Show that $|f(0)| \leq \frac{1}{4}$ for every holomorphic function $f:\Bbb D \to \Bbb D$ such that $|f(\frac{1}{2})|+|f(-\frac{1}{2})|=0$
If $f \in \operatorname{Hol}(D)$, $f(\frac{1}{2}) + f(-\frac{1}{2}) = 0$, prove that $|f(0)| \leq \frac{1}{4}$
Why does (0 < 5 < 3) return true? When do you use at the office? And when do you use in the office? What's the difference between the phrases? "...his parents' dream of *him* achieving a Cambridge degree." What is the function of "him" here? I have a problem analysing this sentence from the point of finite/nonfinite clauses, clause elements and their functions:     He does not want to destroy his parents' dream of him achieving a Cambridge degree.   I am especially interested in the: dream of him achieving a Cambridge degree.  I know that 'achieving a Cambridge degree' is a non-finite -ing participle clause. However what is its function? And what is the function of 'of him'? Is it a postmodification? Finding minimum bounding extent of given pixel value within raster? Launching an Applet fails? How does the secondary effect of the Heat Metal spell work? 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I'm sure i7-3632QM is supported (same socket (BGA1224), same TDP (35W) and microcode found in BIOS (306A9.PAT)).  So my question is: 1) is it possible to de-solder the current CPU without damaging it, and to solder the new CPU without damaging it and the motherboard ? 2) if so, what tools are necessary? who can do that at a reasonnable cost?  Until now, I was unable to find anyone able (or willing) to do that (I'm located in France, and I have tried a local fablab, electronics shops, TV repair shops, ...). Any hint would be appreciated. random access file in java I have the following fields:   Inventory control (16 byte record)   Product ID code (int – 4 bytes) Quantity in stock (int – 4 bytes) Price (double – 8 bytes)    How do I create a fixed length random access file using the above lengths? I tried some examples online, but I either get an EOF exception or random address values when I try to access them.  I tried some more examples and couldn't understand the concept very well. I'm trying a project with it and will try to explore more on it.  Here is some example data. There might be holes in the data where No. in stock could be 23 == 023.            Quantity ID. No.   In Stock   Price  -------   --------   ------  1001       476      $28.35  1002       240      $32.56  1003       517      $51.27  1004       284      $23.75  1005       165      $32.25   Thanks for the help. Let $(x_n)$ be a sequence of real numbers.  Prove that if there exists $x$ such that every subsequence $(x_{n_k})$ of $(x_n)$ has a convergent (sub-)subsequence $(x_{n_{k_l}})$ to $x$, then the original sequence $(x_n)$ itself converges to $x$ .              Thanks for any help. If we set $A$ and $B$. Assuming that there exist an injective map from $A$ to $B$ and an injective map from $B$ to $A$. How to prove that there is a bijection between $A$ and $B$. 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What should be my next step What is a tty, and how do I access a tty? How to let `dpkg -i` install dependencies for me? How To quickly do derivatives with respect to matrices Whats a quick way to work the below (and problems similar) out?   For me to take this derivative it involves a lot of time and boring calculation, there has to be a better way.    This is taken from the solutions to Chris Bishop's Pattern Recognition and Machine learning: