tpo45 integrated writing

本文探讨了关于2亿年前可能存在蜜蜂的争论。虽然没有直接的蜜蜂化石证据,但考虑到当时的树脂保存条件有限,不能排除蜜蜂的存在。早期蜜蜂可能依赖非开花植物生存,并且在开花植物出现后逐渐形成紧密的关系。化学分析表明,化石巢穴中存在与现代蜜蜂巢室相同的防水物质,为蜜蜂建造提供了有力证据。

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It's perfectly possible that the nests found inside the fossilized trees were made by bees 200 million years ago. The arguments used by the skeptics are not convincing.

The professor in the listening part totally refutes the reading statement.

 

First, it's true we have no fossil remains of actual bees that date to 200 million years ago. But maybe the reason for that is that bees could not be preserved as fossils at that time. Fossil bees have typically been preserved in fossilized tree resin, a sticky liquid produced by trees.

However, trees with this type of resin were very rare 200 million years ago. Such trees became common much later. So, the fact that we have no bee remains that are 200 million years old doesn't mean that bees did not exist at that time. Maybe bees existed, but since there were almost no trees producing the right kind of resin, the bees could not be preserved.

 

First of all, no fossils of bees at that early time were found not necessarily means that there was no bees at that early time. Because bees may not be preserved for so long. Additionally, to be well-preserved, bees must combine with a certain resin released by a kind of tree. However, at that early time, this kind of tree was not very common or simply didn't exist. So, the chance of bees to become well-preserved fossil is very limited.

 

 

Second, while it's true that bees have a close mutual relationship with flowering plants today, it's quite possible that bees existed before flowering plants appeared on Earth. Those very early bees may have been feeding on non-flowering plants that preceded flowering plants during evolutionary history. The early bees could have fed on non-flowering plants such as ferns, or pine trees. Later, when flowering plants evolved, bees may have adapted to feeding on them, and this new relationship may have remained stable ever since.

Secondly, bees may feed on some non-flowering species at that early time. Even though, at that time, there wasn't any flower plant and modern bees have a pretty close relationship with flowering plants today, ancient bees could simply rely on the species that not flowered, like pine tree. After the flower trees appeared at 125 million years, the bees began to start the close relationship with the flower plant.

 

Third, even though the fossilized chambers lack spiral caps, there's chemical evidence that supports the theory that bees built the chambers. Modern bees protect their nest chambers against water by using a special waterproofing substance that has a distinctive chemical composition. When the fossilized chambers were chemically analyzed, it turned out that they contained the same kind of waterproofing material that's used by modern bees.

 

 

 

 

Thirdly, the chemical constitutions of chambers of the nest are very similar to their modern-day counterparts. It is true that the fossilized chambers lack spiral caps. However, after careful examination, similar water-resistant structures are found in both the modern-day bees' chambers and the fossil ones. Furthermore, the chemical analysis shows that the samples of both modern chambers and fossil ones shared the same combination. This evidence is more decisive to show the chambers were actually made by bees.

资源下载链接为: https://pan.quark.cn/s/9e7ef05254f8 行列式是线性代数的核心概念,在求解线性方程组、分析矩阵特性以及几何计算中都极为关键。本教程将讲解如何用C++实现行列式的计算,重点在于如何输出分数形式的结果。 行列式定义如下:对于n阶方阵A=(a_ij),其行列式由主对角线元素的乘积,按行或列的奇偶性赋予正负号后求和得到,记作det(A)。例如,2×2矩阵的行列式为det(A)=a11×a22-a12×a21,而更高阶矩阵的行列式可通过Laplace展开或Sarrus规则递归计算。 在C++中实现行列式计算时,首先需定义矩阵类或结构体,用二维数组存储矩阵元素,并实现初始化、加法、乘法、转置等操作。为支持分数形式输出,需引入分数类,包含分子和分母两个整数,并提供与整数、浮点数的转换以及加、减、乘、除等运算。C++中可借助std::pair表示分数,或自定义结构体并重载运算符。 计算行列式的函数实现上,3×3及以下矩阵可直接按定义计算,更大矩阵可采用Laplace展开或高斯 - 约旦消元法。Laplace展开是沿某行或列展开,将矩阵分解为多个小矩阵的行列式乘积,再递归计算。在处理分数输出时,需注意避免无限循环和除零错误,如在分数运算前先约简,确保分子分母互质,且所有计算基于整数进行,最后再转为浮点数,以避免浮点数误差。 为提升代码可读性和可维护性,建议采用面向对象编程,将矩阵类和分数类封装,每个类有明确功能和接口,便于后续扩展如矩阵求逆、计算特征值等功能。 总结C++实现行列式计算的关键步骤:一是定义矩阵类和分数类;二是实现矩阵基本操作;三是设计行列式计算函数;四是用分数类处理精确计算;五是编写测试用例验证程序正确性。通过这些步骤,可构建一个高效准确的行列式计算程序,支持分数形式计算,为C++编程和线性代数应用奠定基础。
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