Physical Sciences and Mathematics | Open Access Articles

Bohr Density Of Simple Linear Group Orbits, Roger Howe, François Ziegler

François Ziegler

We show that any non-zero orbit under a non-compact, simple, irreducible linear group is dense in the Bohr compactification of the ambient space.

Go to article

Local Well-Posedness Of Periodic Fifth Order Kdv-Type Equations, Yi Hu, Xiaochun Li

Yi Hu

In this paper, the local well-posedness of periodic fifth order dispersive equation with nonlinear term P1(u)∂xu + P2(u)∂xu∂xu. Here P1(u) and P2(u) are polynomials of u. We also get some new Strichartz estimates.

Go to article

Primary Spaces, Mackey’S Obstruction, And The Generalized Barycentric Decomposition, Patrick Iglesias-Zemmour, François Ziegler

François Ziegler

We call a hamiltonian N-space primary if its moment map is onto a single coadjoint orbit. The question has long been open whether such spaces always split as (homogeneous) × (trivial), as an analogy with representation theory might suggest. For instance, Souriau’s barycentric decomposition theorem asserts just this when N is a Heisenberg group. For general N, we give explicit examples which do not split, and show instead that primary spaces are always flat bundles over the coadjoint orbit. This provides the missing piece for a full “Mackey theory” of hamiltonian G-spaces, where G is an overgroup in which N …

Go to article

Generalizations Of The Inverse Weibull And Related Distributions With Applications, Broderick O. Oluyede, Tao Yang

Broderick O. Oluyede

In this paper, the generalized inverse Weibull distribution including the exponentiated or proportional reverse hazard and Kumaraswamy generalized inverse Weibull distributionsare presented. Properties of these distributions including the behavior of the hazard and reverse hazard functions, moments, coefficients of variation, skewness, andkurtosis, entropy, Fisher information matrix are studied. Estimates of the model parameters via method of maximum likelihood (ML), and method of moments (MOM) are presented for complete and censored data. Numerical examples are also presented.

Go to article

Localized Quantum States, François Ziegler

François Ziegler

Let X be a symplectic manifold and Aut(L) the automorphism group of a Kostant-Souriau line bundle on X. *Quantum states for X*, as defined by J.-M. Souriau in the 1990s, are certain positive-definite functions on Aut(L) or, less ambitiously, on any "large enough" subgroup G of Aut(L). This definition has two major drawbacks: when G=Aut(L) there are no known examples; and when G is a Lie subgroup the notion is, as we shall see, far from selective enough. In this paper we introduce the concept of a quantum state *localized at Y*, where Y is a coadjoint orbit of a …

Go to article

Multiscale Geometric Modeling Of Macromolecules I: Cartesian Representation, Kelin Xia, Xin Feng, Zhan Chen, Yiying Tong, Guo-Wei Wei

Zhan Chen

This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace–Beltrami flows for biomolecular surface evolution and formation. The …

Go to article

Numerical Studies Of The Generalized L1 Greedy Algorithm For Sparse Signals, Fangjun Arroyo, Edward Arroyo, Xiezhang Li, Jiehua Zhu

Xiezhang Li

The generalized l1 greedy algorithm was recently introduced and used to reconstruct medical images in computerized tomography in the compressed sensing framework via total variation minimization. Experimental results showed that this algorithm is superior to the reweighted l1-minimization and l1 greedy algorithms in reconstructing these medical images. In this paper the effectiveness of the generalized l1 greedy algorithm in finding random sparse signals from underdetermined linear systems is investigated. A series of numerical experiments demonstrate that the generalized l1 greedy algorithm is superior to the reweighted l1-minimization and l1 greedy algorithms in the successful recovery of randomly generated Gaussian sparse …

Go to article

Symplectic Harmonic Theory And The Federer-Fleming Deformation Theorem, Yi Lin

Yi Lin

In this article, we initiate a geometric measure theoretic approach to symplectic Hodge theory. In particular, we apply one of the central results in geometric measure theory, the Federer-Fleming deformation theorem, together with the cohomology theory of normal cur- rents on a differential manifold, to establish a fundamental property on symplectic Harmonic forms. We show that on a closed symplectic manifold, every real primitive cohomology class of positive degrees admits a symplectic Harmonic representative not supported on the entire mani- fold. As an application, we use it to investigate the support of symplectic Harmonic representatives of Thom classes, and give …

Go to article

Discrete Fourier Restriction Associated With Kdv Equations, Yi Hu, Xiaochun Li

Yi Hu

In this paper, we consider a discrete restriction associated with KdV equations. Some new Strichartz estimates are obtained. We also establish the local well-posedness for the periodic generalized Korteweg-de Vries equation with nonlinear term $F(u)\p_x u$ provided F∈C5 and the initial data ϕ∈Hs with s>1/2.

Go to article

Invertibility Of Submatrices Of Pascal's Matrix And Birkhoff Interpolation, Scott N. Kersey

Scott N. Kersey

The inﬁnite (upper triangular) Pascal matrix is T = [ ji] for 0 ≤ i, j. It is easy to see that that submatrix T (0 : n, 0 : n) is triangular with determinant 1, hence in particular, it is invertible. But what about other submatrices T (r, x) for selections r = [r0, . . . , rd] and x = [x0, . . . , xd] of the rows and columns of T ? The goal of this paper is provide a necessary and suﬃcient condition for invertibility based on a connection to polynomial interpolation. In particular, …

Go to article

Liftings And Quasi-Liftings Of Dg Modules, Saeed Nasseh, Sean Sather-Wagstaff

Saeed Nasseh

We prove lifting results for DG modules that are akin to Auslander, Ding, and Solbergʼs famous lifting results for modules.

Go to article

A Note On Symmetry In The Vanishing Of Ext, Saeed Nasseh, Massoud Tousi

Saeed Nasseh

In [1] Avramov and Buchweitz proved that for finitely generated modules M and N over a complete intersection local ring R, ExtiR(M,N)=0 for all i>>0 implies ExtiR(N, M)=0 for all i>>0. In this note we give some generalizations of this result. Indeed we prove the above mentioned result when (1) M is finitely generated and N is arbitrary, (2) M is arbitrary and N has finite length and (3) M is complete and N is finitely generated.

Go to article

Dual Bases Functions In Subspaces, Scott N. Kersey

Scott N. Kersey

In this paper we study dual bases functions in subspaces. These are bases which are dual to functionals on larger linear space. Our goal is construct and derive properties of certain bases obtained from the construction, with primary focus on polynomial spaces in B-form. When they exist, our bases are always affine (not convex), and we define a symmetric configuration that converges to Lagrange polynomial bases. Because of affineness of our bases, we are able to derive certain approximation theoretic results involving quasi-interpolation and a Bernstein-type operator. In a broad sense, it is the aim of this paper to present …

Go to article

Variational Multiscale Models For Charge Transport, Guo-Wei Wei, Qiong Zheng, Zhan Chen, Kelin Xia

Zhan Chen

This work presents a few variational multiscale models for charge transport in complex physical, chemical, and biological systems and engineering devices, such as fuel cells, solar cells, battery cells, nanofluidics, transistors, and ion channels. An essential ingredient of the present models, introduced in an earlier paper [Bull. Math. Biol., 72 (2010), pp. 1562--1622], is the use of the differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain from the microscopic domain, while dynamically coupling discrete and continuum descriptions. Our main strategy is to construct the total energy functional of a charge transport system to …

Go to article

Balance With Unbounded Complexes, Edgar E. Enochs, Sergio Estrada, Alina Iacob

Alina Iacob

Given a double complex X there are spectral sequences with the E2 terms being either HI (HII(X)) or HII(HI(X)). But if HI(X)=HII(X)=0, then both spectral sequences have all their terms 0. This can happen even though there is nonzero (co)homology of interest associated withX. This is frequently the case when dealing with Tate (co)homology. So, in this situation the spectral sequences may not give any information about the (co)homology of interest. In this article, we give a different way of …

Go to article

Factorizations Of Local Homomorphisms, Saeed Nasseh

Saeed Nasseh

Let f:R→S be a homomorphism of commutative rings. Many techniques for studying R-modules focus on finitely generated modules. As a consequence, these techniques are not well-suited for studying S as an R-module. However, a technique of Avramov, Foxby, and Herzog sometimes allows one to replace the original homomorphism with a surjective one R′→S where R and R′ are tightly connected. In this setting, S is a cyclic R′-module, so one can study it using finitely generated techniques. I will give a general introduction to such factorizations, followed by a discussion of …

Go to article

Vatdt: Visual Assessment Of Cluster Tendency Using Diagonal Tracing, Yingkang Hu

Yingkang Hu

The visual assessment of tendency (VAT) technique, for visually finding the number of meaningful clusters in data, developed by J. C. Bezdek, R. J. Hathaway and J. M. Huband, is very useful, but there is room for improvements. Instead of displaying the ordered dissimilarity matrix (ODM) as a 2D gray-level image for human interpretation as is done by VAT, we trace the changes in dissimilarities along the diagonal of the ODM. This changes the 2D data structure (matrices) into 1D arrays, displayed as what we call the tendency curves, which enables one to concentrate only on one variable, namely the …

Go to article

Log-Concavity And Symplectic Flows, Yi Lin, Alvaro Pelayo

Yi Lin

Let M be a compact, connected symplectic 2n-dimensional manifold on which an(n-2)-dimensional torus T acts effectively and Hamiltonianly. Under the assumption that there is an effective complementary 2-torus acting on M with symplectic orbits, we show that the Duistermaat-Heckman measure of the T-action is log-concave. This verifies the logarithmic concavity conjecture for a class of inequivalent T-actions. Then we use this conjecture to prove the following: if there is an effective symplectic action of an (n-2)-dimensional torus T on a compact, connected symplectic 2n-dimensional manifold that admits an effective complementary symplectic action of a 2-torus with symplectic orbits, then the …

Go to article

Differential Geometry Based Solvation Model Ii: Lagrangian Formulation, Zhan Chen, Nathan A. Baker, Guo-Wei Wei

Zhan Chen

Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation models. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages …

Go to article

Note On Highly Connected Monochromatic Subgraphs In 2-Colored Complete Graphs, Shinya Fujita, Colton Magnant

Colton Magnant

In this note, we improve upon some recent results concerning the existence of large monochromatic, highly connected subgraphs in a 2-coloring of a complete graph. In particular, we show that if n≥6.5(k−1), then in any 2-coloring of the edges of Kn, there exists a monochromatic k-connected subgraph of order at least n−2(k−1). Our result improves upon several recent results by a variety of authors.

Go to article

Coloring Rectangular Blocks In 3-Space, Colton Magnant, Daniel M. Martin

Colton Magnant

If rooms in an office building are allowed to be any rectangular solid, how many colors does it take to paint any configuration of rooms so that no two rooms sharing a wall or ceiling/floor get the same color? In this work, we provide a new construction which shows this number can be arbitrarily large.

Go to article

Differential Geometry Based Solvation Model I: Eulerian Formulation, Zhan Chen, Nathan A. Baker, Guo-Wei Wei

Zhan Chen

This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent–solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the solvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal …

Go to article

One-Dimensional Wave Equations Defined By Fractal Laplacians, John Fun-Choi Chan, Sze-Man Ngai, Alexander Teplyaev

Sze-Man Ngai

We study one-dimensional wave equations deﬁned by a class of fractal Laplacians. These Laplacians are deﬁned by fractal measures generated by iterated function systems with overlaps. We prove the existence and uniqueness of weak solutions. We also study numerical computations of the solutions and prove the convergence of the approximation scheme. This is a joint work with John F. Chan and Alexander Teplyaev.

Go to article

Generalized Complex Hamiltonian Torus Actions: Examples And Constraints, Thomas Baird, Yi Lin

Yi Lin

Consider an effective Hamiltonian torus action T×M→M on a topologically twisted,generalized complex manifold M of dimension 2n. We prove that the rank(T)≤n−2 and that the topological twisting survives Hamiltonian reduction. We then construct a large new class of such actions satisfying rank(T)=n−2, using a surgery procedure on toric manifolds.

Go to article

Chvátal-Erdös Type Theorems, Ralph J. Faudree, Jill R. Faudree, Ronald J. Gould, Michael S. Jacobson, Colton Magnant

Colton Magnant

The Chvátal-Erdös theorems imply that if G is a graph of order n ≥ 3 with κ(G) ≥ α(G), then G is hamiltonian, and if κ(G) > α(G), then G is hamiltonian-connected. We generalize these results by replacing the connectivity and independence number conditions with a weaker minimum degree and independence number condition in the presence of sufficient connectivity. More specifically, it is noted that if G is a graph of order n and k ≥ 2 is a positive integer such that κ(G) ≥ k, δ(G) > (n+k2-k)/(k+1), and δ(G) ≥ α(G)+k-2, then G is hamiltonian. It is shown that if …

Go to article

Towards An Automation Of The Circle Method, Andrew Sills

Andrew V. Sills

The derivation of the Hardy-Ramanujan-Rademacher formula for the number of partitions of n is reviewed. Next, the steps for ﬁnding analogous formulas for certain restricted classes of partitions or overpartitions is examined, bearing in mind how these calculations can be automated in a CAS. Finally, a number of new formulas of this type which were conjectured with the aid of Mathematica are presented along with results of a test for their numerical accuracy.

Go to article

Homological Dimensions And Regular Rings, Alina Iacob, Srikanth B. Iyengar

Alina Iacob

A question of Avramov and Foxby concerning injective dimension of complexes is settled in the affirmative for the class of noetherian rings. A key step in the proof is to recast the problem on hand into one about the homotopy category of complexes of injective modules. Analogous results for flat dimension and projective dimension are also established.

Go to article

Analysis On The Strip-Based Projection Model For Discrete Tomography, Jiehua Zhu, Xiezhang Li, Yangbo Ye, Ge Wang

Xiezhang Li

Discrete tomography deals with image reconstruction of an object with finitely many gray levels (such as two). Different approaches are used to model the raw detector reading. The most popular models are line projection with a lattice of points and strip projection with a lattice of pixels/cells. The line-based projection model fits some applications but involves a major approximation since the x-ray beams of finite widths are simplified as line integrals. The strip-based projection model formulates projection equations according to the fractional areas of the intersection of each strip-shaped beam and the rectangular grid of an image to be reconstructed, …

Go to article

Extraction Of The Neutron Magnetic Form Factor From Quasielastic 3He(E , E') At Q2=0.1-0.6 (Gev/C)2, B. Anderson, L. Auberbach, T. Averett, W. Bertozzi, T. Black, J. Calarco, L. Cardman, G. D. Cates, Z. W. Chai, J. P. Chen, Seonho Choi, E. Chudakov, S. Churchwell, G. S. Corrado, C. Crawford, A. Deur, P. Djawotho, D. Dutta, J. M. Finn, H. Gao, J. Golak, J. Gomez, V. G. Gorbenko, J. O. Hansen, F. W. Hersman, D. W. Higinbotham, R. Holmes, C. R. Howell, E. Hughes, B. Humensky, S. Incerti, C. W. De Jager, J. S. Jensen, X. Jiang, C. E. Jones, M. Jones, R. Kahl, H. Kamada, A. Kievsky, I. Kominis, W. Korsch, K. Kramer, G. Kumbartzki, M. Kuss, Enkeleida K. Lakuriqi, M. Liang, N. Liyanange, J. Lerose, S. Malov, D. J. Margaziotis, J. W. Martin, K. Mccormick, R. D. Mckeown, K. Mcilhany, Z. E. Meziani, R. Michaels, G. W. Miller, J. Mitchell, S. Nanda, E. Pace, T. Pavlin, G. G. Petratos, R. I. Pomatsalyuk, D. Pripstein, D. Prout, R. D. Ransome, Y. Roblin, M. Rvachev, A. Saha, G. Salme, M. Schnee, J. Seely, T. Shin, K. Slifer, P. A. Souder, S. Strauch, R. Suleiman, M. Sutter, B. Tipton, L. Todor, M. Viviani, R. Gilman, A. V. Glamazdin, C. Glashausser, B. Vlahovic, J. Watson, C. F. Williamson, H. Witala, B. Wojsekhowski, F. Xiong, X. Wu, J. Yeh, P. Zolmierczuk

Enkeleida K. Lakuriqi

We have measured the transverse asymmetry AT' in the quasielastic 3He(e,e') process with high precision at Q2 values from 0.1 to 0.6 (GeV/c)2. The neutron magnetic form factor GnM was extracted at Q2 values of 0.1 and 0.2(GeV/c)2 using a nonrelativistic Faddeev calculation which includes both final-state interactions (FSI) and meson-exchange currents (MEC). Theoretical uncertainties due to the FSI and MEC effects were constrained with a precision measurement of the spin-dependent asymmetry in the threshold region of 3He(e,e'). We also extracted the neutron magnetic form factor …

Go to article

Closure Under Transfinite Extensions, Edgar E. Enochs, Alina Iacob, Overtoun Jenda

Alina Iacob

The closure under extensions of a class of objects in an abelian category is often an important property of that class. Recently the closure of such classes under transfinite extensions (both direct and inverse) has begun to play an important role in several areas of mathematics, for example in Quillen’s theory of model categories and in the theory of cotorsion pairs. In this paper we prove that several important classes are closed under transfinite extensions

Go to article

Full-Text Articles in Physical Sciences and Mathematics

Bohr Density Of Simple Linear Group Orbits, Roger Howe, François Ziegler

François Ziegler

Local Well-Posedness Of Periodic Fifth Order Kdv-Type Equations, Yi Hu, Xiaochun Li

Yi Hu

Primary Spaces, Mackey’S Obstruction, And The Generalized Barycentric Decomposition, Patrick Iglesias-Zemmour, François Ziegler

François Ziegler

Generalizations Of The Inverse Weibull And Related Distributions With Applications, Broderick O. Oluyede, Tao Yang

Broderick O. Oluyede

Localized Quantum States, François Ziegler

François Ziegler

Multiscale Geometric Modeling Of Macromolecules I: Cartesian Representation, Kelin Xia, Xin Feng, Zhan Chen, Yiying Tong, Guo-Wei Wei

Zhan Chen

Numerical Studies Of The Generalized L1 Greedy Algorithm For Sparse Signals, Fangjun Arroyo, Edward Arroyo, Xiezhang Li, Jiehua Zhu

Xiezhang Li

Symplectic Harmonic Theory And The Federer-Fleming Deformation Theorem, Yi Lin

Yi Lin

Discrete Fourier Restriction Associated With Kdv Equations, Yi Hu, Xiaochun Li

Yi Hu

Invertibility Of Submatrices Of Pascal's Matrix And Birkhoff Interpolation, Scott N. Kersey

Scott N. Kersey

Liftings And Quasi-Liftings Of Dg Modules, Saeed Nasseh, Sean Sather-Wagstaff

Saeed Nasseh

A Note On Symmetry In The Vanishing Of Ext, Saeed Nasseh, Massoud Tousi

Saeed Nasseh

Dual Bases Functions In Subspaces, Scott N. Kersey

Scott N. Kersey

Variational Multiscale Models For Charge Transport, Guo-Wei Wei, Qiong Zheng, Zhan Chen, Kelin Xia

Zhan Chen

Balance With Unbounded Complexes, Edgar E. Enochs, Sergio Estrada, Alina Iacob

Alina Iacob

Factorizations Of Local Homomorphisms, Saeed Nasseh

Saeed Nasseh

Vatdt: Visual Assessment Of Cluster Tendency Using Diagonal Tracing, Yingkang Hu

Yingkang Hu

Log-Concavity And Symplectic Flows, Yi Lin, Alvaro Pelayo

Yi Lin

Differential Geometry Based Solvation Model Ii: Lagrangian Formulation, Zhan Chen, Nathan A. Baker, Guo-Wei Wei

Zhan Chen

Note On Highly Connected Monochromatic Subgraphs In 2-Colored Complete Graphs, Shinya Fujita, Colton Magnant

Colton Magnant

Coloring Rectangular Blocks In 3-Space, Colton Magnant, Daniel M. Martin

Colton Magnant

Differential Geometry Based Solvation Model I: Eulerian Formulation, Zhan Chen, Nathan A. Baker, Guo-Wei Wei

Zhan Chen

One-Dimensional Wave Equations Defined By Fractal Laplacians, John Fun-Choi Chan, Sze-Man Ngai, Alexander Teplyaev

Sze-Man Ngai

Generalized Complex Hamiltonian Torus Actions: Examples And Constraints, Thomas Baird, Yi Lin

Yi Lin

Chvátal-Erdös Type Theorems, Ralph J. Faudree, Jill R. Faudree, Ronald J. Gould, Michael S. Jacobson, Colton Magnant

Colton Magnant

Towards An Automation Of The Circle Method, Andrew Sills

Andrew V. Sills

Homological Dimensions And Regular Rings, Alina Iacob, Srikanth B. Iyengar

Alina Iacob

Analysis On The Strip-Based Projection Model For Discrete Tomography, Jiehua Zhu, Xiezhang Li, Yangbo Ye, Ge Wang

Xiezhang Li

Enkeleida K. Lakuriqi

Closure Under Transfinite Extensions, Edgar E. Enochs, Alina Iacob, Overtoun Jenda

Alina Iacob