初高中数学教学有效衔接的问题设计——以“绝对值”拓展教学为例

以“绝对值”拓展教学为例,设计“绝对值”拓展教学思维导图,并通过立足知识源起、巧设学习支架、触及思维远点进行问题设计,探索如何在教学中进行有效衔接、平稳跨越、适度拔节,从而使学生在经历知识的深化与拓展、技能的丰富与精进的同时,体会数学活动所蕴含的思想方法,积累具有普适性的处理问题和解决问题的路径和经验.

“绝对值”复习中的能力培养

学生进入初三下学期,怎样才能做到系统复习而不只是对知识的简单回顾、重复?怎样才能避免搞"题海战"而又能提高学生的解题能力,我想试以"绝对值"的复习为例谈一点我个人的看法.

Empirical Bayes Absolute Error Loss Estimation for Parameter of One-Side Truncation Distribution Families

In this paper we propose an absolute error loss EB estimator for parameter of one-side truncation distribution families. Under some conditions we have proved that the convergence rates of its Bayes risk is o, where 0<λ,r≤1,Mn≤lnln n (for large n),Mn→∞ as n→∞.

Concave Minimization for Sparse Solutions of Absolute Value Equations

Based on concave function, the problem of finding the sparse solution of absolute value equations is relaxed to a concave programming, and its corresponding algorithm is proposed, whose main part is solving a series of linear programming. It is proved that a sparse solution can be found under the assumption that the connected matrixes have range space property(RSP). Numerical experiments are also conducted to verify the efficiency of the proposed algorithm.

POLYNOMIAL COEFFICIENT FINDING FOR ROOT-MUSIC

Abs Root-MUSIC （MUltiple Signal Classification） is the polynomial rooting form of MUSIC, namely, the spectrum peak searching is resplaced by the polynomial rooting in MUSIC implementation. The coefficients finding of the polynomial is the critical problem for Root-MUSIC and its improvements By analyzing the Root-MUSIC algorithm thoughly, the finding method of the polynomial coefficient is deduced and the concrete calculation formula is given, so that the speed of polynomial finding roots will get the bigger exaltation. The particular simulations are given and attest correctness of the theory analysis and also indicate that the proposed algorithm has preferable estimating performance.

Effect of Initial Frequency Chirp on Supercontinuum Generation in Dispersion-flattened Fibers

Supercontinuum generation in dispersion-flattened fibers is studied theoretically. It is found that the flat spectral width of the supereontinuum generation in normal dispersion-flattened fiber can be increased from 66 nm to over 100 nm when the absolute value of the initial frequency chirps is increased from zero to 10. It is further found that initial frequency chirps are adverse to flat and wideband supercontinuum generation in anomalous dispersion-flattened fiber, and when the absolute value of the frequency chirps is increased to a certain degree, supercontinuum spectrum even can not be achieved.

Determination of indices and critical values of gas parameters of the first gas outburst in a coal seam of the Xieqiao Mine

Based on the important role in mine safety played by parameters of the first gas outburst, we propose a method of combining historic data, theoretical analysis and experimental research for the purpose of crit- ical values of gas parameters of the first gas outburst in a coal seam of the Xieqiao Mine. According to a characteristic analysis and a summary of the rules of coal and gas outbursts in the No.8 coal seam of a Hua- inan mine, we have investigated their effect on coal and gas outbursts in terms such as ground stress, gas, and coal structure. We have selected gas parameters and determined the critical values of each of the fol- lowing indices： gas content as 7.7 m^3/t, tectonic coal as 0.8 m thick, the absolute gas emission as 2 m3/min, the rate of change as 0.7 m3/min, the gas desorption index of a drilling chip KI as 0.26 mL/（g min^1/2） and the values of desorption indexes Ah2 as 200 Pa. From a verification of the production, the results indicate that application of each index and their critical values significantly improve the level of safety in the pro- duction process, relieve the burden upon the mine, save much labor and bring clear economic benefits.

Generalized Domination in Ordered Banach Algebras

The following problem in an OBA （ordered Banach algebra） has been studied by various authors： If a and b are positiveelements in an OBA such that 0 ≤ α ≤ b and ifb has a certain property, under what conditions does a inherit that property？ This will be referred to as the domination problem. In this paper we will introduce absolute value ｜.｜ in an OBA and obtain results for the domination problem under the more general inequality ｜α｜ ≤｜b｜. We will show that these results are applicable to positive operators on a Banach lattice. Furthermore, it will be demonstrated that some known results for the domination problem in OBAs continue to hold true if 0 ≤ α≤ b is replaced by ｜a｜≤｜b｜.

Life History of the Lenkoran Capoeta Capoeta Gracilis （Keyserling, 1981） in the Atrak River, Northern Iran

Within the wide distribution of Lenkoran in Iran, populations of the species inhabit variety of habitats. The authors hypothesized that each river may contribute to habitat-specific variation in life history of the fish. To test this, a total of 378 specimens of Capoeta capoeta gracilis caught in the Atrak river （northern Iran） from Dec. 2007 to Nov. 2008 were examined for life history attributes. The population has a 5-year life cycle. Weight-length relationship （WLR） was estimated as W = 0.0127TL28981 for males, W = 0.0083TL3998 for females and W = 0.0084TL3942 for the population, being allometric negative for males and positive for females and the population. The VBGF fit to back-calculated size at age data were： Lt = 22.11 （1-e-0.19（t＋135））, Lt = 25.37 （1-e-0.18（t＋125）） and Lt = 24.92 （1-e-018（1＋122）） for males, females and sexes combined respectively. Sex ratio was significant from the parity, females dominated. The reproductive season, evaluated from GSI, extended from Apr. to July, with the highest peak in May for males and in Apr. for females. The absolute fecundity ranged between 458-5,743 eggs with a mean of 1,375.06 eggs. Fecundity relative to total weight fluctuated from 14.90 to 132.58, with a mean value of 48.79 eggs·g-1. The diameter of oocytes ranged from 0.53 to 2.40 mm with a mean value of 1.46. The life history patterns of C. c. gracilis in the considered population imply that the many population characteristics of this species in the river differ markedly from those of other rivers of its range distribution in northern Iran. Probably, respond to environmental characteristics to improve fitness locally is the more suitable choice for differentiated life history strategies of the species in the river.

Modification of the land surface energy balance relationship by introducing vertical sensible heat advection and soil heat storage over the Loess Plateau

Little is known about the surface energy balance problem for a complex underlying surface.Taking data from the Loess Plateau Land-surface Processes Experiment(LOPEX) and investigating the characteristics of the surface energy balance over a complex underlying surface,this paper calculates the soil heat storage and vertical sensible heat advection,analyzes their contributions to the surface energy imbalance,and discusses the mechanism by which the vertical velocity and temperature gradient in the surface layer affect the vertical sensible heat advection transfer.We found that the vertical velocity in the surface layer provides the necessary dynamic power for vertical sensible heat advection,and a relatively strong temperature gradient is the energy source generating vertical sensible heat advection.Under an ascending condition,the effect of vertical sensible heat advection on the surface energy budget is more obvious.It is also found that when the soil heat storage term and the vertical sensible heat advection term are added to the energy balance equation,the imbalance significantly improves.The peak of average diurnal residuals decreases from 125.1 to 41.5 W m-2,the daily average absolute value of residuals falls from 59.0 to 26.4 W m-2,and the surface energy balance closure increases from 78.4% to 94.0%.

Tensor absolute value equations

This paper is concerned with solving some structured multi-linear systems, which are called tensor absolute value equations. This kind of absolute value equations is closely related to tensor complementarity problems and is a generalization of the well-known absolute value equations in the matrix case. We prove that tensor absolute value equations are equivalent to some special structured tensor complementary problems. Some sufficient conditions are given to guarantee the existence of solutions for tensor absolute value equations. We also propose a Levenberg-Marquardt-type algorithm for solving some given tensor absolute value equations and preliminary numerical results are reported to indicate the efficiency of the proposed algorithm.

SUMMATION OF ABSOLUTE VALUE TEST FOR MULTIPLE OUTCOME COMPARISON WITH MODERATE EFFECT

In biomedical research,in order to evaluate the effect of a drug,investigators often need to compare the differences between one treatment group and another one by using multiple outcomes.The rank-sum tests can handle the case where the outcome differences between two groups are in the same direction.If they are not,MAX can handle it and is very useful when one/some of the differences is/are relatively larger than the others.When the individual outcome difference between two groups is moderate,a new method,summation of the absolute value of rank-based test for each outcome,is proposed in this work.Power comparison with the existing methods based on simulation studies and a real example show that the proposed test is a robust test,and works well when the difference for each outcome is moderate.The authors also derive some theoretical results for comparing the power between MAX and the the proposed method.

Weak Orlicz spaces:Some basic properties and their applications to harmonic analysis

We study some basic properties of weak Orlicz spaces and their applications to harmonic analysis.We first discuss the absolute continuity of the quasi-norm and its normality,then prove the boundedness of several maximal operators.We also establish a kind of Marcinkiewicz-type interpolation theorem between weak Orlicz spaces.As applications,the weak type analogues of several classical inequalities in harmonic analysis is obtained.

The determination of thermal junction potential difference

A novel method has been designed and exploited to determine the thermal junction potential difference(TJPD) between two acids or alkalies of the same composition but with different temperature. The absolute value of measured TJPD between two strong acids(or alkalies) maintained at different temperatures increases with increasing of the temperature difference between the two electrolytes over the range from 0 to 40 °C. In strong acids, the hot end always has the lower potential while in strong alkalies, the cold end has the lower potential. This is because the ions of fast diffusion rate contribute most to the TJPD. Our results demonstrate the importance of the correction for TJPD in deriving the kinetic parameters when studying the temperature effect on reaction kinetics.

A discussion of Hong-Stein model

In this paper,we discuss a kind of behavioral asset pricing model,called Hong-Stein model.Although this model succeeded in explaining the momentum and reversal effects,we find it usually reaches two extremes:the absolute value of autocorrelation of return sequence is so large that the direction of returns could be easily forecasted,or the value is so small that the elements in return sequence are almost independent of each other.The empirical results show that these two extremes are not supported by the real market data.

GOAL PROGRAMMING ALGORITHM FOR A TYPE OF LEAST ABSOLUTE VALUE REGRESSION PROBLEM

This paper develops goal programming algorithm to solve a type of least absolute value (LAV) problem. Firstly, we simplify the simplex algorithm by proving the existence of solutions of the problem. Then, we present a goal programming algorithm on the basis of the original techniques. Theoretical analysis and numerical results indicate that the new method contains a lower number of deviation variables and consumes less computational time as compared to current LAV methods.

Numerical predictions and stability analysis of cavitating draft tube vortices at high head in a model Francis turbine

Draft tube vortex is one of the main causes of hydraulic instability in hydraulic reaction turbines,in particular Francis turbines.A method of cavitation calculations was proposed to predict the pressure fluctuations induced by draft tube vortices in a model Francis turbine,by solving RANS equations with RNG k-turbulence model and ZGB cavitation model,with modified turbulence viscosity.Three cases with different flow rates at high head were studied.In the study case of part load,two modes of revolutions with the same rotating direction,revolution around the axis of the draft tube cone,and revolution around the core of the vortex rope,can be recognized.The elliptical shaped vortex rope causes anisotropic characteristics of pressure fluctuations around the centerline of the draft tube cone.By analyzing the phase angles of the pressure fluctuations,the role of the vortex rope as an exciter in the oscillating case can be recognized.An analysis of Batchelor instability,i.e.instability in q-vortex like flow structure,has been carried out on the draft tube vortices in these three cases.It can be concluded that the trajectory for study case with part load lies in the region of absolute instability(AI),and it lies in the region of convective instability(CI)for study case with design flow rate.Trajectory for study case with over load lies in the AI region at the inlet of the draft tube,and enters CI region near the end of the elbow.