Bouncing negative-tension branes

It is shown that negative tension branes in higher dimensions may lead to an effective lower dimensional theory where the gauge-invariant vector fields associated with the fluctuations of the metric are always massless and localized on the brane. Explicit five-dimensional examples of this phenomenon are provided. Furthermore, it is shown that higher dimensional gauge fields can also be localized on these configurations with the zero mode separated from the massive tower by a gap.

Resonant transmission through a double domain wall in magnetic nanowires

Multibrane worlds and modification of gravity at large scales

Click to increase image sizeClick to decrease image size Additional informationNotes on contributorsShif BerhanuSHIF BERHANU graduated with a B.Sc. degree from Addis Ababa University, Ethiopia, in 1980. In 1987 he received his Ph.D. from Rutgers University under the direction of Francois Trevès. He is a professor of mathematics at Temple University. Berhanu's main area of research involves complex vector fields, that is, firstorder partial differential operators with complex-valued coefficients. Currently, he, P. Cordaro, and J. Hounie are collaborating to write a book on the subject of complex vector fields.Ahmed MohammedAHMED MOHAMMED received his B.Sc. in 1983 and M.Sc. in 1986 from Addis Ababa University, Ethiopia. He obtained his Ph.D. in 1995 from Temple University under the guidance of Professor Cristian E. Gutierrez. Between 1995 and 2000, he taught in the Department of Mathematics and Computer Science at Kuwait University, Kuwait. He held a visiting position at Temple University from 2000 to 2002. Currently he is an associate professor in the Department of Mathematical Sciences at Ball State University. If he is not doing mathematics in his office or teaching a class, chances are you'll find him at the Starbucks in the university book store.

Haptic devices allow a user to feel either reaction forces from virtual interactions or reaction forces reflected from a remote site during a bilateral teleoperation task. Also, guiding forces can be exerted to train the user in the performance of a virtual task or to assist him/her to safely teleoperate a robot. The generation of guiding forces relies on the existence of a motion plan that provides the direction to be followed to reach the goal from any free configuration of the configuration space ( ${\mathcal C}$ -space). This paper proposes a method to obtain such a plan that interleaves a sampling-based exploration of ${\mathcal C}$ -space with an efficient computation of harmonic functions. A deterministic sampling sequence (with a bias based on harmonic function values) is used to obtain a hierarchical cell decomposition model of ${\mathcal C}$ -space. A harmonic function is iteratively computed over the partially known model using a novel approach. The harmonic function is the navigation function used as motion plan. The approach has been implemented in a planner (called the Kautham planner) that, given an initial and a goal configuration, provides: (a) a channel of cells connecting the cell that contains the initial configuration with the cell that contains the goal configuration; (b) two harmonic functions over the whole ${\mathcal C}$ -space, one that guides motions towards the channel and another that guides motions within the channel towards the goal; and (c) a path computed over a roadmap built with the free samples of the channel. The harmonic functions and the solution path are then used to generate the guiding forces for the haptic device. The planning approach is illustrated with examples on 2D and 3D workspaces.

Our main objective is to study how braneworld models of higher codimension differ from the 5D case and traditional Kaluza-Klein compactifications. We first derive the classical dynamics describing the physical fluctuations in a wide class of models incorporating gravity, non-Abelian gauge fields, the dilaton and two-form potential, as well as 3-brane sources. Next, we use these results to study braneworld compactifications in 6D supergravity, focusing on the bosonic fields in the minimal model; composed of the supergravity-tensor multiplet and the U(1) gauge multiplet whose flux supports the compactification. For unwarped models sourced by positive tension branes, a harmonic analysis allows us to solve the large, coupled, differential system completely and obtain the full 4D spin-2,1 and 0 particle spectra, establishing (marginal) stability and a qualitative behaviour similar to the smooth sphere compactification. We also find interesting results for models with negative tension branes; extra massless Kaluza-Klein vector fields can appear in the spectra, beyond those expected from the isometries in the internal space. These fields imply an enhanced gauge symmetry in the low energy 4D effective theory obtained by truncating to the massless sector, which is explicitly broken as higher modes are excited, until the full 6D symmetries are restored far above the Kaluza-Klein scale. Remarkably, the low energy effective theory does not seem to distinguish between a compactification on a smooth sphere and these singular, deformed spheres.

We describe the spontaneous creation of the brane world in AdS 5 with external field. The resulting brane world consists of a flat 4d spatially finite expanding universe and curved expanding "regulator" branes. No negative tension branes are involved.

The purpose of this paper is to show certain links between univariate interpolation by algebraic polynomials and the representation of polyharmonic functions. This allows us to construct cubature formulae for multivariate functions having highest order of precision with respect to the class of polyharmonic functions. We obtain a Gauss type cubature formula that uses m m values of linear functionals (integrals over hyperspheres) and is exact for all 2 m 2m -harmonic functions, and consequently, for all algebraic polynomials of n n variables of degree 4 m − 1 4m-1 .

In this paper we study the distribution of values of harmonic functions in non-Euclidean disks. We introduce the notion of a P′-sequence, which enables us to characterize the class of normal harmonic functions defined in the unit disk. Moreover, we obtain sufficient conditions for the existence of such sequences and give examples which show that these conditions are essential in the stated theorems.

We study the connection between the dimension of certain spaces of harmonic functions on a group and its geometric and algebraic properties. Our main result shows that (for sufficiently “nice” random walk measures) a connected, compactly generated, locally compact group has polynomial volume growth if and only if the space of linear growth harmonic functions has finite dimension. This characterization is interesting in light of the fact that Gromov’s theorem regarding finitely generated groups of polynomial growth does not have an analog in the connected case. That is, there are examples of connected groups of polynomial growth that are not nilpotent by compact. Also, the analogous result for the discrete case has only been established for solvable groups and is still open for general finitely generated groups.

Open sets D D in R N ( N ≥ 3 ) {R^N}\;(N \geq 3) with the property that D ¯ \bar D is a closed annulus { x : r 1 ≤ ‖ x ‖ ≤ r 2 } \{ x:{r_1} \leq \;\left \| x\right \| \; \leq {r_2}\} are characterized by quadrature formulae involving mean values of certain harmonic functions. One such characterization is used to give a criterion for the existence of a best harmonic L 1 {L^1} approximant to a function which is subharmonic (and satisfies some other conditions) in an annulus.

0. A classical result of Fatou states that if u(z) is harmonic and bounded in lzl < 1 then u has a nontangential limit at almost every point ei?. The same conclusion holds if u is only bounded from below. These results have a local analogue -namely, if u(z) is harmonic in lzl < 1 and at each point ei0 of a measurable set E there is some cone in which u(z) is bounded from either above or below then u(z) has a nontangential limit at almost every eiO & E. With the aid of conformal mapping one can show the above results hold for regions of the plane more general than lzl < 1. Methods similar to those used for lzl < 1 may be applied to functions which are harmonic in the unit ball of Euclidean (n + 1)-space. However, since we lack a conformal mapping theorem for more general domains DcE +1 the situation there is more technically complicated. Known results for certain kinds of domains D c E, + 1 are due to Brelot and Doob [2], Calderon [3], Carleson [4] and Widman [7], and the purpose of this paper is to obtain nontangential boundary values for functions which are harmonic in still more general types of domains D' En + 1 and bounded from above or below in cones. The domains which we consider are all regular domains for the solution of the Dirichlet problem. For a regular domain D, our result may be stated as follows. Let EC aD and suppose for each Q E E there is a cone with vertex Q which is exterior to D. Then if u is harmonic in D and is bounded from above or below in a cone with vertex Q for each Q E E, u has a finite nontangential limit at each Q E E except for a set of harmonic measure zero. It is natural that the exceptional set be one of harmonic measure zero since if Ec AD is any set of harmonic measure zero it is easy to construct a positive harmonic function with boundary value +oo at each point of E. Our main result is a consequence of the basic result that if u is harmonic and bounded in a starlike Lipschitz domain D, then u has a finite nontangential limit at each Q E AD except for a set of harmonic measure zero. In ?1 of this paper we define the terms starlike Lipschitz domain, nontangential limit, and harmonic measure. We also include some elementary consequences of these definitions and some essential theorems on the differentiation of integrals.

CHAPTER V - VARIOUS GENERALIZED BOUNDARY VALUE PROBLEMS

This volume contains the proceedings of the International Conference on Algebra and Related Topics, held from July 2–5, 2018, at Mohammed V University, Rabat, Morocco. Linear reserver problems demand the characterization of linear maps between algebras that leave invariant certain properties or certain subsets or relations. One of the most intractable unsolved problems is Kaplansky's conjecture: every surjective unital invertibility preserving linear map between two semisimple Banach algebras is a Jordan homomorphism. Recently, there has been an upsurge of interest in nonlinear preservers, where the maps studied are no longer assumed linear but instead a weak algebraic condition is somehow involved through the preserving property. This volume contains several articles on various aspects of preservers, including such topics as Jordan isomorphisms, Aluthge transform, joint numerical radius on C*-algebras, advertible complete algebras, and Gelfand-Mazur algebras. The volume also contains a survey on recent progress on local spectrum-preserving maps. Several articles in the volume present results about weighted spaces and algebras of holomorphic or harmonic functions, including biduality in weighted spaces of analytic functions, interpolation in the analytic Wiener algebra, and weighted composition operators on non-locally convex weighted spaces

Analysis of deep beams and shear walls by finite strip method with C0 continuous displacement functions