拓展

Using the theories of probability, algebra and spectral theory comprehensively, we investigate some related characteristics of logic functions in cryptography: Firstly, we introduce m order generalized s - correlation immunity of Boolean vector functions and prove that the higher order generalized ε- correlation immunity can guarantee the lower order generalized ε- correlation immunity. Then by applying decomposition formula of joint distribution of Boolean random vectors, we give a spectrum criterion of m order generalized e - correlation immunity of Boolean vector functions. Furthermore, we show that the algebraic degree of m order generalized e - correlation immune Boolean vector functions is not restricted by the correlation immune orders.

本文主要运用概率论的思想和方法，并结合代数学和频谱理论的相关知识，对密码学中逻辑函数的有关性质进行了研究，主要包括以下三个方面的内容：首先，对布尔向量函数的相关免疫性进行了拓展，给出了k维布尔向量函数m阶广义ε-相关免疫的概念，证明了布尔向量函数的高阶广义ε-相关免疫性蕴含低阶广义ε-相关免疫性，并根据布尔随机向量联合分布分解式得到了布尔向量函数m阶广义ε-相关免疫的一个谱判别条件，还说明了m阶广义ε-相关免疫布尔向量函数的代数次数不受相关免疫阶数的制约。

Other entrepreneurs choose to bootstrap because they want more freedom to develop the company as they see fit.

还有些初创企业家选择自我积累的原因是他们需要在拓展公司业务上面拥有更大的自由度。

Some of this research stretches the boundaries of what we know.

一些研究拓展了我们的认识范围。

Our investigations subsume the case of functions of bounded variation as special case and improve Guo and Khan\'s result[12]by giving a better asympotic estimate.

本章结果拓展了Guo和Khan[12]的研究工作，使之适用于更广泛的函数类，而且给出了一个更好的渐进估计。

You were just saying how you wanted to, you know, push the bounds of decency...

你刚刚说出了你所想要的，嗯，拓展最大的利益考量。。。

Started the new way that manpower capital theory studies to the research of manpower capital property right, extended the bracer of manpower capital theory.

对人力资本产权的研究开创了人力资本理论研究的新方向，拓展了人力资本理论的保护带。

Tina: I agree. Whoever told her to branch out into acting must have been crazy!

蒂娜：没错。叫她拓展事业去演戏的人一定是疯了！

She's leaving the company to branch out on her own.

她离开公司去拓展自己的事业。

Circumstance has handed you an opportunity to branch out. You should make good use of it.

现在环境给了你一个拓展生活圈的机会，你应该善用它。

After your own blog is established, you can branch out to writing on other blogs.

在你建立好自己的博客后，你就可以逐渐拓展到其他博客上进行写作。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。