A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
A kinematic method selects the deformation Laplacian for fluid dynamics on Riemannian manifolds.
Global stability proved for Navier-Stokes equations on hyperbolic space.
On curved spaces, viscous fluids reach equilibrium quickly.
Proves a special case of the Gaussian kinematic formula using large sphere limits.
In this research, Artificial Neural Networks (ANNs) have been used as a powerful tool to solve the inverse kinematic equations of a parallel robot. For this purpose, we have developed the kinematic equations of a Tricept parallel kinematic mechanism with two rotational and one translational degrees of freedom (DoF). Us…
Proposes KStar Diffuser for kinematics-aware bimanual robotic manipulation.
Paper studies viscosity solutions in unique Martinet spaces.
The paper uses complex-valued functions to simplify plane differential geometry and kinematics.
New formulas for measuring geometric properties of definable sets.
Paper proposes a smart neck-band for detecting neck postures using integrated kinematic and kinetic data.
Proves existence and uniqueness of viscosity solutions to complex Hessian equations on compact Hermitian manifolds.
Smooth solutions found for a specific type of Yamabe problem.
This paper establishes the existence of a unique nonnegative continuous viscosity solution to the HJB equation associated with a Markovian linear-quadratic control problems with singular terminal state constraint and possibly unbounded cost coefficients. The existence result is based on a novel comparison principle for…
The thesis explores kinematical symmetries beyond Lorentzian spacetime.
The paper concerns singular solutions of nonlinear elliptic equations, which include removable singularities for viscosity solutions, a strengthening of the Hopf Lemma including parabolic equations, Strong maximum principle and Hopf Lemma for viscosity solutions including also parabolic equations.
Convex solutions to a specific equation are smooth when the phase is smooth enough.
We establish the estimates of modulus of continuity for viscosity solutions of nonlinear evolution equations on manifolds, extending previous work of B. Andrews and J. Clutterbuck for regular solutions on manifolds \cite{AC3} and the first author's recent work for viscosity solutions in Euclidean spaces \cite{me1}.
In this work we consider viscosity solutions to second order partial differential equations on Riemannian manifolds. We prove maximum principles for solutions to Dirichlet problem on a compact Riemannian manifold with boundary. Using a different method, we generalize maximum principles of Omori and Yau to a viscosity v…
Explains non-lorentzian theories and their dynamics.
Model predicts viscosity of multicomponent systems efficiently.
We introduce different bases for the vector space of -invariant, translation invariant continuous valuations on the quaternionic plane and determine a complete set of kinematic formulas.
Study explores kinematics of surfaces under metric restrictions.
Study the geometry and dynamics of skew evolutes and involutes, related to bicycle kinematics.
Self-driving vehicles (SDVs) hold great potential for improving traffic safety and are poised to positively affect the quality of life of millions of people. To unlock this potential one of the critical aspects of the autonomous technology is understanding and predicting future movement of vehicles surrounding the SDV.…
Researchers prove formulas for flag area measures, extending previous work.
The existence of kinematic formulas for area measures with respect to any connected, closed subgroup of the orthogonal group acting transitively on the unit sphere is established. In particular, the kinematic operator for area measures is shown to have the structure of a co-product. In the case of the unitary group the…
We develop an alternative approach to Degenerate complex Monge-Ampère equations on compact Kähler manifolds based on the concept of viscosity solutions and compare systematically viscosity concepts with pluripotential theoretic ones. We generalize to the Kähler case a theorem due to Dinew and Zhang in the projective ca…
In this contribution we review results on the kinematics of a quantum system localized on a connected configuration manifold and compatible dynamics for the quantum system including external fields and leading to non-linear Schrödinger equations for pure states.
Viscosity solutions are suitable notions in the study of nonlinear PDEs justified by estimates established via the maximum principle or the comparison principle. Here we prove that the isoperimetric profile functions of Riemannian manifolds with Ricci lower bound are viscosity super-solutions of some nonlinear differen…
A kinematics of the motion of a car is reformulated in terms of the theory of gauge potentials (connection on principal bundle). E(2)-connection originates in the no-slipping contact of the car with a road.
New kinematic model for a spin-rolling sphere using Darboux frame.
In this paper, we investigate the moduli of continuity for viscosity solutions of a wide class of nonsingular quasilinear evolution equations and also for the level set mean curvature flow, which is an example of singular degenerate equations. We prove that the modulus of continuity is a viscosity subsolution of some o…
We consider the kinematics of specific fluid spacetimes admitting timelike congruences of Ricci Solitons. These fluids includes string cloud, string fluid, perfect fluid, radially symmetric fluid, anisotropic fluid and relativistic magneto-fluid. Results are obtained and important physical aspects are discussed.
New proofs for curvature problems using a viscosity approach.
We establish interior regularity for convex viscosity solutions of the special Lagrangian equation. Our result states that all such solutions are real analytic in the interior of the domain.
We apply ideas from viscosity theory to establish the existence of a unique global weak solution to the generalized Kahler-Ricci flow in the setting of commuting complex structures. Our results are restricted to the case of a smooth manifold with smooth background data. We discuss the possibility of extending these res…
We prove that higher moment maps on area measures of a euclidean vector space are injective, while the kernel of the centroid map equals the image of the first variation map. Based on this, we introduce the space of smooth dual area measures on a finite-dimensional euclidean vector space and prove that it admits a natu…
Paper aims to minimize ruin probability in insurance companies using Sparre Andersen model.
Paper generates synthetic radar signatures for motion classification.
This is the content of the lectures given by the author at the winter school KAWA3 held at the University of Barcelona in 2012 from January 30 to February 3. The main goal was to give an account of viscosity techniques and to apply them to degenerate Complex Monge-Ampère equations following recent works of P. Eyssidieu…
Generalizes kinematical Lie algebras for isotropic spacetimes.
Generic level sets in mean curvature flow are BV solutions.
Abstract: Survey on quadratic Hessian equations, their properties, and open problems.
We study viscosity solutions to complex hessian equations. In the local case, we consider a bounded domain in the standard Kähler form in and Under some suitable conditions on , we prove that the equation $(dd^c \varphi)^m\wedgeβ^{n-m}=F(x,\varphi)β^n,\ \f=…
We consider the problem of inverse kinematics (IK), where one wants to find the parameters of a given kinematic skeleton that best explain a set of observed 3D joint locations. The kinematic skeleton has a tree structure, where each node is a joint that has an associated geometric transformation that is propagated to a…
Sharp Lipschitz bounds and gradient estimates for fully nonlinear parabolic equations.
New equations reveal viscosity from boundary measurements.
We observe that the comparison result of Barles-Biton-Ley for viscosity solutions of a class of nonlinear parabolic equations can be applied to a geometric fully nonlinear parabolic equation which arises from the graphic solutions for the Lagrangian mean curvature flow.