We demonstrate that the exact form-factors of the Calogero-Sutherland model which were recently found in [10] in confirmation of the congectures earlier made by Haldane (Ref. [9]) can be reproduced in the framework of some bosonization procedure in momentum space. This observation implies a possibility of an exact bosonization of this model describing one-dimensional anyons.

In this paper we consider the Jacobian conjecture for a map f of complex affine spaces of dimension n. It is well-known that if f is proper then the conjecture will hold. Using topological arguments, specifically Smith theory, we show that the conjecture holds if and only if f is proper onto its image.

It turns out that various algebraic computations can be reduced to the same type of computations: one has to study the series of integrals ∫ K f(k)g(k) dk, where f, g are complex valued K-finite functions on a compact Lie group K. So it is tempting to state a general conjecture about the behavior of such integrals, and to investigate the consequences of the conjecture. Main conjecture: Let K be...

Corresponding author: Edward Chia-Cheng Lai PhD School of Pharmacy Institute of Clinical Pharmacy and Pharmaceutical Sciences College of Medicine National Cheng Kung University No. 1, University Road Tainan 701, Taiwan Phone: +886-6-2353535 E-mail: tb8991010@mail. ncku.edu.tw 1 Department of Pharmacy, Chang Gung Memorial Hospital, Keelung, Taiwan 2 School of Pharmacy, Institute of Clinical Phar...

YA-MIN CHENG, MD,YI CHEN, MD, YU-YUN HSU, YUEH-CHIN CHENG, MING-JENN CHEN, MD , YI-CHIANG HSU, PHD Department of Obstetrics and Gynecology Institute of Clinical Medicine, National Cheng Kung University, Tainan, Taiwan. Cardiovascular Center, Tainan Municipal Hospital, Taiwan Department of Nursing Institute of Biomedical Engineering, College of Medicine, National Cheng Kung University, Tainan, T...

this note introduces a new general conjecture correlating the dimensionality dt of an infinitelattice with n nodes to the asymptotic value of its wiener index w(n). in the limit of large nthe general asymptotic behavior w(n)≈ns is proposed, where the exponent s and dt are relatedby the conjectured formula s=2+1/dt allowing a new definition of dimensionality dw=(s-2)-1.being related to the topol...

For a simple digraph G without directed triangles or digons, let β(G) be the size of the smallest subset X ⊆ E(G) such that G \ X has no directed cycles, and let γ(G) be the number of unordered pairs of nonadjacent vertices in G. In 2008, Chudnovsky, Seymour, and Sullivan showed that β(G) ≤ γ(G), and conjectured that β(G) ≤ γ(G)/2. Recently, Dunkum, Hamburger, and Pór proved that β(G) ≤ 0.88γ(G...

Yueh-Nan Chen,1,* Shin-Liang Chen,1 Neill Lambert,2 Che-Ming Li,3 Guang-Yin Chen,4 and Franco Nori2,5 1Department of Physics and National Center for Theoretical Sciences, National Cheng-Kung University, Tainan 701, Taiwan 2CEMS, RIKEN, Saitama, 351-0198, Japan 3Department of Engineering Science, National Cheng-Kung University, Tainan 701, Taiwan 4Department of Physics, National Chung Hsing Univ...

In the present study, two new compositions of convergence order six are presented for solving nonlinear equations. The first method is obtained from third-order one given by Homeier using linear interpolation, and second Traub divided differences. requires three evaluations function evaluation derivative, thereby enhancing efficiency index. method, computation a derivative reduced approximating...