A new adaptive binarization technique using fuzzy integrals improves image quality.
problem Improving image thresholding quality.
method FLAT (Fuzzy Local Adaptive Thresholding) based on fuzzy integrals.
result The proposed FLAT method produces better image quality than traditional algorithms and neural networks.
We present a new Liouville-integrable natural Hamiltonian system on the (cotangent bundle of the) two-dimensional sphere. The second integral is cubic in the momenta.
New method to derive integrable systems from existing Lax systems.
problem Deriving new integrable systems from existing ones.
method Systematic method of deriving new integrable systems from a given one.
result Examples of new integrable systems derived, including the dispersionless Hirota equation, the general heavenly equation, and the web equations.
The paper finds new metrics for geodesic flows with rational integrals.
problem Finding Riemannian metrics with rational integrals for geodesic flows.
method Explicit construction of metrics and integrals.
result New examples of metrics with rational integrals are provided.
New integrable systems derived from Nijenhuis geometry.
problem Developing new integrable systems from Nijenhuis geometry.
method Constructing a new series of multicomponent integrable PDE systems.
result Many famous integrable systems are contained within the new series.
Integral currents with boundary of finite mass are integral.
problem Integral currents with boundary of finite mass are integral.
method De Giorgi's structure theorem for integer-valued BV functions and a cylindrical projection argument. result Integral currents with boundary of finite mass are integral.
New vector fields integrate first-order ODEs.
problem Integrating first-order ODEs.
method Relation between Riemannian manifolds and ODEs integration.
result Integration procedure for first-order ODEs.
New integral estimates on substatic manifolds improve Alexandrov Theorem.
problem Improving integral estimates on substatic manifolds.
method Introducing a new vector field with nonnegative divergence.
result Generalization and improvement of integral estimates leading to Alexandrov Theorem.
There are new integrable cases due to the construction from the previous version.
Defines a new integration method for 1D currents, proving a generalized FTC.
problem Developing a new integration method for 1D integral currents.
method Integrates 1D integral currents using a Henstock-Kurzweil type approach.
result Proves a generalized Fundamental Theorem of Calculus for these currents.
Maxwell meets Korn: A New Coercive Inequality for Tensor Fields with Square-Integrable Exterior Derivative
New tensors help solve magnetic flow integrability.
problem Integrability of magnetic flows on specific manifolds.
method Introduced magnetic Killing symmetric tensors to construct first integrals.
result Proved integrability of invariant magnetic flows on 2-step nilmanifolds.
There is a well-known example of integrable conservative system on S2, the case of Kovalevskaya in the dynamics of a rigid body, possessing an integral of fourth degree in momenta. Goryachev proposed a one-parameter family of examples of conservative systems on S2 possessing an integral of fourth degree in moment…
We introduce a novel systematic construction for integrable (3+1)-dimensional dispersionless systems using nonisospectral Lax pairs that involve contact vector fields. In particular, we present new large classes of (3+1)-dimensional integrable dispersionless systems associated to the Lax pairs which are polynomial and …
Geometric theory of integration developed in SDG.
problem Combining infinitesimal contributions to finite quantities.
method Analysis of differential forms and new operators in SDG.
result Discovery of new types of differential forms and operators.
We propose a new condition ℵ which enables to get new results on integrable geodesic flows on closed surfaces. This paper has two parts. In the first, we strengthen Kozlov's theorem on non-integrability on surfaces of higher genus. In the second, we study integrable geodesic flows on 2-torus. Our main result for…
It has been proved that on 2-dimensional orientable compact manifolds of genus g>1 there is no integrable geodesic flow with an integral polynomial in momenta. There is a conjecture that all integrable geodesic flows on T2 possess an integral quadratic in momenta. All geodesic flows on S2 and T2 possessing i…
New integral-geometric formulae derived from normal densities ring.
problem Smooth versions of BKK theorem.
method Algorithm based on ring of normal densities.
result Smooth versions of BKK theorem obtained.
New method solves complex curvature equations.
problem Solving semilinear scalar curvature equations.
method Mixed convex integration method.
result New proof of scalar curvature result.
New proof of Lie algebroid action equivalence and integrability.
problem Equivalence between Lie algebroid action and integrability.
method Double Lie groupoids and multiplicative foliations.
result Simple characterization of double Lie groupoids inducing Lie groupoid structures.
A general method for analytic inversion of geometric integral transforms is proposed
New framework for logarithmically divergent integrals on manifolds with corners.
problem Logarithmically divergent integrals on manifolds with corners.
method Introduces new geometric framework and morphisms in logarithmic geometry.
result Functorial characterization of regularized integration.
New integrable deformations for topological hierarchies from Frobenius manifolds.
problem Integrable deformations of topological hierarchies from Frobenius manifolds.
method Construction of integrable deformations with polynomial tau-structures.
result Conjecture of universal object for Riemann--Hopf hierarchy.
New integration theory on topological spaces, including fractals.
problem Developing a universal integration theory for arbitrary topological spaces.
method Introducing a new integration framework using unital magma valued functions and measures.
result Integration, differentiation, and orientation defined for arbitrary topological spaces.
We provide a unified approach that encompasses some integral formulas for functions of the visual angle of a compact convex set due to Crofton, Hurwitz and Masotti. The basic tool is an integral formula that also allows us to integrate new functions of the visual angle. As well we establish some upper and lower bounds …
Paper evaluates squared-exponential covariance function for Gaussian processes with integral observations.
problem Evaluating double line integrals of the squared exponential covariance function in Gaussian processes.
method Proposes a new approach to reduce double integrals to a single integral using the error function and efficiently computed with numerical techniques.
result Shows superior numerical robustness and accuracy compared to existing methods.
New symplectic scheme speeds up RMHMC.
problem Reducing computational burden in RMHMC.
method Explicit symplectic integration for non-separable Hamiltonians.
result Significant reduction in higher-order derivative calculations.
Study integrability in Poisson and Dirac structures from quotients.
problem Integrability of quotient constructions in Poisson and Dirac geometry.
method Analysis of Poisson and Dirac structures from quotient constructions.
result Explicit constructions of Lie groupoids integrating specific geometric structures.
Sharp criterion for Chern-Gauss-Bonnet integral using Q curvature.
problem Quantifying the Chern-Gauss-Bonnet integral using Q curvature.
method New approach involving singular integral estimation.
result Derivation of asymptotic formula for Q curvature equation.
New minimal surfaces found using Toda lattice and integrable systems.
problem Constructing new minimal surfaces with specific genus.
method Using Toda lattice and integrable systems techniques.
result New singly periodic minimal surfaces with genus j(j+1)/2−1. New definition of Born geometry connects to known geometries.
problem Defining and understanding Born geometries.
method Using Künneth structures and recursion operators.
result Born connection derived from Künneth connection for integrable geometries.
Investigates new F-structures and their Cauchy-Riemann properties.
problem Exploring new F-structures satisfying specific polynomial conditions. method Analyzes Cauchy-Riemann structure and integrability conditions.
result Identifies conditions for partial and complete integrability of F-structures. Lie algebroids can not always be integrated into Lie groupoids. We introduce a new object--``Weinstein groupoid'', which is a differentiable stack with groupoid-like axioms. With it, we have solved the integration problem of Lie algebroids. It turns out that every Weinstein groupoid has a Lie algebroid and every Lie al…
The paper proves conditions for Darboux integrability in diagonal hydrodynamic systems.
problem Conditions for Darboux integrability in diagonal hydrodynamic systems.
method Proof of conditions using Laplace transformation sequences and geometric interpretations.
result Diagonal systems of hydrodynamic type are Darboux integrable if and only if the corresponding systems for commuting flows are Darboux integrable.
New definition of Bäcklund transformation for surface isometric deformation.
problem Defining Bäcklund transformation in surface isometric deformation.
method Proving generic 4D integrable rolling distribution splits into 1D family of 3D distributions.
result Introducing new definition of Bäcklund transformation.
New method replaces traditional convex integration for solving geometric problems.
problem Constructing solutions with self-similarity properties in geometric embeddings.
method Introducing Kuiper differential relations and a Corrugation Process to replace traditional convex integration.
result Totally real isometric embeddings exhibit self-similarity and can be uniformly expressed.
New integral transforms solve multilayer heat equations.
problem Solving multilayer heat equations with moving boundaries.
method Expanding Dirac delta function in eigenfunctions, constructing oscillating integral transforms.
result Semi-analytical solutions for various problems.
Defines a new distance for integral current spaces and proves convergence criteria.
problem Defining a new distance metric for integral current spaces.
method Defines a new distance function and proves convergence criteria.
result Establishes the compactness theorem for integral current spaces using a new distance function.
New integral theorems improve density function estimations.
problem Improving density function estimations.
method Integrals based on cyclic functions and Riemann sums, Fourier integral theorem, Monte Carlo methods, variational approach, Cauchy residue theorem.
result Optimal cyclic functions minimize square integrals, improving density estimations.
We develop a class of integrals on a manifold M called exponential iterated integrals, an extension of K. T. Chen's iterated integrals. It is shown that the matrix entries of any upper triangular representation of the fundamental group of M can be expressed via these new integrals. The ring of exponential iterated inte…
New integrators for mechanical systems on Lie groups simplify based on group properties.
problem Designing numerical integrators for mechanical systems on Lie groups.
method Leverage retraction maps and Lie group properties to design structure-preserving integrators.
result Simplified design of integrators for Euler-Poincare and Lie-Poisson equations.
The paper interprets and proves integral formulas for visual angles.
problem Integral formulas of visual angles.
method Integral Geometry approach to Crofton, Hurwitz, and Masotti formulas.
result New simpler proofs of integral formulas.
New integrable matrix PDEs derived from Frölicher-Nijenhuis brackets.
problem Developing integrable systems from tensor field properties.
method Using Frölicher-Nijenhuis brackets to generate bi-differential graded algebras and PDE systems.
result New integrable nonlinear matrix PDEs and systems are derived.
Some years ago Moshé Flato pointed up that it could be interesting to develop the Nambu's idea to generalize Hamiltonian mechanic. An interesting new formalism in that direction was proposed by T. Takhtajan. His theory gave new perspectives concerning deformation quantization, and many authors have developed its mathem…
New curvature equations obstruct integrability of complex structures.
problem Understanding curvature obstructions to integrability of complex structures.
method Direct approach using Nijenhuis tensor derivatives and curvature scalars.
result Certain complex structures cannot coexist with non-flat constant curvature metrics.
The method of contact integrable extensions is used to find new zero-curvature representation for Plebañski's second heavenly equation.
The aim of this paper is to describe a class of conservative systems on S2 possessing an integral cubic in momenta. We prove that this class of systems consists off the case of Goryachev-Chaplygin, the one-parameter family of systems which has been found by the author in the previous paper (dg-ga/9711005) and a new …
A new diffeomorphism invariant of integral homology 3-spheres is defined using a non-abelian 'quaternionic' version of the Seiberg-Witten equations.