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Mathematics

University of New Haven

Mathematics Faculty Publications

Articles 1 - 15 of 15

Full-Text Articles in Physical Sciences and Mathematics

Bochner-Kähler And Bach Flat Manifolds, Amalendu Ghosh, Ramesh Sharma Jan 2019

Bochner-Kähler And Bach Flat Manifolds, Amalendu Ghosh, Ramesh Sharma

Mathematics Faculty Publications

We have classified Bochner-Kähler manifolds of real dimension > 4, which are also Bach flat. In the 4-dimensional case, we have shown that, if the scalar curvature is harmonic, then it is constant. Finally, we show that the gradient of scalar curvature of any Bochner-Kähler manifold is an infinitesimal harmonic transformation, and if it is conformal then the scalar curvature is constant.

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Gradient Ricci Solitons With A Conformal Vector Field, Ramesh Sharma Aug 2018

Gradient Ricci Solitons With A Conformal Vector Field, Ramesh Sharma

Mathematics Faculty Publications

We show that a connected gradient Ricci soliton (M,g,f,λ) with constant scalar curvature and admitting a non-homothetic conformal vector field V leaving the potential vector field invariant, is Einstein and the potential function f is constant. For locally conformally flat case and non-homothetic V we show without constant scalar curvature assumption, that f is constant and g has constant curvature.

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Fractional Generalizations Of Zakai Equation And Some Solution Methods, Sabir Umarov, Fred Daum, Kenric Nelson Apr 2018

Fractional Generalizations Of Zakai Equation And Some Solution Methods, Sabir Umarov, Fred Daum, Kenric Nelson

Mathematics Faculty Publications

The paper discusses fractional generalizations of Zakai equations arising in filtering problems. The derivation of the fractional Zakai equation, existence and uniqueness of its solution, as well as some methods of solution to the fractional filtering problem, including fractional version of the particle flow method, are presented.

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Some Remarks On Ricci Solitons, Ramesh Sharma, S Balasubramanian, N. Uday Kiran Dec 2017

Some Remarks On Ricci Solitons, Ramesh Sharma, S Balasubramanian, N. Uday Kiran

Mathematics Faculty Publications

We obtain an intrinsic formula of a Ricci soliton vector field and a differential condition for the non-steady case to be gradient. Next we provide a condition for a Ricci soliton on a Kaehler manifold to be a Kaehler–Ricci soliton. Finally we give an example supporting the first result.

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Sasakian Manifolds With Purely Transversal Bach Tensor, Amalendu Ghosh, Ramesh Sharma Oct 2017

Sasakian Manifolds With Purely Transversal Bach Tensor, Amalendu Ghosh, Ramesh Sharma

Mathematics Faculty Publications

We show that a (2n + 1)-dimensional Sasakian manifold (M, g) with a purely transversal Bach tensor has constant scalar curvature ≥2n(2n+1), equality holding if and only if (M, g) is Einstein. For dimension 3, M is locally isometric to the unit sphere S3. For dimension 5, if in addition (M, g) is complete, then it has positive Ricci curvature and is compact with finite fundamental group π1(M).

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Some Results On Almost Ricci Solitons And Geodesic Vector Fields., Ramesh Sharma Jan 2017

Some Results On Almost Ricci Solitons And Geodesic Vector Fields., Ramesh Sharma

Mathematics Faculty Publications

We show that a compact almost Ricci soliton whose soliton vector field is divergence-free is Einstein and its soliton vector field is Killing. Next we show that an almost Ricci soliton reduces to Ricci soliton if and only if the associated vector field is geodesic. Finally, we prove that a contact metric manifold is K-contact if and only if its Reeb vector field is geodesic.

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Cosmological Models Through Spatial Ricci Flow, Ramesh Sharma May 2016

Cosmological Models Through Spatial Ricci Flow, Ramesh Sharma

Mathematics Faculty Publications

We consider the synchronization of the Einstein’s flow with the Ricci-flow of the standard spatial slices of the Robertson–Walker space–time and show that associated perfect fluid solution has a quadratic equation of state and is either spherical and collapsing, or hyperbolic and expanding.
Read More: http://www.worldscientific.com/doi/abs/10.1142/S0219887816500699

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Random Sampling Of Skewed Distributions Implies Taylor’S Power Law Of Fluctuation Scaling, Joel E. Cohen, Meng Xu Jun 2015

Random Sampling Of Skewed Distributions Implies Taylor’S Power Law Of Fluctuation Scaling, Joel E. Cohen, Meng Xu

Mathematics Faculty Publications

Taylor’s law (TL), a widely verified quantitative pattern in ecology and other sciences, describes the variance in a species’ population density (or other nonnegative quantity) as a power-law function of the mean density (or other nonnegative quantity): Approximately, variance = a(mean)b, a > 0. Multiple mechanisms have been proposed to explain and interpret TL. Here, we show analytically that observations randomly sampled in blocks from any skewed frequency distribution with four finite moments give rise to TL. We do not claim this is the only way TL arises. We give approximate formulae for the TL parameters and their …

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Fractional Generalizations Of Filtering Problems And Their Associated Fractional Zakai Equation, Sabir Umarov, Fred Daum, Kenric Nelson Jan 2014

Fractional Generalizations Of Filtering Problems And Their Associated Fractional Zakai Equation, Sabir Umarov, Fred Daum, Kenric Nelson

Mathematics Faculty Publications

In this paper we discuss fractional generalizations of the filtering problem. The ”fractional” nature comes from time-changed state or observation processes, basic ingredients of the filtering problem. The mathematical feature of the fractional filtering problem emerges as the Riemann-Liouville or Caputo-Djrbashian fractional derivative in the associated Zakai equation. We discuss fractional generalizations of the nonlinear filtering problem whose state and observation processes are driven by time-changed Brownian motion or/and Lévy process.

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Almost Contact Lagrangian Submanifolds Of Nearly Kaehler 6-Sphere, Ramesh Sharma, Sharief Deshmukh, Falleh Al-Solamy Jan 2014

Almost Contact Lagrangian Submanifolds Of Nearly Kaehler 6-Sphere, Ramesh Sharma, Sharief Deshmukh, Falleh Al-Solamy

Mathematics Faculty Publications

For a Lagrangian submanifold M of S 6 with nearly Kaehler structure, we provide conditions for a canonically induced almost contact metric structure on M by a unit vector field, to be Sasakian. Assuming M contact metric, we show that it is Sasakian if and only if the second fundamental form annihilates the Reeb vector field ξ, furthermore, if the Sasakian submanifold M is parallel along ξ, then it is the totally geodesic 3-sphere. We conclude with a condition that reduces the normal canonical almost contact metric structure on M to Sasakian or cosymplectic structure.

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Almost Ricci Solitons And K-Contact Geometry, Ramesh Sharma Jan 2014

Almost Ricci Solitons And K-Contact Geometry, Ramesh Sharma

Mathematics Faculty Publications

We give a short Lie-derivative theoretic proof of the following recent result of Barros et al. “A compact non-trivial almost Ricci soliton with constant scalar curvature is gradient, and isometric to a Euclidean sphere”. Next, we obtain the result: a complete almost Ricci soliton whose metric g is K-contact and flow vector field X is contact, becomes a Ricci soliton with constant scalar curvature. In particular, for X strict, g becomes compact Sasakian Einstein.

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Sasakian Metric As A Ricci Soliton And Related Results, Ramesh Sharma, Amalendu Ghosh Jan 2014

Sasakian Metric As A Ricci Soliton And Related Results, Ramesh Sharma, Amalendu Ghosh

Mathematics Faculty Publications

We prove the following results: (i) a Sasakian metric as a non-trivial Ricci soliton is null η-Einstein, and expanding. Such a characterization permits us to identify the Sasakian metric on the Heisenberg group H2n+1 as an explicit example of (non-trivial) Ricci soliton of such type. (ii) If an η-Einstein contact metric manifold M has a vector field V leaving the structure tensor and the scalar curvature invariant, then either V is an infinitesimal automorphism, or M is D-homothetically fixed K-contact.

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Contact Hypersurfaces Of A Bochner-Kaehler Manifold, Amalendu Ghosh, Ramesh Sharma Jan 2013

Contact Hypersurfaces Of A Bochner-Kaehler Manifold, Amalendu Ghosh, Ramesh Sharma

Mathematics Faculty Publications

We have studied contact metric hypersurfaces of a Bochner-Kaehler manifold and obtained the following two results: (1) A contact metric constant mean curvature (C M C) hypersurface of a Bochner-Kaehler manifold is a (k, µ)-contact manifold, and (2) If M is a compact contact metric C M C hypersurface of a Bochner-Kaehler manifold with a conformal vector field V that is neither tangential nor normal anywhere, then it is totally umbilical and Sasakian, and under certain conditions on V , is isometric to a unit sphere.

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Conformal Classification Of (K, Μ)-Contact Manifolds, Ramesh Sharma, Luc Vrancken Jan 2010

Conformal Classification Of (K, Μ)-Contact Manifolds, Ramesh Sharma, Luc Vrancken

Mathematics Faculty Publications

First we improve a result of Tanno that says "If a conformal vector field on a contact metric manifold M is a strictly infinitesimal contact transformation, then it is an infinitesimal automorphism of M" by waiving the "strictness" in the hypothesis. Next, we prove that a (k, μ)-contact manifold admitting a non-Killing conformal vector field is either Sasakian or has k = –n – 1, μ = 1 in dimension > 3; and Sasakian or flat in dimension 3. In particular, we show that (i) among all compact simply connected (k, μ)-contact manifolds of dimension > 3, only the unit sphere S2n+1 …

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Monte Carlo Random Walk Simulations Based On Distributed Order Differential Equations With Applications In Cell Biology, Erik Andries, Sabir Umarov, Stanly Steinberg Jan 2006

Monte Carlo Random Walk Simulations Based On Distributed Order Differential Equations With Applications In Cell Biology, Erik Andries, Sabir Umarov, Stanly Steinberg

Mathematics Faculty Publications

In this paper the multi-dimensional random walk models governed by distributed fractional order differential equations and multi-term fractional order differential equations are constructed. The scaling limits of these random walks to a diffusion process in the sense of distributions is proved. Simulations based upon multi-term fractional order differential equations are performed.

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