We obtain sharp estimates involving the mean curvatures of higher order of a complete bounded hypersurface immersed in a complete Riemannian manifold. Similar results are also given for complete spacelike hypersurfaces in Lorentzian ambient spaces.
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This article presents the further steps of the previously done studies taking into consideration the k-th order extensions of a complex manifold. In the previous studies higher order vertical and complete lifts of structures on the complex manifold were introduced. Presently, k-th extended spaces of a product manifold …
Study proves inequalities for eigenvalues of fourth-order elliptic operators on Riemannian manifolds.
problem Eigenvalue inequalities for fourth-order elliptic operators on Riemannian manifolds.
method Proves inequalities using Payne-Pólya-Weinberger-Yang type for eigenvalues of fourth-order elliptic operators in divergence form on complete Riemannian manifolds.
result Generalizes eigenvalue inequalities for the clamped plate problem to complete Riemannian manifolds.
We give different proofs and prove new results on the non complete solvability of some systems of complex first order p.d.e.'s, especially related to the analysis on CR manifolds.
We prove several Liouville-type non-existence theorems for higher order Codazzi tensors and classical Codazzi tensors on complete and compact Riemannian manifolds, in particular. These results will be obtained by using theorems of the connections between the geometry of a complete smooth manifold and the global behavio…
We give a complete description of all order 1 invariants of planar curves.
Neural autoregressive models are explicit density estimators that achieve state-of-the-art likelihoods for generative modeling. The D-dimensional data distribution is factorized into an autoregressive product of one-dimensional conditional distributions according to the chain rule. Data completion is a more involved ta…
We find the complete set of fundamental invariants for systems of ordinary differential equations of order under the group of point transformations generalizing similar results for contact invariants of a single ODE and point invariants of systems of the second and the third order. It turns out that starting fr…
In this paper, we investigate the sample size requirement for a general class of nuclear norm minimization methods for higher order tensor completion. We introduce a class of tensor norms by allowing for different levels of coherence, which allows us to leverage the incoherence of a tensor. In particular, we show that …
Study on completeness of Sobolev metrics on manifold-valued curves.
problem Completeness of Sobolev metrics on spaces of manifold-valued curves.
method Analysis of reparametrization invariant Sobolev metrics of order .
result Sobolev immersions are metrically and geodesically complete for several important cases of metrics.
For complete shrinking (gradient) Ricci solitons, we observe a quantification of Wylie's result that the fundamental group is finite.
New invariants show stronger virtual knot sets.
problem Classifying virtual knots using invariants.
method Defining -order invariants using forbidden moves.
result Set of -order invariants is strictly stronger.
LMConv improves autoregressive models for image generation and completion.
problem Limited generation order in autoregressive models restricts their applicability.
method Introduces LMConv, a modified 2D convolution that allows arbitrary masks to be applied to weights.
result LMConv achieves improved performance on image density estimation and coherent completions.
Fix a prime number ell. In this paper we develop the theory of relative pro-ell completion of discrete and profinite groups -- a natural generalization of the classical notion of pro-ell completion -- and show that the pro-ell completion of the Torelli group does not inject into the relative pro-ell completion of the c…
By using a certain second order differential equation, the notion of adapted coordinates on Finsler manifolds is defined and some classifications of complete Finsler manifolds are found. Some examples of Finsler metrics, with positive constant sectional curvature, not necessarily of Randers type nor projectively flat, …
Inter-order relations between moments of a Student distribution, with an application to -quantilesmath.ST
The paper derives formulas for moments of a Student t distribution and applies them to quantify -quantiles.
problem Understanding the moments and quantiles of a Student t distribution.
method Developed formulas for partial and complete moments, and derived relationships between -quantiles.
result For a Student t distribution, the -quantile and -quantile coincide at any confidence level.
In his 1954 paper about the initial value problem for 2D hyperbolic nonlinear PDEs, P. Lax declared that he had "a strong reason to believe" that there must exist a well-defined class of "not genuinely nonlinear" nonlinear PDEs. In 1978 G. Boillat coined the term "completely exceptional" to denote it. In the case of $2…
Constructs a function to prove meromorphic differential strata don't have complete subvarieties.
problem Proving meromorphic differential strata don't contain complete subvarieties.
method Explicit construction of a strictly plurisubharmonic function.
result Proves meromorphic differential strata do not contain positive-dimensional complete subvarieties.
Alternative proof for non-existence of complete curves in differential strata.
problem Non-existence of complete algebraic curves in strata of holomorphic differentials.
method Using positivity of divisor classes on moduli spaces of curves.
result Alternative proof confirming Gendron's result on non-existence.
For a bounded domain in a complete Riemannian manifold , we study estimates for lower order eigenvalues of a clamped plate problem. We obtain universal inequalities for lower order eigenvalues. We would like to remark that our results are sharp.
A new tensor completion method handles missing data with missing not at random entries.
problem Handling missing data in tensors where the probability of observation depends on other entries.
method Estimate propensities using convex relaxation, then use higher-order SVD with inverse propensities weights.
result Finite-sample error bounds on the completed tensor are provided.
Complete invariant defined for doodles on a sphere.
problem Doodles on a 2-sphere.
method Coefficients in series of chord diagrams.
result Finite type invariants of order at most 2n.
Study on Brownian motion on discrete curve spaces, proving stochastic completeness.
problem Analyzing Brownian motion on spaces of discrete curves.
method Introduced and studied Brownian motion on spaces of discrete regular curves with Sobolev-type metrics.
result All geodesically complete spaces of discrete regular curves are stochastically complete.
We give a complete description of all order 1 invariants of spherical curves. We also identify the subspaces of all J-invariants and S-invariants, and present two equalities satisfied by any spherical curve.
On complete embedded translating solitons of the mean curvature flow that are of finite genusmath.DG
We desingularise the union of Grim paraboloids along Costa-Hoffman-Meeks surfaces in order to obtain complete embedded translating solitons of the mean curvature flow with ends and arbitrary finite genus.
Study on minimal surfaces with constraints on index and branching order.
problem Existence and geometry of complete branched minimal surfaces.
method Intrinsic monotonicity of area formulas, scale-invariant weak chord-arc estimates.
result Derivation of weak chord-arc type results for minimal surfaces.
The paper analyzes reinforcement learning methods for estimating weights and quality functions with fast convergence rates.
problem Estimating weights and quality functions in reinforcement learning with function approximation.
method The paper uses minimax methods for estimating marginal importance weights and q-functions.
result The minimax approach enables fast rates of convergence for weights and quality functions, achieving first-order efficiency.
We show that the local equivalence problem for second-order ordinary differential equations under point transformations is completely characterized by differential invariants of order at most 10 and that this upper bound is sharp. We also show that, modulo Cartan duality and point transformations, the Painlevé-I equati…
In this paper we analyze the problem of uniqueness for spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson-Walker spacetimes. We consider first the case of compact spacelike hypersurfaces, completing some previous results given in [2]. We next extend these results to the complete …
The study extends Obata's theorem and classifies Finsler manifolds with transnormal functions.
problem Classifying Finsler manifolds based on geometric properties.
method Extending Obata's theorem and using a second order differential equation.
result Complete Finsler manifolds of positive constant flag curvature are homeomorphic to spheres.
We use the solution space of a pair of ODEs of at least second order to construct a smooth surface in Euclidean space. We describe when this surface is a proper embedding which is geodesically complete with finite total Gauss curvature. If the associated roots of the ODEs are real and distinct, we give a universal uppe…
Study explores robust Orlicz spaces in finance, showing separability implications.
problem Understanding robustness in financial and economic contexts.
method Distinguished two constructions of robust Orlicz spaces: top-down and bottom-up.
result Separability of robust Orlicz spaces has strong implications for dominatedness and order completeness.
We show that Plebanski's second heavenly equation, when written as a first-order nonlinear evolutionary system, admits multi-Hamiltonian structure. Therefore by Magri's theorem it is a completely integrable system. Thus it is an example of a completely integrable system in four dimensions.
Scalable method completes ill-conditioned matrices from few samples.
problem Matrix completion from few samples for ill-conditioned matrices.
method Iterative algorithm combining IRLS, smoothing Newton, and proximal gradient methods.
result Local quadratic convergence rate and well-conditioned linear systems.
This paper measures and compares the tail risks of limit and market orders using Extreme Value Theory. The analysis examines realised tail outcomes using the Dealing 2000-2 electronic broking system based on completed transactions rather than the more common analysis of indicative quotes. In general, limit and market o…
Proposes a new method for completing swap cycles in decentralized exchanges.
problem Completing swap cycles in decentralized exchanges efficiently and without slippage.
method Introduces an asset matrix formulation to verify and complete CoW cycles using graph traversal and imbalance correction.
result Demonstrates efficient discovery and insertion of synthetic orders for atomic cycle closure.
Study on loops on non-orientable surfaces, determining cardinality and order.
problem Determining the cardinality and order of maximal complete 1-systems of loops on non-orientable surfaces.
method Proved the cardinality of maximal systems of arcs pairwise-intersecting at most once on a non-orientable surface is , and used this to determine the cardinality of maximal complete 1-systems of loops.
result Exact cardinality of maximal complete 1-systems of loops on punctured projective planes is determined.
Results of R. Stanley and M. Masuda completely characterize the h-vectors of simplicial posets whose order complexes are spheres. In this paper we examine the corresponding question in the case where the order complex is a ball. Using the face rings of these posets, we develop a series of new conditions on their h-vect…
The paper calculates a specific weight system for chord diagrams with a particular graph structure.
problem Calculating a specific weight system for chord diagrams with a complete bipartite graph structure.
method Using a Lie algebra and its weight system, the authors derive a function on chord diagrams.
result The authors compute the weight system for chord diagrams with a complete bipartite graph structure.
Predicting the completion time of business process instances would be a very helpful aid when managing processes under service level agreement constraints. The ability to know in advance the trend of running process instances would allow business managers to react in time, in order to prevent delays or undesirable situ…
We prove the existence of a solution of the Yamabe equation on complete manifolds with finite volume and positive Yamabe invariant. In order to circumvent the standard methods on closed manifolds which heavily rely on global (compact) Sobolev embeddings we approximate the solution by eigenfunctions of certain conformal…
New tensor completion method converges linearly and is highly practical.
problem Recovering low-rank tensors from sparse observations.
method Adapted alternating minimization to tensor setting.
result Linear convergence even with highly correlated factors.
We study completeness properties of Sobolev metrics on the space of immersed curves and on the shape space of unparametrized curves. We show that Sobolev metrics of order are metrically complete on the space of Sobolev immersions of the same regularity and that any two curves i…
Study biderivations in complete Leibniz algebras, extending Lie algebra results.
problem Defining and studying biderivations in complete Leibniz algebras.
method Analyze biderivations according to two definitions, provide conditions for biderivations, and compare symmetric and skew-symmetric biderivations.
result Necessary and sufficient conditions for biderivations in Leibniz algebras are provided.
Study proves higher-order conformal forms don't exist in odd dimensions.
problem Proving non-existence of higher-order conformal forms in odd dimensions.
method Analyzing conformal hypersurface embeddings and differential order invariants.
result General non-existence of higher-order conformal forms in odd dimensions.
The aim of this paper is twofold. First, we extend the results of [33] concerning the existence and uniqueness of second-order reflected 2BSDEs to the case of two obstacles. Under some regularity assumptions on one of the barriers, similar to the ones in [10], and when the two barriers are completely separated, we prov…
New method for tensor completion using nonconvex dual total variation.
problem Tensor completion from partial measurements with exponential-family noise.
method Proposed dual-TV (DTV) regularizers for tensor completion under exponential-family noise.
result Theoretical upper bounds on recovery error for tensor completion.
In this paper we give Hamilton's Laplacian estimates for the heat equation on complete noncompact manifolds with nonnegative Ricci curvature. As an application, combining Li-Yau's lower and upper bounds of the heat kernel, we give an estimate on Laplacian form of the heat kernel on complete manifolds with nonnegative R…