algebraic curves – Laurent Tail divisor definition

I am reading Rick Miranda’s Book and now he defines a Laurent tail divisor as being a finite formal sum $sum_pr_p(z_p).p$ where $r_p$ is a Laurent polynomial in the coordinate $z_p$. Then he goes on to define a map $alpha_D : mathcal{M}(X)rightarrow tau(D)(X)$ defined by sending the meromorphic function $f$ to the sum $sum_p r_p.p $ where $r_p$ is the truncation of the laurent series $f(z_p)$ of $f$ in terms of $z_p$, removing all terms of order $-D(p)$ or higher, now my question is how do we know that the sum $sum_p r_p.p$ will be finite so that it will be in the set of laurent tail divisors? Since we defined them as a being finite.

Thanks in advance.

Where can I find a similar view from a hotel room like Costa Rica looking at Whale Tail National Park?

This is called "Lattice House in Puntarenas Costa Rica. Absolutely beautiful. In the background is the" Whale Tail "National Park. But I have already visited Costa Rice before. Where can I find a similar view in

  1. Hawaii

  2. Japan

  3. Australia

  4. New Zealand?

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Head & tail Games Collection Earn from 200% (earn 5-7 $ / day)

I collect some websites that contain head & tail.


1. Find the story

2. If you win from 199% – 250%, the story loses 3-4 times -> play. If you win 300-400, the story loses 6-7 times -> play.

3. Change IP

4. Change the site bet

5. Play again

List of sites:

Good luck


dnd 5e: Can a Tiefling self-mutilate to remove its horns / tail, and if so, does it hurt?

Yes, the horns and tail of a tiefling could be removed

No material specifies that they cannot, nor any mechanical effect or penalty for such mutilated typing. The closest we have is that the DMG, on page 272, includes an optional rule on persistent injuries that has examples that include severed limbs. For example, losing an arm:

You lose an arm or a hand. You can no longer hold anything with both hands, and you can hold only one object at a time. Magic like the regeneration spell can restore the lost appendix.

Therefore, losing a part of the body does not lead to a permanent loss of HP. However, another example is the "oozing wound", which reduces its maximum HP over time until the wound heals by magic or otherwise, so a maimed draw could suffer such damage due to lack of proper medical care:

Suppurating wound Its maximum hit point is reduced by 1 every 24 hours that the wound persists. If your maximum hit point drops to 0, you die. The wound heals if you receive magic healing. Alternatively, someone can tend to the wound and do a DC 15 Wisdom (Medicine) check once every 24 hours. After ten successes, the wound heals.

For a major head / face injury such as that caused by removing the horns, the "horrible scar" injury may be appropriate:

Horrible scar. It is disfigured to the extent that the wound cannot be easily hidden. You have a disadvantage in the Charisma controls (Persuasion)
and advantage in Charisma controls (Intimidation). Level 6 magic healing or higher, like healing and regenerating, removes the scar.

I'd also be inclined to say that a tifling that suddenly lacks its tail should be at a disadvantage in acrobatics and athletics testing for at least a while, since for any creature with such a large tail it will significantly affect its balance, but it could get used to with some time.

In any case, whether or not permanent hit point is incurred, removal of the appendages would be a significant physical trauma that would definitely cause damage to the hit point at that time, which would need to be healed like any other.

No, they will not grow again without magical assistance.

In nature, damaged horns may or may not grow back depending on the extent of damage done and the type of horn. True horns, like those owned by goats and cattle, are live bones with a keratin exterior and have a blood supply and such. They are not like antlers (which are dead bones, shedding and regrowing every year) or other horn-like growths (like rhinoceros, which are pure keratin and will regrow if cut, like a fingernail).

The depictions of tiefling horns in official works of art are more like true horns in the style of bovine animals. Splinters to the outside of a true horn will likely regrow and limited damage to the bone nucleus could heal, but if it breaks or is completely removed, they will not re-grow on their own (although a broken horn can fix like bone broken and can heal again together).

A severed tail is unlikely to grow back much, if most creatures that lose the tail can grow a very short stump again at best.

In both cases, be subject to Regeneration the spell would immediately cause the lost appendages to start regenerating:

The severed body members of the target (fingers, legs, tails, etc.), if any, are restored after 2 minutes.

Based on this question, a character probably can't choose which parts of the body it would regenerate if affected by the spell, so regeneration of the horns and tail would occur even if the subject found that an undesirable effect.

In the general case, assume that people heal as they do in real life unless otherwise noted. If you pull out a person's teeth, they don't grow back, nor do you cut parts of their ears.

What are long tail and short tail keywords?

What are long tail and short tail keywords?

unit: snake tail in snake game not working properly

I am making a simple snake game in Unity 2D. And the snake's tail doesn't follow just behind the snake's head as it should.

This is what is happening:

This is my code:

using System.Collections;

using System.Collections.Generic;
using UnityEngine;
using System.Linq;

SnakeMovement public class: MonoBehavior

private Vector3 fp;   //First touch position
private Vector3 lp;   //Last touch position

private float dragDistance;  //minimum distance for a swipe to be registered
private float speed = 13f;

private Rigidbody2D rb;
private Vector2 moveVelocity;

public GameObject tail;

public List tailPositions;

void Start() {
    dragDistance = Screen.height * 5 / 100; //dragDistance is 5% height of the screen
    rb = GetComponent();

void Update() {

    if (Input.touchCount == 1) // user is touching the screen with a single touch
        Touch touch = Input.GetTouch(0); // get the touch
        if (touch.phase == TouchPhase.Began) //check for the first touch
            fp = touch.position;
            lp = touch.position;
        else if (touch.phase == TouchPhase.Moved) // update the last position based on where they moved
            lp = touch.position;
        else if (touch.phase == TouchPhase.Ended) //check if the finger is removed from the screen
            lp = touch.position;  //last touch position. Ommitted if you use list

            //Check if drag distance is greater than ?% of the screen height
            if (Mathf.Abs(lp.x - fp.x) > dragDistance || Mathf.Abs(lp.y - fp.y) > dragDistance)
            {//It's a drag
             //check if the drag is vertical or horizontal

                if (Mathf.Abs(lp.x - fp.x) > Mathf.Abs(lp.y - fp.y)) {   //If the horizontal movement is greater than the vertical movement...
                    if ((lp.x > fp.x)) {   //Right swipe
                        if(moveVelocity != Vector2.left) {
                            moveVelocity = Vector2.right;
                    else {   //Left swipe
                        if(moveVelocity != Vector2.right) {
                            moveVelocity = Vector2.left;
                else {   //the vertical movement is greater than the horizontal movement
                    if (lp.y > fp.y) {   //Up swipe
                        if(moveVelocity != Vector2.down) {
                            moveVelocity = Vector2.up;
                    else {   //Down swipe
                        if(moveVelocity != Vector2.up) {
                            moveVelocity = Vector2.down;



void FixedUpdate() {
    Vector3 lastPos = transform.position;

    rb.MovePosition(rb.position + moveVelocity * speed * Time.deltaTime);

    if (tailPositions.Count >= 1) {
        tailPositions.Last().position = lastPos;
        tailPositions.Insert(0, tailPositions.Last ());
        tailPositions.RemoveAt(tailPositions.Count - 1);

void OnTriggerEnter2D(Collider2D trigger) {
    Vector2 spawnPos = new Vector2(5, 5);

    if (trigger.tag == "Food") {
        GameObject newTail = Instantiate(tail, spawnPos, Quaternion.identity) as GameObject;
        newTail.transform.parent = GameObject.Find("Tail Holder").transform;


Thank you very much for taking the time to help me.

Who uses Long Tail Pro and Benefits?

I am considering Long tail pro and wondering who has experience with it and finds it beneficial.

How to find long tail keywords?

ttp: // "">

How to find long tail keywords? The | Web Hosting Talk

& # 39;);
var sidebar_align = & # 39; right & # 39 ;;
var content_container_margin = parseInt (& # 39; 350px & # 39;);
var sidebar_width = parseInt (& # 39; 330px & # 39;);
// ->

  1. How to find long tail keywords?

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java – Codility Fish solution (tail)

Today I tried a Codility "Fish" exercise (, and I have to say I found it:
1) Not necessarily "easy" as the page implies, AND
2) Very satisfactory to realize at the end.

My solution is a bit playful, and I was wondering if anyone could take a look and let me know if this is a correct way to solve this problem. All comments will be appreciated.

import java.util.ArrayDeque;

// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");

class Solution {
    public int solution(int() A, int() B) {

        ArrayDeque safetyPool = new ArrayDeque();
        ArrayDeque activePool = new ArrayDeque();

        for (int i = 0; i < A.length; i++) {
            activePool.offer(Fish.cFish(A(i), B(i)));

        while(!activePool.isEmpty()) {
            // System.out.println(safetyPool + " " + activePool);
            Fish safeFish = safetyPool.peekLast();
            Fish swimmingFish = activePool.peekFirst();

            if (safeFish != null) {
                if (safeFish.dir == 1) {
                    if (safeFish.dir != swimmingFish.dir) {
                        if (safeFish.att > swimmingFish.att) {
                        } else {
                    } else {
                } else {
            } else {
        return safetyPool.size();

class Fish {
    public int att;
    public int dir;

    public Fish(int att, int dir) {
        this.att = att;
        this.dir = dir;

    public static Fish cFish(int att, int dir) {
        return new Fish(att, dir);

    public String toString() {
        return String.format("Fish(att: %d, dir: %d)", att, dir);

Use of long tail keyword padding

Keyword padding is bad, right? But what if you add keywords that make sense together in a long tail keyword?

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