there is no entire function f(z) which verifies that |f(z)| > |z| for every z ∈ C.
Function $f(z)$ such that $|f(z)| > |z|$ for every $z\in\mathbb{C}, 1/f(z)$
Creating Workflow -> Error Proving Cauchy condensation test I have to prove the  by tomorrow and I am really unconfident about what I did:  $$\sum_{n=1}^\infty a_n\text{ converges } \iff \sum_{n=1}^\infty 2^n a_{2^n}\text{ converges}$$  I did the following:  Let $(b_n)$ be a sequence as follow: $b_{2^k+m}:=a_{2^k}$ with $k\in\mathbb N_0$ and $0\leq m&lt;2^k$.  It's $a_{n+1}\leq a_n$ and so $0\leq a_{n+p}\leq a_n$ for all $n,p\in\mathbb N$.  So $\sum\limits_{n=1}^\infty b_n$ converges by the majorizing series $\sum\limits_{n=1}^\infty a_n$. And it's $\sum\limits_{n=0}^\infty b_n=\sum\limits_{n=0}^\infty\sum\limits_{m=0}^{2^n-1}a_{2^{n+1}}=\sum\limits_{n=1}^\infty 2^{n-1}a_{2^n}$ so $\Rightarrow$ is done.  For $\Leftarrow$ consider $c_{2^k+m}:=a_{2^k}$ with $k\in\mathbb N_0$ and $0\leq m&lt;2^k$.  It's $|a_n|\leq c_n$ and $\sum\limits_{n=0}^\infty c_n=\sum\limits_{n=0}^\infty\sum\limits_{m=0}^{2^n-1}a_{2^{n}}=\sum\limits_{n=1}^\infty 2^{n}a_{2^n}$ and so $\sum\limits_{n=1}^\infty a_n$ converges by the majorizing series $\sum\limits_{n=0}^\infty c_n$.  Is this in form and content correct? My connection was fine until now, but my wired connection is not working in Ubuntu 12.04.  I have installed Ubuntu 12.04 along side Windows 7 partition and the connection works on Windows but not on Ubuntu 12.04. I have no problem with wireless connection as well.  The problem is specific to the wired connection on Ubuntu 12.04. I have included a few details below.  ifconfig  eth0      Link encap:Ethernet  HWaddr 00:1e:ec:8d:f0:03             inet6 addr: fe80::21e:ecff:fe8d:f003/64 Scope:Link           UP BROADCAST RUNNING MULTICAST  MTU:1500  Metric:1           RX packets:1 errors:0 dropped:0 overruns:0 frame:0           TX packets:376 errors:0 dropped:0 overruns:0 carrier:0           collisions:0 txqueuelen:1000            RX bytes:316 (316.0 B)  TX bytes:33769 (33.7 KB)           Interrupt:19   eth2      Link encap:Ethernet  HWaddr 00:21:00:4e:ac:58             inet6 addr: fe80::221:ff:fe4e:ac58/64 Scope:Link           UP BROADCAST MULTICAST  MTU:1500  Metric:1           RX packets:1660 errors:0 dropped:0 overruns:0 frame:28           TX packets:1846 errors:61 dropped:0 overruns:0 carrier:0           collisions:0 txqueuelen:1000            RX bytes:1372676 (1.3 MB)  TX bytes:254576 (254.5 KB)           Interrupt:18   lo        Link encap:Local Loopback             inet addr:127.0.0.1  Mask:255.0.0.0           inet6 addr: ::1/128 Scope:Host           UP LOOPBACK RUNNING  MTU:16436  Metric:1           RX packets:1862 errors:0 dropped:0 overruns:0 frame:0           TX packets:1862 errors:0 dropped:0 overruns:0 carrier:0           collisions:0 txqueuelen:0            RX bytes:155767 (155.7 KB)  TX bytes:155767 (155.7 KB)     sudo lshw -C network    *-network                       description: Wireless interface        product: BCM4312 802.11b/g LP-PHY        vendor: Broadcom Corporation        physical id: 0        bus info: pci@0000:03:00.0        logical name: eth2        version: 01        serial: 00:21:00:4e:ac:58        width: 64 bits        clock: 33MHz        capabilities: pm msi pciexpress bus_master cap_list ethernet physical wireless        configuration: broadcast=yes driver=wl0 driverversion=5.100.82.38 ip=10.0.0.3 latency=0 multicast=yes wireless=IEEE 802.11bg        resources: irq:18 memory:99700000-99703fff    *-network        description: Ethernet interface        product: RTL8101E/RTL8102E PCI Express Fast Ethernet controller        vendor: Realtek Semiconductor Co., Ltd.        physical id: 0        bus info: pci@0000:04:00.0        logical name: eth0        version: 02        serial: 00:1e:ec:8d:f0:03        size: 100Mbit/s        capacity: 100Mbit/s        width: 64 bits        clock: 33MHz        capabilities: pm msi pciexpress msix vpd bus_master cap_list rom ethernet physical tp mii 10bt 10bt-fd 100bt 100bt-fd autonegotiation        configuration: autonegotiation=on broadcast=yes driver=r8169 driverversion=2.3LK-NAPI duplex=full firmware=N/A latency=0 link=yes multicast=yes port=MII speed=100Mbit/s        resources: irq:19 ioport:3000(size=256) memory:93410000-93410fff memory:93400000-9340ffff memory:93420000-9343ffff Show sub reasons in close review queue Currently close vote review queue shows the top level close reason in the header, but some close reasons, for instance, off topic have very different sub reasons. For instance, "demonstrate minimal understanding" is different from "This question belongs on a different site in the stack exchange network".  It would be nice if sub close reasons were also shown. System.currentTimeMillis() vs. new Date() vs. Calendar.getInstance().getTime() In Java, what are the performance and resource implications of using  System.currentTimeMillis()    vs.   new Date()    vs.   Calendar.getInstance().getTime()   As I understand it, System.currentTimeMillis() is the most efficient. However, in most applications, that long value would need to be converted to a Date or some similar object to do anything meaningful to humans. How to prove that $\lim\limits_{h \to 0} \frac{a^h - 1}{h} = \ln a$ In order to find the derivative of a exponential function, on its general form $a^x$ by the definition, I used limits.  $\begin{align*} \frac{d}{dx} a^x &amp; = \lim_{h \to 0} \left [ \frac{a^{x+h}-a^x}{h} \right ]\\  \\ &amp; =\lim_{h \to 0} \left [ \frac{a^x \cdot a^h-a^x}{h} \right ] \\  \\  &amp;=\lim_{h \to 0} \left [ \frac{a^x \cdot (a^h-1)}{h} \right ] \\  \\ &amp;=a^x \cdot \lim_{h \to 0} \left [\frac {a^h-1}{h} \right ] \end{align*}$  I know that this last limit is equal to $\ln(a)$ but how can I prove it by using basic Algebra and Exponential and Logarithms properties? Thanks Is there a word for a person who avoids their responsibilities? Proof of the formula $1+x+x^2+x^3+ \cdots +x^n =\frac{x^{n+1}-1}{x-1}$ If I have a native C++ windows program (i.e. the entry point is WinMain) how do I view output from console functions like std::cout? RX 590 IN Blender and Cycles Render I don't know why, but I cant render anything in CUDA and OptiX but OpenCL work fine. I cant use Cycles render because it's very laggy. I have newest  version of Blender and an RX 590 Red Dragon 8gb. Why does that happen?  How can I turn on my gpu? The bounty I offered on  is now in its grace period and the information box tells me:     you must award this bounty as soon as possible   But there are no answers - what do I do? Site blocked by content filter I run a large and high trafficked WordPress powered platform. One of my editors informed me that our site is blocked at his workspace as a "games site". They use WebCat to filter the traffic.  The issue here is that our platform is not a gaming site, although it does have a games category that covers news. And that is a very minor part of the site.  My question is, what can I do to unblock the site? How does WebCat work? Do they use a universal database to filter the traffic (meaning that the site is blocked on all workspace with WebCat) etc. Obviously they need to improve their filtering algorithm. Meaning of hash symbol in pin name I'm reading the datasheet of a PSRAM (available ). In the top-right hand corner all the pins are listed. Some of the pin names end with a hash, e.g. LB#, OE#.  What does the # notation mean for pins? Why $\sqrt{-1 \times -1} \neq \sqrt{-1}^2$? Why are so many important verbs irregular? Is a Schengen visa/transit visa required for a transit flight through two Schengen airports? I am travelling form Delhi (DEL) to San Francisco (SFO), I have to make a connection flight in Vienna that would take me to Frankfurt (FRA). My flight to SFO is from FRA, I have one ticket for entire journey and the flights are operated by Lufthansa or its subsidiaries.  Do I need a transit visa? My flight arrives at Vienna international airport and leaves from the same, and for second leg it arrives at Frankfurt international airport.  I asked this question as an addendum to my  but was advised to make a new post.  I hold Indian passport and valid US visa. What is a "slug" in Django? How do I use itertools.groupby()? I haven't been able to find an understandable explanation of how to actually use Python's itertools.groupby() function.  What I'm trying to do is this:  Take a list - in this case, the children of an objectified lxml element Divide it into groups based on some criteria Then later iterate over each of these groups separately.  I've reviewed , but I've had trouble trying to apply them beyond a simple list of numbers. So, how do I use of itertools.groupby()?  Is there another technique I should be using?  Pointers to good &quot;prerequisite&quot; reading would also be appreciated. I was wondering if there is a simpler way to find the last to digits of a power such as $3^{45}$. I reduced it modulo 100 to get the answer, which is 43. But I was curious if there was a simpler, or more eloquent way to get this result.  Here's my method:  Using the fact that $3^4=81\equiv -19 \pmod{100}$ and $19^5=2,476,099\equiv -1 \pmod{100}$  $$ 3^{45}\equiv 3(3^4)^{11}\equiv 3(-19)^{11}\equiv 3(-19)(19^5)^2\equiv 3(-19)(-1)^2 \equiv -57 \equiv 43 \pmod {100} $$  I just felt like this was sort of a messy way to find out that the last two digits are 43. White screen of death: Fatal error: Allowed memory size of X bytes exhausted I have a issue with my Drupal installation, for example:   when I enable or disable the modules, It redirects me to a blank page, when I create a new content type and save it, redirects me to a blank page, when I add a new view and save it, it redirects me to a blank page, when I try to clear the cache, it redirects me back to a blank page, or in similar cases.   Basically all the confirmation pages redirect me to a white screen. When I refresh it again, it shows me the page. I tried to increase the PHP memory value but it doesn't help.  Are there any other solutions for this?  The error which I'm having:      Fatal error: Allowed memory size of 100663296 bytes exhausted (tried to allocate 8192 bytes) in sites/all/modules/views/plugins/views_plugin_localization_none.inc on line 1