Tensor models and 3-ary algebras

Tensor models are the generalization of matrix models, and are studied as models of quantum gravity in general dimensions. In this paper, I discuss the algebraic structure in the fuzzy space interpretation of the tensor models which have a tensor with three indices as its only dynamical variable. The algebraic structure is studied mainly from the perspective of 3-ary algebras. It is shown that the tensor models have algebraic expressions, and that their symmetries are represented by 3-ary algebras. It is also shown that the 3-ary algebras of coordinates, which appear in the nonassociative fuzzy flat spacetimes corresponding to a certain class of configurations with Gaussian functions in the tensor models, form Lie triple systems, and the associated Lie algebras are shown to agree with those of the Snyder's noncommutative spacetimes. The Poincare transformations on the fuzzy flat spacetimes are shown to be generated by 3-ary algebras.Comment: 21 pages, no essential changes of contents, but explanations added for clarit

User's guide to the Mission Analysis Evaluation and Space Trajectory Operations program (MAESTRO)

The MAESTRO system is a mission analysis tool designed to present to the user information necessary to make the various decisions required in the design and execution of a spaceflight mission. The system was designed so that it can be used in both the pre-launch mission planning phase of a mission and during the flight as an in-flight decision making tool. A description of each of the following modes is presented: (1) trajectory propagation mode; (2) retro-fire determination mode; (3) midcourse analysis determination mode; (4) Monte Carlo mode; (5) verification mode; (6) orbit stability mode; and (7) post injection trim mode. A description of the inputs necessary to run the program mode is given along with a sample case

Multi-instantons in seven dimensions

We consider the self-dual Yang-Mills equations in seven dimensions. Modifying the t'Hooft construction of instantons in $d=4$, we find $N$-instanton $7d$ solutions which depend on $8N$ effective parameters and are $E_{6}$-invariant.Comment: 9 pages, LaTeX, no figure

Treatment of failed articular cartilage reconstructive procedures of the knee: A systematic review

Background: Symptomatic articular cartilage lesions of the knee are common and are being treated surgically with increasing frequency. While many studies have reported outcomes following a variety of cartilage restoration procedures, few have investigated outcomes of revision surgery after a failed attempt at cartilage repair or reconstruction. Purpose: To investigate outcomes of revision cartilage restoration procedures for symptomatic articular cartilage lesions of the knee following a previously failed cartilage reconstructive procedure. Study Design: Systematic review; Level of evidence, 4. Methods: A literature search was performed by use of the PubMed, EMBASE, and MEDLINE/Ovid databases for relevant articles published between 1975 and 2017 that evaluated patients undergoing revision cartilage restoration procedure(s) and reported outcomes using validated outcome measures. For studies meeting inclusion criteria, relevant information was extracted. Results: Ten studies met the inclusion criteria. Lesions most commonly occurred in the medial femoral condyle (MFC) (52.8%), with marrow stimulation techniques (MST) the index procedure most frequently performed (70.7%). Three studies demonstrated inferior outcomes of autologous chondrocyte implantation (ACI) following a previous failed cartilage procedure compared with primary ACI. One study comparing osteochondral allograft (OCA) transplant following failed microfracture (MFX) with primary OCA transplant demonstrated similar clinical outcomes and graft survival at midterm follow-up. No studies reported outcomes following osteochondral autograft transfer (OAT) or newer techniques. Conclusion: This systematic review of the literature reporting outcomes following revision articular cartilage restoration procedures (most commonly involving the MFC) demonstrated a high proportion of patients who underwent prior MST. Evidence is sufficient to suggest that caution should be taken in performing ACI in the setting of prior MST, likely secondary to subchondral bone compromise. OCA appears to be a good revision treatment option even if the subchondral bone has been violated from prior surgery or fracture. </jats:sec

Towards the theory of coherent hard dijet production on hadrons and nuclei

We carry out a detailed calculation of the cross section of pion diffraction dissociation into two jets with large transverse momenta, originating from a hard gluon exchange between the pion constituents. Both the quark and the gluon contribution are considered and in the latter case we present calculations both in covariant and in axial gauges. We find that the standard collinear factorization does not hold in this reaction. The structure of non-factorizable contributions is discussed and the results are compared with the experimental data. Our conclusion is that the existing theoretical uncertainties do not allow, for the time being, for a quantitative extraction of the pion distribution amplitude.Comment: 45 pages, latex, 17 figures, final version to appear in Nuclear Physics

The Ginzburg-Landau Free Energy Functional of Color Superconductivity at Weak Coupling

We derive the Ginzburg-Landau free energy functional of color superconductivity in terms of the thermal diagrams of QCD in its perturbative region. The zero mode of the quadratic term coefficient yields the same transition temperature, including the pre-exponential factor, as the one obtained previously from the Fredholm determinant of the two quark scattering amplitude. All coefficients of the free energy can be made identical to those of a BCS model by setting the Fermi velocity of the latter equal to the speed of light. We also calculate the induced symmetric color condensate near $T_c$ and find that it scales as the cubic power of the dominant antisymmetric color component. We show that in the presence of an inhomogeneity and a nonzero gauge potential, while the color-flavor locked condensate dominates in the bulk, the unlocked condensate, the octet, emerges as a result of a simultaneous color-flavor rotation in the core region of a vortex filament or at the junction of super and normal phases.Comment: 32 pages, Plain Tex, 3 figure

Effective Gap Equation for the Inhomogeneous LOFF Superconductive Phase

We present an approximate gap equation for different crystalline structures of the LOFF phase of high density QCD at T=0. This equation is derived by using an effective condensate term obtained by averaging the inhomogeneous condensate over distances of the order of the crystal lattice size. The approximation is expected to work better far off any second order phase transition. As a function of the difference of the chemical potentials of the up and down quarks, $\delta\mu$, we get that the octahedron is energetically favored from $\delta\mu=\Delta_0/\sqrt 2$ to $0.95\Delta_0$, where $\Delta_0$ is the gap for the homogeneous phase, while in the range $0.95\Delta_0-1.32\Delta_0$ the face centered cube prevails. At $\delta\mu=1.32\Delta_0$ a first order phase transition to the normal phase occurs.Comment: 11 pages, 5 figure

Diquark Condensates and Compact Star Cooling

The effect of color superconductivity on the cooling of quark stars and neutron stars with large quark cores is investigated. Various known and new quark-neutrino processes are studied. As a result, stars being in the color flavor locked (CFL) color superconducting phase cool down extremely fast. Quark stars with no crust cool down too rapidly in disagreement with X-ray data. The cooling of stars being in the N_f =2 color superconducting (2SC) phase with a crust is compatible with existing X-ray data. Also the cooling history of stars with hypothetic pion condensate nuclei and a crust does not contradict the data.Comment: 10 pages, 5 figures, accepted for publication in Ap

Replication: A Design Principle for Field Research

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