Unipotent representations of real classical groups

Let $\mathbf G$ be a complex orthogonal or complex symplectic group, and let $G$ be a real form of $\mathbf G$, namely $G$ is a real orthogonal group, a real symplectic group, a quaternionic orthogonal group, or a quaternionic symplectic group. For a fixed parity $\mathbb p\in \mathbb Z/2\mathbb Z$, we define a set $\mathrm{Nil}^{\mathbb p}_{\mathbf G}(\mathfrak g)$ of nilpotent $\mathbf G$-orbits in $\mathfrak g$ (the Lie algebra of $\mathbf G$). When $\mathbb p$ is the parity of the dimension of the standard module of $\mathbf G$, this is the set of the stably trivial special nilpotent orbits, which includes all rigid special nilpotent orbits. For each $\mathcal O \in \mathrm{Nil}^{\mathbb p}_{\mathbf G}(\mathfrak g)$, we construct all unipotent representations of $G$ (or its metaplectic cover when $G$ is a real symplectic group and $\mathbb p$ is odd) attached to $\mathcal O$ via the method of theta lifting and show in particular that they are unitary

Heat Transfer by Numerical Solution for a Class of Radiating Fins

It has long been known that the heat transfer from a solid body to an ambient fluid can be increased by increasing the surface area of the solid body. Extended surfaces, or fins, are indispensable for compact heat exchangers. Geometrically, fins may be classified as straight fins, annular fins, and rod fins or spines. In most applications of fins, a fluid is circulating inside the fin-supporting pipe while the outside is exposed to another ambient fluid. The purpose of fin analysis is to find the temperature distribution in the fin and the heat transfer from the fin to the ambient fluid, i.e., the fin efficiency, which is the basis of comparing various fin designs. Conduction is the heat transfer mechanism in the fin and convection and radiation occur at the surface. The amount of radiation heat transfer, in accordance with Stefan-Boltzmann\u27s law, is proportional to the difference between the fourth power of the temperature of the fin and the ambient fluid. The fourth-power term makes the fin equation non-linear and difficult to solve analytically. Earlier researchers linearized the radiation term by replacing the fourth power law by an equivalent convection coefficient times the difference of the temperature in order to obtain an analytical solution. (See more in text

MeshAdv: Adversarial Meshes for Visual Recognition

Highly expressive models such as deep neural networks (DNNs) have been widely applied to various applications. However, recent studies show that DNNs are vulnerable to adversarial examples, which are carefully crafted inputs aiming to mislead the predictions. Currently, the majority of these studies have focused on perturbation added to image pixels, while such manipulation is not physically realistic. Some works have tried to overcome this limitation by attaching printable 2D patches or painting patterns onto surfaces, but can be potentially defended because 3D shape features are intact. In this paper, we propose meshAdv to generate "adversarial 3D meshes" from objects that have rich shape features but minimal textural variation. To manipulate the shape or texture of the objects, we make use of a differentiable renderer to compute accurate shading on the shape and propagate the gradient. Extensive experiments show that the generated 3D meshes are effective in attacking both classifiers and object detectors. We evaluate the attack under different viewpoints. In addition, we design a pipeline to perform black-box attack on a photorealistic renderer with unknown rendering parameters.Comment: Published in IEEE CVPR201

Mass effect in polarization investigation at BEPC/BES and the B-factory

We consider the annihilation process of an electron-positron pair into a pair of heavier fermions when the initial electron and position beams are polarized. By calculating the polarization of the final-state particles, we discuss in detail the effect due to the produced particle masses in the $\tau$-charm energy region at BEPC/BES, and also compare the effect with that at the B-factory. Such a study is useful for the design of possible polarization investigation at the BEPC/BES facility and the B-factory.Comment: 7 latex pages, 4 figure