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李云祥 《数学学习与研究(教研版)》2013,(14):103-106
数字冰雹猜想是:对于任意一个自然数N,如果N是偶数,就把它变成N2;如果N是奇数,就把它变成3N+1.按照这个法则运算下去,最终必然得1.这个有趣的猜想引起了许多数学爱好者的兴趣,并做了大量的研究、验证,都没有找到此猜想的一般规律,至今都是数学领域里悬而未解的难题.这个难题如何解决呢?在研究过的大量数字冰雹数列中都有神奇的数字漩涡124,并由此可以推导出数字漩涡公式:n=3n+12x.由数字漩涡公式引导出的三个证明都可以各自独立地证明:当数字冰雹数列中,只有奇数n1,n2(或者奇数n2就是第1个奇数n1本身)时,只有唯一的数字漩涡124.根据证明三推导出证明四,证明四可以证明:当数字冰雹数列中有奇数n1,n2,n3,…,nv时,这样的数字冰雹数列中不存在别的数字漩涡(除数字漩涡124外).证明五可以证明每一个数字冰雹数列最后都必然得1.因此由证明一、二、三、四、五的充分论证就可以证明数字冰雹猜想是正确的. 相似文献
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一道常见例题:有一半径为R的扇形废铁皮,圆心角∠AOB=60°,现将其废物利用,剪成一个内接矩形,如图所示有两种裁法:甲同学让矩形的一边在扇形的一条半径上(如图1),乙同学让矩形的一边与弦AB平行(如图2).请问:哪位同学的裁法能得到面积最大的矩形?图1图2笔者和研究性学习小组的同学们对此例展开后继研究后,收获颇丰.现将过程简述如下.1猜想———创新的起点猜想有一半径为R的扇形,圆心角∠AOB=60°,现将其剪成一个矩形,内接矩形的面积最大.分析此时由于长方形顶点的位置不确定,其裁法也多种多样,但依据前面的研究可猜想:面积最大的矩形必… 相似文献
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文[1]提出了如下一个积型不等式猜想: 设ai＞0(i=1,2,…,n),n≥3,∑ni=1ai=1,k∈N*,则有 相似文献
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涉及三角形边角关系的两个猜想 总被引：1，自引：0，他引：1
以下用a、b 、c 分别表示△ ABC 中角 A 、 B 、C 的对边,文[1]给出了两个猜想: 猜想1若an,bn,cn(n ≤ 4,n∈R?)成等差数列,则 B ≤ 60° . 猜想 2 若0 < n ≤ 4,k ≥1,则 k2 ? k 1≥ (kn2 1)n2 . 猜想 2 的证明: f (k) = ln(k2 ? k 1) ? ln 2 kn 1 , n 2 k2 ? k 1 = (k ? )2 > 0 , 1 3 2 4 对k … 相似文献
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文献[1]提出如下一个代数不等式的猜想:猜想设 a_i>0,i=1,2,…,n,3≤n ∈N,证明或否定:f(a_1,a_2,…,a_n)=(a_1/1 a_1 a_1a_2 … a_1a_2…a_(n-1)) (a_2/1 a_2 a_2a_3 … a_2a_3…a_n) (a_3/1 a_3 a_3a_4 … a_3a_4…a_na_1) …… 相似文献
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李建潮 《中学数学研究(江西师大)》2004,(8):15-16
1.文[1]猜想 文[1]提出如下不等式: 已知x、y、x∈R ,且x y x=1,则 (1/x-x)(1/y-y)(1/z-x)≥(8/3)3.(1)并在文末提出漂亮猜想: 相似文献
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As low-stakes testing contexts increase, low test-taking effort may serve as a serious validity threat. One common solution to this problem is to identify noneffortful responses and treat them as missing during parameter estimation via the effort-moderated item response theory (EM-IRT) model. Although this model has been shown to outperform traditional IRT models (e.g., two-parameter logistic [2PL]) in parameter estimation under simulated conditions, prior research has failed to examine its performance under violations to the model’s assumptions. Therefore, the objective of this simulation study was to examine item and mean ability parameter recovery when violating the assumptions that noneffortful responding occurs randomly (Assumption 1) and is unrelated to the underlying ability of examinees (Assumption 2). Results demonstrated that, across conditions, the EM-IRT model provided robust item parameter estimates to violations of Assumption 1. However, bias values greater than 0.20 SDs were observed for the EM-IRT model when violating Assumption 2; nonetheless, these values were still lower than the 2PL model. In terms of mean ability estimates, model results indicated equal performance between the EM-IRT and 2PL models across conditions. Across both models, mean ability estimates were found to be biased by more than 0.25 SDs when violating Assumption 2. However, our accompanying empirical study suggested that this biasing occurred under extreme conditions that may not be present in some operational settings. Overall, these results suggest that the EM-IRT model provides superior item and equal mean ability parameter estimates in the presence of model violations under realistic conditions when compared with the 2PL model. 相似文献
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当前,在给小学生特别是低年级小学生制作语文阅读资源时需要对阅读材料进行注音。目前使用的注音工具主要是WORD办公软件的注音工具,该工具一次只能对有限的文本(50个字符)进行全文注音,且无法由使用者自定义需要注音的字,给注音带来诸多不便。针对这一问题,本研究研制了基于Web的自定义注音工具,该工具可以由课件制作人员设定生字范围或填写自己认为需要注音的汉字来对任意长度的文本注音,并可设定拼音的呈现格式(拼音在汉字上方及拼音在汉字右侧),在注音灵活性、排版等方面优于国内其他注音工具。 相似文献
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Rebecca Bull Wendy Anne Davidson Emily Nordmann 《Learning and individual differences》2010,20(3):246-250
Lateralization of the brain is strongly influenced by prenatal androgens, with differential exposure thought to account for cognitive sex differences. This study investigated sex and individual differences and relationships between 2D:4D (the ratio of the 2nd to 4th digit [digit ratio] as a proxy indicator of prenatal testosterone exposure), visual-spatial memory, and numerical skills in 5-year-old children. No sex differences were found in any of the numerical or visual-spatial tasks. Visual-spatial memory was positively correlated with arithmetic score. Girls with a lower (more masculinised) 2D:4D had better number sense and visual-spatial skills, whilst boys with lower 2D:4D had better arithmetic skills. This suggests that prenatal testosterone exposure may have differential effects on the visual-spatial and numerical skills of girls and boys. 相似文献
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Jessica H. Milton Margaret M. Flores Vanessa M. Hinton Caroline Dunn Craig B. Darch 《Learning disabilities research & practice》2023,38(1):15-25
This study investigated the effects of a place value intervention with third-grade students with learning disabilities. The intervention added content to a research-based intervention using the concrete-representational-abstract (CRA) sequence. The added content reflected current mathematics standards for third grade. Students’ place value understanding was measured using probes in which students had to identify the value of each digit within a three-digit number, round three-digit numbers to the nearest 10 or 100, and write three equations showing an expanded form of a three-digit number. A single-case, multiple-probe-across-students design showed a functional relation between CRA and completion of items requiring place value understanding. Students completed a generalization task by estimating the sum of a given equation. 相似文献
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以两位数、三位数、四位数等为例，综述了各位数的偶数表示为两个质数之和的组合形式的发展趋势．得出了一个偶数，无论以两质数之和，或以两纯奇数之和，或以一个质数与一个纯奇数之和去表示．总是偶数越大表示为两数之和的组合数越发具有多样性的共同的规律．由此提出了对“哥德巴赫猜想”深信不疑的根据． 相似文献
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贾善翔著的《南华真经直音》是宋代汉语语音史研究的重要材料,但由于各种原因一直未受到学术界的关注。《南华真经直音》与《广韵》声类相比,贾善翔音切反映了宋代通语语音的演变和当时四川方言的一些特点。 相似文献
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Mark E. Wildmon Christopher H. Skinner Merilee McCurdy Sanpier Sims 《Psychology in the schools》1999,36(4):319-325
The purpose of the current study was to replicate and extend research on academic assignment preference by presenting high school students with control assignments containing eight 2‐digit × 2‐digit + 2‐digit × 2‐digit mathematics reading problems, experimental assignments that contained eight equivalent 2‐digit × 2‐digit + 2‐digit × 2‐digit problems, and three additional interspersed 4‐digit + 4‐digit mathematics reading problems. After spending 10 minutes and 40 seconds working on each assignment, significantly more high school students ranked the experimental assignments as being less difficult. When given a choice between the two assignments for homework, significantly more students chose a new experimental assignment. No differences were found on accuracy levels across assignments. Although the experimental assignments contained more problems, the students preferred the experimental over the control assignments. Discussion focuses on future research designed to investigate the applied implications of the interspersal technique within educational settings. © 1999 John Wiley & Sons, Inc. 相似文献
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This study examines a wide range of numerical representations (i.e., quantity, knowledge of multiplication facts, and use of parity information) in adult deaf signers. We introduce a modified version of the number bisection task, with sequential stimulus presentation, which allows for a systematic examination of mathematical skills in deaf individuals in different modalities (number signs in streaming video vs. Arabic digit displays). Reaction times and accuracy measures indicated that deaf signers make use of several representations simultaneously when bisecting number triplets, paralleling earlier findings in hearing individuals. Furthermore, some differences were obtained between the 2 display modalities, with effects being less prominent in the Arabic digit mode, suggesting that mathematical abilities in deaf signers should be assessed in their native sign language. 相似文献
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In Experiment 1, goldfish trained with alternation of reward (R) and nonreward (N) for responding to a single color gave clear evidence of patterning (more rapid responding on R than on N trials). In Experiment 2, patterning was found for each of two colors alternately rewarded and nonrewarded in the sequence blue R, yellow R, blue N, yellow N, …. Changes in performance with subsequent changes in the sequence of the two colors suggested that the patterning was based on carryover rather than on associative memory of R and N. 相似文献
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基于一种新的非参数方法计算了HDR (high data rate)无线网络的吞吐率容量区域. 首先把HDR吞吐率容量区域的计算问题转化为一个不带参数的数学优化问题, 然后通过贪婪算法求解得到该优化问题的解, 从而最终给出了HDR吞吐率容量区域的非参数解析刻划. 与传统的参数化方法的庞大计算量相比, 该方法的计算复杂度降低很多, 最多只需要计算N(M2-M 1)N-1个线性约束即可, 其中N为用户数, M为系统支持速率数. 数值计算例子验证了这种非参数方法的正确性. 相似文献