Lack of trinification in Z_3 orbifolds of the SO(32) heterotic string

We report results relating to the trinification scenario in some explicit string constructions that contain SU(3)^3 as a gauge symmetry. These models are obtained from symmetric Z_3 orbifolds of the SO(32) heterotic string with one discrete Wilson line. We highlight the obstacles that were encountered: the absence of the usual Higgs sector that would break SU(3)^3 \to SU(3)_c \times SU(2)_L \times U(1)_Y; the presence of exotics that would generically befoul gauge coupling unification and lead to fractionally-charged states in the low energy spectrum.Comment: 1+7 pages, comments and refs adde

Exact Potts Model Partition Functions for Strips of the Honeycomb Lattice

We present exact calculations of the Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature-like variable $v$ on $n$-vertex strip graphs $G$ of the honeycomb lattice for a variety of transverse widths equal to $L_y$ vertices and for arbitrarily great length, with free longitudinal boundary conditions and free and periodic transverse boundary conditions. These partition functions have the form $Z(G,q,v)=\sum_{j=1}^{N_{Z,G,\lambda}} c_{Z,G,j}(\lambda_{Z,G,j})^m$, where $m$ denotes the number of repeated subgraphs in the longitudinal direction. We give general formulas for $N_{Z,G,j}$ for arbitrary $L_y$. We also present plots of zeros of the partition function in the $q$ plane for various values of $v$ and in the $v$ plane for various values of $q$. Explicit results for partition functions are given in the text for $L_y=2,3$ (free) and $L_y=4$ (cylindrical), and plots of partition function zeros are given for $L_y$ up to 5 (free) and $L_y=6$ (cylindrical). Plots of the internal energy and specific heat per site for infinite-length strips are also presented.Comment: 39 pages, 34 eps figures, 3 sty file

A semi-direct solver for compressible 3-dimensional rotational flow

An iterative procedure is presented for solving steady inviscid 3-D subsonic rotational flow problems. The procedure combines concepts from classical secondary flow theory with an extension to 3-D of a novel semi-direct Cauchy-Riemann solver. It is developed for generalized coordinates and can be exercised using standard finite difference procedures. The stability criterion of the iterative procedure is discussed along with its ability to capture the evolution of inviscid secondary flow in a turning channel

Structure of the Partition Function and Transfer Matrices for the Potts Model in a Magnetic Field on Lattice Strips

We determine the general structure of the partition function of the $q$-state Potts model in an external magnetic field, $Z(G,q,v,w)$ for arbitrary $q$, temperature variable $v$, and magnetic field variable $w$, on cyclic, M\"obius, and free strip graphs $G$ of the square (sq), triangular (tri), and honeycomb (hc) lattices with width $L_y$ and arbitrarily great length $L_x$. For the cyclic case we prove that the partition function has the form $Z(\Lambda,L_y \times L_x,q,v,w)=\sum_{d=0}^{L_y} \tilde c^{(d)} Tr[(T_{Z,\Lambda,L_y,d})^m]$, where $\Lambda$ denotes the lattice type, $\tilde c^{(d)}$ are specified polynomials of degree $d$ in $q$, $T_{Z,\Lambda,L_y,d}$ is the corresponding transfer matrix, and $m=L_x$ ($L_x/2$) for $\Lambda=sq, tri (hc)$, respectively. An analogous formula is given for M\"obius strips, while only $T_{Z,\Lambda,L_y,d=0}$ appears for free strips. We exhibit a method for calculating $T_{Z,\Lambda,L_y,d}$ for arbitrary $L_y$ and give illustrative examples. Explicit results for arbitrary $L_y$ are presented for $T_{Z,\Lambda,L_y,d}$ with $d=L_y$ and $d=L_y-1$. We find very simple formulas for the determinant $det(T_{Z,\Lambda,L_y,d})$. We also give results for self-dual cyclic strips of the square lattice.Comment: Reference added to a relevant paper by F. Y. W

Distance-two labelings of digraphs

For positive integers $j\ge k$, an $L(j,k)$-labeling of a digraph $D$ is a function $f$ from $V(D)$ into the set of nonnegative integers such that $|f(x)-f(y)|\ge j$ if $x$ is adjacent to $y$ in $D$ and $|f(x)-f(y)|\ge k$ if $x$ is of distant two to $y$ in $D$. Elements of the image of $f$ are called labels. The $L(j,k)$-labeling problem is to determine the $\vec{\lambda}_{j,k}$-number $\vec{\lambda}_{j,k}(D)$ of a digraph $D$, which is the minimum of the maximum label used in an $L(j,k)$-labeling of $D$. This paper studies $\vec{\lambda}_{j,k}$- numbers of digraphs. In particular, we determine $\vec{\lambda}_{j,k}$- numbers of digraphs whose longest dipath is of length at most 2, and $\vec{\lambda}_{j,k}$-numbers of ditrees having dipaths of length 4. We also give bounds for $\vec{\lambda}_{j,k}$-numbers of bipartite digraphs whose longest dipath is of length 3. Finally, we present a linear-time algorithm for determining $\vec{\lambda}_{j,1}$-numbers of ditrees whose longest dipath is of length 3.Comment: 12 pages; presented in SIAM Coference on Discrete Mathematics, June 13-16, 2004, Loews Vanderbilt Plaza Hotel, Nashville, TN, US

Optimization the initial weights of artificial neural networks via genetic algorithm applied to hip bone fracture prediction

This paper aims to find the optimal set of initial weights to enhance the accuracy of artificial neural networks (ANNs) by using genetic algorithms (GA). The sample in this study included 228 patients with first low-trauma hip fracture and 215 patients without hip fracture, both of them were interviewed with 78 questions. We used logistic regression to select 5 important factors (i.e., bone mineral density, experience of fracture, average hand grip strength, intake of coffee, and peak expiratory flow rate) for building artificial neural networks to predict the probabilities of hip fractures. Three-layer (one hidden layer) ANNs models with back-propagation training algorithms were adopted. The purpose in this paper is to find the optimal initial weights of neural networks via genetic algorithm to improve the predictability. Area under the ROC curve (AUC) was used to assess the performance of neural networks. The study results showed the genetic algorithm obtained an AUC of 0.858±0.00493 on modeling data and 0.802 ± 0.03318 on testing data. They were slightly better than the results of our previous study (0.868±0.00387 and 0.796±0.02559, resp.). Thus, the preliminary study for only using simple GA has been proved to be effective for improving the accuracy of artificial neural networks.This research was supported by the National Science Council (NSC) of Taiwan (Grant no. NSC98-2915-I-155-005), the Department of Education grant of Excellent Teaching Program of Yuan Ze University (Grant no. 217517) and the Center for Dynamical Biomarkers and Translational Medicine supported by National Science Council (Grant no. NSC 100- 2911-I-008-001)

Organic chemistry on Titan

Observations of nonequilibrium phenomena on the Saturn satellite Titan indicate the occurrence of organic chemical evolution. Greenhouse and thermal inversion models of Titan's atmosphere provide environmental constraints within which various pathways for organic chemical synthesis are assessed. Experimental results and theoretical modeling studies suggest that the organic chemistry of the satellite may be dominated by two atmospheric processes: energetic-particle bombardment and photochemistry. Reactions initiated in various levels of the atmosphere by cosmic ray, Saturn wind, and solar wind particle bombardment of a CH4 - N2 atmospheric mixture can account for the C2-hydrocarbons, the UV-visible-absorbing stratospheric haze, and the reddish color of the satellite. Photochemical reactions of CH4 can also account for the presence of C2-hydrocarbons. In the lower Titan atmosphere, photochemical processes will be important if surface temperatures are sufficiently high for gaseous NH3 to exist. Hot H-atom reactions initiated by photo-dissociation of NH3 can couple the chemical reactions of NH3 and CH4 and produce organic matter