arXiv research

Novel proof of Shepp's theorem using martingales.

New urn problem considers unknown sampling method.

Improved tracking of tangled point sources using Riemannian metrics.

In this work, we expand the idea of Samuelson[3] and Shepp[2,5,6] for stock optimization using the Bachelier model [4] as our models for the stock price at the money (X[stock price]= K[strike price]) for the American call and put options [1]. At the money (X= K) for American options, the expected payoff of both the cal…

Study utility maximization with delayed information in continuous time Gaussian markets.

During the Great Recession, Democrats in the United States argued that government spending could be utilized to "grease the wheels" of the economy in order to create wealth and to increase employment; Republicans, on the other hand, contended that government spending is wasteful and discouraged investment, thereby incr…

Fix two points $x,\bar{x}\in S^2$ and two directions (without orientation) $η,\barη$ of the velocities in these points. In this paper we are interested to the problem of minimizing the cost $J[γ]=\int_0^T g_{γ(t)}(\dotγ(t),\dotγ(t))+ K^2_{γ(t)}g_{γ(t)}(\dotγ(t),\dotγ(t)) ~dt$ along all smooth curves starting from $x…

Optimizes selling bonds with non-negative prices using a Brownian bridge model.

The paper solves optimal control problems for various convex sets using convex trigonometry.

Theorem analogues proven using Artin's approximation theorem.

AI generates theorems and proofs for training theorem provers.

Global inverse function theorem proved easily using Riemannian geometry.

A new comparison theorem for geometric spaces.

The paper proves a new theorem in Riemannian geometry and offers a new proof for Toponogov's theorem in Alexandrov geometry.

Revises a theorem by Thurston, finding a counter-example and a weaker version.

The paper proves three circles theorems and Liouville type theorems for subharmonic and holomorphic functions.

Paper develops formulas and theorems in Hermitian geometry.

Fixed-point theorems for set-valued maps using homological methods.

Proves Markov theorem for trivalent braids using L-move approach.

Proofs for Moon's theorem and its generalization.

New measure proves Poncelet-type theorems.

New theorem for doodles on sphere, similar to Markov's.

Investigates proving geometric theorems over complex and real numbers using tilings.

Analyzes Saito vanishing theorem using $L^{2}$ methods.

Extends calculus theorem to higher dimensions.

Extends symplectic reduction and theorem to Lie algebroids.

Paper generalizes complex Brunn-Minkowski theory and proves new extension theorems.

Proves Thurston's bounded image theorem for Haken manifolds.

Method upgrades limit theorems to mixing limit theorems for dynamical systems.

Formulates Index III lemma and Rauch III theorem with applications.

In LM, we proved a family version of the famous Witten rigidity theorems and several family vanishing theorems for elliptic genera. In this paper, we gerenalize our theorems LM in two directions. First we establish a family rigidity theorem for the Dirac operator on loop space twisted by general positive energy loop gr…

The paper explains the topological origin of the distinction between incidence theorems over division rings and fields.

INT benchmark tests theorem proving agents' ability to generalize to unseen theorems.

Proves two theorems on odd-dimensional manifolds with boundary.

Sharp convergence theorem for sphere submanifolds proved.

Abstracts a theorem for non-smooth maps in infinite dimensions.

Atiyah-Singer theorem links math fields, predicts topological insights.

Paper proves compactness and rigidity of $λ$-surfaces in 3D.

Generalizes Simon's theorem to spacetime and hyperbolic manifolds.

Notes on a theorem with broad applications in dynamical systems.

The paper proves injectivity and vanishing theorems on compact Kahler manifolds.

Paper generalizes a theorem for real analytic singularities.

The paper proves sphere theorems for submanifolds in Kähler manifolds.

The paper proves an equivariant Kastler-Kalau-Walze theorem for various spin manifolds.

Several proofs of Fáry--Milnor theorem are presented.

Reviews g-theorem and hard Lefschetz theorem for face rings.

The paper generalizes the Liouville theorem for minimal hypersurfaces with finite index.

The paper extends cyclic cocycles and proves relative index theorems for partitioned manifolds.