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Schengen Visa Refusal: Justification for the purpose and conditions of the intended stay was not provided Schengen refusal formulae can be difficult to understand sometimes.    When an applicant receives a refusal with "Justification for the purpose and conditions of the intended stay was not provided", what does it mean? I don't understand this. These identities are given in the online notes for MIT's 18.01 calculus class. It's related to taking the sum of two trig functions and transforming them into a single trig function. I can use the formulas to do this, but I am having trouble finding anything on the internet to use a proof for my understanding.  Thanks for any responses!  EDITED (added after the first answer):  Sorry, the identity goes like this:  $A\sin{k(x-c)}=a\sin{kx}+b\cos{kx}$ ,  with the relationships  $a=A\cos{kc}$ , $b=-A\sin{kc}$ , $A=\sqrt{a^2+b^2}$ , and $\tan{kc}=-b/a$ Does $G\cong G/H$ imply that $H$ is trivial? My exterior door deadbolt has gotten stuck - it'll open with the lever but not the key. By spraying WD-40 inside the lock, I've been able to get it to work but it's very stiff. I'd like to remove the lock and inspect the inside, either to clean/lube it or replace it. But I can't figure out how to remove the lock; there's no obvious way to do this. (I'm used to seeing two screws on the inside of the deadbolt, usually under the lever arms when it's horizontal.)    How do I remove this? I can loosen the cover plate on the inside but it doesn't do anything other than rotate a few degrees. Determine if Type is a pointer in a template function Living forever in D&D (via spells)? I was thinking of a way for a humanoid (PC or NPC) to live forever in a D&amp;D setting, but through rather "common" and reproducible means, such that they will be available to many. By this logic I exclude cases such as a god giving immortality (or some other intervention) or a unique item granting an endless lifespan etc.  To cover all bases I will note that miracle and wish cannot do this directly, nor can true resurrection (and its lesser brethren) "restore to life a creature who has died of old age".  I had came up with the following ruse:   Reach your deathbed with at least 2 HD (or levels). Have someone kill you so that the cause of death will not be "old age". Have a druid cast reincarnate on you into a young body. You "recall the majority of your former life". I assume your memories, personality/identity and experiences are preserved.   Rinse and repeat. It's not that difficult to recover the 1 HD lost through the course of almost a lifetime. The material components are worth 1,000 gp - might not be easy to get, but surely possible.  Furthermore, it is stated that "A wish or a miracle spell can restore a reincarnated character to his or her original form.". I assume the "original form" is the aged humanoid at his or her deathbed - not the direction we are looking for, unless it means that the humanoid restores his race only.  Is there a flaw in this plan? Is there another way of doing it? Gaming the system for Populist badges If $\mathop{\mathrm{Spec}}A$ is not connected then there is a nontrivial idempotent Defining the appropriate Projected Coordinate System Backtrack, Wi-Fi not working I've installed Backtrack 5R3 KDE, and I realized that my wireless is not working, but wired is working fine.  Here's the lshw output:     *-network         description: Ethernet interface         product: RTL8101E/RTL8102E PCI Express Fast Ethernet controller         vendor: Realtek Semiconductor Co., Ltd.         physical id: 0         bus info: pci@0000:02:00.0         logical name: eth0         version: 05         serial: 04:7d:7b:b7:46:f8         size: 100MB/s         capacity: 100MB/s         width: 64 bits         clock: 33MHz         capabilities: pm msi pciexpress msix vpd bus_master cap_list 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=rtl_nic/rtl8105e-1.fw ip=192.168.2.2 latency=0 link=yes multicast=yes port=MII speed=100MB/s         resources: irq:42 ioport:2000(size=256) memory:f0404000-f0404fff memory:f0400000-f0403fff   lspci output:      00:00.0 Host bridge: Intel Corporation 2nd Generation Core Processor Family DRAM Controller (rev 09) 00:02.0 VGA compatible controller: Intel Corporation 2nd Generation Core Processor Family Integrated Graphics Controller (rev 09) 00:14.0 USB Controller: Intel Corporation Panther Point USB xHCI Host Controller (rev 04) 00:16.0 Communication controller: Intel Corporation Panther Point MEI Controller #1 (rev 04) 00:1a.0 USB Controller: Intel Corporation Panther Point USB Enhanced Host Controller #2 (rev 04) 00:1b.0 Audio device: Intel Corporation Panther Point High Definition Audio Controller (rev 04) 00:1c.0 PCI bridge: Intel Corporation Panther Point PCI Express Root Port 1 (rev c4) 00:1c.1 PCI bridge: Intel Corporation Panther Point PCI Express Root Port 2 (rev c4) 00:1d.0 USB Controller: Intel Corporation Panther Point USB Enhanced Host Controller #1 (rev 04) 00:1f.0 ISA bridge: Intel Corporation Panther Point LPC Controller (rev 04) 00:1f.2 SATA controller: Intel Corporation Panther Point 6 port SATA AHCI Controller (rev 04) 00:1f.3 SMBus: Intel Corporation Panther Point SMBus Controller (rev 04) 02:00.0 Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8101E/RTL8102E PCI Express Fast Ethernet controller (rev 05) Is there a way to make Git mark a file as conflicted? My current desktop reso is 1366x768    In cs 1.6 I have selected display option as Normal and Resolution as 1024x768.     In this settings I don't get those vertical black side bars which make the playing screen square.     Atm it is rectangular but I wanted square.    How do I get the vertical black bars while playing cs 1.6? The question asks to compute:   $$\sum_{k=0}^{n-1}\dfrac{\alpha_k}{2-\alpha_k}$$   where $\alpha_0, \alpha_1, \ldots, \alpha_{n-1}$ are the $n$-th roots of unity.   I started off by simplifiyng and got it as:  $$=-n+2\left(\sum_{k=0}^{n-1} \dfrac{1}{2-\alpha_k}\right)$$  Now I was stuck. I can rationalise the denominator, but we know $\alpha_k$ has both real and complex components, so it can't be simplified by rationalising. What else can be done? What are the most appropriate datum and projection I could use for the Gulf coast region - spanning  Louisiana, Mississippi, Alabama, and Florida? I have to analyze block group data along the coast. Is there a way to target the arrow from an OP bow via command block? I am trying to make an effect trail for a specific weapon in MC, a bow with power 120.  I want to use a command block to target any arrow with the damage it should be doing (63) and summon a trail of splash potions.  I also want to kill any arrow entities that have inGround=True  Is there any way to do this or do I have to come up with something else?  Attempt:  /execute @e[type=Arrow,damage=63,inGround=0] ~ ~ ~ summon ThrownPotion ~ ~ ~ {Potion:{id:potion,Damage:8197}} /kill @e[type=Arrow,inGround=True]   Each unfortunately just affects all arrows.  Is this even possible? If the imaginary part of an entire function is never zero, the function is constant Let $f : \mathbb{C} \to \{z\in\mathbb{C}:\Im(z)\neq0\} $ entire . Show that $f$ is constant.  I took $g(z)=\frac{1}{f(z)}$ and I think that g is bounded, therefore it is constant (due to Louville's theorem) but how do I prove it? Is $|g(z)|=\frac{1}{|f(z)|}=\frac{1}{u^2+v^2}\le M$ valid? Are there alternatives to LibreOffice? How do I adjust the Clock Indicator format? What I have now is:  /testfor @a {SelectedItemSlot:0,Inventory:[{Slot:0b,id:"diamond_pickaxe"}]}   How can I use the /testfor command to test a specific slot for a specific item that is enchanted? Matching Gmail filters on BCC mail