Homotopy Method for the Large, Sparse, Real Nonsymmetric Eigenvalue Problem

A homotopy method to compute the eigenpairs, i.e., the eigenvectors and eigenvalues, of a given real matrix A1 is presented. From the eigenpairs of some real matrix A0, the eigenpairs of A(t) ≡ (1 − t)A0 + tA1 are followed at successive "times" from t = 0 to t = 1 using continuation. At t = 1, the eigenpairs of the desired matrix A1 are found. The following phenomena are present when following the eigenpairs of a general nonsymmetric matrix: • bifurcation, • ill conditioning due to nonorthogonal eigenvectors, • jumping of eigenpaths. These can present considerable computational difficulties. Since each eigenpair can be followed independently, this algorithm is ideal for concurrent computers. The homotopy method has the potential to compete with other algorithms for computing a few eigenvalues of large, sparse matrices. It may be a useful tool for determining the stability of a solution of a PDE. Some numerical results will be presented

Bilateral Anterior Shoulder Dislocation

Introduction: Unilateral anterior shoulder dislocation is one of the most common problems encountered in orthopedic practice. However, simultaneous bilateral anterior dislocation of the shoulders is quite rare. Case Presentation: We report a case of a 75-year-old woman presented with simultaneous bilateral anterior shoulder dislocation following a trauma, complicated with a traction injury to the posterior cord of the brachial plexus. Conclusions: Bilateral anterior shoulder dislocation is very rare. The excessive traction force during closed reduction may lead to nerve palsy. Clear documentation of neurovascular status and adequate imaging before and after a reduction should be performed

Proximal Fifth Metatarsal Fractures: Anatomy, Classification, Treatment and Complications

Context: Fractures of proximal fifth metatarsal are one of the most common fractures of the foot. Evidence Acquisition: A search of PubMed for studies on proximal fifth metatarsal fracture and Jones fracture focusing on the classification and management was performed. The reference list of the retrieved articles was searched for additional related studies. Results: The vascular supply and soft tissue anatomy of the fifth metatarsal explains the increased risk of delayed union and non-union in fractures at the metaphyseal-diaphyseal junction. Lawrence and Botte classify proximal fifth metatarsal fractures according to their location: tuberosity avulsion fractures (zone 1), fractures at metaphyseal-diaphyseal junction extending into the fourth-fifth intermetatarsal joint (zone 2) and proximal diaphyseal fractures (zone 3). Zone 1 fractures are treated conservatively with functional immobilization and early mobilization with excellent outcome. For zone 2 and zone 3 fractures, acute forms can be treated conservatively but with a risk of delayed union time and time for return to function. Therefore, early surgical fixation with intramedullary screw is advised in athletic individuals. For cases presented with signs of delayed union and non-union, surgical treatment with or without bone grafting is recommended. Complications of these fractures and their management are discussed in this report. Conclusions: Lawrence and Botte’s classification of proximal fifth metatarsal fractures is recommended by experts, due to its implication on prognosis and treatment strategy. Zone 1 fractures should be treated conservatively due to their excellent healing potential. Early operative treatment is advised for zone 2 and zone 3 fractures, especially in the athletic group. Complications of delayed union, non-union and refractures should be treated by revision fixation and bone grafting

Split Fracture: A Complication of Cerclage Wiring of Acute Patellar Fracture

Introduction: Iatrogenic patellar fracture is reported as a complication of patella procedures, such as medial patellofemoral ligament reconstruction, reconstruction of the anterior cruciate ligament of the knee using bone-patellar tendon-bone technique, and resurfacing the patella in total knee arthroplasty. Case Presentation: A 65-year-old lady with right patella fracture was treated with open reduction and cerclage wiring. An iatrogenic split fracture was noted during tension of the cerclage wire and was successfully managed by screw fixation of the split fracture. Conclusions: Split fracture is a rare complication of circumferential cerclage wiring of patellar fracture. The surgeon should be aware of the contributing factors in order to avoid this complication

Effect of next-nearest neighbor coupling on the optical spectra in bilayer graphene

We investigate the dependence of the optical conductivity of bilayer graphene (BLG) on the intra- and inter-layer interactions using the most complete model to date. We show that the next nearest-neighbor intralayer coupling introduces new features in the low-energy spectrum that are highly sensitive to sample doping, changing significantly the ``universal'' conductance. Further, its interplay with interlayer couplings leads to an anisotropy in conductance in the ultraviolet range. We propose that experimental measurement of the optical conductivity of intrinsic and doped BLG will provide a good benchmark for the relative importance of intra- and inter-layer couplings at different doping levels.Comment: 5 pages, 5 figure

The Role of Artificial Intelligence for Business Value

An increasing number of organizations are investing in Artificial intelligence (AI), but not all AI implementation leads to improved performance. To contribute to organizational business value, two components of AI resources, AI assets and AI capabilities, should be complementary in the business value creation process. In this study, based on IT business value literature and through the lens of dynamic capabilities, the role of AI resources in organizational value creation is explored. It is proposed that AI resources would enable organizations to develop process-oriented dynamic capabilities (PDCs), contributing to business value. This study will examine how organizations build AI capabilities and the roles of AI resources in creating business values through case studies. This research will offer a framework that guides and assists practitioners in utilising AI resources and building AI capabilities. A deeper understanding of the subject through this study also enriches the growing body of literature on AI

Advanced Abrasive Waterjet for Multimode Machining

Abrasive waterjet (AWJ) possesses inherent technological and manufacturing advantages unmatched by most machine tools. Recent advancements in AWJ processes have enhanced those merits. Multidisciplinary advancements include process automation, position accuracy, cutting models, range of part dimensions, ergonomics, user and environmental friendliness, feature recognition, and others. Among the technological merits, AWJ is material independent and a cold cutting tool, capable of preserving the structural and chemical integrity of parent materials. For heat sensitive materials, AWJ often cuts over 10 times faster than thermal cutting tools such as lasers and electrode discharge machining. Unlike photochemical etching, AWJ is environmentally friendly, producing no toxic byproducts. Additionally, AWJ requires only a single tool assisted with accessories to qualify for multimode machining; it is cost effective with fast turnaround for small and large lots alike. Recent advancements together with relevant R&D, engineering, and industrial applications will be presented for precision multimode machining from macro to micro scales

Numerical studies of the fractional quantum Hall effect in systems with tunable interactions

The discovery of the fractional quantum Hall effect in GaAs-based semiconductor devices has lead to new advances in condensed matter physics, in particular the possibility for exotic, topological phases of matter that possess fractional, and even non-Abelian, statistics of quasiparticles. One of the main limitations of the experimental systems based on GaAs has been the lack of tunability of the effective interactions between two-dimensional electrons, which made it difficult to stabilize some of the more fragile states, or induce phase transitions in a controlled manner. Here we review the recent studies that have explored the effects of tunability of the interactions offered by alternative two-dimensional systems, characterized by non-trivial Berry phases and including graphene, bilayer graphene and topological insulators. The tunability in these systems is achieved via external fields that change the mass gap, or by screening via dielectric plate in the vicinity of the device. Our study points to a number of different ways to manipulate the effective interactions, and engineer phase transitions between quantum Hall liquids and compressible states in a controlled manner.Comment: 9 pages, 4 figures, updated references; review for the CCP2011 conference, to appear in "Journal of Physics: Conference Series

Pair production of the T-odd leptons at the LHC

The T-odd leptons predicted by the littlest $Higgs$ model with T-parity can be pair produced via the subprocesses $gg\to \ell^{+}_{H}\ell^{-}_{H}$, $q\bar{q}\to \ell^{+}_{H}\ell^{-}_{H}$, $\gamma\gamma\to \ell^{+}_{H}\ell^{-}_{H}$ and $VV \to \ell^{+}_{H}\ell^{-}_{H}$ ($V$=$W$ or $Z$) at the $CERN$ Large Hadron Collider $(LHC)$. We estimate the hadronic production cross sections for all of these processes and give a simply phenomenology analysis. We find that the cross sections for most of the above processes are very small. However, the value of the cross section for the $Drell-Yan$ process $q\bar{q}\to \ell^{+}_{H}\ell^{-}_{H}$ can reach $270fb$.Comment: 12 pages, 2 figure