Elliptic Pairing Research Articles

Extensions of tempered representations

Let π, π′ be irreducible tempered representations of an affine Hecke algebra $${\mathcal{H}}$$ with positive parameters. We compute the higher extension groups Ext $${{}_\mathcal{H}^n (\pi,\pi')}$$ explicitly in terms of the representations of analytic R-groups corresponding to π and π′. The result has immediate applications to the computation of the Euler–Poincaré pairing EP (π, π′), the alternating sum of the dimensions of the Ext-groups. The resulting formula for EP(π, π′) is equal to Arthur’s formula for the elliptic pairing of tempered characters in the setting of reductive p-adic groups. Our proof applies equally well to affine Hecke algebras and to reductive groups over non-archimedean local fields of arbitrary characteristic. This sheds new light on the formula of Arthur and gives a new proof of Kazhdan’s orthogonality conjecture for the Euler–Poincaré pairing of admissible characters.

Study on High-Order Elliptical Gear Parametric Design, Automatic Modeling and Motion Simulation

In this paper, the high-order elliptical gear design principle and methods were studied based on Solidworks API to accomplish high-order elliptical gear parametrical design, machining simulation and automatic modeling. Elliptical gear pair simulation was carried out for verification. The high-order elliptical gear modeling method proposed was to use gear hob type of envelope processing method with the advantages of being able to process concaved pitch curve of high-order elliptical gear. The idea of this design process can also be extended to other types of non-circular gear design and modeling.

Elliptical Gears Parametric Design and Motion Simulation

Based on the design theory of non-circular gears, using Visual Basic 6.0 Programming language secondary developed SolidWorks software, a system of elliptical gears parametric design and motion simulation was developed. 3D parametric modeling and motion simulation of elliptical gears can be achieved by this system. The development process of system is introduced in detail, and an example which designed a transmission with two identical three rank elliptical gears was given to illustrate the system operation process in detail. Using elliptical gears pair ratio cyclical curves acquired, compared with theoretical transmission ratio can verify design whether meet the requirements. Complex design and calculation and difficult 3D modeling problems of elliptical gears are solved, and this system can also improve design precision, shorten the development cycle, and guarantee the quality of products.

LOCAL BENCHMARKS FOR THE EVOLUTION OF MAJOR-MERGER GALAXIES—SPITZEROBSERVATIONS OF AK-BAND SELECTED SAMPLE

We present Spitzer observations for a sample of close major-merger galaxy pairs (KPAIR sample) selected from cross-matches between the Two Micron All Sky Survey and Sloan Digital Sky Survey Data Release 3. The goals are to study the star formation activity in these galaxies and to set a local bench mark for the cosmic evolution of close major mergers. The Spitzer KPAIR sample (27 pairs, 54 galaxies) includes all spectroscopically confirmed spiral–spiral (S+S) and spiral–elliptical (S+E) pairs in a parent sample that is complete for primaries brighter than K = 12.5 mag, projected separations of 5 h−1 kpc ⩽ s ⩽ 20 h−1 kpc, and mass ratios ⩽2.5. The Spitzer data, consisting of images in seven bands (3.6, 4.5, 5.8, 8, 24, 70, 160 μm), show very diversified IR emission properties. Compared to single spiral galaxies in a control sample, only spiral galaxies in S+S pairs show significantly enhanced specific star formation rate (sSFR = SFR/M), whereas spiral galaxies in S+E pairs do not. Furthermore, the SFR enhancement of spiral galaxies in S+S pairs is highly mass-dependent. Only those with M ≳ 1010.5 M☉ show significant enhancement. Relatively low-mass (M ∼ 1010 M☉) spirals in S+S pairs have about the same SFR/M compared to their counterparts in the control sample, while those with 1011 M☉ have on average a ∼3 times higher SFR/M than single spirals. There is evidence for a correlation between the global star formation activities (but not the nuclear activities) of the component galaxies in massive S+S major-merger pairs (the "Holmberg effect"). There is no significant difference in the SFR/M between the primaries and the secondaries, nor between spirals of SEP < 1 and those of SEP ⩾ 1, SEP being the normalized separation parameter. The contribution of KPAIR galaxies to the cosmic SFR density in the local universe is only 1.7%, and amounts to .

Zero-knowledge identification scheme based on Weil pairing

Zero knowledge turned out to be a useful tool for many cryptographic applications. Many cryptographic protocols based on bilinear pairings, namely the Weil and Tate pairings, have been proposed recently. In this paper, first elliptic curves and weil pairing would be introduced. In addition a new zero-knowledge identification scheme based on weil pairing is proposed. Finally, our scheme is compared with some identification schemes. Also we have described zero-knowledge property of the scheme and evaluation security analysis of proposed scheme.

Galaxy Interactions and Their Cosmic and Morphological Evolution

Merger theory, in its extreme form, postulates that ellipticals are the products of mergers of spirals. While the morphology-clustercentric relationship (Whitmoreet al., 1993), indicates that the morphological fractions are unaffected by the local properties of the clusters, considerable observational evidence has surfaced in favor of the existence of marginally bound pairs; that are the source of the most frequent collisions (Chengaluret al., 1996 and references therein). To test the global impact of galaxy collisions on their evolution we have studied many collisions between spirals and ellipticals, as well as spiral and elliptical pairs. The details of the models and methods are in Chatterjee &amp; Magalinsky, 2002; and we refer to it. Marginally bound, eccentric orbits are found to maintain their eccentricities for a long time; which is supported by analytical research (Magalinsky &amp; Chatterjee, 2000). The calculation of collision frequency indicates that only of the order of 5% of ellipticals can be formed in this way. A remarkable phenomenon is that the fraction of blue galaxies around z = 0.3 to 0.5 is more than in the present epoch – the B-O effect (Butcher &amp; Oemler, 1978). While observations indicate that the effect is primarily due to an increase in galaxies with perturbed morphology (e.g., Faberet al., 1995), in the same environment we find a homogeneous population of normal red galaxies, that have almost finished their star formation.

The directional contact distance of two ellipsoids: Coarse-grained potentials for anisotropic interactions

We obtain the distance of closest approach of the surfaces of two arbitrary ellipsoids valid at any orientation and separation measured along their intercenter vector. This directional distance is derived from the elliptic contact function. The geometric meaning behind this approach is clarified. An elliptic pair potential for modeling arbitrary mixtures of elliptic particles, whether hard or soft, is proposed based on this distance. Comparisons with Gay-Berne potentials are discussed. Analytic expressions for the forces and torques acting on the elliptic particles are given.

Mass of Galaxies in Pairs

We have compared the frequency distribution of the dynamical observedquantity log (Vz2rp), for a sample of 46 pairs of elliptical galaxies, to the distribution of this quantity obtained from numerical simulations of pairs of galaxies. From such an analysis, where we have considered the structure of the galaxies and its influence in the orbital evolution of the system, we have obtained the characteristic mass and the mass-luminosity ratio for the sample. Our results show that the hypothesis of point-mass in elliptical orbits is, for this sample, an approximation as good as the model that takes into account the structure of the galaxies. The statistical method used here gives an estimate of a more reliable mass, it minimizes the contamination of spurious pairs and it considers adequately the contribution of the physical pairs. We have obtained a characteristic mass to the 46 elliptical pairs of 1.68 × 1012 ± 7.01 ×1011 M⊙ with M/L = 17.6 ± 7.3 (H0 = 60 km s-1Mpc-1).

An X‐Ray Temperature Map of the Merging Cluster Abell 2255

We present a spatially resolved map of intracluster gas temperatures in the rich cluster Abell 2255, using ROSAT PSPC data. The intracluster gas is strongly nonisothermal and the temperature distribution supports the conclusions of Burns and coworkers that Abell 2255 is currently undergoing a merger. The hottest regions are near the core, northwest of the center. A map of the ratio of softer to harder X-ray photons reveals an anomalously soft region northeast of the center, coincident with a radio ridge discovered by Burns and coworkers in 1995. We suggest that this cooler region is associated with an infalling group of galaxies that is giving rise to the radio ridge. Meanwhile, a much more substantial recent merger between comparably sized subcluster components can account for the more global merger signatures, which include the extensive central radio halo, the large-scale gas temperature variations, the pair of central-dominant ellipticals, elliptical X-ray isophotes offset from these dominant galaxies, and the very high velocity dispersion of galaxies in the cluster.

Optical Properties of the Radio Source B2 0828+32

A small number of radio galaxies have two sets of classical double radio lobes with the radio axes aligned in different directions. Furthermore differences in the properties of the radio lobes such as the surface brightness and spectral index indicate that the two sets of double radio structure have different ages. The radio ejection axis has therefore changed direction with time. In the first two known radio galaxies of this type, 3C 315 and B2 0055+26, the host galaxy is a member of a close pair of ellipticals in a common optical envelope suggesting that the complex radio structure is caused by gravitational interaction.

A dynamical study of the frequency of merging galaxies

A study of the expected frequency of merging galaxies, involving disk-sphere systems, is conducted by use of the impulsive approximation. The results indicate that the expected frequencies of such galaxies is several orders of magnitude smaller than the observational value, if mergers taking place in a single crossing time or orbital period are considered. The expected frequency of elliptical pairs and spiral-elliptical pairs in merger is of the same order of magnitude, indicating that the two types of collisions are equally frequent.

Dynamics of Groups around Interacting Double Ellipticals: Measuring Dark Matter Haloes

Binary galaxies, as binary stars, are important to measure masses, as suggested by Page (1952). Because three orbit parameters are measurable for galaxies at one instant of time, severe uncertainties remain in the orbit and mass determinations. These uncertainties can partly be overcome by statistical studies of selected samples and/or n-body simulations. Close double galaxies (and isolated galaxies) could also be useful to estimate dynamical masses if we can find test particles around them.Interacting elliptical pairs or dumb-bell galaxies are found with a large range, between 0-1200 km s-1, of relative radial velocities. Standard 2-body orbit calculations, highly uncertain due to projection factors, suggest for the largest velocity differences very large galaxy masses, if the systems are bound and stationary. However, recent n-body simulations model these binaries as galaxies captured from hyperbolic orbits, requiring masses of order a few times 1011M⊙) (Borne et al. 1988), but producing systems that are short lived.

Morphology of interacting elliptical galaxy pairs

CCD-photometry of 20 elliptical galaxy pairs was obtained in order to study the effects of galaxy interactions. Deviations from undisturbed brightness profiles are interpreted in terms of ongoing tidal interaction. The deviations include asymmetrical isophotes, distortions of the outer isophotes, twisting of the major axes of the outer isophotes with respect to the line connecting both galaxy centers, nonconcentric isophotes and extended or truncated brightness profiles.