The paper classifies graph surfaces of product production functions in isotropic 3-space.
problem Understanding the geometry of production functions in economics.
method Analysis of graph surfaces in isotropic 3-space with constant curvature.
result Several classification results for product production functions in isotropic 3-space.
In this paper, we completely classify homogeneous production functions with an arbitrary number of inputs whose production hypersurfaces are flat. As an immediate consequence, we obtain a complete classification of homogeneous production functions with two inputs whose production surfaces are developable.
The study classifies geometric properties of quasi-product production models.
problem Understanding geometric properties of quasi-product production models.
method Analysis of graph hypersurfaces and classification results.
result Obtained classification results on quasi-product production functions.
The paper modifies a warped product space to find conditions for constant height functions.
problem Finding sufficient conditions for the height function to be constant in a modified warped product space.
method The paper modifies the warped product space by adding a warping function and discusses the sufficient condition for the height of immersed surfaces.
result The paper establishes a sufficient condition for the height function to be constant in the modified warped product space.
Proves a theorem for a specific type of warped product space.
problem Analyzing warped product spaces.
method Uses the warped function \( f(r) = \cosh\left(r\sqrt{\frac{\lambda}{n-2}}
ight) \) to prove the theorem.
result Proves an almost splitting theorem for the specified warped product space.
Productions functions map the inputs of a firm or a productive system onto its outputs. This article expounds generalizations of the production function that include state variables, organizational structures and increasing returns to scale. These extensions are needed in order to explain the regularities of the empiri…
Estimates production function of Iran's mining sector, finding capital and labor intensive.
problem Estimating production function of Iran's mining sector.
method Used co-integration method and time-series data for 1976-2006, augmented Dickey-Fuller and Phillips-Perron tests for stationarity.
result Elasticity of production with respect to capital and labor are 0.44 and 0.41, respectively; technological progress positively affects output.
Paper calculates volatility distribution for cumulative production.
problem Volatility distribution for cumulative production.
method Generalizes study of volatility with arbitrary distribution function.
result Exact probability distribution function for volatility.
The article studies groups generated by products and wreath products, focusing on first Betti numbers of Morse function orbits.
problem Calculating first Betti numbers of orbit groups generated by products and wreath products.
method Analyzes algebraic properties of specific groups G, proving ranks of center and quotient by commutator subgroup coincide. result The rank of the quotient by commutator subgroup is a first Betti number of the orbit of Morse function.
Paper examines stability of quadratic curvature functionals on product Einstein manifolds.
problem Understanding stability of critical points of quadratic curvature functionals on product Einstein manifolds.
method Analyzes Riemannian functionals defined by L2-norms of Ricci, scalar, Weyl, and Riemannian curvatures. result Product of a spherical space form and a compact hyperbolic manifold is unstable for some quadratic functionals if the first eigenvalue of the Laplacian of the hyperbolic manifold is sufficiently small.
Precise computations of Dehn functions for subgroups of free group products.
problem Computing precise Dehn functions for subgroups of direct products of free groups.
method Analyzing specific subgroups and using algebraic methods to compute Dehn functions.
result Quartic and quadratic Dehn functions for specific subgroups of free group products.
Characterizes Ricci almost solitons on semi-Riemannian warped products.
problem Characterizing Ricci almost solitons on semi-Riemannian warped products.
method Characterization using potential function dependence and fiber properties.
result Fiber is necessarily an Einstein manifold; base and warped product are also Einstein manifolds under certain conditions.
Heterogeneity of economic agents is emphasized in a new trend of macroeconomics. Accordingly the new emerging discipline requires one to replace the production function, one of key ideas in the conventional economics, by an alternative which can take an explicit account of distribution of firms' production activities. …
The paper proves Schauder estimates on cone products and characterizes harmonic functions.
problem Proving Schauder estimates for metric products of cones.
method Characterizing harmonic functions and using local approximations to measure Hölder continuity.
result Interior Schauder estimates for the Laplacian on cone products are proven.
The paper classifies hypersurfaces with specific curvature for economic applications.
problem Classifying hypersurfaces with null Gauss-Kronocker curvature.
method Complete classification of homothetical hypersurfaces in Euclidean space.
result Applications to production functions in economics.
Mathematically, a homothetic function is a function of the form f(x)=F(h(x1,...,xn)), where h is a homogeneous function of any degree d=0 and F is a monotonically increasing function. In economics homothetic functions are production functions whose marginal technical rate of substitution is homogeneo…
The paper examines conditions for compactness in sequences of warped product length spaces.
problem Conditions for compactness in sequences of warped product length spaces.
method Analyzes conditions on warping functions for compactness and Lipschitz bounds.
result Necessary conditions for compactness and Lipschitz bounds are identified.
New method detects non-product domains using squeezing function.
problem Detecting non-product bounded pseudoconvex domains.
method New application of squeezing function and optimal estimates.
result Identifies new family of holomorphic homogeneous regular domains.
We prove that complete warped product Einstein metrics with isometric bases, simply connected space form fibers, and the same Ricci curvature and dimension are isometric. In the compact case we also prove that the warping functions must be the same up to scaling, while in the non-compact case there are simple examples …
The paper proves rigidity for hypersurfaces with constant shifted curvature functions in warped product manifolds.
problem Characterizing and proving rigidity for hypersurfaces with constant shifted curvature functions.
method Using integral inequalities and Minkowski-type formulas, the paper derives rigidity theorems in sub-static warped product manifolds.
result The paper provides new characterizations and rigidity results for hypersurfaces with constant shifted curvature functions in warped product manifolds.
The study examines properties of gradient Yamabe solitons on warped product manifolds.
problem Investigating properties of gradient Yamabe solitons on warped product manifolds.
method Utilizing the maximum principle and modified Li-Yau's technique, the study finds gradient estimates for the warping function.
result The study finds three different gradient estimates for the warping function, one for each sign of the scalar curvature of the fiber manifold.
To obtain groups with bounded harmonic functions (which are not hyperbolic), one of the most frequent way is to look at some semi-direct products (\eg lamplighter groups). The aim here is to show that many of these semi-direct products do not admit harmonic functions with gradient in ℓp, for p∈[1,∞[.
Complete classification of isoparametric hypersurfaces in product spaces of space forms.
problem Classifying isoparametric hypersurfaces in product spaces of space forms.
method Proving constant product angle function and removing constant principal curvatures condition.
result Complete classification of isoparametric hypersurfaces in product spaces of space forms.
New rigidity found for 3D warped product domains.
problem Finding rigidity conditions for warped product domains.
method Developed scalar curvature rigidity for a general class of domains.
result Identified domains satisfying a boundary condition analogous to logarithmic concavity.
The study examines Einstein-Finsler spaces using Minkowskian products.
problem Characterizing Einstein-Finsler spaces through Minkowskian products.
method Proving conditions for Einstein-Finsler spaces in terms of Minkowskian products.
result If a Minkowskian product Finsler manifold is Einstein, then either the product manifold is Ricci flat or both quotient manifolds are Einstein with same scalar functions.
We give explicit formulas for the intertwinors on the scalar functions over the product of spheres with the natural pseudo-Riemannian product metric using the spectrum generating technique. As a consequence, this provides another proof of the even order conformally invariant differential operator formulas obtained earl…
Study on special symmetries in biwarped product 3-manifolds.
problem Characterizing Killing vector fields on biwarped product-type 3-manifolds.
method Derived system of equations for Killing fields and described their structure.
result Families of solutions found, including explicit examples.
Study on biwarped product submanifolds in Kähler manifolds, proving their existence and characterizing them.
problem Existence and characterization of biwarped product submanifolds in Kähler manifolds.
method Analyzing multiply warped product submanifolds, providing examples, and establishing inequalities.
result Existence and characterization of non-trivial biwarped product submanifolds in Kähler manifolds.
The study defines and constructs hypersurfaces in a product of two space forms.
problem Characterizing hypersurfaces in a product of two space forms.
method Explicit construction using parallel families of hypersurfaces and isoparametric hypersurfaces.
result Classification of hypersurfaces with constant mean curvature and constant product angle function.
Sharp growth estimates for warping functions in warped product manifolds.
problem Estimating growth of warping functions in warped product manifolds.
method Applying an average method in PDE to establish sharp inequalities.
result Sharp inequalities between mean curvature and sectional curvatures of the ambient manifold.
Study on warped products in contact skew-CR submanifolds with inequality and examples.
problem Analyzing warped products in contact skew-CR submanifolds.
method Established an inequality for the squared norm of the second fundamental form.
result Derived inequality and provided non-trivial examples.
Study of mean curvature flows in product manifolds with graph structures.
problem Understanding mean curvature flows in product manifolds.
method Analysis of mean curvature type flows of graphs in product manifolds \(N imes R\), establishing long-term existence and convergence with specific conditions.
result Established long-term existence and convergence of mean curvature flows with specified conditions.
Characterizes warping functions in Einstein Poisson warped spaces.
problem Existence and nonexistence of warping functions with constant scalar curvature.
method Analyzes various dimensions of base space and constant scalar curvature conditions.
result Characterizes warping functions for different dimensions of base space.
The GJMS operators of special Einstein products are factored into simpler operators and applied to solve the Q-Yamabe problem.
problem Factorization of GJMS operators in special Einstein products.
method Factorization of GJMS operators as a composition of second- and fourth-order differential operators.
result The Green's function for the GJMS operator of order 2k is positive for certain special Einstein products.
We discuss conformal deformation and warped products on some open manifolds. We discuss how these can be applied to construct Riemannian metrics with specific scalar curvature functions.
Researchers determine Dehn functions of specific nilpotent groups.
problem Understanding the Dehn functions of central products of nilpotent groups.
method Analyzing families of filiform and Lie groups to determine Dehn functions.
result Confirms conjecture and provides evidence for lower Dehn functions in central products.
The paper proves rigidity for submanifolds in warped product manifolds.
problem Rigidity of submanifolds in warped product manifolds.
method Dihedral extremality and rigidity theorem for submanifolds with polyhedral boundary.
result Dihedral rigidity results for hyperbolic polyhedra in flat warped product spaces.
Adaptive time decay functions improve financial product recommendation accuracy.
problem Inaccurate recommendations due to static historical data in finance.
method Time-dependent collaborative filtering with personalized decay functions.
result Significant improvements over state-of-the-art benchmarks in financial product recommendation.
We derive one unified formula for Ricci curvature tensor on arbitrary warped product manifold by introducing a new notation for the lift vector and the Levi-Civita connection.This formula is helpful to further consider Ricci flow (RF) and hyperbolic geometric flow (HGF) and evolution equations on warped product manifol…
Study on warped product Yamabe solitons with constant fiber curvature.
problem Characterizing nontrivial warped product Yamabe gradient solitons.
method Investigation of warped product manifolds, derivation of scalar curvature estimates.
result Nontrivial warped product Yamabe gradient solitons have constant scalar curvature in the fiber.
We establish a cubic lower bound on the Dehn function of a certain finitely presented subgroup of a direct product of 3 free groups.
Game theory helps analyze ESOs/EBIs in production and service sectors.
problem Economic incentives affect traditional production/service functions and create intangible capital.
method Uses game theory to analyze interactions in ESO/EBI transactions.
result No perfect Nash Equilibria for two-stage games involving many participants.
Arithmetic groups have polynomially bounded Dehn functions in certain products of Lie groups.
problem Understanding the Dehn functions of arithmetic groups in products of Lie groups.
method Utilizing results from Bestvina-Eskin-Wortman and Cornulier-Tessera.
result Arithmetic groups defined over global fields with specific properties have polynomially bounded Dehn functions.
Study investigates Kähler metrics and base metrics of Ricci solitons, classifying and characterizing them.
problem Investigating Kähler metrics and base metrics of Ricci solitons and quasi-solitons.
method Analyzes Kähler metrics conformal to gradient Ricci solitons and base metrics of warped product Ricci solitons (quasi-solitons). Uses functional dependence of soliton potentials and additional assumptions.
result Partial classification of Kähler metrics in dimension n≥4 and characterization of quasi-soliton metrics as Riemannian products under additional genericity hypothesis. The paper explores volume product and slicing conjectures using convex body deformations.
problem Volume product and slicing conjectures in convex geometry.
method Study of variational aspects of volume product functional under projective deformations.
result Provides a proof of a theorem by Klartag and identifies critical convex bodies.
The paper classifies hypersurfaces in H2imesH2 with constant curvature.
problem Classifying hypersurfaces in H2imesH2 with constant sectional curvature. method Analyzing the geometry of H2imesH2 and constructing specific examples. result Examples of hypersurfaces in H2imesH2 with non-constant product angle function. Researchers prove inner product recovery is impossible in latent space models.
problem Recovering inner products in latent space models with random geometric graphs.
method Rate-distortion theory applied to Gaussian or spherical latent locations.
result Impossible to recover inner products if dimensionality exceeds nh(p), matching positive results' conditions. Researchers find a way to bound the complexity of certain subgroup geometric invariants.
problem Understanding the geometric invariants of subgroups of direct products of free groups.
method Generalizing techniques for 'pushing fillings' into normal subgroups.
result Finitely presented subgroups of direct products of three free groups and subgroups of finiteness type Fn−1 in a direct product of n free groups have Dehn functions bounded above by N9.