搜索结果：The Angle orthodontist

In the last two decades, much effort has been dedicated to studying curves and surfaces according to their angle with a given direction. However, most findings were obtained using a case-by-case approach, and it is often unclear what are consequences of the specificities of the ambient manifold and what could be generic. In this work, we propose a theoretical framework to unify parts of these findings. We study curves and surfaces by prescribing the angle they make with a parallel transported vector field. We show that the characterization of Euclidean helices in terms of their curvature and torsion is also valid in any Riemannian manifold. Among other properties, we prove that surfaces making a constant angle with a parallel transported direction are extrinsically flat ruled surfaces. We also investigate the relation between their geodesics and the so-called slant helices; we prove that surfaces of constant angle are the rectifying surface of a slant helix, i.e., the ruled surface with rulings given by the Darboux vector field of the directrix. We characterize rectifying surfaces of constant angle; in other words, when their geodesics are slant helices. As a corollary, we show tha

In addition to the well-known quantum chromodynamical theta angle, we show that the Standard Model has another theta angle which is invariant under arbitrary chiral rotations of quarks and leptons. The new theta angle can be identified with the quantum electrodynamical theta angle, which should be viewed as an independent parameter of the Standard Model, and may be observable in spacetime with non-simply connected features, either beyond the visible universe or in an effective background from a laboratory setup.

The nature of the phase transition in a system of self-propelling particles has been extensively studied during the last few decades. A theoretical model was proposed by T. Vicsek, {\it et. al.} [Phys. Rev. Lett. {\bf 75}, 1226 (1995)] with a simple rule for updating the direction of motion of each particle. Based on the Vicsek's model (VM) [1], in this work, we consider a group of animals as particles moving freely on a two-dimensional space. Due to the fact that the viewable area of animals depends on the species, we consider the motion of each individual within an angle $\varphi=Φ/2$ ($Φ$ is called angle of view) of a circle centered at its position, of radius $R$. We obtained a phase diagram in the space ($\varphi$, $η_c$) with $η_c$ being the critical noise. We show that, the phase transition exists only in the case of a wide view's angle $\varphi \geq 0.5π$. The flocking of animals is an universal behavior of the species of prey, but not the one of the predator. Our simulation results are in good agreement with experimental observation [2].

We theoretically investigate the apparent contact angle and contact angle hysteresis of a droplet placed on a liquid infused surface. We show that the apparent contact angle is not uniquely defined by material parameters, but also has a strong dependence on the relative size between the droplet and its surrounding wetting ridge formed by the infusing liquid. We derive a closed form expression for the contact angle in the limit of vanishing wetting ridge, and compute the correction for small but finite ridge, which corresponds to an effective line tension term. We also predict contact angle hysteresis on liquid infused surfaces generated by the pinning of the contact lines by the surface corrugations. Our analytical expressions for both the apparent contact angle and contact angle hysteresis can be interpreted as `weighted sums' between the contact angles of the infusing liquid relative to the droplet and surrounding gas phases, where the weighting coefficients are given by ratios of the fluid surface tensions.

We consider an extension of the Standard Model that was proposed recently by one of the current authors (PQH), which admits magnetic monopoles with a mass of order of a few TeV. We impose, in addition to topological quantization in the SU(2) sector of the model, the Dirac Quantization Condition (DQC) required for consistency of the quantum theory of a charged electron in the presence of the monopole. This leads to the prediction ${\rm sin}^2θ_W = 1/4$, where $θ_W$ is the weak mixing angle at the energy scale set by the monopole mass. A leading-order renormalization-group analysis yields the value of ${\rm sin}^2 θ_W \simeq 0.231$ at the $Z$-boson mass, as measured by experiment, under suitable conditions on the spectrum of the extra particles in the model.

A multivariate likelihood method to measure electroweak couplings with the Drell-Yan process at the LHC is presented. The process is described by the dilepton rapidity, invariant mass, and decay angle distributions. The decay angle ambiguity due to the unknown assignment of the scattered constituent quark and antiquark to the two protons in a collision is resolved statistically using correlations between the observables. The method is applied to a sample of dimuon events from proton-proton collisions at sqrt(s) = 7 TeV collected by the CMS experiment at the LHC, corresponding to an integrated luminosity of 1.1 inverse femtobarns. From the dominant u-ubar, d-dbar to gamma*/Z to opposite sign dimuons process, the effective weak mixing angle parameter is measured to be sin^2(theta[eff]) = 0.2287 +/- 0.0020 (stat.) +/- 0.0025 (syst.). This result is consistent with measurements from other processes, as expected within the standard model.

In this paper, we discuss the Lagrangian angle and the Kähler angle of immersed surfaces in $\mathbb C^2$. Firstly, we provide an extension of Lagrangian angle, Maslov form and Maslov class to more general surfaces in $\mathbb C^2$ than Lagrangian surfaces, and then naturally extend a theorem by J.-M. Morvan to surfaces of constant Kähler angle, together with an application showing that the Maslov class of a compact self-shrinker surface with constant Kähler angle is generally non-vanishing. Secondly, we obtain two pinching results for the Kähler angle which imply rigidity theorems of self-shrinkers with Kähler angle under the condition that $\int_M |h|^2e^{-\frac{|x|^2}{2}}dV_M<\infty$, where $h$ and $x$ denote, respectively, the second fundamental form and the position vector of the surface.

In the "classical" adventitious angle problem, for a given set of three angles $a$, $b$, and $c$ measured in integral degrees in an isosceles triangle, a fourth angle $θ$ (the derived angle), also measured in integral degrees, is sought. We generalize the problem to find $θ$ in fractional degrees. We show that the triplet $(a, b, c) = (45^\circ, 45^\circ, 15^\circ)$ is the only combination that leads to $θ= 7\frac{1}{2}^\circ$ as the fractional derived angle.

The CosmoQuest virtual community science platform facilitates the creation and implementation of astronomical research projects performed by citizen scientists. One such project, called Moon Mappers, aids in determining the feasibility of producing crowd-sourced cratering statistics of the surface of the Moon. Lunar crater population statistics are an important metric used to understand the formation and evolutionary history of lunar surface features, to estimate relative and absolute model ages of regions on the Moon's surface, and to establish chronologies for other planetary surfaces via extrapolation from the lunar record. It has been suggested and shown that solar incidence angle has an effect on the identification of craters, particularly at meter scales. We have used high-resolution image data taken by the Lunar Reconnaissance Orbiter's Narrow-Angle Camera of the Apollo 15 landing site over a range of solar incidence angles and have compiled catalogs of crater identifications obtained by minimally trained members of the general public participating in CosmoQuest's Moon Mappers project. We have studied the effects of solar incidence angle spanning from approximately 27.5 deg

We report on the final electroweak measurements performed with data taken at the Z resonance by the experiments operating at the electron-positron colliders SLC and LEP. The data consist of 17 million Z decays accumulated by the ALEPH, DELPHI, L3 and OPAL experiments at LEP, and 600 thousand Z decays by the SLD experiment using a polarised beam at SLC. The measurements include cross-sections, forward-backward asymmetries and polarised asymmetries. The mass and width of the Z boson, $\MZ$ and $\GZ$, and its couplings to fermions, for example the $ρ$ parameter and the effective electroweak mixing angle, are precisely measured. The number of light neutrino species is determined to be 2.9840+/-0.0082. The results are compared to the predictions of the Standard Model. Electroweak radiative corrections beyond the running of the QED and QCD coupling constants are observed with a significance of five standard deviations, and in agreement with the Standard Model. Of the many Z-pole measurements, the forward-backward asymmetry in b-quark production shows the largest difference with respect to its Standard Model expectation, at the level of 2.8 standard deviations. Through radiative correctio

In this paper, we will describe the space spanned by the angle-sums of polytopes, recorded in the alpha-vector. We will consider the angles sums of simplices and the angles sums and face numbers of simplicial polytopes and general polytopes. We will construct families of polytopes whose angle sums span the spaces of polytopes defined by the Gram and Perles equations, analogues of the Euler and Dehn-Sommerville equations. We show that the dimensions of the affine span of the space of angle sums of simplices is floor[(d-1)/2] + 1, and that of the angle sums and face numbers of simplicial polytopes and general polytopes are d-1 and 2d-3 respectively.

We propose a novel quark mass matrix texture-pair with five free parameters, which fits the four quark mass ratios $m_s/m_b$, $m_d/m_b$, $m_c/m_t$, $m_u/m_t$, and the four CKM quark mixing observables. The matrices each have one texture zero, but the main innovation here is a ``geometric'' ansatz exploiting a pair of small complex expansion parameters, based on the geometry of the Unitarity Triangle. The fit to the observables is in good agreement with current experimental values renormalised to $\sim\!\!10^4$ TeV, and offers decisive tests against future high-precision measurements of the unitarity triangle angles at the weak scale. We identify two novel symmetries of these mass matrices which explain the phenomenologically-successful relations $α\equivφ_2\simeq\tfracπ{2}$ and $β\equivφ_1\simeq\tfracπ{8}$.

The GRANITE III camera of the Whipple Cherenkov Telescope at the Fred Lawrence Whipple Observatory on Mount Hopkins, Arizona (2300 m a.s.l.) has the highest angular resolution of all cameras used on this telescope so far. The central region of the camera has 379 pixels with an individual angular diameter of 0.12 degrees. This makes the instrument especially suitable for observations of gamma-induced air-showers at large zenith angles since the increase in average distance to the shower maximum leads to smaller shower images in the focal plane of the telescope. We examine the performance of the telescope for observations of gamma-induced air-showers at zenith angles up to 63 degrees based on observations of Mkn 421 and using Monte Carlo Simulations. An improvement to the standard data analysis is suggested.

Motivated by recent advances in the fabrication of twisted bilayers of 2D materials, we consider the low-energy properties of a twisted pair of two-dimensional nodal superconductors. We study both the cases of singlet and triplet superconductors. It is demonstrated that the Bogoliubov-de Gennes (BdG) quasiparticle dispersion undergoes dramatic reconstruction due to the twist. In particular, the velocity of the neutral massless Dirac excitations near the gap nodes is strongly renormalized by the interlayer hopping and vanishes at a ``magic angle'' where in the limit of a circular Fermi surface a quadratic band touching is formed. In addition, it is shown that the BdG disperion can be tuned with an interlayer displacement field, magnetic field, and current, which can suppress the velocity renormalization, create finite BdG Fermi surfaces, or open a gap, respectively. Finally, interactions between quasiparticles are shown to lead to the emergence of a correlated superconducting state breaking time-reversal symmetry in the vicinity of the magic angle. Estimates of the magic angle in a variety of nodal superconductors are presented, ranging from the cuprates to the organic and heavy fer

Recently T2K gives hint in favor of large reactor angle. Most of the models, with tri-bimaximal mixing at the leading order, can not reproduce such a large mixing angle since they predict typically corrections for the reactor angle of the order of the Cabibbo angle. In this letter, we discuss the possibility to have large reactor angle within the T2K region with maximal atmospheric mixing angle and trimaximal solar mixing angle, through the deviation from tri-bimaximal. We derive the structure of neutrino mass matrix that leads to the large reactor angle leaving maximal atmospheric angle and trimaximal solar angle. It is shown that such a structure of neutrino mass matrix can arise in a model with S4 flavor symmetry.

Angular correlations between heavy-quarks provide a unique probe of the quark-gluon plasma created in ultra-relativistic heavy-ion collisions. Results are presented of a measurement of the azimuthal angle correlations between muons originating from semileptonic decays of heavy-quarks produced in 5.02 TeV Pb+Pb and $pp$ collisions at the LHC. The muons are measured with transverse momenta and pseudorapidities satisfying $p_{\mathrm{T}}^μ> 4$ GeV and $|η^μ|<2.4$, respectively. The distributions of azimuthal angle separation, $Δφ$, for muon pairs having pseudorapidity separation $|Δη|>0.8$, are measured in different Pb+Pb centrality intervals and compared to the same distribution measured in $pp$ collisions at the same center-of-mass energy. Results are presented separately for muon pairs with opposite-sign charges, same-sign charges, and all pairs. A clear peak is observed in all $Δφ$ distributions at $Δφ\simπ$, consistent with the parent heavy-quark pairs being produced via hard-scattering processes. The widths of that peak, characterized using Cauchy-Lorentz fits to the $Δφ$ distributions, are found to not vary significantly as a function of Pb+Pb collision centrality and

High-quality text embedding is pivotal in improving semantic textual similarity (STS) tasks, which are crucial components in Large Language Model (LLM) applications. However, a common challenge existing text embedding models face is the problem of vanishing gradients, primarily due to their reliance on the cosine function in the optimization objective, which has saturation zones. To address this issue, this paper proposes a novel angle-optimized text embedding model called AnglE. The core idea of AnglE is to introduce angle optimization in a complex space. This novel approach effectively mitigates the adverse effects of the saturation zone in the cosine function, which can impede gradient and hinder optimization processes. To set up a comprehensive STS evaluation, we experimented on existing short-text STS datasets and a newly collected long-text STS dataset from GitHub Issues. Furthermore, we examine domain-specific STS scenarios with limited labeled data and explore how AnglE works with LLM-annotated data. Extensive experiments were conducted on various tasks including short-text STS, long-text STS, and domain-specific STS tasks. The results show that AnglE outperforms the state-

We have measured the ratio $R_φ=BR(φ\to η^{\prime} γ)/BR(φ\to ηγ)$ by looking for the radiative decays $φ\to η^{\prime} γ$ and $φ\to ηγ$ in the final states $π^+π^-$ 7 $γ$'s and 7 $γ$'s respectively, in a sample of $\sim 1.3\cdot 10^{9}$ $φ$ mesons produced at the Frascati $φ$-factory. We obtain $R_φ=(4.77\pm0.09_{stat}\pm0.19_{sys})\cdot 10^{-3}$ from which we derive $BR(φ\to η^{\prime} γ)=(6.20\pm0.11_{stat}\pm0.25_{sys})\cdot 10^{-5}$. In the hypothesis of no gluonium content we extract the pseudoscalar mixing angle in the quark-flavor basis $φ_P=(41.4\pm0.3_{stat}\pm0.7_{sys}\pm0.6_{th})^{\circ}$. Combining the value of $R_φ$ with other constraints, we estimate the gluonium fractional content of $η^{\prime}$ meson as $Z^2 = 0.14\pm0.04$ and the mixing angle $φ_P = (39.7\pm0.7)^{\circ}$.

The distribution and orientation of energy inside jets is predicted to be an experimental handle on colour connections between the hard--scatter quarks and gluons initiating the jets. This Letter presents a measurement of the distribution of one such variable, the jet pull angle. The pull angle is measured for jets produced in $t\bar{t}$ events with one $W$ boson decaying leptonically and the other decaying to jets using 20.3 fb$^{-1}$ of data recorded with the ATLAS detector at a centre-of-mass energy of $\sqrt{s}=8$ TeV at the LHC. The jet pull angle distribution is corrected for detector resolution and acceptance effects and is compared to various models.