization of a large, sparse matrix A is frequently computed using Givens rotations. The precise order in which the rotations are applied can affect the amount of storage required. We present an ordering for the Givens rotations that, when A has the Hall property, is optimal with regard to storage for Q (a so-called “tight” ordering) and that preserves sparsity by restricting fill to those locations in R that are necessarily nonzero. This ordering is of particular interest when A does not have the strong Hall property and is not permuted into block upper trapezoidal form. We describe a bipartite graph model of sparse matrix structures and summarize the characterization of the structures of the factors Q and R. We define the product of structures of matrices, determine the product of the structures of a sequence of Givens rotations, and specify a tight ordering for these transformations.

Almost free groups and the M. Hall property

Almost free groups and the M. Hall property

Sparsity Analysis of the $QR$ Factorization

Given only the zero–nonzero pattern of an $m \times n$ matrix A of full column rank, which entries of Q and which entries of R in its $QR$ factorization must be zero, and which entries may be nonzero? A complete answer to this question is given, which involves an interesting interplay between combinatorial structure and the algebra implicit in orthogonality. To this end some new sparse structural concepts are introduced, and an algorithm to determine the structure of Q is given. The structure of R then follows immediately from that of Q and A. The computable zero/nonzero structures for the matrices Q and R are proven to be tight, and the conditions on the pattern for A are the weakest possible (namely, that it allows matrices A with full column rank). This complements existing work that focussed upon R and then only under an additional combinatorial assumption (the strong Hall property).

Finitely generated groups with M. Hall property

Finitely generated groups with M. Hall property

Oxidation in a molybdenite deposit, Nye County, Nevada

The Hall Molybdenum deposit near Tonopah, Nevada, has been developed for 1,200 feet in length, and has an average width of 53 feet. It lies in schist along the southern margin of an alaskite stock. Molybdenite, its oxidation product ferrimolybdite, pyrite, chalcopyrite, and limonitic ocher are associated with abundant quartz veins in the contact zone.The region is arid, and the topography is of moderate relief.The oxidized zone is 95 to 150 feet deep, and the bottom of oxidation parallels the surface drainage gradient. The water table lies below the lowest workings, which are 200 feet beneath the bottom of oxidation.In the oxide zone 30 to 40 per cent of the total molybdenum is in the form of sulphide, whereas in the sulphide zone 87 per cent or more of the metal is present in that form. Total assay values, however, show no significant change in passing from one zone to the other.Conditions at the Hall Property favored thorough oxidation, but molybenite oxidizes slowly, and the metal clearly does not migrate readily in any form. In comparison with other molybdenite deposits, oxidation of the Hall orebody has more than average relative importance.The amount and depth of oxidation of molybdenite should be carefully considered in the examination of prospects, because no commercial process has been put in use to recover the metal from the oxide.