Arithmetic-arboreal residue structures induced by Prufer extensions : An axiomatic approach

We present an axiomatic framework for the residue structures induced by Prufer extensions with a stress upon the intimate connection between their arithmetic and arboreal theoretic properties. The main result of the paper provides an adjunction relationship between two naturally defined functors relating Prufer extensions and superrigid directed commutative regular quasi-semirings.Comment: 56 page

On the Importance of Displacement History in Soft-Body Contact Models

Two approaches are commonly used for handling frictional contact within the framework of the discrete element method (DEM). One relies on the complementarity method (CM) to enforce a nonpenetration condition and the Coulomb dry-friction model at the interface between two bodies in mutual contact. The second approach, called the penalty method (PM), invokes an elasticity argument to produce a frictional contact force that factors in the local deformation and relative motion of the bodies in contact. We give a brief presentation of a DEM-PM contact model that includes multi-time-step tangential contact displacement history. We show that its implementation in an open-source simulation capability called Chrono is capable of accurately reproducing results from physical tests typical of the field of geomechanics, i.e., direct shear tests on a monodisperse material. Keeping track of the tangential contact displacement history emerges as a key element of the model. We show that identical simulations using contact models that include either no tangential contact displacement history or only single-time-step tangential contact displacement history are unable to accurately model the direct shear test

Dynamic Graphs on the GPU

We present a fast dynamic graph data structure for the GPU. Our dynamic graph structure uses one hash table per vertex to store adjacency lists and achieves 3.4–14.8x faster insertion rates over the state of the art across a diverse set of large datasets, as well as deletion speedups up to 7.8x. The data structure supports queries and dynamic updates through both edge and vertex insertion and deletion. In addition, we define a comprehensive evaluation strategy based on operations, workloads, and applications that we believe better characterize and evaluate dynamic graph data structures

Factors Related to Declining Attendance at the Adult Sabbath School in the North American Division of Seventh-day Adventist Church

Problem. From the time of its inception in the 1850s until the early part of the 20th century, the Adventist Sabbath School in North America was highly attended. During those times Sabbath School reached the highest attendance rate when Sabbath School membership was sometimes even larger than church membership. Following that time, the attendance rate at Sabbath School has significantly declined. Currently it is estimated that less than 25% of the Seventh-day Adventist Church membership in North America attends Sabbath School on a regular basis. This study explores factors related to declining attendance at the adult Sabbath School in the North American Division of the Seventh-day Adventist Church. Purpose. The purpose of this study was to examine the relationships between Sabbath School Attendance in the North American Division of the Seventh-day Adventist Church and the following five groups of factors: Achievement, Satisfaction, Socio-cultural, Institutional, and General Perceptions. Methodology. This descriptive study employed non-experimental, quantitative survey methodology. The survey included 1,451 church members and 59 pastors in the Seventh-day Adventist Church, from a cluster sample in all nine unions in the North American Division. The statistical analysis utilized multiple one-way analysis of variance (ANOVA), correlation analysis, and Chi-square tests applied to a two-stage process to determine the relationship(s) between Sabbath School Attendance and the five groups of factors mentioned above. Results. In response to the 4,958 Member Surveys and 64 Pastor Surveys distributed, 1,451 (30%) Member Surveys and 59 (92%) Pastor Surveys were returned and correctly completed. The study revealed that seven out of eight Institutional Factors were significantly related to Sabbath School Achievement, and six out of the same eight Institutional Factors were related to Sabbath School Satisfaction. Furthermore, the study revealed that five out of eight Institutional Factors, five out of five Sabbath School Achievement and Sabbath School Satisfaction Factors, three out of six Socio-cultural Factors, and five out of six General Perception Factors were significantly related to Sabbath School Attendance. Conclusions. Although there is no simple answer to the declining attendance at the adult Sabbath School in North America, this study reveals that 23 out of 30 factors studied were significantly related to Sabbath School Attendance. The only common institutional factor related to Sabbath School Achievement, Sabbath School Satisfaction, and Sabbath School Attendance was Teaching Style. Those taught interactively are more likely to achieve more, be more satisfied, and attend Sabbath School more frequently

Domain wall in a chiral p-wave superconductor: a pathway for electrical current

Superconductors with p+ip pairing symmetry are characterized by chiral edge states, but these are difficult to detect in equilibrium since the resulting magnetic field is screened by the Meissner effect. Nonequilibrium detection is hindered by the fact that the edge excitations are unpaired Majorana fermions, which cannot transport charge near the Fermi level. Here we show that the boundary between p_x+ip_y and p_x-ip_y domains forms a one-way channel for electrical charge. We derive a product rule for the domain wall conductance, which allows to cancel the effect of a tunnel barrier between metal electrodes and superconductor and provides a unique signature of topological superconductors in the chiral p-wave symmetry class.Comment: 6 pages, 3 figure

Optimal control of time-dependent targets

In this work, we investigate how and to which extent a quantum system can be driven along a prescribed path in Hilbert space by a suitably shaped laser pulse. To calculate the optimal, i.e., the variationally best pulse, a properly defined functional is maximized. This leads to a monotonically convergent algorithm which is computationally not more expensive than the standard optimal-control techniques to push a system, without specifying the path, from a given initial to a given final state. The method is successfully applied to drive the time-dependent density along a given trajectory in real space and to control the time-dependent occupation numbers of a two-level system and of a one-dimensional model for the hydrogen atom.Comment: less typo

Strong coupling from the Hubbard model

It was recently observed that the one dimensional half-filled Hubbard model reproduces the known part of the perturbative spectrum of planar N=4 super Yang-Mills in the SU(2) sector. Assuming that this identification is valid beyond perturbation theory, we investigate the behavior of this spectrum as the 't Hooft parameter \lambda becomes large. We show that the full dimension \Delta of the Konishi superpartner is the solution of a sixth order polynomial while \Delta for a bare dimension 5 operator is the solution of a cubic. In both cases the equations can be solved easily as a series expansion for both small and large \lambda and the equations can be inverted to express \lambda as an explicit function of \Delta. We then consider more general operators and show how \Delta depends on \lambda in the strong coupling limit. We are also able to distinguish those states in the Hubbard model which correspond to the gauge invariant operators for all values of \lambda. Finally, we compare our results with known results for strings on AdS_5\times S^5, where we find agreement for a range of R-charges.Comment: 14 pages; v2: 17 pages, 2 figures, appendix and references added; typos fixed, minor changes; v3 fixed figures; v4 more references added, minor correctio