arXiv subjects

Lin Zhang

Publications and source records attributed to Lin Zhang.

460 records · Page 26Linked to original sources

arXiv2009

Approximation Algorithms for Link Scheduling with Physical Interference Model in Wireless Multi-hop Networks

The link scheduling in wireless multi-hop networks is addressed. Different from most of work that adopt the protocol interference model which merely take consideration of packet collisions, our proposed algorithms use the physical interference model to reflect the aggregated signal to interference and noise ratio (SINR), which is a more accurate abstraction of the real scenario. We first propose a centralized scheduling method based on the Integer Linear Programming (ILP) and resolve it by an approximate solution based on the randomized rounding method. The probability bound of getting a guaranteed approximate factor is given. We then extend the centralized algorithm to a distributed solution, which is favorable in wireless networks. It is proven that with the distributed scheduling method, all links can transmit without interference, and the approximate ratio of the algorithm is also given.

cs.NI↗

arXiv2008

Logarithmic tensor product theory for generalized modules for a conformal vertex algebra

We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ''conformal vertex algebra'' or even more generally, for a "Möbius vertex algebra.'' We do not require the module categories to be semisimple, and we accommodate modules with generalized weight spaces. As in the earlier series of papers, our tensor product functors depend on a complex variable, but in the present generality, the logarithm of the complex variable is required; the general representation theory of vertex operator algebras requires logarithmic structure. The first part of this work is devoted to the study of logarithmic intertwining operators and their role in the construction of the tensor product functors. The remainder of this work is devoted to the construction of the appropriate natural associativity isomorphisms between triple tensor product functors, to the proof of their fundamental properties, and to the construction of the resulting braided tensor category structure. This work includes the complete proofs in the present generality and can be read independently of the earlier series of papers.

math.QA↗

arXiv2007

Vertex tensor category structure on a category of Kazhdan--Lusztig

We incorporate a category of certain modules for an affine Lie algebra, of a certain fixed non-positive-integral level, considered by Kazhdan and Lusztig, into the representation theory of vertex operator algebras, by using the logarithmic tensor product theory for generalized modules for a vertex operator algebra developed by Huang, Lepowsky and the author. We do this by proving that the conditions for applying this general logarithmic tensor product theory hold. As a consequence, we prove that this category has a natural vertex tensor category structure, and in particular we obtain a new, vertex-algebraic, construction of the natural associativity isomorphisms and proof of their properties.

math.QA↗

arXiv2006

Logarithmic tensor product theory for generalized modules for a conformal vertex algebra, Part I

We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ``conformal vertex algebra'' or even more generally, for a "Möbius vertex algebra.'' We do not require the module categories to be semisimple, and we accommodate modules with generalized weight spaces. As in the earlier series of papers, our tensor product functors depend on a complex variable, but in the present generality, the logarithm of the complex variable is involved. This first part is devoted to the study of logarithmic intertwining operators and their role in the construction of the tensor product functors. Part II of this work will be devoted to the construction of the appropriate natural associativity isomorphisms between triple tensor product functors, to the proof of their fundamental properties, and to the construction of the resulting braided tensor category structure. This work includes the complete proofs in the present generality and can be read independently of the earlier series of papers.

math.QA↗

arXiv2006

A logarithmic generalization of tensor product theory for modules for a vertex operator algebra

We describe a logarithmic tensor product theory for certain module categories for a ``conformal vertex algebra.'' In this theory, which is a natural, although intricate, generalization of earlier work of Huang and Lepowsky, we do not require the module categories to be semisimple, and we accommodate modules with generalized weight spaces. The corresponding intertwining operators contain logarithms of the variables.

math.QA↗

arXiv2006

Broadband SBS Slow Light in an Optical Fiber

We investigate slow-light via stimulated Brillouin scattering in a room temperature optical fiber that is pumped by a spectrally broadened laser. Broadening the spectrum of the pump field increases the linewidth $Δω_p$ of the Stokes amplifying resonance, thereby increasing the slow-light bandwidth. One physical bandwidth limitation occurs when the linewidth becomes several times larger than the Brillouin frequency shift $Ω_B$ so that the anti-Stokes absorbing resonance cancels out substantially the Stokes amplifying resonance and hence the slow-light effect. We find that partial overlap of the Stokes and anti-Stokes resonances can actually lead to an enhancement of the slow-light delay - bandwidth product when $Δω_p \simeq 1.3 Ω_B$. Using this general approach, we increase the Brillouin slow-light bandwidth to over 12 GHz from its nominal linewidth of $\sim$30 MHz obtained for monochromatic pumping. We controllably delay 75-ps-long pulses by up to 47 ps and study the data pattern dependence of the broadband SBS slow-light system.

physics.optics↗

arXiv2004

On the concepts of intertwining operator and tensor product module in vertex operator algebra theory

We produce counterexamples to show that in the definition of the notion of intertwining operator for modules for a vertex operator algebra, the commutator formula cannot in general be used as a replacement axiom for the Jacobi identity. We further give a sufficient condition for the commutator formula to imply the Jacobi identity in this definition. Using these results we illuminate the crucial role of the condition called the ``compatibility condition'' in the construction of the tensor product module in vertex operator algebra theory, as carried out in work of Huang and Lepowsky. In particular, we prove by means of suitable counterexamples that the compatibility condition was indeed needed in this theory.

math.QA↗

arXiv2002

On the Number of Positive Solutions to a Class of Integral Equations

By using the complete discrimination system for polynomials, we study the number of positive solutions in {\small $C[0,1]$} to the integral equation {\small $ϕ(x)=\int_0^1k(x,y)ϕ^n(y)dy$}, where {\small $k(x,y)=ϕ_1(x)ϕ_1(y)+ϕ_2(x)ϕ_2(y), ϕ_i(x)>0, ϕ_i(y)>0, 0<x,y<1, i=1,2,$} are continuous functions on {\small $[0,1]$}, {\small $n$} is a positive integer. We prove the following results: when {\small $n= 1$}, either there does not exist, or there exist infinitely many positive solutions in {\small $C[0,1]$}; when {\small $n\geq 2$}, there exist at least {\small 1}, at most {\small $n+1$} positive solutions in {\small $C[0,1]$}. Necessary and sufficient conditions are derived for the cases: 1) {\small $n= 1$}, there exist positive solutions; 2) {\small $n\geq 2$}, there exist exactly {\small $m(m\in \{1,2,...,n+1\})$} positive solutions. Our results generalize the existing results in the literature, and their usefulness is shown by examples presented in this paper.

math-ph↗

arXiv1997

Quantum Reed-Muller Codes

This paper presents a set of quantum Reed-Muller codes which are typically 100 times more effective than existing quantum Reed-Muller codes.

quant-ph↗

arXiv1997

V-Algebras and Their Free Field Realizations

The V-algebras are the non-local matrix generalization of the well-known W-algebras. Their classical realizations are given by the second Poisson brackets associated with the matrix pseudodifferential operators. In this paper, by using the general Miura transformation, we give the decomposition theorems for the second Poisson brackets, from which we are able to construct the free field realizations for a class of V-algebras including V_{(2k,2)}-algebras that corresponds to the Lie algebra of C_k-type as the particular examples. The reduction of our discussion to the scalar case provides the similar result for the W_{BKP}-algebra.

hep-th↗