arXiv research

Study improves dividend discount model using VAR process.

We compute two vector field models of the Carnot algebra with the growth vector (2,3,5,8), and an infinitesimal symmetry of the corresponding sub-Riemannian structure.

This paper is a starting point towards computing the Hausdorff dimension of submanifolds and the Hausdorff volume of small balls in a sub-Riemannian manifold with singular points. We first consider the case of a strongly equiregular submanifold, i.e., a smooth submanifold N for which the growth vector of the distributi…

The study generalizes a specific geometric correspondence to higher dimensions.

We study local control of the mechanism with the growth vector (4,7). We study controllability and extremal trajectories on the nilpotent approximation as an example of the control theory on Lie group. We give solutions of the system an show examples of local extremal trajectories.

Derives a new maximum principle for Riemannian manifolds with volume growth constraints.

Consider vector valued harmonic maps of at most linear growth, defined on a complete non-compact Riemannian manifold with non-negative Ricci curvature. For the norm square of the pull-back of the target volume form by such maps, we report a strong maximum principle, and equalities among its supremum, its asymptotic ave…

Ancient solutions on a strip are constant if polynomial, and have finite-dimensional space for slower growth.

In this article, we study properly immersed complete noncompact submanifolds in a complete shrinking gradient Ricci soliton with weighted mean curvature vector bounded in norm. We prove that such a submanifold must have polynomial volume growth under some mild assumption on the potential function. On the other hand, if…

New $G_2$ symmetry found in 8D distribution with 6D square.

We analyse the asymptotical growth of Vassiliev invariants on non-periodic flow lines of ergodic vector fields on domains of $\R^3$. More precisely, we show that the asymptotics of Vassiliev invariants is completely determined by the helicity of the vector field. As an application, we determine the asymptotic Alexander…

We consider vector fields $X$ on a closed manifold $M$ with rest points of Morse type. For such vector fields we define the property of exponential growth. A cohomology class $ξ\in H^1(M;\mathbb R)$ which is Lyapunov for $X$ defines counting functions for isolated instantons and closed trajectories. If $X$ has exponent…

We give lower bounds for the growth of the number of Reeb chords and for the volume growth of Reeb flows on spherizations over closed manifolds M that are not of finite type, have virtually polycyclic fundamental group, and satisfy a mild assumption on the homology of the based loop space. For the special case of geode…

We consider a vector field $X$ on a closed manifold which admits a Lyapunov one form. We assume $X$ has Morse type zeros, satisfies the Morse--Smale transversality condition and has non-degenerate closed trajectories only. For a closed one form $η$, considered as flat connection on the trivial line bundle, the differen…

Germs of Goursat distributions can be classified according to a geometric coding called an RVT code. Jean (1996) and Mormul (2004) have shown that this coding carries precisely the same data as the small growth vector. Montgomery and Zhitomirskii (2010) have shown that such germs correspond to finite jets of Legendrian…

Efficient algorithms solve large-scale DRSVM problems.

The paper proves that certain modified conformal vector fields are trivial on compact and non-compact manifolds.

Study examines boundedness of oscillating singular integrals on specific Lie groups.

Analytic torsion and Reidemeister torsion help show exponential growth of torsion in cohomology.

Effective plant growth and yield prediction is an essential task for greenhouse growers and for agriculture in general. Developing models which can effectively model growth and yield can help growers improve the environmental control for better production, match supply and market demand and lower costs. Recent developm…

The study examines how gamma positivity and PL homeomorphism types affect simplicial spheres.

Constructs complete metrics and solitons on complex vector bundles.

Study Kähler geometry on vector bundles over elliptic curves.

Geometric structures on surfaces relate to 2-plane distributions in 5D.

Study of hyperbolic behavior in complex manifolds with specific vector bundles.

The study examines the normal growth exponent of submanifolds in negatively curved manifolds.

It is well known that the compactifications of the canonical contact systems living on real jet spaces $J^{\,r}(1,1)$, $r \ge 2$, are locally universal Goursat distributions, $Δ^r$, living on compact manifolds (called Goursat monsters) having open dense jet-like ($J^{\,r}(1,1)$-like) parts. By virtue of the results of …

B.-Y. Chen famously conjectured that every submanifold of Euclidean space with harmonic mean curvature vector is minimal. In this note we establish a much more general statement for a large class of submanifolds satisfying a growth condition at infinity. We discuss in particular two popular competing natural interpreta…

This paper explores geometric and analytic aspects of Lojasiewicz inequalities on vector bundles.

Given for instance a finite volume negatively curved Riemannian manifold $M$, we give a precise relation between the logarithmic growth rates of the excursions into cusps neighborhoods of the strong unstable leaves of negatively recurrent unit vectors of $M$ and their linear divergence rates under the geodesic flow. As…

Let G denote a closed, connected, self adjoint, noncompact subgroup of GL(n,R), and let d_{R} denote the canonical right invariant Riemannian metric on G. For v in R^{n} let G_{v} = {g in G : g(v) = v}. We obtain algebraically defined upper and lower bounds for the asymptotic growth rate of g --> log |g(v)| / d_{R}(g,G…

In this paper, we enlarge the space of uniformly supported pseudo-differential operators on some groupoids by considering kernels satisfying certain asymptotic estimates. We show that such enlarged space contains the compact parametrix, and the generalized inverse of uniformly supported operators with Fredholm vector r…

The study of special Lagrangian classes and semistable Mukai vectors on K3 surfaces.

Study examines how COVID-19 affected India's exchange rates and stock market.

We investigate how and when to diversify capital over assets, i.e., the portfolio selection problem, from a signal processing perspective. To this end, we first construct portfolios that achieve the optimal expected growth in i.i.d. discrete-time two-asset markets under proportional transaction costs. We then extend ou…

Vocal disorders have affected several patients all over the world. Due to the inherent difficulty of diagnosing vocal disorders without sophisticated equipment and trained personnel, a number of patients remain undiagnosed. To alleviate the monetary cost of diagnosis, there has been a recent growth in the use of data a…

Study sequences of solutions to Taubes's Seiberg-Witten equations with unbounded energy.

We construct geometric realization for non-exceptional mutation-finite cluster algebras by extending the theory of Fomin and Thurston to skew-symmetrizable case. Cluster variables for these algebras are renormalized lambda lengths on certain hyperbolic orbifolds. We also compute growth rate of these cluster algebras, p…

We address some global solvability issues for classes of smooth nonsingular vector fields $L$ in the plane related to cohomological equations $Lu=f$ in geometry and dynamical systems. The first main result is that $L$ is not surjective in $C^\infty(\R^2)$ iff the geometrical condition -- the existence of separatrix str…

Theory models nonlinear soft tissue elasticity and remodeling using extended Finsler geometry.

Motivated by control-affine systems in optimal control theory, we introduce the notion of a point-affine distribution on a manifold X - i.e., an affine distribution F together with a distinguished vector field contained in F. We compute local invariants for point-affine distributions of constant type when dim(X)=n, ran…

We consider rank 3 distributions with growth vector (3,5,6). The class of such distributions splits into three subclasses: parabolic, hyperbolic and elliptic. In the present paper, we deal with the parabolic case. We provide a classification of such distributions and exhibit connections between them and Gl(2)-structure…

This paper benchmarks econometric and machine learning methods in nowcasting GDP growth.

Abstract Coxeter groups have growth rates that are Perron numbers.

We empirically test the effects of unanticipated fiscal policy shocks on the growth rate and the cyclical component of real private output and reveal different types of asymmetries in fiscal policy implementation. The data used are quarterly U.S. observati ons over the period 1967:1 to 2011:4. In doing so, we use both …

Historical economic growth in countries of the former USSR is analysed. It is shown that Unified Growth Theory is contradicted by the data, which were used, but not analysed, during the formulation of this theory. Unified Growth Theory does not explain the mechanism of economic growth. It explains the mechanism of Malt…

Efficiently estimates private least squares with linear error growth.

The Unified Growth Theory is a puzzling collection of myths based on illusions created by hyperbolic distributions. Some of these myths are discussed. The examination of data shows that the three stages of growth (Malthusian Regime, Post-Malthusian Regime and Modern Growth Regime) did not exist and that Industrial Revo…