Bachelor thesis Non-absolute convergence of Newton integral (CZ/ENG)

In this thesis we search for sufficient and necessary conditions for non absolute convergence of Newton integral of function of the form sin(φ(x))/x. Importantly we analyse how the oscilation of the sine function influences the convergence of the integral. We are dealing with continous non-decreasing functions such that limx→∞ φ(x) = ∞. We proved that bilipschitz of φ is not sufficient. Nevertheless, we proved several theorems about sufficient conditions for the convergence of the integral. I have proven following theorem.

theorem - relationship between periodicity and convergence of newton integral

Let \(\psi \) be a function that is \( \underline{2p-periodic} \) and \( \underline{continous} \) on \( \mathbb{R} \), then

\[ \begin{equation*} \int_{1}^{\infty} \frac{\psi(x)}{x} \,dx\, \, \text{convergence} \Leftrightarrow \int_{-p}^{p} \psi(x)\,dx\, =0. \end{equation*} \]


I would like to take the opportunity to voice my opinion on the first defense of my thesis which took place on 12 September 2018, with particular reference to the referee's report. It is a rather unpleasant situation for me because I profoundly disagree with the referee's report. What is more, I didn't get an opportunity to explain my own views on the subject. However, since it is included in the Charles University's repository of theses, I would like to make my opinion public here.

"You should never put up with unjustice, whatever it is "Jan Zajíc, Univerzita Karlova

Unfortunately, the examiner can say whatever he wants in the report on the student's thesis. He can make things up, lie, or otherwise discredit the student - and his review will remain in the public domain of the repository of theses forever. The student has no chance to defend himself. This is how the school system works. The student has no opportunity to express his own views on the examiner's review. The student has the right to comment only briefly on the oral defense and that's all. He has no right to express his view in a written form and openly disagree with the examiner's opinion, as has been explained to me by both the university's lawyer and the vice-dean for education. I was told that the examiner's opinion is very important, whatever it is, which is why it has to remain lodged in the public domain forever and the student must accept it and is not allowed to question it.

However, it is my belief that the examiner's assumptions were often fictional, distorted and misleading. He might have done it on purpose as a result of a personal grudge or he might not have read it carefully enough. In either case, I feel damaged by his report. That is why I later applied for a change of examiner and the head of department granted my application. I then defended my thesis successfully on 7 of February 2019, having corrected made a small correction.