关于Smarandache-Pascal数列的几个猜想

对任意数列{bn},它的Smarandache-Pascal数列是通过{bn}定义的一个新的数列{Tn},其中T1 =b1,T2 = b1 b2,T3 =b1 2b2 b3.一般地,当n≥2时,Tn 1 = ∑ n k=0 Ck n·bk 1,其中Ck n = n! k! (n-k)! 为组合数.利用初 等方法以及组合数和Fibonacci数的性质研究并解决猜想:设{Tn}是由{bn}= {F8n 1}= {F1,F9,F17,…}生成的 Smarandache-Pascal数列,则有恒等式Tn 1 ≡49(Tn -Tn-1),其中n≥2.     

花瓣Fibonacci数的生存函数研究

花瓣与Fibonacci数有着密切关系，根据Fibonacci数与Lucas数的递归关系，给出了关于Fibonacci数的生存函数F（r，x）和S（r，n，x）的定义，得到了关于Fibonacci数的生存函数，揭示了Fibonacci数的内在联系：     

植物叶序中的Fibonacci数与Lucas数的反演

植物的叶序与Fibonacci数和Lucas数有着密切关系,根据Fibonacci数与Lucas数的递推关系,利用母函数的方法,研究Fibonacci数与Lucas数的反演关系,揭示了植物叶序的内在现象。     

关于两个Fibonacci数整除的充要条件的注记

利用数学归纳法提供了2个Fibonacci数整除的充要条件的简捷证明,并给出Fibonacci数的一些重要性质。     

关于行列式化筒方法的探讨

本文系统的分析了各种类型行列式的结构、特点,在此基础之上给出了不同类型行列式具体的化简方法,并讨论了有关化简结果等问题,为行列式的化简问题提供了系统的方法。     

对线性代数中辅助行列式的分析研究

本文研究了线性代数理论证明中辅助行列式的性质和作用,总结出了构造辅助行列式的四种方法以及构造辅助行列式的一般原则。     

推广的范德蒙行列式的某些结果

对范德蒙行列式进行了两种形式的推广,并给出了推广后的范德蒙行列式的计算公式,这些公式的表示式简单明了,便于实际应用.同时探讨了这些结果在多项式函数求根中的应用.     

行列式元素的两个要素

本文指出行列式的元素有数值和下标(行标和列标)两个要素。行列式的许多定理实际上描述了行列式的值与两要素的关系。并指出:在一些定理的证明中,突出行列式元素的两个要素,可使证明思路清晰,简单明了,容易理解。     

一类行列式的计算公式

首次利用Z变换的方法计算得到了一类具有递推关系的特殊行列式的计算公式.并且将该公式应用于这类行列式的计算,得到了一些很好的结果.同时,利用Z变换的方法来计算此类具有递推关系的n阶行列式是一个很好的途径.     

试论递推法在行列式求值中的应用

定义：应用行列式的性质，把一个n阶行列式表示为具有相同结构的较低阶行列式的线性关系式，这种关系式称为递推关系式。根据递推关系式及某个低阶初始行列式的值，便可递推求得所给n阶行列式的值，这种计算行列式的方法称为递推法。     

3种常见优选法在农药配比中的应用及选择分析

从数学优选原理出发,通过3个农药配比试验介绍了黄金分割优选法、菲波那契数列优选法和对分法应用的合理性,减少了试验次数,提高了工作效率。     

Triangular and Fibonacci number patterns driven by stress on core/shell microstructures

Fibonacci number patterns and triangular patterns with intrinsic defects occur frequently on nonplanar surfaces in nature, particularly in plants. By controlling the geometry and the stress upon cooling, these patterns can be reproduced on the surface of microstructures about 10 micrometers in diameter. Spherules of the Ag core/SiOx shell structure, possessing markedly uniform size and shape, self-assembled into the Fibonacci number patterns (5 by 8 and 13 by 21) or the triangular pattern, depending on the geometry of the primary supporting surface. Under proper geometrical constraints, the patterns developed through self-assembly in order to minimize the total strain energy. This demonstrates that highly ordered microstructures can be prepared simultaneously across large areas by stress engineering.     

植物叶序研究的源流与发展

综述了8个世纪以来,人类在研究叶序现象的发生规律和机制方面所取得的主要成就。植物的叶序一般符合斐波纳契序列,并存在黄金分割关系;互生叶序的发散角大多恒定;发散角可以采用多种数学方法进行推导;发散角的形成在光照利用方面具有一定的生态学意义;叶序在形态发生学上具有特定的规律,并与某些植物激素和遗传基因有关,同时植物叶序与其它形态特征之间也具有一定的相关性。     

计算机在高等数学极限理论分析中的应用初探

本文应用计算机技术对高等数学中极限理论分析进行了探讨，以TURBOBASIC语言编制源程序，分别用（ε-N）和（δ-N）表达法，以数字状态显示，直观地揭示出序列极限、函数极限的原理，从而有助于正确理解序列极限、函数极限的定义。     

Isolation of the gene for a glycophorin-binding protein implicated in erythrocyte invasion by a malaria parasite

Plasmodium falciparum, the most lethal of the malarial parasites that infect humans, undergoes three cycles of development in its vertebrate host and elicits stage-specific immune responses. This stage specificity of the immune response has made it difficult to isolate antigens that would be useful in developing a vaccine against malaria. A complementary DNA clone for a glycophorin-binding protein of Plasmodium falciparum merozoites has been isolated and characterized. The protein interacts with glycophorin, the erythrocyte receptor, during invasion of the host cell by the parasite. Antigenic determinants of this protein expressed in Escherichia coli have been used to produce antibodies to a glycophorin-binding protein. The antibodies show schizont-specific immunofluorescence and react with the merozoite protein. The primary sequence of these determinants reveals a 150-nucleotide tandem-repeating sequence coding for a 50-amino-acid repeat. The characterization of the Plasmodium falciparum glycophorin-binding protein represents one approach toward designing serologic agents to block the parasite's development in the vertebrate host.     

The science of patterns

The rapid growth of computing and applications has helped cross-fertilize the mathematical sciences, yielding an unprecedented abundance of new methods, theories, and models. Examples from statistical science, core mathematics, and applied mathematics illustrate these changes, which have both broadened and enriched the relation between mathematics and science. No longer just the study of number and space, mathematical science has become the science of patterns, with theory built on relations among patterns and on applications derived from the fit between pattern and observation.     

Theodore von karman and applied mathematics in america

The emergence of applied mathematics as a discipline in the United States is traditionally associated with World War II. Hungarian-born Theodore von Kármán was among those who had waged a long and vigorous campaign well before the war to make applied mathematics respectable to engineers and mathematicians. While advocating the use of mathematics and physics to solve applied problems, he challenged the prevailing philosophy of engineering programs, locked horns with recalcitrant journal editors, and generally encountered the obstacles to building a discipline that cuts across conventional boundaries.     

Phyllotaxis and the fibonacci series

The principal conclusion is that Fibonacci phyllotaxis follows as a mathematical necessity from the combination of an expanding apex and a suitable spacing mechanism for positioning new leaves. I have considered an inhibitory spacing mechanism at some length, as it is a plausible candidate. However, the same treatment would apply equally well to depletion of, or competition for, a compound by developing leaves, and could no doubt accommodate other ingredients. The mathematical principles involved are clear when it is assumed that only two leaves (the contacts) position a new leaf. There is some experimental evidence for this assumption. Nonetheless, it is not a precondition for Fibonacci phyllotaxis, since a computer model shows that this pattern is generated even when many leaves contribute to inhibition at a given point. Indeed, the Fibonacci pattern seems to be a robust and stable mathematical phenomenon, a finding which goes some way to explaining its widespread occurrence throughout the plant kingdom.