Study space-like and time-like surfaces in Robertson-Walker space-times with positive nullity.
problem Characterize space-like and time-like surfaces in Robertson-Walker space-times with positive relative nullity.
method Provide necessary and sufficient conditions, local classification theorems, and analyze special spaces.
result Local classification theorems for space-like and time-like surfaces in L14(f,0) with positive relative nullity. Study on moduli space of metrics with positive scalar curvature.
problem Topology of moduli space of metrics with positive scalar curvature.
method Analyzes the moduli space of concordances of metrics with positive scalar curvature.
result Shows non-trivial homotopy groups in the moduli space.
The paper proves conditions for positive scalar curvature and Yamabe constant on noncompact cylinders.
problem Conditions for positive scalar curvature and Yamabe constant on noncompact cylinders.
method Analyzes complete metrics with positive scalar curvature and Yamabe constant on noncompact cylinders.
result Positive scalar curvature and Yamabe constant conditions are satisfied under specific geometric and conformal class constraints.
Paper tackles survival data analysis with positive and unlabeled observations.
problem Traditional survival analysis yields biased results with positive-unlabeled data.
method Developed parametric, nonparametric, and machine learning models for positive and unlabeled survival data.
result Proposed estimation method provides valid results for positive-unlabeled survival data.
Study finds metrics with positive intermediate Ricci curvature on specific low-dimensional manifolds.
problem Existence of invariant metrics with positive intermediate Ricci curvature on low-dimensional cohomogeneity one manifolds.
method Construction of invariant metrics with positive intermediate Ricci curvature on specific manifolds.
result Invariant metrics with positive 4th-intermediate Ricci curvature exist but not for 3rd-intermediate Ricci curvature on certain manifolds.
New upper bound on Jones polynomial for fibered positive links.
problem Classifying positive and non-positive knots of crossing number ≤ 12.
method Proved a new upper bound on the maximum degree of Jones polynomial for fibered positive knots.
result Maximum degree of Jones polynomial for fibered positive knots is at most four times the minimum degree.
The paper extends the spacetime positive mass theorem to multiple time dimensions.
problem Proving the nonnegativity of mass in spacetimes with multiple time dimensions.
method Generalizing the spacetime positive mass theorem to include multiple time dimensions and showing mass nonnegativity through energy inequalities.
result Equality in the energy inequality implies a foliation by flat submanifolds.
Classifies self-similar solutions for heat equations with positive speed.
problem Classifying self-similar solutions for semilinear heat equations.
method Analyzes the semilinear heat equation ut=Δu+∣u∣p−1u for p>1. result Finite time blowing up solutions converge to a positive constant after rescaling.
In this paper, we prove a differential Harnack inequality for positive solutions of time-dependent heat equations with potentials. We also prove a gradient estimate for the positive solution of the time-dependent heat equation.
Bayesian analysis of financial time series using R-INLA.
problem Analyzing interdependencies between stock volatility measures.
method Flexible level correlated model (LCM) with INLA approximation.
result Fast approximate Bayesian modeling of positive-valued time series.
We prove that Ricci flows with almost maximal extinction time must be nearly round, provided that they have positive isotropic curvature when crossed with R2. As an application, we show that positively curved metrics on S3 and RP3 with almost maximal width must be nearly round.
Proves positive energy conjecture for a specific metric class.
problem Proving the positive energy conjecture for a class of AHM metrics.
method Analyzes asymptotically Horowitz-Myers (AHM) metrics on R2imesTn−2. result Generalizes previous results on positive energy conjecture.
We constructively prove the existence of time-discrete consumption processes for stochastic money accounts that fulfill a pre-specified positively homogeneous projection property (PHPP) and let the account always be positive and exactly zero at the end. One possible example is consumption rates forming a martingale und…
Introduces Θ-positivity in Lie groups, generalizing Lusztig's positivity.
problem Generalizing Lusztig's total positivity to a broader class of Lie groups.
method Introduces and studies Θ-positivity in real simple Lie groups. result Four families of Lie groups admit Θ-positive structures. This paper is devoted to the study of the evolution of positively curved metrics on the Wallach spaces SU(3)/Tmax, Sp(3)/Sp(1)×Sp(1)×Sp(1), and F4/Spin(8). We prove that for all Wallach spaces, the normalized Ricci flow evolves all generic invariant Riemannian metrics with positive sectional curv…
Study shows long-term flow on special manifolds with positive Yamabe constant.
problem Analyzing long-time behavior of Yamabe flow on singular spaces.
method Formulated axioms for long-time existence, used parabolic Moser iteration for bounds.
result Established long-time existence of normalized Yamabe flow on specified manifolds.
Polynomial-time algorithm for homotoping arcs or curves into efficient position.
problem Finding efficient position for arcs or curves on surfaces.
method Polynomial-time algorithm using local homotopies.
result Polynomial-time efficient position achieved for surfaces of positive complexity.
Improved solver maintains positivity and accuracy across all time steps.
problem Linear second-order schemes for Fokker-Planck equation cannot preserve positivity.
method Flux-Corrected Diagonal Frog (FCDF) framework using nonlinear extension and iterative limiter.
result FCDF schemes are unconditionally positive across all time steps and maintain second-order accuracy.
Survey on Kähler-Ricci flow solutions.
problem Existence of solutions for Kähler-Ricci flow.
method Survey of recent developments.
result Discussion of solutions existing for all positive times.
We develop Square Root Graphical Models (SQR), a novel class of parametric graphical models that provides multivariate generalizations of univariate exponential family distributions. Previous multivariate graphical models [Yang et al. 2015] did not allow positive dependencies for the exponential and Poisson generalizat…
Curvature flows in hyperbolic space preserve positive sectional curvature and contract to a point.
problem Preserving positive sectional curvature in contracting curvature flows in hyperbolic space.
method Homogeneous speed flow with positive sectional curvature, including kth mean curvature flow. result Positive sectional curvature is preserved and the hypersurface contracts to a round point in finite time.
Prove existence of SO(3)imesSO(8)-invariant Einstein metric on S3imesS7
problem Prove existence of SO(3)imesSO(8)-invariant Einstein metric on S3imesS7 method Prove existence of SO(3)imesSO(8)-invariant Einstein metric on S3imesS7 result Prove existence of SO(3)imesSO(8)-invariant Einstein metric on S3imesS7 In this paper, we introduce the flag-wise positively curved condition for Finsler spaces (the (FP) Condition), which means that in each tangent plane, we can find a flag pole in this plane such that the corresponding flag has positive flag curvature. Applying the Killing navigation technique, we find a list of compact …
Two positive scalar curvature metrics g0, g1 on a manifold M are psc-isotopic if they are homotopic through metrics of positive scalar curvature. It is well known that if two metrics g0, g1 of positive scalar curvature on a closed compact manifold M are psc-isotopic, then they are psc-concordant: i.e., …
We consider a discrete-time, linear state equation with delay which arises as a model for a trader's account value when buying and selling a risky asset in a financial market. The state equation includes a nonnegative feedback gain α and a sequence v(k) which models asset returns which are within known bounds but o…
Proves positive mass theorems for specific ALF and ALG manifolds.
problem Proving positive mass theorems for ALF and ALG manifolds.
method Reduces the problem to non-existence of positive scalar curvature metrics on closed manifolds.
result Shows that incompressible conditions for S1 and T2 are sufficient for nonnegativity of mass. We observe that an analogue of the Positive Mass Theorem in the time-symmetric case for three-space-time-dimensional general relativity follows trivially from the Gauss-Bonnet theorem. In this case we also have that the spatial slice is diffeomorphic to $\Real^2$.
New curvature concept shows certain manifolds can't have positive curvature.
problem Understanding manifolds that can't have positive curvature metrics.
method Introducing m-intermediate curvature and using stable weighted slicings. result Manifolds Nn=Mn−mimesTm do not admit positive m-intermediate curvature for n≤7. We introduce Θ-positivity, a new notion of positivity in real semisimple Lie groups. The notion of Θ-positivity generalizes at the same time Lusztig's total positivity in split real Lie groups as well as well known concepts of positivity in Lie groups of Hermitian type. We show that there are two other families of …
New mass-type invariants for cosmological space-times.
problem Characterize de Sitter solutions in space-times with a cosmological constant.
method Introduce new mass-type invariants and prove positive mass theorems.
result 1-harmonic Mass provides new characterizations and inequalities.
The paper proves complex geometry results for manifolds of the form X × R², answering a 1994 conjecture.
problem Proving complex geometry results for manifolds of the form X × R².
method Using Riemannian and complex geometry techniques, the authors show the existence of metrics with positive scalar curvature.
result The paper answers a 1994 Rosenberg-Stolz conjecture for X × R², extending results to noncompact manifolds.
Finite time for Ricci flow on certain manifolds.
problem Finite time of Ricci flow on specific manifolds.
method Analysis of homogeneous Ricci flows on noncompact manifolds.
result Finite extinction time for a family of homogeneous Ricci flows.
This paper finds a metric on \(S^2 imes T^2\) with strictly positive biorthogonal curvature using an affine connection with antisymmetric torsion.
problem Existence of a Riemannian metric on \(S^2 imes T^2\) with strictly positive biorthogonal curvature.
method Introducing an affine connection with antisymmetric torsion calibrated via non-trivial cohomology classes, which allows overcoming topological constraints.
result Demonstrates the construction of a metric on \(S^2 imes T^2\) with strictly positive biorthogonal curvature.
Study free circle actions on specific 7-manifolds with positive Ricci curvature.
problem Classify and construct metrics on manifolds with a specific cohomology ring.
method Classify manifolds, construct free circle actions, and find positive Ricci curvature metrics.
result Almost all manifolds admit infinitely many non-equivalent free circle actions with positive Ricci curvature.
Study the positive mass theorem for certain asymptotic manifolds.
problem Positive mass theorem for specific types of asymptotic manifolds.
method Compactification and analysis of Riemannian manifolds.
result Established conditions for the positive mass theorem.
In this paper, position vectors of a time-like curve with respect to standard frame of Minkowski space E13 are studied in terms of Frenet equations. First, we prove that position vector of every time-like space curve in Minkowski space E13 satisfies a vector differential equation of fourth order. The general so…
Learning a classifier with control on the false-positive rate plays a critical role in many machine learning applications. Existing approaches either introduce prior knowledge dependent label cost or tune parameters based on traditional classifiers, which lack consistency in methodology because they do not strictly adh…
The study constructs metrics with positive 2nd Ricci curvature on various manifolds.
problem Constructing metrics with positive 2nd Ricci curvature on closed manifolds.
method Generalization of the concept of fatness to ensure the existence of metrics with positive 2nd Ricci curvature on certain homogeneous bundles.
result Infinitely many examples of manifolds with positive 2nd Ricci curvature, including non-simply connected spaces.
Extends double linear policy with time-varying weights and proves robust positive expectation.
problem Ensuring robustness in policy optimization with time-varying parameters.
method Employed a novel elementary symmetric polynomials characterization approach to prove robust positive expectation (RPE). Derived explicit expressions for expected cumulative gain-loss and variance.
result Proved the robust positive expectation property holds for the extended double linear policy.
Totally geodesic submanifolds in product spaces imply special curvature properties.
problem Characterizing manifolds based on the existence of totally geodesic submanifolds.
method Analyzing totally geodesic submanifolds in products of non-positively curved manifolds with transversality conditions.
result If infinitely or just a single dense such submanifolds exist, the manifold must be locally symmetric.
A Sasakian structure on a manifold is called {\it positive} if its basic first Chern class can be represented by a positive (1,1)-form with respect to its transverse holomorphic CR-structure. We prove a theorem that says that every positive Sasakian structure can be deformed to a Sasakian structure whose metric has pos…
Classifies 3-manifolds with uniformly positive scalar curvature.
problem Classifying 3-manifolds with uniformly positive scalar curvature.
method Analyzes properties of 3-manifolds with mean convex boundaries and uniformly positive scalar curvature.
result 3-manifolds with uniformly positive scalar curvature are homeomorphic to sums of spherical 3-manifolds and S1imesS2. New geometric framework for positive semidefinite matrices of fixed rank.
problem Statistical analysis of positive semidefinite matrices of fixed rank.
method Introducing a manifold S(n,p)∗ with Riemannian geometry and Lie group structure. result Analytical closed forms for geodesics and Fréchet means.
Since the introduction and the public availability of the \textsc{ucr} time series benchmark data sets, numerous Time Series Classification (TSC) methods has been designed, evaluated and compared to each others. We suggest a critical view of TSC performance evaluation protocols put in place in recent TSC literature. Th…
We prove that every complete connected immersed surface with positive extrinsic curvature K in H2×R must be properly embedded, homeomorphic to a sphere or a plane and, in the latter case, study the behavior of the end. Then, we focus our attention on surfaces with positive constant extrinsic curvature (K−s…
New k-means method clusters radar image sequences using SPD matrices.
problem Clustering radar image sequences efficiently.
method Developed k-means on SPD matrices for non-Euclidean data. result Effective clustering of radar image sequences via SPD matrices.
Built on a recent work of Almaraz, Barbosa, de Lima on positive mass theorems on asymptotically flat manifods with a noncompact boundary, we apply free boundary minimal surface techniques to prove their positive mass theorem and study the existence of positive scalar curvature metrics with mean convex boundary on a con…
In this paper, based on an intrinsic definition of asymptotically AdS space-times, we show that the standard anti-de Sitter space-time is the unique strictly stationary asymptotically AdS solution to the vacuum Einstein equations with negative cosmological constant in dimension less than 7. Instead of using the positiv…