arXiv research

We construct cup and cap products in intersection (co)homology with field coefficients. The existence of the cap product allows us to give a new proof of Poincare duality in intersection (co)homology which is similar in spirit to the usual proof for ordinary (co)homology of manifolds.

We show that there is a well-defined cap-product structure on the Fintushel-Stern spectral sequence. Hence we obtain the induced cap-product structure on the ${\BZ}_8$-graded instanton Floer homology. The cap-product structure provides an essentially new property of the instanton Floer homology, from a topological poin…

Study investigates minimal surfaces in spherical caps, extending previous findings.

The paper studies parallel surfaces of cuspidal cross caps and their degeneracy.

New flow for capillary surfaces converges to spherical caps.

For a normal covering over a closed oriented topological manifold we give a proof of the L2-signature theorem with twisted coefficients, using Lipschitz structures and the Lipschitz signature operator introduced by Teleman. We also prove that the L-theory isomorphism conjecture as well as the C^*_max-version of the Bau…

The paper models SaaS products as insurance, offering new pricing tools.

Perfect pairing for tropical cycles on integral affine manifolds.

This paper works out fair values of stock loan model with automatic termination clause, cap and margin. This stock loan is treated as a generalized perpetual American option with possibly negative interest rate and some constraints. Since it helps a bank to control the risk, the banks charge less service fees compared …

In this paper, we shall show a condition for that a chart is C-move equivalent to the product of two charts, the union of two charts $Γ^*$ and $Γ^{**}$ which are contained in disks $D^*$ and $D^{**}$ with $D^*\cap D^{**}=\emptyset$.

Investigates minimal genus of second homology classes in RAAGs, finding bounds and specific cases.

In this paper we first introduce two new financial products: stock loan and capped stock loan. Then we develop a pure variational inequality method to establish explicitly the values of these stock loans. Finally, we work out ranges of fair values of parameters associated with the loans.

We consider symplectic Floer homology in the lowest nontrivial dimension, that is to say, for area-preserving diffeomorphisms of surfaces. Particular attention is paid to the quantum cap product; we show that it distinguishes the trivial element of the mapping class group from any nontrivial one.

We study the spherical cap packing problem with a probabilistic approach. Such probabilistic considerations result in an asymptotic sharp universal uniform bound on the maximal inner product between any set of unit vectors and a stochastically independent uniformly distributed unit vector. When the set of unit vectors …

We revisit Spakula's uniform K-homology, construct the external product for it and use this to deduce homotopy invariance of uniform K-homology. We define uniform K-theory and on manifolds of bounded geometry we give an interpretation of it via vector bundles of bounded geometry. We further construct a cap product with…

The paper uses LSMC to price capped American options with time-dependent caps.

It is classically known that generic smooth maps of R^2 into R^3 admit only cross cap singularities. This suggests that the class of cross caps might be an important object in differential geometry. We show that the standard cross cap (u,uv,v^2) has non-trivial isometric deformations with infinite dimensional freedom. …

Study symmetry of cross-cap surfaces with folding maps.

Paper classifies symmetries of cross caps using invariants.

This paper proves geodesic curvature measures are bounded for curves near cross cap singularities.

Two cross caps in Euclidean $3$-space are said to be formally isometric if their Taylor expansions of the first fundamental forms coincide by taking a suitable local coordinate system. For a given $C^\infty$ cross cap $f$, we give a method to find all cross caps which are formally isometric to $f$. As an application, w…

We give a variational proof of the existence and uniqueness of a convex cap with the given upper boundary. The proof uses the concavity of the total scalar curvature functional on the space of generalized convex caps. As a byproduct, we prove that generalized convex caps with the fixed boundary are globally rigid, that…

This study improves mid-cap equity performance with a data-driven, market-neutral approach.

3D spherical caps are rigid under certain perturbations.

Improved LDA with capped l_{2,1}-norm reduces outlier sensitivity.

In the paper we consider the following conjecture: if a finite group $G$ possesses a solvable $π$-Hall subgroup $H$, then there exist elements $x,y,z,t\in G$ such that the identity $H\cap H^x\cap H^y\cap H^z\cap H^t=O_π(G)$ holds. The minimal counter example is shown to be an almost simple group of Lie type.

Study analyzes order transitions in high, medium, and low market cap stocks using Markov chains.

Study of free boundary minimal Möbius bands in spherical caps.

Proposes a diagnostic method to evaluate factor models using cap-axis integrals.

Proposes a diagnostic method to evaluate factor models using cap-axis integrals.

Let $M$ be a smooth closed $4k$-manifold whose Yamabe invariant $Y(M)$ is nonpositive. We show that $Y(M\sharp l \Bbb HP^k\sharp m \bar{\Bbb HP^k})=Y(M),$ where $l,m$ are nonnegative integers, and $\Bbb HP^k$ is the quaternionic projective space. When $k=4$, we also have $$Y(M\sharp l CaP^2\sharp m \bar{CaP^2})=Y(M),…

This paper examines the valuation of American capped call options with two-level caps. The structure of the immediate exercise region is significantly more complex than in the classical case with constant cap. When the cap grows over time, making extensive use of probabilistic arguments and local time, we show that the…

The paper uses Floer homology to study twist coefficients and their behavior after capping off.

CAP adapts optimization to class attributes for better fairness.

This work studies the chord length distribution, in the case where both ends lie on a $N$-dimensional hypersphere ($N \geq 2$). Actually, after connecting this distribution to the recently estimated surface of a hyperspherical cap \cite{SLi11}, closed-form expressions of both the probability density function and the cu…

The paper constructs metrics with negative curvature on complex manifolds.

Study counts and equidistributes tori in Kleinian group self-joinings.

Investors face constraints in Heston's model; optimal allocation differs from naive capped strategy.

A global agreement on how to reduce and cap human footprint, especially their GHG emissions, is very unlikely in near future. At the same time, bilateral agreements would be inefficient because of their neural and balanced nature. Therefore, unilateral actions would have attracted attention as a practical option. Howev…

New method distinguishes 4-manifold types using trisections.

We prove relative versions of the symplectic capping theorem and sufficiency of Giroux's criterion for Stein fillability and use these to study the 4-genus of knots.

The paper shows how to use hyperplanes and hyperballs interchangeably using inversive geometry.

FSD-CAP improves graph feature imputation under high missing rates.

This study examines return and risk of Puerto Rico stock market IRA products.

The study finds the optimal metrics for free boundary minimal surfaces in spherical caps.

Let $(G,h)$ be a nilpotent Lie group endowed with a left invariant Riemannian metric, $\mathfrak{g}$ its Euclidean Lie algebra and $Z(\mathfrak{g})$ the center of $\mathfrak{g}$. By using an orthonormal basis adapted to the splitting $\mathfrak{g}=(Z(\mathfrak{g})\cap[\mathfrak{g},\mathfrak{g}])\oplus O^+\oplus (Z(\mat…

CAP algorithm controls FCR in online selective prediction.

We study PCA as a stochastic optimization problem and propose a novel stochastic approximation algorithm which we refer to as "Matrix Stochastic Gradient" (MSG), as well as a practical variant, Capped MSG. We study the method both theoretically and empirically.