Do you want to publish a course? Click here

On Maximum Norm of Exterior Product and A Conjecture of C.N. Yang

149   0   0.0 ( 0 )
 Added by Zhilin Luo
 Publication date 2014
  fields Physics
and research's language is English
 Authors Zhilin Luo




Ask ChatGPT about the research

Let $V$ be a finite dimensional inner product space over $mathbb{R}$ with dimension $n$, where $nin mathbb{N}$, $wedge^{r}V$ be the exterior algebra of $V$, the problem is to find $max_{| xi | = 1, | eta | = 1}| xi wedge eta |$ where $k,l$ $in mathbb{N},$ $forall xi in wedge^{k}V, eta in wedge^{l}V.$ This is a problem suggested by the famous Nobel Prize Winner C.N. Yang. He solved this problem for $kleq 2$ in [1], and made the following textbf{conjecture} in [2] : If $n=2m$, $k=2r$, $l=2s$, then the maximum is achieved when $xi_{max} = frac{omega^{k}}{| omega^{k}|}, eta_{max} = frac{omega^{l}}{| omega^{l}|}$, where $ omega = Sigma_{i=1}^m e_{2i-1}wedge e_{2i}, $ and ${e_{k}}_{k=1}^{2m}$ is an orthonormal basis of V. From a physicists point of view, this problem is just the dual version of the easier part of the well-known Beauzamy-Bombieri inequality for product of polynomials in many variables, which is discussed in [4]. Here the duality is referred as the well known Bose-Fermi correspondence, where we consider the skew-symmetric algebra(alternative forms) instead of the familiar symmetric algebra(polynomials in many variables) In this paper, for two cases we give estimations of the maximum of exterior products, and the Yangs conjecture is answered partially under some special cases.



rate research

Read More

We study a bilinear multiplication rule on 2x2 matrices which is intermediate between the ordinary matrix product and the Hadamard matrix product, and we relate this to the hyperbolic motion group of the plane.
265 - P. Aniello , A. Ibort , V. Manko 2009
Using the formalism of quantizers and dequantizers, we show that the characters of irreducible unitary representations of finite and compact groups provide kernels for star products of complex-valued functions of the group elements. Examples of permutation groups of two and three elements, as well as the SU(2) group, are considered. The k-deformed star products of functions on finite and compact groups are presented. The explicit form of the quantizers and dequantizers, and the duality symmetry of the considered star products are discussed.
We analyze the Moyal star product in deformation quantization from the resurgence theory perspective. By putting algebraic conditions on Borel transforms, one can define the space of ``algebro-resurgent series (a subspace of $1$-Gevrey formal series in $ihbar/2$ with coefficients in $C{q,p}$), which we show is stable under Moyal star product.
182 - Antonio Russo 2011
We prove that the steady--state Navier--Stokes problem in a plane Lipschitz domain $Omega$ exterior to a bounded and simply connected set has a $D$-solution provided the boundary datum $a in L^2(partialOmega)$ satisfies ${1over 2pi}|int_{partialOmega}acdot |<1$. If $Omega$ is of class $C^{1,1}$, we can assume $ain W^{-1/4,4}(partialOmega)$. Moreover, we show that for every $D$--solution $(u,p)$ of the Navier--Stokes equations it holds $ abla p = o(r^{-1}), abla_k p = O(r^{epsilon-3/2}), abla_ku = O(r^{epsilon-3/4})$, for all $kin{Bbb N}setminus{1}$ and for all positive $epsilon$, and if the flux of $u$ through a circumference surrounding $complementOmega$ is zero, then there is a constant vector $u_0$ such that $u=u_0+o(1)$.
250 - P.Cruz , E.L. Lakshtanov 2008
We have constructed a sequence of solutions of the Helmholtz equation forming an orthogonal sequence on a given surface. Coefficients of these functions depend on an explicit algebraic formulae from the coefficient of the surface. Moreover, for exterior Helmholtz equation we have constructed an explicit normal derivative of the Dirichlet Green function. In the same way the Dirichlet-to-Neumann operator is constructed. We proved that normalized coefficients are uniformly bounded from zero.
comments
Fetching comments Fetching comments
Sign in to be able to follow your search criteria
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا