相关论文: Is G a conversion factor or a fundamental unit?

We analyze the problem of comparing unitary transformations. The task is to decide, with minimal resources and maximal reliability, whether two given unitary transformations are identical or different. It is possible to make such…

Dimensional analysis provides many simple and useful tools for various situations in science. The objective of this paper is to investigate its relations to functions, i.e., the dimensions for functions that yield physical quantities and…

There are no two identical leaves in the world, so how to find effective markers or features to distinguish them is an important issue. Function transformation, such as f(x,y) and f(x,y,z), can transform two, three, or multiple…

Consider any sequence of finite groups $A^t$, where $t$ takes values in an integer index set $\mathbf{Z}$. A group system $A$ is a set of sequences with components in $A^t$ that forms a group under componentwise addition in $A^t$, for each…

If D is a category and k is a commutative ring, the functors from D to k-Mod can be thought of as representations of D. By definition, D is dimension zero over k if its finitely generated representations have finite length. We characterize…

Let p be a prime, K a field of characteristic p, G a locally finite p-group, KG the group algebra, and V the group of the units of KG with augmentation 1. The anti-automorphism g\mapsto g^{-1} of G extends linearly to KG; this extension…

For more than half a century, moments have attracted lot ot interest in the pattern recognition community.The moments of a distribution (an object) provide several of its characteristics as center of gravity, orientation, disparity, volume.…

In \cite{Ioana:vNsuperrigidity}, Ioana introduced three new invariants of type II$_1$ factors: the one-sided fundamental group, the endomorphism semigroup and the set of right-finite bimodules. In \cite{Ioana:vNsuperrigidity}, he does not…

Gauging a symmetry can be thought of as the insertion of a spacetime-filling defect. Accordingly, we regard each gaugeable symmetry in a theory as defining a $-1$-form symmetry via condensation. The resulting operators, called gauge…

Within the HQET, the heavy to light vector meson transitions are systematically analyzed to the order of 1/m_Q. Besides the four universal functions at the leading order, there are twenty-two independent universal form factors at the order…

We call an operator algebra A {\em reversible} if A with reversed multiplication is also an abstract operator algebra (in the modern operator space sense). This class of operator algebras is intimately related to the {\em symmetric operator…

The central impediment to reducing multidimensional integrals of transition amplitudes to analytic form, or at least to a fewer number of integral dimensions, is the presence of magnitudes of coordinate vector differences (square roots of…

Some problems of quantum information, cloning, estimation and testing of states, universal coding etc., are special example of the following `state convertibility' problem. In this paper, we consider the dual of this problem, 'observable…

The $q$-deformed Araki-Woods von Neumann algebras $\Gamma_q(\mathcal{H}_\mathbb{R}, U_t)^{\prime \prime}$ are factors for all $q\in (-1,1)$ whenever $dim(\mathcal{H}_\mathbb{R})\geq 3$. When $dim(\mathcal{H}_\mathbb{R})=2$ they are factors…

In this paper the theory of time-dependent and time-independent canonical transformations is considered from a geometric perspective. Both the geometric formalism and the coordinate based approach are described in detail. In particular,…

Let G be a simple finite graph such that each vertex has an integer value and different vertices have different values. Let S be a finite non-empty set of primes. We call G an S-graph if any two vertices are connected by an edge if and only…

We prove that if $G$ is a finite simple group which is the unit group of a ring, then $G$ is isomorphic to either (a) a cyclic group of order 2; (b) a cyclic group of prime order $2^k -1$ for some $k$; or (c) a projective special linear…

We show that the Green biset functor $R_{\mathbb{C}}$ of complex characters over $\mathbb{Z}$, is not separable, i.e. it is not projective as a bimodule over itself. Also, we show that $RB_G$, the Burnside biset functor shifted by a finite…

A nontrivial element in a group is a generalized torsion element if some nonempty finite product of its conjugates is the identity. We prove that any generalized torsion element in a free product of torsion-free groups is conjugate to a…

The Fourier transform is naturally defined for integrable functrions. Otherwise, it should be stipulated in which sense the Fourier transform is understood. We consider some class of radial and, generally saying, nonintegrable functions.…