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### Cone Monotonicity: Structure Theorem, Properties, and Comparisons to Other Notions of Monotonicity

Heather A. Van Dyke, Kevin R. Vixie, Thomas J. Asaki
2013 Abstract and Applied Analysis
In search of a meaningful 2-dimensional analog to monotonicity, we introduce two new definitions and give examples of and discuss the relationship between these definitions and others that we found in  ...  the literature.  ...  The definition for normal monotone requires that the function be monotone along the entire intersection of a one dimensional line and the the domain of .  ...

### How singular are moment generating functions? [article]

Eberhard Mayerhofer
2011 arXiv   pre-print
This short note concerns the possible singular behaviour of moment generating functions of finite measures at the boundary of their domain of existence. We look closer at Example 7.3 in O.  ...  Barndorff-Nielsen's book "Information and Exponential Families in Statistical Theory (1978)" and elaborate on the type of exhibited singularity.  ...  The final section 3 poses a problem about singularities of moment generating functions along the boundary of their existence domains.  ...

### Mayer-Vietoris property for relative symplectic cohomology [article]

Umut Varolgunes
2020 arXiv   pre-print
This is tailored to work under certain integrability assumptions, the weakest of which introduces a new geometric object called a barrier - roughly, a one parameter family of rank 2 coisotropic submanifolds  ...  In this paper, we construct a Hamiltonian Floer theory based invariant called relative symplectic cohomology, which assigns a module over the Novikov ring to compact subsets of closed symplectic manifolds  ...  Then, we can find a smooth function : R → R such that:• ≥ • and have no critical points along the boundaries of their domain of definition Let ⊂ ({ ∈ ′ ∩ ′′ | ( ) = ( )}) be a compact set such that ′  ...

### Boundary element dynamical energy analysis: A versatile method for solving two or three dimensional wave problems in the high frequency limit

David J. Chappell, Gregor Tanner, Stefano Giani
2012 Journal of Computational Physics
The main challenge is the high dimensionality of the problem: we determine the wave energy density both as a function of the spatial coordinate and momentum (or direction) space.  ...  Dynamical energy analysis was recently introduced as a new method for determining the distribution of mechanical and acoustic wave energy in complex built up structures.  ...  The authors also wish to thank inuTech Gmbh, Nürnberg for Diffpack guidance and licences and Hanya Ben Hamdin and Dmitrii Maksimov for helpful discussions.  ...

### Some six-dimensional rigid forms

Mathieu Dutour, Frank Vallentin
2005 arXiv   pre-print
Furthermore, we found out that for d <= 5 the adjacency graph of primitive L-type domains is an infinite tree on which GL_d(Z) acts.  ...  On the other hand, we demonstrate that in d = 6 we face a combinatorial explosion.  ...  From Voronoi's algorithm for finding all primitive L-type domains we get the facets of every primitive L-type domain. By converting the facet description we find all extreme rays.  ...

### Application of Random Walk Methods to Wave Propagation

B. V. Budaev
2002 Quarterly Journal of Mechanics and Applied Mathematics
We start our analysis of the Helmholtz equation following closely the scheme of the ray method, but instead of approximating the resulting second-order auxiliary equation by a firstorder equation, we study  ...  of Wiener functional integration, and the theory of stochastic processes.  ...  Acknowledgements This research was supported by NSF grant 9730779 and by the William S. Floyd Jr Distinguished Professorship in Engineering held by the second author.  ...

### In–out decomposition of boundary integral equations

Stephen C Creagh, Hanya Ben Hamdin, Gregor Tanner
2013 Journal of Physics A: Mathematical and Theoretical
We propose a reformulation of the boundary integral equations for the Helmholtz equation in a domain in terms of incoming and outgoing boundary waves.  ...  As an application, we show how the decomposition may be used to calculate Goos-H\"anchen shifts of ray dynamics in billiards with variable boundary conditions and for dielectric cavities.  ...  EP/F036574/1 and the hospitality of the MPIPKS, Dresden, where part of this work was completed while participating in the Advanced Study Group Dynamical Tunneling.  ...

### Numerical Solution of the Tomography Problem in Domains with Obstacles [article]

Kamen Lozev
2012 arXiv   pre-print
We study numerical methods of tomography in domains with a reflecting obstacle.  ...  It will be shown that tomography with sets containing both broken rays, i.e. rays reflecting at the obstacle, as well as unbroken rays, has a smaller error between the original and reconstructed image  ...  Acknowledgments I would like to thank my wife for her support, comments and suggestions. I would like to thank Professor Gregory Eskin for suggesting this problem and for his continuous guidance.  ...

### How should we improve the ray-tracing method?

B. V. Budaev
2011 St. Petersburg Mathematical Journal
equation in the form of the expectation of a certain functional on the space of Brownian random walks).  ...  The possibility is discussed to improve the ray approximation up to an exact representation of a wave field by the Feynman-Kac probabilistic formula (this formula gives an exact solution of the Helmholtz  ...  , the diffraction problem on an arbitrary polygon, the three-dimensional problem of diffraction on a plane sectorial screen, as well as a more general problem of diffraction on a pyramid of infinite length  ...

### A boundary integral method for modelling vibroacoustic energy distributions in uncertain built up structures

Janis Bajars, David J. Chappell
2018 Journal of Computational Physics
A phase-space boundary integral method is developed for modelling stochastic highfrequency acoustic and vibrational energy transport in both single and multi-domain problems.  ...  Numerical results for a series of coupled domain problems are presented, and demonstrate the potential for future applications to larger scale problems from industry.  ...  Acknowledgements We would like to thank Dr Oscar Bandtlow and Professor Gregor Tanner for stimulating discussions. Support from the EPSRC (grant no. EP/M027201/1) is gratefully acknowledged.  ...

### Bounded λ-harmonic functions in domains of H^n with asymptotic boundary with fractional dimension [article]

Leonardo Prange Bonorino, Patrícia Kruse Klaser
2015 arXiv   pre-print
We prove that if the (n-1)/2 Hausdorff measure of the asymptotic boundary of a domain Ω is zero, then there is no bounded λ-harmonic function of Ω for λ∈ [0,λ_1(H^n)], where λ_1(H^n)=(n-1)^2/4.  ...  Conversely, for any s>(n-1)/2, we prove the existence of domains with asymptotic boundary of dimension s for which there are bounded λ_1-harmonic functions that decay exponentially at infinity.  ...  A horosphere in H n is a (n−1)−dimensional submanifold of H n obtained as the limit set of a sequence of geodesic spheres centered along a geodeisic ray γ(t) that contain γ(0).  ...

### Modeling of silicon solar cells performances by MATLAB

Cherouana ABDELBAKI, Labbani REBIHA
2015 International Journal of Computational and Experimental Science and Engineering
We reformulate the boundary integral equations for the Helmholtz equation in terms of incoming and outgoing boundary waves independently of the boundary conditions and decomposing the green functions into  ...  For demonstration purposes, we apply a semiclassical form of the operator (corresponding to a high-frequency approximation) to polygonal coupled-cavity configurations with abrupt changes of the material  ...  Acknowledgement HBH acknowledges support by the Libyan Ministry of Education. SCC acknowledges support from EPSRC under grant no. EP/F036574/1.  ...

### Radiative transfer in decomposed domains

T. Heinemann, W. Dobler, Å. Nordlund, A. Brandenburg
2006 Astronomy and Astrophysics
The waiting time of idle processors during the nonlocal communication part does not have a severe impact on the scaling.  ...  The integral formulation of the transfer equation is used to divide the problem into a local but compute-intensive part for calculating the intensity and optical depth integrals, and a nonlocal part for  ...  The work of ÅN was supported by grant number 21-01-0557 from the Danish Research Council for Nature and Universe (FNU). Computing time was provided by the Danish Scientific Computing Center (DCSC).  ...

### A Simplified Fourier Method for Nonhydrostatic Mountain Waves

Dave Broutman, James W. Rottman, Stephen D. Eckermann
2003 Journal of the Atmospheric Sciences
Resonant modes are handled with a small amount of damping, and caustics are handled with a uniformly valid approximation involving the Airy function.  ...  The approximation involves using ray theory to simplify the vertical eigenfunctions. The generalization to nonhydrostatic waves requires special treatment for resonant modes and caustics.  ...  We thank John Lindeman for providing the numerical simulations presented in Figs. 5 and 6. SDE acknowledges support for this research from the Office of Naval Research.  ...

### Finite element method for modeling radiative transfer in semitransparent graded index cylindrical medium

L. Zhang, J.M. Zhao, L.H. Liu
2009 Journal of Quantitative Spectroscopy and Radiative Transfer
To overcome the RTEGC-led numerical singularity at the origin of cylindrical coordinate system, a pole condition is proposed as a special mathematical boundary condition.  ...  Both Galerkin finite element method (GFEM) and least squares finite element method (LSFEM) are developed and their performances are compared for solving the radiative transfer equation of graded index  ...  Acknowledgment The support of this work by the National Nature Science Foundation of China (50620120442) is gratefully acknowledged.  ...
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