Euclidean solutions of Yang-Mills-dilaton theory

Classical solutions of the Yang-Mills-dilaton theory in Euclidean space-time are investigated. Our analytical and numerical results imply existence of infinite number of branches of dyonic type solutions labelled by the number of nodes of gauge field amplitude $W$. We find that the branches of solutions exist in finite region of parameter space and discuss this issue in detail in different dilaton field normalization.Comment: 16 pages, 11 figures, references added, matches published vesio

Distributed Estimation of Graph Spectrum

In this paper, we develop a two-stage distributed algorithm that enables nodes in a graph to cooperatively estimate the spectrum of a matrix $W$ associated with the graph, which includes the adjacency and Laplacian matrices as special cases. In the first stage, the algorithm uses a discrete-time linear iteration and the Cayley-Hamilton theorem to convert the problem into one of solving a set of linear equations, where each equation is known to a node. In the second stage, if the nodes happen to know that $W$ is cyclic, the algorithm uses a Lyapunov approach to asymptotically solve the equations with an exponential rate of convergence. If they do not know whether $W$ is cyclic, the algorithm uses a random perturbation approach and a structural controllability result to approximately solve the equations with an error that can be made small. Finally, we provide simulation results that illustrate the algorithm.Comment: 15 pages, 2 figure

Elements with finite Coxeter part in an affine Weyl group

Let $W_a$ be an affine Weyl group and $\eta:W_a\longrightarrow W_0$ be the natural projection to the corresponding finite Weyl group. We say that $w\in W_a$ has finite Coxeter part if $\eta(w)$ is conjugate to a Coxeter element of $W_0$. The elements with finite Coxeter part is a union of conjugacy classes of $W_a$. We show that for each conjugacy class $\mathcal{O}$ of $W_a$ with finite Coxeter part there exits a unique maximal proper parabolic subgroup $W_J$ of $W_a$, such that the set of minimal length elements in $\mathcal{O}$ is exactly the set of Coxeter elements in $W_J$. Similar results hold for twisted conjugacy classes.Comment: 9 page

Lax Operator for the Quantised Orthosymplectic Superalgebra U_q[osp(2|n)]

Each quantum superalgebra is a quasi-triangular Hopf superalgebra, so contains a \textit{universal $R$-matrix} in the tensor product algebra which satisfies the Yang-Baxter equation. Applying the vector representation $\pi$, which acts on the vector module $V$, to one side of a universal $R$-matrix gives a Lax operator. In this paper a Lax operator is constructed for the $C$-type quantum superalgebras $U_q[osp(2|n)]$. This can in turn be used to find a solution to the Yang-Baxter equation acting on $V \otimes V \otimes W$ where $W$ is an arbitrary $U_q[osp(2|n)]$ module. The case $W=V$ is included here as an example.Comment: 15 page

Kajian Mutu Mi Instan yang Terbuat dari Tepung Jagung Lokal Riau dan Pati Sagu

The purpose of this study was to obtain the best ratio of corn flour and sago starch on the quality of instant noodles. A completely randomized design with five treatments and flour replications was used. The treatment consist were JST1 (corn flour 60% : sago starch 30% : tapioca 10%), JST2 (corn flour 55% : sago starch 35% : tapioca 10%), JST3 (corn flour 50% : sago starch 40% : tapioca 10%), JST4 (corn flour 45% : sago starch 45% : tapioca 10%) and JST5 (corn flour 40% : sago starch 50% : tapioca 10%). The results show that the ratio of corn flour and sago starch were significantly affected the quality of instant noodles. The best treatment of this study was JST2 with, water content before frying of 10,73% (w/w), moisture content after frying of 6,39% (w/w), protein content of 7,42% (w/w), total acid number of 0,14% (w/w), the intackness of 95,36% (w/w), and rehydration time 10 of minutes 6 seconds

Euclidean solutions of Yang-Mills theory coupled to a massive dilaton

The Euclidean version of Yang-Mills theory coupled to a massive dilaton is investigated. Our analytical and numerical results imply existence of infinite number of branches of globally regular, spherically symmetric, dyonic type solutions for any values of dilaton mass $m$. Solutions on different branches are labelled by the number of nodes of gauge field amplitude $W$. They have finite reduced action and provide new saddle points in the Euclidean path integral.Comment: 16 pages 8 figure