Upper and lower bounds for the energy of bipartite graphs

Using Lagrange's multiplier rule, we find upper and lower bounds of the energy of a bipartite graph G, in terms of the number of vertices, edges and the spectral moment of fourth order. Moreover, the upper bound is attained in a graph G if and only if G is the graph of a symmetric balanced incomplete block design (BIBD). Also, we determine the graphs for which the lower bound is sharp.     

Concerning seven and eight mutually orthogonal Latin squares

In this paper, three new direct Mutually Orthogonal Latin Squares (MOLS) constructions are presented for 7 MOLS(24), 7 MOLS(75) and 8 MOLS(36); then using recursive methods, several new constructions for 7 and 8 MOLS are obtained. These reduce the largest value for which 7 MOLS are unknown from 780 to 570, and the largest odd value for which 8 MOLS are unknown from 1935 to 419. © 2003 Wiley Periodicals, Inc.     

Block transitive Steiner systems with more than one point orbit

For all ‘reasonable’ finite t, k, and s, we construct a t‐(?₀, k, 1) design and a group of automorphisms which is transitive on blocks and has s orbits on points. In particular, there is a 2‐(?0, 4, 1) design with a block‐transitive group of automorphisms having two point orbits. This answers a question of P. J. Cameron and C. E. Praeger. The construction is presented in a purely combinatorial way, but is a by‐product of a new way of looking at a model‐theoretic construction of E. Hrushovski. © 2004 Wiley Periodicals, Inc.     

Formula 1 – A Mathematical Microworld with CAS: Analysis of Learning Opportunities and Experiences with Students

In this article we describe a mathematical microworld for investigating car motion on a racing course and its use with a group of grade 12 students. The microworld is concerned with the mathematical construction of courses and functions which describe car motion. It is implemented in the computer algebra system, Maple^®, which provides the means to represent courses and functions symbolically and graphically. We describe the learning opportunities offered by the microworld in relation to the research literature on functions. Various facets and layers of the function concept are addressed in the microworld, and we suggest how work in the microworld might help in overcoming some well-known misconceptions.This revised version was published online in September 2005 with corrections to the Cover Date.     

混合效应模型中的D-最优设计

本研究的是混合效应-Ⅱ模型，首先，给出二阶模型存在D-最优回归设计点的必要条件。其次，组合D-最优回归设计和D-最优区组设计BIBD构造D-最优设计并给出寻找新的D-最优设计点的方法。以两种有代表性的组合误差分布为例，阐明新的D-最优设计点的获得过程，并给出了数值结果。     

Internal standardization for the determination of cadmium,cobalt, chromium and manganese in saline produced water from petroleum industry by inductively coupled plasma optical emission spectrometry after cloud point extraction

In the present paper a procedure is proposed for the determination of traces of Cd, Co, Mn and Cr in petroleum industry produced water by inductively coupled plasma optical emission spectrometry. The procedure is based on cloud point extraction of these metals, as their dithizonate complexes, into the surfactant-rich phase of octylphenoxypolyethoxyethanol surfactant (Triton X-114). Extractions were carried out in solutions with salinities between 10‰ and 70‰. Since residual salinity in the surfactant-rich phase caused differences in its transport to the plasma, yttrium was used as an internal standard to correct for this effect. The simultaneous metal extraction procedure was optimized by response surface methodology using a Doehlert design and desirability function. Enhancement factors of 21, 21, 9 and 19, along with limits of quantification of 0.093, 0.20, 0.73 and 1.2 μg L^− 1, and precision expressed as relative standard deviation (n = 8, 20.0 μg L^− 1) of 5.8, 1.2, 1.7 and 5.7% were obtained for Cd, Co, Mn and Cr, respectively. The accuracy was evaluated by spike recovery tests on the high salinity water samples with salinity of 40 and 63‰.     

干电池供电式电子标准电池的设计

标准电池是度量电源电动势的标准仪器．利用RC4191和MC1403精密的低压稳压特性，设计一款电子稳压式的标准电池，既可克服传统汞镉标准电池的缺点，又能保证相同精度的实验性能要求．     

Pseudoaffinity, de Boor algorithm, and blossoms

In order to ensure existence of a de Boor algorithm (hence of a B-spline basis) in a given spline space with (n+1)-dimensional sections, it is important to be able to generate each spline by restriction to the diagonal of a symmetric function of n variables supposed to be pseudoaffine w.r. to each variable. We proved that a way to obtain these three properties (symmetry, n-pseudoaffinity, diagonal property) is to suppose the existence of blossoms on the set of admissible n-tuples, given that blossoms are defined in a geometric way by means of intersections of osculating flats. In the present paper, we examine the converse: do symmetry, n-pseudoaffinity, and diagonal property imply existence of blossoms?     

Difference Families in Z2d+1⊕Z2d+1 and Infinite Translation Designs in Z⊕Z

We analyse 3-subset difference families of Z_2d+1⊕Z_2d+1 arising as reductions (mod 2d+1) of particular families of 3-subsets of Z⊕Z. The latter structures, namely perfect d-families, can be viewed as 2-dimensional analogues of difference triangle sets having the least scope. Indeed, every perfect d-family is a set of base blocks which, under the natural action of the translation group Z⊕Z, cover all edges {(x,y),(x′,y′)} such that |x−x′|, |y−y′|≤d. In particular, such a family realises a translation invariant (G,K₃)-design, where V(G)=Z⊕Z and the edges satisfy the above constraint. For that reason, we regard perfect families as part of the hereby defined translation designs, which comprise and slightly generalise many structures already existing in the literature. The geometric context allows some suggestive additional definitions. The main result of the paper is the construction of two infinite classes of d-families. Furthermore, we provide two sporadic examples and show that a d-family may exist only if d≡0,3,8,11 (mod 12).     

Vehicle density and velocity estimation on highways for on-ramp metering control

A scheme for vehicle density and velocity estimation in a stretch of highway based on a modified cell transmission model [C. F. Daganzo, Transportation Research, Part B, 28B(4),269–287, 1994. Elsevier is presented. The scheme is intended for use with on-ramp metering control algorithms, providing local knowledge of densities and velocities that is helpful to improve on-ramp metering control performance. Estimation of density is obtained by nonlinear estimators, while velocity estimation is obtained by gradient algorithms. There is one density–velocity estimator for free traffic flow and other for congested traffic flow. Both estimator schemes work in parallel. The final estimation of density and velocity results from a convex combination of the predictions of the two estimators. This combination depends on occupancy or density measurements at the boundaries of the stretch and is produced by a fuzzy inference system. Stability and convergence of the density and velocity estimation scheme is proved by Lyapunov based techniques. Simulation results comparing measured and estimated traffic data are presented. They confirm good performance of the estimators. Research sponsored by grants UNAM PAPIIT IN110403 and CONACYT 47583.