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Orbital two-channel Kondo effect in epitaxial ferromagnetic L10-MnAl filmsJun 14 2015Jul 21 2015We report the first experimental realization of orbital two-channel Kondo (2CK) effect from two-level systems (TLSs) in epitaxial L10-MnAl films with giant perpendicular magnetic anisotropy. The resistivity exhibits a low-temperature (T) upturn with a ... More

Magneto-electroluminescence of organic heterostructures: Analytical theory and spectrally resolved measurementsOct 16 2014The effect of a magnetic field on the electroluminescence of organic light emitting devices originates from the hyperfine interaction between the electron/hole polarons and the hydrogen nuclei of the host molecules. In this paper, we present an analytical ... More

Radial Velocity Curves of Ellipsoidal Red Giant Binaries in the Large Magellanic CloudMar 20 2015Ellipsoidal red giant binaries are close binary systems where an unseen, relatively close companion distorts the red giant, leading to light variations as the red giant moves around its orbit. These binaries are likely to be the immediate evolutionary ... More

Demuth's path to randomnessApr 17 2014Jul 17 2014Osvald Demuth (1936--1988) studied constructive analysis from the viewpoint of the Russian school of constructive mathematics. In the course of his work he introduced various notions of effective null set which, when phrased in classical language, yield ... More

Optical spectroscopy study of Nd(O,F)BiS2 single crystalsJun 23 2014We present an optical spectroscopy study on F-substituted NdOBiS$_2$ superconducting single crystals grown using KCl/LiCl flux method. The measurement reveals a simple metallic response with a relatively low screened plasma edge near 5000 \cm. The plasma ... More

Edge Shear Flows and Particle Transport near the Density Limit in the HL-2A TokamakMay 03 2017Jan 17 2018Edge shear flow and its effect on regulating turbulent transport have long been suspected to play an important role in plasmas operating near the Greenwald density limit $ n_G $. In this study, equilibrium profiles as well as the turbulent particle flux ... More

Breakdown of single spin-fluid model in heavily hole-doped superconductor CsFe2As2May 28 2017Although Fe-based superconductors are multiorbital correlated electronic systems, previous nuclei magnetic resonance (NMR) measurement suggests that a single spin-fluid model is sufficient to describe its spin behavior. Here, we firstly observed the breakdown ... More

Spectrally-resolved hyperfine interactions between polaron and nuclear spins in organic light emitting diodes: Magneto-EL studiesSep 12 2014We use spectrally-resolved magneto-electroluminescence (EL) measurements to study the energy dependence of hyperfine interactions between polaron and nuclear spins in organic LEDs. Using layered devices based on Bphen/MTDATA -- a well-known exciplex emitter ... More

Observation of anomalous temperature dependence of spectrum on small Fermi surfaces in a BiS2-based superconductorFeb 08 2014We performed an angle-resolved photoemission spectroscopy study of the BiS2-based superconductor Nd(O,F)BiS2. Two small electron-like Fermi surfaces around X (pi, 0) are observed, which enclose 2.4% and 1.1% of the Brillouin zone area, respectively, corresponding ... More

Binding energies of hydrogen-like impurities in a semiconductor in intense terahertz laser fieldsApr 11 2003A detailed theoretical study is presented for the influence of linearly polarised intense terahertz (THz) laser radiation on energy states of hydrogen-like impurities in semiconductors. The dependence of the binding energy for 1s and 2p states on intensity ... More

The Orbital Nature of 81 Ellipsoidal Red Giant Binaries in the Large Magellanic CloudFeb 08 2017In this paper, we collect a sample of 81 ellipsoidal red giant binaries in the Large Magellanic Cloud (LMC), and we study their orbital natures individually and statistically. The sample contains 59 systems with circular orbits and 22 systems with eccentric ... More

Predicting the Fate of Binary Red Giants Using the Observed Sequence E Star Population: Binary Planetary Nebula Nuclei and Post-RGB StarsApr 12 2012Sequence E variables are close binary red giants that show ellipsoidal light variations. They are likely the immediate precursors of planetary nebulae (PNe) with close binary central. We have made a Monte Carlo simulation to determine the fraction of ... More

Predicting the Evolutionary Descendents of Sequence E StarsNov 18 2011Sequence E variables are close binary red giants that show ellipsoidal light variations. They are likely to terminate their red giant evolution by a common envelope (CE) event when the red giant fills its Roche lobe, and produce close binary Planetary ... More

Raman scattering investigation of the electron-phonon coupling in superconducting Nd(O,F)BiS$_2$Jul 25 2014We have performed polarized Raman scattering measurements on the newly discovered superconductor Nd(O,F)BiS$_2$ ($T_c = 4$ K). We observe 2 Raman active modes, with frequencies in accordance with first-principles calculations. One A$_{1g}$ phonon mode ... More

Structural and electrical properties of tantalum nitride thin films fabricated by using reactive radio-frequency magnetron sputteringMay 29 2003May 30 2003TaN thin film is an attractive interlayer as well as a diffusion barrier layer in [FeN/TaN](n) multilayers for the application as potential write-head materials in high-density magnetic recording. We synthesized two series of TaN films on glass and Si ... More

Anomalous Hall effect in L10-MnAl films with controllable orbital two-channel Kondo effectJan 28 2016Feb 03 2016The anomalous Hall effect (AHE) in strongly disordered magnetic systems has been buried in persistent confusion despite its long history. We report the AHE in perpendicularly magnetized L10-MnAl epitaxial films with variable orbital two-channel Kondo ... More

Revealing the hidden order in BaTi2As2O via nuclear magnetic resonanceJun 29 2018In low-dimensional metallic systems, lattice distortion is usually coupled to a density-wave-like electronic instability due to Fermi surface nesting (FSN) and strong electron-phonon coupling. However, the ordering of other electronic degrees of freedom ... More

Improved prospects for the detection of new Large Magellanic Cloud planetary nebulaeMar 10 2011The Large Magellanic Cloud (LMC) contains the nearest large extragalactic population of planetary nebulae (PNe). A shallow viewing angle and low interstellar reddening towards the LMC potentially means a larger, more complete flux-limited population can ... More

Quantum state engineering with flux-biased Josephson phase qubits by Stark-chirped rapid adiabatic passagesJul 01 2010Jul 12 2010In this paper, the scheme of quantum computing based on Stark chirped rapid adiabatic passage (SCRAP) technique [L. F. Wei et al., Phys. Rev. Lett. 100, 113601 (2008)] is extensively applied to implement the quantum-state manipulations in the flux-biased ... More

Critical Percolation Probabilities for the Next-Nearest-Neighboring Site Problems on Sierpinski CarpetsJun 03 2003In this paper, we compute the next-nearest-neighboring site percolation (Connections exist not only between nearest-neighboring sites, but also between next-nearest-neighboring sites.) probabilities Pc on the two-dimensional Sierpinski carpets, using ... More

A spin-orbital-intertwined nematic state in FeSeMar 14 2019Spin-orbit coupling (SOC) due to the relativistic motion of electrons is a fundamental interaction to intertwine spin and orbital degrees of freedom in solids. Recently, the fingerprint of SOC on the low-energy electronic structure has been observed in ... More

Adaptive Channel Allocation Spectrum Etiquette for Cognitive Radio NetworksFeb 07 2006In this work, we propose a game theoretic framework to analyze the behavior of cognitive radios for distributed adaptive channel allocation. We define two different objective functions for the spectrum sharing games, which capture the utility of selfish ... More

Interplay of Spin-Orbit Interactions, Dimensionality, and Octahedral Rotations in Semimetallic SrIrO$_3$Jan 09 2015We employ reactive molecular-beam epitaxy to synthesize the metastable perovskite SrIrO$_{3}$ and utilize {\it in situ} angle-resolved photoemission to reveal its electronic structure as an exotic narrow-band semimetal. We discover remarkably narrow bands ... More

Experimental Discovery of the First Nonsymmorphic Topological Insulator KHgSbMay 22 2016Topological insulators (TIs) host novel states of quantum matter, distinguished from trivial insulators by the presence of nontrivial conducting boundary states connecting the valence and conduction bulk bands. Up to date, all the TIs discovered experimentally ... More

Experimental evidence of large-gap two-dimensional topological insulator on the surface of ZrTe5Jan 26 2016Two-dimensional (2D) topological insulators (TIs) with a large bulk band-gap are promising for experimental studies of the quantum spin Hall effect and for spintronic device applications. Despite considerable theoretical efforts in predicting large-gap ... More

Scaling p_T distributions for p and \bar{p} produced in Au+Au collisions at RHICApr 09 2007Oct 12 2007With the experimental data from STAR and PHENIX on the centrality dependence of the $p_T$ spectra of protons and anti-protons produced at mid-rapidity in Au+Au collisions at 200 GeV, we show that for protons and anti-protons there exists a scaling distribution ... More

Meromorphic cubic differentials and convex projective structuresMar 09 2015Extending the Labourie-Loftin correspondence, we establish, on any punctured oriented surface of finite type, a one-to-one correspondence between convex projective structures with specific types of ends and punctured Riemann surface structures endowed ... More

Linear Optimization with Cones of Moments and Nonnegative PolynomialsMay 13 2013Jul 17 2014Let A be a finite subset of N^n and R[x]_A be the space of real polynomials whose monomial powers are from A. Let K be a compact basic semialgebraic set of R^n such that R[x]_A contains a polynomial that is positive on K. Denote by P_A(K) the cone of ... More

Meromorphic cubic differentials and convex projective structuresMar 09 2015Jan 06 2017Extending the Labourie-Loftin correspondence, we establish, on any punctured oriented surface of finite type, a one-to-one correspondence between convex projective structures with specific types of ends and punctured Riemann surface structures endowed ... More

The quasi-Poisson Goldman formulaJan 22 2013Feb 10 2013We prove a quasi-Poisson bracket formula for the space of representations of the fundamental groupoid of a surface with boundary, which generalizes Goldman's Poisson bracket formula. We also deduce a similar formula for quasi-Poisson cross-sections.

Calculus of Cost FunctionsMar 05 2017Cost functions provide a framework for constructions of sets Turing below the halting problem that are close to computable. We carry out a systematic study of cost functions. We relate their algebraic properties to their expressive strength. We show that ... More

On the Hilbert geometry of simplicial Tits setsNov 05 2011Jul 11 2014The moduli space of convex projective structures on a simplicial hyperbolic Coxeter orbifold is either a point or the real line. Answering a question of M. Crampon, we prove that in the latter case, when one goes to infinity in the moduli space, the entropy ... More

Karoubi's Construction for Motivic Cohomology OperationsMar 19 2006We use an analogue of Karoubi's construction in the motivic situation to give some cohomology operations in motivic cohomology. We prove many properties of these operations, and we show that they coincide, up to some nonzero constants, with the reduced ... More

Left-orderablity for surgeries on $(-2,3,2s+1)$-pretzel knotsFeb 28 2018In this paper, we prove that the fundamental group of the manifold obtained by Dehn surgery along a $(-2,3,2s+1)$-pretzel knot ($s\ge 3$) with slope $\frac{p}{q}$ is not left orderable if $\frac{p}{q}\ge 2s+3$, and that it is left orderable if $\frac{p}{q}$ ... More

On characteristic integrals of Toda field theoriesMar 05 2013Apr 06 2014Characteristic integrals of Toda field theories associated to simple Lie algebras are presented in the most explicit forms, both in terms of the formulas and in terms of the proofs.

Logic Blog 2012Feb 15 2013The 2012 logic blog has focussed on the following: Randomness and computable analysis/ergodic theory; Systematizing algorithmic randomness notions; Traceability; Higher randomness; Calibrating the complexity of equivalence relations from computability ... More

Logic Blog 2011Mar 23 2014This year's logic blog has focussed on: 1. Demuth randomness 2. traceability 3. The connection of computable analysis and randomness 4. $K$-triviality in metric spaces.

Logic Blog 2013Mar 23 2014Jun 19 2014The 2013 logic blog has focussed on the following: 1. Higher randomness. Among others, the Borel complexity of $\Pi^1_1$ randomness and higher weak 2 randomness is determined. 2. Reverse mathematics and its relationship to randomness. For instance, what ... More

Calibrating the complexity of Delta 2 sets via their changesFeb 03 2013The computational complexity of a Delta 2 set will be calibrated by the amount of changes needed for any of its computable approximations. Firstly, we study Martin-Loef random sets, where we quantify the changes of initial segments. Secondly, we look ... More

The complexity of isomorphism between countably based profinite groupsApr 03 2016A topological group G is profinite if it is compact and totally disconnected. Equivalently, G is the inverse limit of a surjective system of finite groups carrying the discrete topology. We discuss how to represent a countably based profinite group as ... More

Rescaling Limits in Non-Archimedean DynamicsDec 03 2016Suppose $\{f_t\}$ is an analytic one-parameter family of rational maps defined over a non-Archimedean field $K$. We prove a finiteness theorem for the set of rescalings for $\{f_t\}$. This complements results of J. Kiwi.

Iteration at the Boundary of Newton MapsMar 21 2018Let $\{N_t\}$ be a holomorphic family of degree $d\ge 3$ Newton maps. By studying the related Berkovich dynamics, we obtain an estimate of the weak limit of the maximal measures of $N_t$. Moreover, we give a complete description of the rescaling limits ... More

Logic Blog 2016Mar 05 2017Mar 09 2017This year's logic blog contains a variety of results, some of them available only here. Highlights include the resolution of the Gamma question by Monin, and a number of entries on topological group theory and its connection to logic. There's also a new ... More

Optimality Conditions and Finite Convergence of Lasserre's HierarchyJun 01 2012Apr 15 2013Lasserre's hierarchy is a sequence of semidefinite relaxations for solving polynomial optimization problems globally. This paper studies the relationship between optimality conditions in nonlinear programming theory and finite convergence of Lasserre's ... More

Symmetric Tensor Nuclear NormsMay 28 2016This paper studies nuclear norms of symmetric tensors. As recently shown by Friedland and Lim, the nuclear norm of a symmetric tensor can be achieved at a symmetric decomposition. We discuss how to compute symmetric tensor nuclear norms, depending on ... More

Nearly Low Rank Tensors and Their ApproximationsDec 23 2014The low rank tensor approximation problem (LRTAP) is to find a tensor whose rank is small and that is close to a given one. This paper studies the LRTAP when the tensor to be approximated is close to a low rank one. Both symmetric and nonsymmetric tensors ... More

Discriminants and Nonnegative PolynomialsFeb 10 2010Apr 23 2010For a semialgebraic set K in R^n, let P_d(K) be the cone of polynomials in R^n of degrees at most d that are nonnegative on K. This paper studies the geometry of its boundary. When K=R^n and d is even, we show that its boundary lies on the irreducible ... More

Polynomial Matrix Inequality and Semidefinite RepresentationAug 03 2009Mar 28 2011Consider a convex set S defined by a matrix inequality of polynomials or rational functions over a domain. The set S is called semidefinite programming (SDP) representable or just semidefinite representable if it equals the projection of a higher dimensional ... More

Secondary Chern-Euler forms and the Law of Vector FieldsSep 25 2009Aug 14 2010The Law of Vector Fields is a term coined by Gottlieb for a relative Poincar\'e-Hopf theorem. It was first proved by Morse and expresses the Euler characteristic of a manifold with boundary in terms of the indices of a generic vector field and the inner ... More

Secondary Chern-Euler class for general submanifoldJun 22 2009Jul 13 2009We define and study the secondary Chern-Euler class for a general submanifold of a Riemannian manifold. Using this class, we define and study index for a vector field with non-isolated singularities on a submanifold. As an application, our studies give ... More

On isomorphism numbers of "$F$-crystals"Mar 09 2014In this note, we show that for an ``$F$-crystal" (the equal characteristic analogue of $F$-crystals), its {\it isomorphism number} and its {\it level torsion} coincide. This confirms a conjure of Vasiu \cite{Va} in the equal characteristic case.

The convolution algebra structure on $K^G(\mathcal{B} \times \mathcal{B})$Nov 08 2011We show that the convolution algebra $K^G(\mathcal{B} \times \mathcal{B})$ is isomorphic to the Based ring of the lowest two-sided cell of the extended affine Weyl group associated to $G$, where $G$ is a connected reductive algebraic group over the field ... More

Logic Blog 2015fFeb 14 2016The 2015 Logic Blog contains a large variety of results connected to logic, some of them unlikely to be submitted to a journal. For the first time there is a group theory part. There are results in higher randomness, and in computable ergodic theory.

Lowness, randomness, and computable analysisJul 24 2016Analytic concepts contribute to our understanding of randomness of reals via algorithmic tests. They also influence the interplay between randomness and lowness notions. We provide a survey, written on the occasion of Rod Downey's 60th birthday.

Rescaling Limits in Non-Archimedean DynamicsDec 03 2016Jan 20 2018Suppose $\{f_t\}$ is an analytic one-parameter family of rational maps defined over a non-Archimedean field $K$. We prove a finiteness theorem for the set of rescalings for $\{f_t\}$. This complements results of J. Kiwi.

Entropy degeneration of convex projective surfacesMar 15 2015Nov 17 2015We show that the volume entropy of the Hilbert metric on a closed convex projective surface tends to zero as the corresponding Pick differential tends to infinity. The proof is based on the theorem, due to Benoist and Hulin, that the Hilbert metric and ... More

Polynomial Optimization with Real VarietiesNov 08 2012Jun 04 2013We consider the optimization problem of minimizing a polynomial f(x) subject to polynomial constraints h(x)=0, g(x)>=0. Lasserre's hierarchy is a sequence of sum of squares relaxations for finding the global minimum. Let K be the feasible set. We prove ... More

Convex Hulls of Quadratically Parameterized Sets With Quadratic ConstraintsOct 11 2011Let V be a semialgebraic set parameterized by quadratic polynomials over a quadratic set T. This paper studies semidefinite representation of its convex hull by projections of spectrahedra (defined by linear matrix inequalities). When T is defined by ... More

Tight Relaxations for Polynomial Optimization and Lagrange Multiplier ExpressionsJan 06 2017Apr 06 2018This paper proposes tight semidefinite relaxations for polynomial optimization. The optimality conditions are investigated. We show that generally Lagrange multipliers can be expressed as polynomial functions in decision variables over the set of critical ... More

Local Versus Global Conditions in Polynomial OptimizationMay 01 2015This paper reviews local and global optimality conditions in polynomial optimization. We summarize the relationship between them.

Sum of Squares Method for Sensor Network LocalizationMay 24 2006Sep 18 2007This paper has been withdrawn by the author due to its publication

The Space-like Surfaces with Vanishing Conformal Form in the Conformal SpaceAug 15 2011The conformal geometry of surfaces in the conformal space $\mathbf Q^n_1$ is studied. We classify the space-like surfaces in $\mathbf Q^n_1$ with vanishing conformal form up to conformal equivalence.

Classification of solutions to Toda systems of types $C$ and $B$ with singular sourcesAug 25 2015In this paper, the classification in [Lin,Wei,Ye] of solutions to Toda systems of type $A$ with singular sources is generalized to Toda systems of types $C$ and $B$. Like in the $A$ case, the solution space is shown to be parametrized by the abelian subgroup ... More

X-rays from Proton Bremsstrahlung: Evidence from Fusion Reactors and Its Implication in AstrophysicsOct 20 2009In a fusion reactor, a proton and a neutron generated in previous reactions may again fuse with each other. Or they can in turn fuse with or be captured by an un-reacted deuteron. The average center-of-mass (COM) energy for such reaction is around 10 ... More

Subtle Features in Transport Properties: Evidence for a Possible Coexistence of Holes and Electrons in Cuprate SuperconductorsMar 06 2000Mar 08 2000Transport properties of high transition temperature (high Tc) cuprate superconductors are investigated within a two-band model. The doping dependent Hall coefficients of La_{2-x}Sr_xCuO_4 (LSCO) and Nd_{2-x}Ce_xCuO_4 (NCCO) are explained by assuming the ... More

Logic Blog 2014Apr 30 2015The 2014 Logic Blog starts with open questions from the May IMS program in Singapore. It contains results on randomness, including answers to some open questions in higher randomness. There are structural results on equivalence relations, and metric spaces. ... More

Compactifications of the moduli spaces of Newton mapsMar 22 2018We study various compactifications of moduli space of Newton maps. Mainly, we focus on GIT compactifiaction and Deligne-Mumford compactification. Then we explore the relations among these compactifications.

Indeterminacy Loci of Iterate MapsSep 05 2017We consider the indeterminacy locus $I(\Phi_n)$ of the iterate map $\Phi_n:\overline{M}_d-rightarrow\overline{M}_{d^n}$, where $\overline{M}_d$ is the GIT compactification of the moduli space $M_d$ of degree $d$ complex rational maps. We give natural ... More

Weak Solutions of the Chern-Ricci flow on compact complex surfacesJan 18 2017In this note, we prove the existence of weak solutions of the Chern-Ricci flow through blow downs of exceptional curves, as well as backwards smooth convergence away from the exceptional curves on compact complex surfaces. The smoothing property for the ... More

Logic Blog 2017Apr 15 2018The blog is somewhat shorter than in previous years, It contains new insights in a variety of areas, including computability, quantum algorithmic version of the SMB theorem, descriptions of groups (both discrete and profinite), metric spaces. There are ... More

Low Rank Symmetric Tensor ApproximationsSep 06 2017For a given symmetric tensor, we aim at finding a new one whose symmetric rank is small and that is close to the given one. There exist linear relations among the entries of low rank symmetric tensors. Such linear relations can be expressed by polynomials, ... More

The Hierarchy of Local Minimums in Polynomial OptimizationNov 17 2013Nov 25 2014This paper studies the hierarchy of local minimums of a polynomial in the space. For this purpose, we first compute H-minimums, for which the first and second order optimality conditions are satisfied. To compute each H-minimum, we construct a sequence ... More

Certifying Convergence of Lasserre's Hierarchy via Flat TruncationJun 13 2011Aug 06 2012This paper studies how to certify the convergence of Lasserre's hierarchy of semidefinite programming relaxations for solving multivariate polynomial optimization. We propose flat truncation as a general certificate for this purpose. Assume the set of ... More

An Exact Jacobian SDP Relaxation for Polynomial OptimizationJun 11 2010Given polynomials f(x), g_i(x), h_j(x), we study how to minimize f on the semialgebraic set S = { x \in R^n: h_1(x)=...=h_{m_1}(x) =0, g_1(x) >= 0, ..., g_{m_2}(x) >= 0}. Let f_{min} be the minimum of f on S. Suppose S is nonsingular and f_{min} is achievable ... More

First Order Conditions for Semidefinite Representations of Convex Sets Defined by Rational or Singular PolynomialsJun 28 2008A set is called semidefinite representable or semidefinite programming (SDP) representable if it can be represented as the projection of a higher dimensional set which is represented by some Linear Matrix Inequality (LMI). This paper discuss the semidefinite ... More

An Application of Maximum Principle to space-like Hypersurfaces with Constant Mean Curvature in Anti-de Sitter SpaceAug 16 2011In this paper, we study complete hypersurfaces with constant mean curvature in anti-de Sitter space $H^{n+1}_1(-1)$. we prove that if a complete space-like hypersurface with constant mean curvature $x:\mathbf M\rightarrow H^{n+1}_1(-1) $ has two distinct ... More

An Alternative Explanation on the Two Relaxation Rates in Cuprate SuperconductorsNov 22 2000Dec 05 2000Transport properties of high transition temperature (high-Tc) superconductors have been shown to have two distinct relaxation rates. We argue that this apparent inconsistence can be resolved with an effective carrier density n linear in temperature T. ... More

Variational bounds on the ground-state energy of three electrons and one hole in two-dimensionDec 31 2000Jan 09 2001We consider a model of three electrons and one hole confined in a two-dimensional (2D) plane, interacting with one another through Coulomb forces. Using a Ritz variational method we find an upper bound of \approx -0.0112me^4/8\pi^2 \epsilon ^2 \hbar ^2 ... More

Intrinsic construction of invariant functions on simple Lie algebrasMar 05 2013Apr 06 2014An algorithm for constructing primitive adjoint-invariant functions on a complex simple Lie algebra is presented. The construction is intrinsic in the sense that it does not resort to any representation. A primitive invariant function on the whole Lie ... More

On the Minimum Area of Null Homotopies of Curves Traced TwiceNov 29 2014Dec 31 2014We provide an efficient algorithm to compute the minimum area of a homotopy between two closed plane curves, given that they divide the plane into finite number of regions. For any positive real number $\varepsilon>0$, we construct a closed plane curve ... More

A Functor Converting Equivariant Homology to HomotopyMar 18 2006Aug 01 2007In this paper, we prove an equivariant version of the classical Dold-Thom theorem. Associated to a finite group, a CW-complex on which this group acts and a covariant coefficient system in the sense of Bredon, we functorially construct a topological abelian ... More

The A-truncated K-moment problemOct 25 2012Aug 28 2014Let A be a finite subset of N^n, and K be a compact semialgebraic set in R^n. An A-tms is a vector y indexed by elements in A. The A-truncated K-moment problem (A-TKMP) studies whether a given A-tms y admits a K-measure or not. This paper proposes a numerical ... More

Connected components of closed affine Deligne-Lusztig varieties in affine GrassmanniansNov 15 2015We determine the set of connected components of closed affine Deligne-Lusztig varieties for hyperspecial maximal parahoric subgroups of unramified connected reductive groups. This extends the work by Viehmann for split reductive groups, and the work by ... More

Fundamental elements of an affine Weyl groupOct 08 2013Jun 03 2014Fundamental elements are certain special elements of affine Weyl groups introduced by Gortz, Haines, Kottwitz and Reuman. They play an important role in the study of affine Deligne-Lusztig varieties. In this paper, we obtain characterizations of the ... More

On Sha's secondary Chern-Euler classJan 17 2009Feb 08 2010For a manifold with boundary, the restriction of Chern's transgression form of the Euler curvature form over the boundary is closed. Its cohomology class is called the secondary Chern-Euler class and used by Sha to formulate a relative Poincar\'e-Hopf ... More

Coding Methods in Computability Theory and Complexity TheoryAug 29 2013A major part of computability theory focuses on the analysis of a few structures of central importance. As a tool, the method of coding with first-order formulas has been applied with great success. For instance, in the c.e. Turing degrees, it has been ... More

Regularity of A Complex Monge-Ampère Equation on Hermitian ManifoldsNov 18 2013We obtain higher order estimates for a parabolic flow on a compact Hermitian manifold. As an application, we prove that a bounded $\hat{\omega}$-plurisubharmonic solution of an elliptic complex Monge-Amp\`{e}re equation is smooth under an assumption on ... More

Logic Blog 2018Feb 23 2019Mar 14 2019Some notions from algorithmic randomness are extended to measures and to quantum states. There is a lot on group theory and its relation to logic. This includes some new results on oligomorphic groups. There's also metric spaces and Scott rank, and interpretability. ... More

Generating Polynomials and Symmetric Tensor DecompositionsAug 25 2014Oct 02 2015This paper studies symmetric tensor decompositions. For symmetric tensors, there exist linear relations of recursive patterns among their entries. Such a relation can be represented by a polynomial, which is called a generating polynomial. The homogenization ... More

Poles of cubic differentials and ends of convex $\mathbb{RP}^2$-surfacesJun 17 2018Jun 19 2018On any oriented surface, the affine sphere construction gives a one-to-one correspondence between convex $\mathbb{RP}^2$-structures and holomorphic cubic differentials. Generalizing results of Benoist-Hulin, Loftin and Dumas-Wolf, we show that poles of ... More

Regular Submanifolds in the Conformal Space ${\mathbb Q}^n_p$Aug 15 2011There is a Lorenzian group acting on the conformal space ${\mathbb Q}^n_p$. We study the regular submanifolds in the conformal space ${\mathbb Q}^n_p$ and construct general submanifold theory in the conformal space ${\mathbb Q}^n_p$. Finally we give the ... More

Topologically slice $(1,1)$-knots which are not smoothly sliceJan 23 2019We prove that there are infinitely many $(1,1)$-knots which are topologically slice, but not smoothly slice, which was a conjecture proposed by B\'ela Andr\'as R\'acz.

Toda field theories and integral curves of standard differential systemsOct 16 2015Aug 08 2016This paper establishes three relations between the Toda field theory associated to a simple Lie algebra and the integral curves of the standard differential system on the corresponding complete flag variety. The motivation comes from the viewpoint on ... More

Solving Toda field theories and related algebraic and differential propertiesMar 05 2013Toda field theories are important integrable systems. They can be regarded as constrained WZNW models, and this viewpoint helps to give their explicit general solutions, especially when a Drinfeld-Sokolov gauge is used. The main objective of this paper ... More

Zeta functions of trinomial curves and maximal curvesAug 10 2014We determine the zeta functions of trinomial curves in terms of Gauss sums and Jacobi sums, and we obtain an explicit formula of the genus of a trinomial curve over a finite field, then we study the conditions for a trinomial curve to be a maximal curve ... More

On transgression in associated bundlesJun 22 2009Feb 03 2011We formulate and prove a formula for transgressing characteristic forms in general associated bundles following a method of Chern. As applications, we derive D. Johnson's explicit formula for such general transgression and Chern's first transgression ... More

Irreducible components of affine Deligne-Lusztig varietiesSep 11 2018Nov 18 2018By extending the method of semi-modules developed by de Jong, Oort, Viehmann and Hamacher, we introduce a stratification for the affne Deligne-Lusztig variety (in the affne Grassmannian) attached to attached to a minuscule cocharacter and a basic element. ... More

Semi-modules and irreducible components of affine Deligne-Lusztig varietiesFeb 13 2018Feb 21 2018Let $G$ be the Weil restriction of a general linear group. By extending the method of semi-modules developed by de Jong, Oort, Viehmann and Hamacher, we obtain a stratification of the affine Deligne-Lusztig varieties for $G$ (in the affine Grassmannian) ... More

A stochastic approach to a new type of parabolic variational inequalitiesMar 21 2012Mar 23 2012We study the following quasilinear partial differential equation with two subdifferential operators: $${\frac{\partial u}{\partial s}(s,x)} + (\mathcal{L}u)(s,x,u(s,x),(\nabla u(s,x))^\ast\sigma(s,x,u(s,x))) + f(s,x,u(s,x),(\nabla u(s,x))^\ast\sigma(s,x,u(s,x))) ... More

Thickness monitoring of graphene on SiC using low-energy electron diffractionFeb 04 2010The formation of epitaxial graphene on SiC is monitored in-situ using low-energy electron diffraction (LEED). The possibility of using LEED as an in-situ thickness monitor of the graphene is examined. The ratio of primary diffraction spot intensities ... More