A case study on the quadratic function problem solving process of middle school students with different unit coordination stages

We consider the minimal number of AND and OR gates in monotone circuits for quadratic boolean functions, i.e. disjunctions of length-2 monomials. The single level conjecture claims that monotone single level circuits, i.e. circuits which have only one level of AND gates, for quadratic functions are not much larger than arbitrary monotone circuits. In this paper we disprove the conjecture: there are quadratic functions in n variables whose monotone circuits have linear size whereas their monotone single level circuits require ).

The present paper extends previous findings already published where the relationships among total porosity, bulk density, compressive strength, and thermal conductivity were analysed. The paper brings more accuracy into some original mathematical relationships and takes into account two additional physical properties (pore volume and the median pore radius). It has been found that the relationships between physical properties and a dose of any admixture added to brick clay could be better described using a quadratic function. The relationships between pairs of physical characteristics can be described by three types of mathematical function (linear, exponential, and power). The amount of admixture used, the firing temperature, and type of clay affect the value of the coefficients but not the type of functions.

Psychiatry

The purpose of this study is to design an instructional sequence triggering students’ quantitative reasoning in the process of learning quadratic functions. The study was conducted as a design-based research, following a cyclical process. The study consisted of three phases of the design, implementation, and analysis phases and the implementation phase consisted of two consecutive cycles. While the first cycle was carried out to evaluate the success of the instructional sequence in supporting student learning in a class with ten 10th students, the second cycle was carried out with two 10th grade students. The video recordings taken during the teaching experiments, the researchers’ observation notes, the clinical interviews, and the students’ reflective journals constituted the data sources of the study. In the data analysis process of the study, the constant comparison method simultaneously conducted with the data collection process was used and also a retrospective analysis of the teaching experiments data was conducted after completing the cycles. Because the tasks were grounded in real-life contexts involving dynamic situations, they contributed to the students’ understanding of functional relations and helped them construct the idea of covarying change in the functions. It is suggested that mathematics teachers revise and use the instructional sequence according to their own classroom context with the aim of supporting their students’ understanding of quadratic functions.

The theory of spin-wave resonance in gradient ferromagnetic films with magnetic parameters varying in space described by both concave and convex quadratic functions is developed. Gradient structures such as a potential well, a potential barrier, and a monotonic change in potential between the film surfaces for both quadratic functions are considered. The waveforms of oscillations mn(z), the laws of the dependence of discrete frequencies ωn, and relative susceptibilities χn/χ10 of spin-wave resonances on the resonance number n are studied. It is shown that the law ωn∝n for n<nc, where nc is the resonance level near the upper edge of the gradient inhomogeneity, which is well known for a parabolic potential well, is also valid for the potential barrier and for the monotonic change in potential, if these structures are formed by a concave quadratic function. It is shown that the law ωn∝(n−1/2)1/2, which we numerically derived and approximated by the analytical formula, is valid for all three structures formed by a convex quadratic function. It is shown that the magnetic susceptibility χn of spin-wave resonances for n<nc is much greater than the susceptibility of resonances in a uniform film. An experimental study of both laws ωn(n) and χn(n) would allow one to determine the type of quadratic function that formed the gradient structure and the form of this structure. The possibility of creating gradient films with different laws ωn(n) and the high magnitude of the high-frequency magnetic susceptibility χn(n) at n<nc make these metamaterials promising for practical applications.

The transformation of the power generation industry from coal-based to more sustainable energy sources is an irreversible trend. In China, the coal-fired power plant, as the main electric power supply facility at present, needs to know its own sustainability level to face the future competition. A hybrid multi-criteria decision making (MCDM) model is proposed in this paper to assess the sustainability levels of the existing Chinese coal-fired power units. The areal grey relational analysis (AGRA) method is involved in the hybrid model, and a combined weighting method is used to determine the priorities of the criteria. The combining weight fuses the fuzzy rough set (FRS) and entropy objective weighting method together with the analytic hierarchy process (AHP) subjective weighting method by game theory. Moreover, an AHP weighting uncertainty analysis using Monte Carlo (MC) simulation is introduced to measure the uncertainty of the results, and a 95 percent confidence interval (CI) is defined as the uncertainty measurement of the alternatives. A case study about eight coal-fired power units is carried out with a criteria system, which contains five aspects in an operational perspective, such as the flexibility, economic, environmental, reliability and technical criterion. The sustainability assessment is performed at the unit level, and the results give a priority rank of the eight alternatives; additionally, the uncertainty analysis supplies the extra information from a statistical perspective. This work expands a novel hybrid MCDM method to the sustainability assessment of the power generation systems, and it may be a benefit to the energy enterprises in assessing the sustainability at the unit level and enhance its ability in future sustainable development.

Quadratic response functions are derived and implemented for a vibrational configuration interaction state. Combined electronic and vibrational quadratic response functions are derived using Born-Oppenheimer vibronic product wave functions. Computational tractable expressions are derived for determining the total quadratic response contribution as a sum of contributions involving both electronic and vibrational linear and quadratic response functions. In the general frequency-dependent case this includes a new and more troublesome type of electronic linear response function. Pilot calculations for the FH, H(2)O, CH(2)O, and pyrrole molecules demonstrate the importance of vibrational contributions for accurate comparison to experiment and that the vibrational contributions in some cases can be very large. The calculation of transition properties between vibrational states is combined with sum-over-states expressions for analysis purposes. On the basis of this some simple analysis methods are suggested. Also, a preliminary study of the effect of finite lifetimes on quadratic response functions is presented.

This chapter describes how teacher engagement in a learning community designed to examine their own teaching and student learning can make significant contributions to improving mathematics education. Child Study/Lesson Study (CS/LS), a new form of professional development, combines significant components of Japanese Lesson Study with clinical interviews to create opportunities for teachers to engage in critical reflections on teaching and learning. Student responses during clinical interviews often challenge teacher assumptions of how students make sense of and learn from a given lesson. Furthermore, teachers benefit from clinical interview information on the nature of student concepts, thinking strategies, and misconceptions. A case study which includes teachers discussing children’s mathematical thinking is included to model how clinical interviews accelerate meaningful professional discourse during lesson study sessions.

We consider bilevel problem in the following formulation. The follower problem is a convex quadratic problem which linearly depends on the leader variable. The leader problem is a quadratic problem. We are looking for an optimistic solution. Optimal value function of the follower problem is used to reformulate bilevel problem as a standard (one-level) optimization problem. By this way we obtain a nonconvex multiextremal problem with implicit nonconvex constraint generated by the optimal value function. We show how to construct an explicit piecewise quadratic function which is support to the optimal value function at a given point. Usage of the support functions allows us to approximate the implicit one-level problem by a number of explicit nonconvex quadratic problems. In our talk we describe an iterative procedure based on such approximation.

Despite natural light, near-façade structures’ impact on Natural Ventilation (NV) performance, reducing cooling demand, is usually ignored by designers. This article aims to characterize interactions between balconies’ design features (i.e. depth, unit level, and wind incident) and near-façade buildings on single-sided NV performance in a case study, representing medium to high-rise apartments in dominant cooling climates, utilizing validated Computational Fluid Dynamics (CFD) simulations. Results show that nearby buildings, even small structures close to the façade, significantly impact windward flow regime and indoor air movements. Nearby blocks might result in less air entering, which could be moderated by designing deeper balconies. Perpendicular wind incidents to the balcony opening may enormously improve single-sided NV performance. In contrast, wind incidents within higher degrees from perpendicular strongly reduce NV performance. This study provides designers with a method to characterize balcony design features’ effects on NV performance in apartments and improve it concerning urban design.

Best reduction of the quadratic semi-assignment problem

Con la emergencia de nuevos algoritmos para el análisis de redes y la aparición de bases de datos económicas desagregadas a nivel de unidad, se plantea un método distinto a los anteriormente reportados en la literatura especializada para detectar centralidades urbanas.La primera parte define la centralidad urbana y presenta una disertación teórica sobre la condición policéntrica. Posteriormente, se muestran los métodos anteriormente usados para la medición de las centralidades y se describen las nuevas herramientas empleadas en esta investigación. Finalmente, se presentan algunos resultados de este método aplicado como caso de estudio en la ciudad de México.

The unconstrained binary quadratic minimization problem is known to be NP-hard and due to its computational challenge and application capability, it becomes more and more considered and involved by the recent research studies, including both exact and heuristic solution approaches. Our work is in line with what was suggested by Glover et al. (in Eur. J. Oper. Res. 137, 272–287, 2002) who proposed one pass heuristics as alternatives to the well-known Devour Digest Tidy-up procedure (DDT) of Boros et al. (in RRR 39-89, 1989). The “devour” step sets a term of the current representation to 0 or 1, and the “tidy-up” step substitutes the logical consequences derived from the “digest” step into the current quadratic function. We propose several versions of the DDT constructive heuristic based on the alternative representation of the quadratic function. We also present an efficient implementation of local search using one-flip and two-flip moves that simultaneously change the values of one or two binary variables. Computational experiments performed on instances up to 7000 variables show the efficiency of our implementation in terms of quality improvement and CPU use enhancement.

A column generation approach for the unconstrained binary quadratic programming problem

In this study a research model is designed that describes the effects of IS company standards on business performance. This model is based on a pilot case study and on the small amount of literature available on company standards. Subsequently, the descriptive model is used in an in-depth case study at a large financial services corporation. This study is part of a series of case studies that will be used to validate the model. The case study describes the implementation, usage and effects of a HR IS standard. The goal is to provide a HR information infrastructure to support HR processes on a global, Business Unit and local level. The effects of these standards on HR business process performance are identified. To conclude, implications for future research are presented.