Characterizes differential forms and vector fields with constant coefficients on manifolds.
problem Understanding constant coefficient differential forms and vector fields on manifolds.
method Analyzes differential forms and vector fields of specific degrees, proving obstructions and characterizing solutions to partial differential systems.
result Characterizes differential forms and vector fields with constant coefficients of various degrees on smooth manifolds.
The fused lasso is analyzed for high-dimensional piecewise-constant regression coefficients.
problem Estimation of high-dimensional piecewise-constant regression coefficients.
method Formulated a restricted isometry condition for the fused lasso estimator and derived estimation bounds.
result The estimation error can be dominated by either the lasso or the fused lasso rate, depending on the number of non-zero coefficients and piece-wise constant segments.
Gradient almost para-Ricci-like solitons have constant coefficients and scalar curvatures.
problem Characterizing gradient almost para-Ricci-like solitons on para-Sasaki-like Riemannian Π-manifolds. method Proving constant coefficients and scalar curvatures through analysis of soliton properties.
result Constant coefficients and scalar curvatures for gradient almost para-Ricci-like solitons.
Study optimal portfolios for many players in a market model with random coefficients.
problem Optimal portfolio selection for many players under relative performance criteria in a market model with random coefficients.
method Game theory and stochastic optimal control, focusing on CARA and CRRA risk preferences, and extending to continuum of players.
result Existence of forward Nash equilibrium and mean field equilibrium for the n-agent game and corresponding mean field stochastic optimal control problem.
In this paper we use wavelet concepts to show that correlation coefficient between two financial data's is not constant but varies with scale from high correlation value to strongly anti-correlation value This studies is important because correlation coefficient is used to quantify degree of independence between two va…
Proves solvability of general inverse σ_k equations with constant coefficients.
problem Solvability of general inverse σ_k equations with constant coefficients.
method Proves existence of unique solution if a C-subsolution exists.
result Confirms analytical conjecture for deformed Hermitian--Yang--Mills equation.
An investor faced with a contingent claim may eliminate risk by perfect hedging, but as it is often quite expensive, he seeks partial hedging (quantile hedging or efficient hedging) that requires less capital and reduces the risk. Efficient hedging for European call option was considered in the standard Black-Scholes m…
Proves log-concavity of cluster algebra coefficients for type An.
problem Log-concavity of cluster algebra coefficients.
method Introduced atomic theta basis and proved log-concavity for type An. result Proved log-concavity of coefficients for cluster algebra variables of type An. Study on Ricci-like solitons and gradient solitons on specific manifolds.
problem Characterizing solitons on Sasaki-like almost contact B-metric manifolds.
method Introduced and studied Ricci-like solitons with arbitrary potential and gradient solitons. Proved properties of the Ricci tensor and soliton coefficients.
result Gradient almost Ricci-like solitons have constant soliton coefficients.
Extends Kyle model to multiple traders with different time-preference coefficients.
problem Existence and convergence of discrete-time Kyle models with multiple insiders.
method Extends Basak and Cuoco's model to include traders with different time-preference coefficients.
result Parameter restrictions ensure the existence of a Radner equilibrium and long-term survival of traders.
In this article we prove completeness results for Sobolev metrics with nonconstant coefficients on the space of immersed curves and on the space of unparametrized curves. We provide necessary as well as sufficient conditions for the coefficients of the Riemannian metric for the metric to be metrically complete and we c…
We extend a result of Z. Feng and Z. Tu by showing that if one of the coefficients aj, 2≤j≤n, of Rawnlsey's epsilon function associated to a n-dimensional Cartan-Hartogs domain is constant, then the domain is biholomorphically equivalent to the complex hyperbolic space.
Guts determine the leading coefficients of L2-Alexander torsions for 3-manifolds.
problem Determining the leading coefficient of L2-Alexander torsions for 3-manifolds. method Using a new criterion for the convergence of Fuglede-Kadison determinants and the work of Agol and Zhang on guts of 3-manifolds.
result The leading coefficient equals the relative L2-torsion of the guts associated to the cohomology class. Sharp fractional Sobolev inequalities on closed manifolds identified.
problem Critical fractional Sobolev embedding on closed Riemannian manifolds.
method Intrinsic heat-kernel based framework, determining optimal coefficients, proving sharp inequalities.
result Sharp p-power inequality and almost sharp inequality established. Extended model ensures long-term survival of traders in limited stock market participation.
problem Limited stock market participation and survival of traders over long periods.
method Extended Basak and Cuoco (1998) model with different time-preference coefficients.
result Parameter restrictions ensure long-term survival of traders.
The abstract discusses nonuniqueness results for specific Riemannian invariants.
problem Identifying conditions for nonhomothetic conformal rescalings with constant Riemannian invariants.
method Identifying sufficient conditions for finite and infinite geometrically distinct periodic conformal rescalings.
result Improves and establishes nonuniqueness results for various Riemannian invariants.
Novel approach ensures stability of compact schemes for variable PDEs.
problem Ensuring stability of compact schemes for variable coefficient PDEs.
method Difference equation approach to derive stability conditions.
result Derives sufficient condition for unconditional stability.
A linear different operator L is called weakly hypoelliptic if any local solution u of Lu=0 is smooth. We allow for systems, that is, the coefficients may be matrices, not necessarily of square size. This is a huge class of important operators which cover all elliptic, overdetermined elliptic, subelliptic and parabolic…
Paper tests if beta coefficients in AMF model are consistent over time.
problem Testing time-invariance of beta coefficients in AMF model.
method Used AMF model with GIBS algorithm to identify relevant factors, compared to FF5 model.
result AMF model shows time-invariant beta coefficients for most periods, FF5 does not.
Explicit computation of symplectic form for PGLn(R)-Hitchin component.
problem Symplectic structure of PGLn(R)-Hitchin component. method Atiyah-Bott-Goldman symplectic form and global coordinates.
result Coefficients of the symplectic form are constant.
The techniques used in this paper are based on the exterior calculus of Maurer-Cartan forms, and Weingarten surfaces are used to illustrate the methods that apply to quadratic exterior equations with constant coefficients. Isothermic {\it surfaces of constant astigmatism} (non-linear Weingarten surfaces whose differenc…
We classify radial scalar flat metrics with constant third coeffcient of its TYZ expansion. As a byproduct of our analysis we provide a characterization of Simanca's scalar flat metric.
Characterizes Whitney forms on simplices and proves their uniqueness.
problem Characterizing Whitney forms on simplices.
method Proves the uniqueness of differential forms with affine coefficients.
result Whitney forms are the unique differential forms with affine coefficients.
The paper studies geometric constants under modified Ricci flows with variable parameters.
problem Understanding geometric constants under variable coupling parameters in Ricci flows.
method Introduced modified Ricci flows with variable coefficients, derived evolution formulas, and proved monotonicity conditions.
result Conditions for maintaining monotonicity of geometric constants under modified Ricci flows.
Let M be a rational homology sphere plumbed 3-manifold associated with a connected negative definite plumbing graph. We show that its Seiberg-Witten invariants equal certain coefficients of an equivariant multivariable Ehrhart polynomial. For this, we construct the corresponding polytopes from the plumbing graphs toget…
The Finsleroid--Finsler space becomes regular when the norm ∣∣b∣∣=c of the input 1-form b is taken to be an arbitrary positive scalar c(x)<1. By performing required direct evaluations, the respective spray coefficients have been obtained in a simple and transparent form. The adequate continuation into the regul…
A realization of coherent state Lie algebras by first-order differential operators with holomorphic polynomial coefficients on Kähler coherent state orbits is presented. Explicit formulas involving the Bernoulli numbers and the structure constants for the semisimple Lie groups are proved.
We use the natural lifts of the fundamental tensor field g to the cotangent bundle T*M of a Riemannian manifold (M,g), in order to construct an almost Hermitian structure (G,J) of diagonal type on T*M. The obtained almost complex structure J on T*M is integrable if and only if the base manifold has constant sectional c…
Researchers compute trace formula for magnetic Laplacian on hyperbolic surfaces.
problem Analyzing the magnetic Laplacian on compact hyperbolic surfaces.
method Computed the trace formula for magnetic Laplacian energies above the Mane critical level.
result Asymptotic behavior of trace formula coefficients near the Mane critical level.
Derives continuum model from discrete ε-graphs with connectivity functional.
problem Modeling diffusion in networks with varying connectivity.
method Energy-based continuum limit derivation, neural-network reconstruction of connectivity.
result Error between discrete and continuum energies is O(ε), valid even with fluctuations. Let φ∈C∞(Cn) be a given real valued function. We assume that $\pr\ddbarφ$ is non-degenerate of constant signature (n−,n+) on Cn. When q=n−, it is well-known that the Bergman kernel for (0,q) forms with respect to the k-th weight e−2kφ, k>0, admits a full asymptotic expansi…
We consider a general one-factor short rate model, in which the instantaneous interest rate is driven by a univariate diffusion with time independent drift and volatility. We construct recursive formula for the coefficients of the Taylor expansion of the bond price and its logarithm around τ=0, where τ is time to m…
Framework uses deep learning and statistical models to solve PDEs with discontinuous coefficients.
problem Solving PDEs with discontinuous coefficients.
method Two-stage physics-informed deep learning and statistical mixture models.
result Framework achieves adaptability and accurate parameter identification.
We study fractional configurations in gravity theories and Lagrange mechanics. The approach is based on Caputo fractional derivative which gives zero for actions on constants. We elaborate fractional geometric models of physical interactions and we formulate a method of nonholonomic deformations to other types of fract…
This paper mixes constant sum and constant product market makers to improve their features.
problem Improving the balance between stable exchange rates and liquidity in automated market makers.
method Mixing and designing new methods for AMMs with specific features.
result Demonstrates new tools for creating markets with desired characteristics.
We use an elliptic system of equations with complex coefficients for a set of complex-valued tensor fields as a tool to construct infinite-dimensional families of non-singular stationary black holes, real-valued Lorentzian solutions of the Einstein-Maxwell-dilaton-scalar fields-Yang-Mills-Higgs-Chern-Simons-f(R) equa…
This paper addresses parameter estimation for wave equations with Markovian switching.
problem Parameter estimation for wave equations with abrupt changes.
method Bayesian statistical framework using discrete sparse Bayesian learning.
result Strong performance in parameter estimation for variable coefficient PDEs.
Study finds Stäckel equivalence for superintegrable systems via invariant quadrics.
problem Understanding Stäckel equivalence in superintegrable systems.
method Using invariant quadrics to determine Stäckel classes of superintegrable systems.
result Stäckel classes of superintegrable systems can be derived from associated invariant quadrics.
Extends compactness theory to variable-coefficient pseudo-differential operators on manifolds.
problem Compensated compactness for pseudodifferential operators on vector bundles.
method Establishes a theorem for weakly convergent sequences of sections under a pseudo-differential operator.
result Quadratic form converges in distributional sense under certain conditions.
The study finds conditions for a third rank Killing tensor field on a 2D Riemannian torus.
problem Conditions for the existence of a third rank Killing tensor field on a 2D Riemannian torus.
method Analyzes the metric of the torus and uses Fourier coefficients to derive conditions for the function λ.
result Equations relating Fourier coefficients of the function λ determine the existence of a third rank Killing tensor field.
The Volume conjecture claims that the hyperbolic Volume of a knot is determined by the colored Jones polynomial. The purpose of this article is to show a Volume-ish theorem for alternating knots in terms of the Jones polynomial, rather than the colored Jones polynomial: The ratio of the Volume and certain sums of coeff…
Defines invariants for reflection groups and connects them to Frobenius structures.
problem Understanding invariants for reflection groups and their relation to Frobenius structures.
method Defines good basic invariants and shows their connection to Frobenius structures.
result Good basic invariants for reflection groups lead to Frobenius structure constants.
Abelian differentials on Riemann surfaces can be seen as translation surfaces, which are flat surfaces with cone-type singularities. Closed geodesics for the associated flat metrics form cylinders whose number under a given maximal length generically has quadratic asymptotics in this length, with a common coefficient c…
Study constant mean curvature tori in R^3 using spectral data and Whitham deformations.
problem Parameterize spectral data of constant mean curvature tori in R^3.
method Use Whitham deformations, blowups, and spectral data analysis.
result Prove the Wente family is parameterized by the bisector of the right angle.
Sharp uniqueness result for Q-curvature type equation on S^6.
problem Proving uniqueness of axially symmetric solutions to a Q-curvature type equation on S^6.
method New estimates on semi-norm and Gegenbauer coefficients.
result Axially symmetric solutions are constants for a specific range of α.
The standard asset pricing models (the CCAPM and the Epstein-Zin non-expected utility model) counterintuitively predict that equilibrium asset prices can rise if the representative agent's risk aversion increases. If the income effect, which implies enhanced saving as a result of an increase in risk aversion, dominates…
Formula for heat coefficients of curved conic singularities derived from Riemannian metrics.
problem Calculating heat coefficients for surfaces with curved conic singularities.
method Explicit formula derivation for coefficient b1/2(C) under rotationally invariant metrics near conical singularities. result The coefficient b1/2(C) varies irrationally under constant rescalings near the cone point, contrasting with other coefficients. Study rigidifies non-compact manifolds with specific curvature conditions.
problem Analyzing non-compact generalized m-quasi-Einstein manifolds with constant scalar curvature and soliton function.
method Introduced a weighted function and proved its subharmonicity to derive rigidity results.
result Proves manifolds are Euclidean under specific conditions, with constant μ essential.