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- P-balanced growth (4)
- Cauchy-Schwarz Inequality (2)
- P-harmonic maps (2)
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- Bi-harmonic maps (1)
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- Bochner-Weitzenbock formula (1)
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- Finite q-energy in Lq spaces (1)
- First and second variation formulas (1)
- Fourier series (1)
- Fruits (1)
- Gibbs phenomenon (1)
- Hardy-Sobolev type inequalities (1)
- Harmonic forms (1)
- Heat (1)
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Articles 1 - 11 of 11
Full-Text Articles in Analysis
Bi-Harmonic Maps' Existence And P-Balanced Energy And Connections To Harmonic Maps, Lina Wu
Bi-Harmonic Maps' Existence And P-Balanced Energy And Connections To Harmonic Maps, Lina Wu
Publications and Research
We discover a bi-harmonic map’ existence, its energy growth, and its connections to a harmonic map. First, we prove the existence of a nontrivial bi-harmonic map in a unit sphere. Second, we investigate the p-balanced energy growth of biharmonic maps. As the most important energy technical breakthroughs, we propose an innovative energy algorithm called p-balanced energy technique to break the constraints of the existing L^q-energy technique in detecting L^q-energy growth towards boundlessness. The disadvantage of the finite L^q -energy technique in the L ^q spaces is not effective in dealing with infinite L^q- energy in Non-L^q spaces. Third, we study …
Preconditioned Iteractive Solvers For The 2d Helmholtz Equation Via Radial Basis Functions, Lina Wu
Preconditioned Iteractive Solvers For The 2d Helmholtz Equation Via Radial Basis Functions, Lina Wu
Publications and Research
In this paper, we discuss the solution solver for the linear system of equations arising from the discretized 2D Helmholtz equation using the radial basis functions. The coefficient matrix A that is generated from the discretization is dense and often ill-conditioned. This paper uses preconditioned iterative methods such as the General Minimal Residual method (GMRES) to solve the linear system. Different preconditioners are compared. Numerical experiments are conducted in order to provide a comparison of the convergence rates among various preconditioned linear systems. A further observation is made into the eigenvalue distributions and the choice of the shaping parameters during …
Interfacial Dynamics And Ionic Transport Of Radiologic Contrast Media In Carbohydrate Matrix: Utility And Limits Of X-Ray Imaging, Lin Mousa, Hayley Sanchez, Subhendra Sarkar, Zoya Vinokur
Interfacial Dynamics And Ionic Transport Of Radiologic Contrast Media In Carbohydrate Matrix: Utility And Limits Of X-Ray Imaging, Lin Mousa, Hayley Sanchez, Subhendra Sarkar, Zoya Vinokur
Publications and Research
Hello, our names are Lin Mousa and Hayley Sanchez, this semester we participated in a research project dedicated to analyzing the interactions of contrast media with the molecular components of fruits to compare how they would react with the human brain. This project involved the injection of fruits with varying contrasts and the imaging of the diffusion and interactions of the contrast within the fruits with X-rays. With setup technical parameters on the x-ray equipment images were taken with identical setups at an hourly rate for several days. The final results of this experiment indicated that contrasts such as Gadolinium …
R Program For Estimation Of Group Efficiency And Finding Its Gradient. Stochastic Data Envelopment Analysis With A Perfect Object Approach, Alexander Vaninsky
R Program For Estimation Of Group Efficiency And Finding Its Gradient. Stochastic Data Envelopment Analysis With A Perfect Object Approach, Alexander Vaninsky
Publications and Research
The data presented here are related to the research article “Energy-environmental efficiency and optimal restructuring of the global economy” (Vaninsky, 2018) [1]. This article describes how the world economy can be restructured to become more energy-environmental efficient, while still increasing its growth potential. It demonstrates how available energy-environmental and economic information may support policy-making decisions on the atmosphere preservation and climate change prevention. This Data article presents a computer program in R language together with examples of input and output files that serve as a means of implementation of the novel approach suggested in publication[1]. The computer program utilizes stochastic …
Applying P-Balanced Energy Technique To Solve Liouville-Type Problems In Calculus, Lina Wu
Applying P-Balanced Energy Technique To Solve Liouville-Type Problems In Calculus, Lina Wu
Publications and Research
We are interested in solving Liouville-type problems to explore constancy properties for maps or differential forms on Riemannian manifolds. Geometric structures on manifolds, the existence of constancy properties for maps or differential forms, and energy growth for maps or differential forms are intertwined. In this article, we concentrate on discovery of solutions to Liouville-type problems where manifolds are Euclidean spaces (i.e. flat Riemannian manifolds) and maps become real-valued functions. Liouville-type results of vanishing properties for functions are obtained. The original work in our research findings is to extend the q-energy for a function from finite in L^q space to infinite …
Solving Liouville-Type Problems On Manifolds With Poincar´E-Sobolev Inequality By Broadening Q-Energy From Finite To Infinite, Lina Wu
Publications and Research
The aim of this article is to investigate Liouville-type problems on complete non-compact Riemannian manifolds with Poincar´e-Sobolev Inequality. Two significant technical breakthroughs are demonstrated in research findings. The first breakthrough is an extension from non-flat manifolds with non-negative Ricci curvatures to curved manifolds with Ricci curvatures varying among negative values, zero, and positive values. Poincar´e-Sobolev Inequality has been applied to overcome difficulties of an extension on manifolds. Poincar´e-Sobolev Inequality has offered a special structure on curved manifolds with a mix of Ricci curvature signs. The second breakthrough is a generalization of q-energy from finite to infinite. At this point, a …
Equivalence Between A Harmonic Form And A Closed Co-Closed Form In Both Lq And Non-Lq Spaces, Lina Wu
Equivalence Between A Harmonic Form And A Closed Co-Closed Form In Both Lq And Non-Lq Spaces, Lina Wu
Publications and Research
For a differential k-form ω on a complete non-compact manifold, we establish an equivalent relation between a harmonic form and a closed co-closed form. We extend this equivalence from ω in L^2 spaces to ω with 2-balanced growth including L^2 spaces and non-L^2 spaces. Especially for a simple differential k-form ¯ω on a complete non-compact manifold, we generalize this equivalence from ¯ω in L^q spaces to ¯ω with 2-balanced growth including L^q spaces and non-L^q spaces for 2 ≤ q < 3. Our research findings recapture the work of Andreotti and Vesentini. Our ideas and calculation methods in this paper could provide a new way of broadening L^q spaces to non-L^q spaces in a variety of energy for differential forms.
Discovering Liouville-Type Problems For P-Energy Minimizing Maps In Closed Half-Ellipsoids By Calculus Variation Method, Lina Wu
Publications and Research
The goal of this project is to investigate constant properties (called the Liouville-type Problem) for a p-stable map as a local or global minimum of a p-energy functional where the domain is a Euclidean space and the target space is a closed half-ellipsoid. The First and Second Variation Formulas for a p-energy functional has been applied in the Calculus Variation Method as computation techniques. Stokes’ Theorem, Cauchy-Schwarz Inequality, Hardy-Sobolev type Inequalities, and the Bochner Formula as estimation techniques have been used to estimate the lower bound and the upper bound of the derived p-Harmonic Stability Inequality. One challenging point in …
Generalizing Liouville-Type Problems For Differential 1-Forms From Lq Spaces To Non-Lq Spaces, Lina Wu, Ye Li
Generalizing Liouville-Type Problems For Differential 1-Forms From Lq Spaces To Non-Lq Spaces, Lina Wu, Ye Li
Publications and Research
We obtain Liouville-type results for closed and p-pseudo-coclosed differential 1-forms ! with energy of lim inf r!1 1 r2 R B(x0;r) j!jqdv < 1 (that is, 2-finite growth), which extends finite q-energy ( R M j!jqdv < 1) in Lq spaces to infinite q-energy ( R M j!jqdv = 1) in non-Lq spaces. In particular, we recapture mathematicians' vanishing results of Liouville- type theorem for ! with finite q-energy in Lq spaces. Our method in this paper provides a successful way to work on Liouville-type problems for differential forms with a variety of energy conditions in broad spaces.
Semi-Fredholm Solvability In The Framework Of Singular Solutions For The (3+1)-D Protter-Morawetz Problem, Nedyu Popivanov, Todor Popov, Allen Tesdall
Semi-Fredholm Solvability In The Framework Of Singular Solutions For The (3+1)-D Protter-Morawetz Problem, Nedyu Popivanov, Todor Popov, Allen Tesdall
Publications and Research
For the four-dimensional nonhomogeneous wave equation boundary value problems that are multidimensional analogues of Darboux problems in the plane are studied. It is known that for smooth right-hand side functions the unique generalized solution may have a strong power-type singularity at only one point. This singularity is isolated at the vertex �� of the boundary light characteristic cone and does not propagate along the bicharacteristics.The present paper describes asymptotic expansions of the generalized solutions in negative powers of the distance to ��. Some necessary and sufficient conditions for existence of bounded solutions are proven and additionally a priori estimates for …
Multiresolution Inverse Wavelet Reconstruction From A Fourier Partial Sum, Nataniel Greene
Multiresolution Inverse Wavelet Reconstruction From A Fourier Partial Sum, Nataniel Greene
Publications and Research
The Gibbs phenomenon refers to the lack of uniform convergence which occurs in many orthogonal basis approximations to piecewise smooth functions. This lack of uniform convergence manifests itself in spurious oscillations near the points of discontinuity and a low order of convergence away from the discontinuities.In previous work [11,12] we described a numerical procedure for overcoming the Gibbs phenomenon called the Inverse Wavelet Reconstruction method (IWR). The method takes the Fourier coefficients of an oscillatory partial sum and uses them to construct the wavelet coefficients of a non-oscillatory wavelet series. However, we only described the method standard wavelet series and …