Boundary Circle Research Articles

The generalized Lefschetz number of homeomorphisms on punctured disks

We compute the generalized Lefschetz number of orientation-preserving self-homeomorphisms of a compact punctured disk, using the fact that homotopy classes of these homeomorphisms can be identified with braids. This result is applied to study Nielsen-Thurston canonical homeomorphisms on a punctured disk. We determine, for a certain class of braids, the rotation number of the corresponding canonical homeomorphisms on the outer boundary circle. As a consequence of this result on the rotation number, it is shown that the canonical homeomorphisms corresponding to some braids are pseudo-Anosov with associated foliations having no interior singularities.

Disk-annulus transition and localization in random non-Hermitian tridiagonal matrices

Eigenvalues and localization of eigenvectors of non-Hermitian tridiagonal periodic random matrices are studied by means of the Hatano–Nelson deformation. The support of the spectrum undergoes a disk to annulus transition, with inner radius measured by the complex Thouless formula. The inner bounding circle and the annular halo are structures that correspond to the two arcs and wings observed by Hatano and Nelson in deformed Hermitian models, and are explained in terms of localization of eigenstates via a spectral duality and the argument principle. This disk-annulus transition is reminiscent of Feinberg and Zee's transition observed in full complex random matrices.

Restricted partition functions of the two-dimensional Ising model on a half-infinite cylinder

We study the Ising model on a half-infinite cylinder at the critical temperature. On the boundary circle, we fix four intervals of constant signs. Let θ1, θ2, θ3, and θ4 be the positions where the flips occur, labeled counterclockwise in that order. From each θ starts a contour between clusters of opposite signs. The contour leaving θ1 may end only at θ2 or θ4. Using an argument based on conformal field theory, we give the probability distribution that the contour leaving θ1 ends at θ2. The behavior of this function when θ2−θ1→0 is described by a power law with an exponent (53) that belongs to the Kac table but that corresponds to a nonunitarizable highest-weight representation. We check that this prediction agrees with a Monte Carlo simulation.

Theoretical Research and Verification on the Porosity of Semi-Fixed Abrasive Tool

Semi-fixed abrasive tool is a new developed grinding wheel which can adjust abrasive grain near the workpiece-abrasive interface according to the situation of the hard and large grits, damaged surface layer generated by the scratch or crack could be decreased when using semi-fixed wheel. Porosity, one of the most important parameters to evaluate trap effect, was studied based on the analysis of uniform scratch and it’s effect on the polishing time, contact models between circle abrasive grain, line boundary and circle boundary were deduced to investigate the relations between engagement depth and the ratio of normal force to normal elastic stiffness. Theoretical research results show that semi-fixed grinding wheel should be conditioned after it’s compaction for the boundary between abrasive grain and line boundary is unstable, the contact status is stable for internal abrasive grain, predicted porosity value agree well with that measured in the experiment, the shear strength of semi-fixed abrasive tool can meet the demand of lapping and polishing processes.

Numerical study on transient flow in the deep naturally fractured reservoir with high pressure

According to the experimental results and the characteristics of the pressure-sensitive fractured formation, a transient flow model is developed for the deep naturally-fractured reservoirs with different outer boundary conditions. The finite element equations for the model are derived. After generating the unstructured grids in the solution regions, the finite element method is used to calculate the pressure type curves for the pressure-sensitive fractured reservoir with different outer boundaries, such as the infinite boundary, circle boundary and combined linear boundaries, and the characteristics of the type curves are comparatively analyzed. The effects on the pressure curves caused by pressure sensitivity module and the effective radius combined parameter are determined, and the method for calculating the pressure-sensitive reservoir parameters is introduced. By analyzing the real field case in the high temperature and pressure reservoir, the perfect results show that the transient flow model for the pressure-sensitive fractured reservoir in this paper is correct.

Planforms of self‐consistently generated plates in 3D spherical geometry

In the past decade, several studies have documented the effectiveness of plastic yielding in causing a basic approximation of plate tectonic behavior in mantle convection models with strongly temperature dependent viscosity, strong enough to form a rigid lid in the absence of yielding. The vast majority of such research to date has been in either two‐dimensional, or three‐dimensional cartesian geometry. In the present study, mantle convection calculations are performed to investigate the planform of self‐consistent tectonic plates in three‐dimensional spherical geometry. The results are compared to those of similar calculations where a three dimensional cartesian geometry is used. We found that when yield stress of the lithosphere is low (∼20 MPa) a “great circle”‐subduction zone forms. At low‐intermediate yield stresses (∼100 MPa) plates, spreading centers and subduction zones formed and were destroyed over time. At high‐intermediate yield stresses (∼200 MPa) two plates form, separated by a great circle boundary that is a spreading centre on one side and a subduction zone on the other side. At high yield stresses (∼400 MPa) a rigid lid was observed. The great circle subduction zone and the rigid lid are stable over time while at intermediate yield stresses some episodic behavior is observed. The spherical cases showed a higher, more Earth‐like, toroidal‐poloidal ratio of the surface velocity field than the cartesian cases.

Phase transition of electrically charged Ricci-flat black holes

We study phase transition between electrically charged Ricci-flat black holes and AdS soliton spacetime of Horowitz and Myers in five dimensions. Boundary topology for both of them is S1 × S1 × R2. We consider AdS-Reissner-Nordström black hole and R-charged black holes and find that phase transition of these black holes to AdS soliton spacetime depends on the relative size of two boundary circles. We also perform the stability analysis for these black holes. In order to use the AdS/CFT correspondence, we work in the grand canonical ensemble.

The Fredholm Index for Elements of Toeplitz-Composition C*-Algebras

We analyze the essential sectrum and index theory of elements of Toeplitz-composition C*-algebras (algebras generated by the Toeplitz algebra and a single linear-fractional composition operator, acting on the Hardy space of the unit disk). For automorphic composition operators we show that the quotient of the Toeplitz-composition algebra by the compacts is isomorphic to the crossed product C*-algebra for the action of the symbol on the boundary circle. Using this result we obtain sufficient conditions for polynomial elements of the algebra to be Fredholm, by analyzing the spectrum of elements of the crossed product. We also obtain an integral formula for the Fredholm index in terms of a generalized Chern character. Finally we prove an index formula for the case of the non-parabolic, non-automorphic linear fractional maps studied by Kriete, MacCluer and Moorhouse.

On the Gersgorin Theorem Applied To Radar Polarimetry

This contribution is concerned with the mathematical formulation and theoretical background of the Ger‚sgorin theory in the context of Radar Polarimetry. Named after its founder Semian A. Ger‚sgorin the Ger‚sgorin theorem basically states that there are certain regions in the complex plane that can be derived from any n £ n complex matrix by rather simple arithmetic operations. These regions are containing more information, speciflcally its eigenvalues lying within or at the boundaries of circles, where the radii are obtained by the deleted absolute row and/or column sums of the respective n £ n complex matrices.

1705 多重極展開を用いた境界要素法による注目領域の高速解法(OS17.RBFと選点法の新展開(2),ポスターセッションP-3)

A new technique for boundary element analysis of potential problems using a multipole expansion to obtain the solution efficiently only in a target region has been developed. The capability of the present technique was verified by numerical simulations. In this technique, region to be analyzed is divided into target boundaries and non-target boundaries as shown in Figure 1, and the multipole expansion is applied to boundary integral equations on non-target boundaries, and the expansion is truncated at the term where the error bound of the higher terms is guaranteed. This technique decreases the calculation amount by introducing multipole moments as the unknown valuables in place of the unkown flux distribution in the non-target boundaries. To demonstrate the effectiveness of the method, example analysis of doughnut shaped Laplace field › was performed as shown in Figure 2. The outer circle boundary is

Conformal mapping and an inverse impedance boundary value problem

Akduman, Haddar and Kress [1, 12, 15] proposed a conformal mapping approach for solving inverse boundary value problems for the two-dimensional Laplace equation in a doubly connected domain D with interior boundary curve Γ0 and exterior boundary curve Γ1. The inverse problem consists of reconstructing the interior boundary Γ0 from the Cauchy data on Γ1 of a harmonic function satisfying a homogeneous Dirichlet or Neumann boundary condition on the unknown interior boundary curve Γ0. The reconstruction method consists of two parts: In the first step, by successive approximations a nonlocal and nonlinear ordinary differential equation is solved to determine the boundary values of a holomorphic function Ψ on the outer boundary circle C1 of an annulus B. Then in the second step via regularizing a Laurent expansion in the sense of Tikhonov an ill-posed Cauchy problem is solved to determine Ψ in the annulus and the unknown Γ0 as the image Ψ(C0) of the interior boundary circle C0 of B. The present paper extends this approach to the case of a homogeneous impedance boundary condition. The analysis and the numerical implementation of the method differ from the limiting cases of the Dirichlet and Neumann conditions since the impedance problem in the annulus B that is associated with the impedance problem in the original domain D depends on the conformal map Ψ.

Configuration Models For Moduli Spaces of Riemann surfaces with boundary

In this article we consider Riemann surfacesF of genus g ≥ 0 with n ≥ 1 incoming and m ≥ 1 outgoing boundary circles, where on each incoming circle a point is marked. For the moduli space mg*(m, n) of all suchF of genusg ≥ 0 a configuration space model Radh(m, n) is described: it consists of configurations of h = 2g-2+m+n pairs of radial slits distributed over n annuli; certain combinatorial conditions must be satisfied to guarantee the genusg and exactly m outgoing circles. Our main result is a homeomorphism between Radh(m, n) and Mg*(m,n). The space Radh(m, n) is a non-compact manifold, and the complement of a subcomplex in a finite cell complex. This can be used for homological calculations. Furthermore, the family of spaces Radh(m, n ) form an operad, acting on various spaces connected to conformai field theories.

New Approach for Static Gesture Recognition

Static gestures can convey certain meanings and act as specific transitions in dynamic gestures. Therefore, recognizing static gestures is one of the most important aspects of gesture recognition. In this paper, a new approach is presented for recognizing static gestures based on Zernike moments (ZMs) and pseudo-Zernike moments (PZMs). The binary hand silhouette is first accommodated with a minimum bounding circle (MBC). The binary hand silhouette is then decomposed into the finger part and the palm part by morphological operations according to the radius of the MBC. After that, the ZMs & PZMs of the finger part and the palm part with different importance, respectively, are computed based on the center of the MBC. Finally, 1-nearest neighbor techniques are used to perform feature matching between an input feature vector and stored feature vectors for static gesture identification. Results show that the proposed approach performs better than previous methods based on conventional ZMs & PZMs in recognizing static gestures. The proposed technique could be useful in improving the recognition rate, of static gestures.

Time-of-flight secondary ion mass spectrometry chemical imaging analysis of micropatterns of streptavidin and cells without labeling

A bismuth cluster ion-beam-based time-of-flight secondary ion mass spectrometry (TOF-SIMS) has been successfully used to image micropatterns of streptavidin and Chinese hamster ovary (CHO-k1) cells, as received and without any labeling. Three different analysis ion beams (Bi+, Bi3+, and Bi32+) were compared to obtain label-free TOF-SIMS chemical images of micropatterns of streptavidin, which were subsequently used for generating biotinylated cell patterns. Unlike using a Bi+ ion beam, using a Bi3+ or Bi32+ primary analysis ion beam yielded well-contrasted-TOF-SIMS images of streptavidin characteristic secondary ions. A principal component analysis of TOF-SIMS data was performed to generate a chemical image of the streptavidin itself. A chemical specific TOF-SIMS image analysis gave us a better understanding of the localization of cells at the outer boundaries of the streptavidin-patterned circles. Our work suggests that using cluster-ion analysis beams together with multivariate data analysis for TOF-SIMS chemical imaging would be an effectual method for producing label-free chemical images of micropatterns of biomolecules, including proteins and cells.

Wireless Data Broadcast Schemes for Location-Dependent Information Services Under a Geometric Location Model

Indexing techniques are used to implement selective tuning in wireless environments. Indices are broadcast together with data to help mobile clients locate the required information. As a result, clients stay in doze mode most of the time. The drawback of this solution is that broadcast cycles are lengthened due to additional index information. In this paper, we introduce the broadcast-based LDIS scheme (BBS) for the mobile computing environment. In the BBS, broadcasted data objects are sorted sequentially, based on their location, and the server broadcasts the location-dependent data (LDD) without additional indices. Then, we present a data prefetching scheme and OBC (Object Boundary Circle) in order to reduce the client’s tuning time. The performance of the proposed scheme is investigated in relation to various environmental variables, such as the distributions of the data objects, the average speed of the clients, and the size of the service area.

Physical insight into superdiffusive dynamics of Sinai billiard through collision statistics

We report on distinct steady-motion dynamic regimes in chaotic Sinai billiard (SB). A numerical study on elastic reflections from the SB boundary (square wall of length L and circle obstacle of radius R) is carried out for different R / L . The research is based on the exploration of the generalized diffusion equation and on the analysis of wall-collision and the circle-collision distributions observed at late times. The asymptotes for the diffusion coefficient D R and the corresponding diffusion exponent z R are established for all geometries. The universal ( R-independent) diffusion with D 1 ∽ t 1 / 3 and z 1 = 1.5 replaces the ballistic motion regime ( z 0 = 1 ) attributed to square billiard ( R = 0 ). Geometrically, this superdiffusive regime is bounded by small radii 0 < R < R 1 ( R 1 / L = 2 4 ), when both diagonal and non-diagonal Bleher's corridors are open in the correspondent square lattice of Lorentz gas (LG) model. The relaxation dynamics observed is ensured by the universal diffusive propagation of the regular-type and the bouncing-ball-type orbits. Within the random walk scheme, this superdiffusive regime is due to the Lévy flights between the long-distant scatterers. With the increase in circle radius ( R 1 ⩽ R < R 2 , R 2 = L / 2 ), the diagonal corridor closes, but the arc-touching effects continue to bring the long-living bouncing-ball orbits back to the non-diagonal infinite corridors. This transient non-universal dynamics with 1.5 < z R < 2 , also associated with the trapping of regular orbits, seems to be characteristic of non-fully hyperbolic billiard systems. In SB with finite horizon ( R ⩾ R 2 ), all the principal corridors are closed and the interplay between square and circle boundaries generates the known chaotic dynamics, attributed to the fully hyperbolic systems. This is also observed through the normal Brownian diffusion ( z 2 = 2 ) and the Gaussian statistics, proved for both kinds of collisions.

R-charged adS bubble

We construct R-charged adS bubbles in D=5, N=8 supergravity. These bubbles are characterized by four parameters. The asymptotic boundary of these solutions are de Sitter times a circle. By comparing boundary energies, we study the possibility of a transition from certain class of black holes to these bubbles below a critical radius of the boundary circle. We argue that this may occur when four parameters of the bubble satisfy a constraint among themselves.

The arctic circle boundary and the Airy process

We prove that the, appropriately rescaled, boundary of the north polar region in the Aztec diamond converges to the Airy process. The proof uses certain determinantal point processes given by the extended Krawtchouk kernel. We also prove a version of Propp’s conjecture concerning the structure of the tiling at the center of the Aztec diamond. 1. Introduction and results. Domino tilings of the Aztec diamond were introduced in [8, 9]. Asymptotic properties of random domino tilings of the Aztec diamond have been studied in [5, 12, 15]. In particular, in [12] the existence of the so-called arctic circle was proved. The arctic circle is the asymptotic boundary of the disordered so-called temperate region of the tiling. Outside this boundary the tiling forms a completely regular brick wall pattern. The methods in [12] combined with the results in [13] show that the fluctuations of the point of intersection of the boundary of the temperate region with a line converge to the Tracy–Widom distribution of random matrix theory. In this paper we extend this result to show that the fluctuations of the boundary around the arctic circle converges to the Airy process introduced in [23]. The paper is a continuation of the approach used in [14] and [15], where certain point processes with determinantal correlation functions [24] and the Krawtchouk ensemble, were used. We will use the general techniques developed in [16] and investigate an extended point process which also has determinantal correlation functions given by a kernel, which we call the extended Krawtchouk kernel. The Aztec diamond, An, of order n is the union of all lattice squares [m, m+1]×[l, l+1], m, l 2 Z, that lie inside the region {(x1, y1);|x1|+|y1| �

On some heat conduction problem in a periodically two-layered body: Comparative results

The paper deals with some comparison of results obtained within the framework of homogenized model with microlocal parameters [Cz. Woźniak, Int. J. Eng. Sci. 25 (1987) 483–499; S.J. Matysiak, Cz. Woźniak, Acta Mech. 63 (1986) 223–238; S.J. Matysiak, Acta Mech., 78 (1989) 95–108] and within the framework of classical heat conduction equations for a periodically two-layered half-space. The body is assumed to be heated by a constant heat flux on a boundary circle.

Schwarz-Christoffel mapping of multiply connected domains

A Schwarz-Christoffel mapping formula is established for polygonal domains of finite connectivitym≥2 thereby extending the results of Christoffel (1867) and Schwarz (1869) form=1 and Komatu (1945),m=2. A formula forf, the conformal map of the exterior ofm bounded disks to the exterior ofm bounded disjoint polygons, is derived. The derivation characterizes the global preSchwarzianf″ (z)/f′ (z) on the Riemann sphere in terms of its singularities on the sphere and its values on them boundary circles via the reflection principle and then identifies a singularity function with the same boundary behavior. The singularity function is constructed by a “method of images” infinite sequence of iterations of reflecting prevertex singularities from them boundary circles to the whole sphere.