Is a +1 chain shirt strictly inferior to a breastplate?

My character really likes chain shirts. He much prefers them to other armor like for instance a breastplate.

I thought maybe I could make up for his tastes with a piece of magical armor, since usually magic items are considered stronger than mundane ones. But I’m realising that it’s still not quite as good. There are two benefits to mundane armor that I can find, and no benefits to magic armor (besides the AC bonus).

  1. Magic items can be suppressed by the antimagic field spell, and there seems to be no way to make magic armor not work that wouldn’t also work on magic armor. With mundane weapons some creatures will be able to resist, so magic on weapons is great. Not so with magical armor, as far as I know.

  2. A Forge Cleric can use their Blessing of the Forge ability on nonmagical armor, but can’t use it on magical armor.

At 1st level, you gain the ability to imbue magic into a weapon or armor. At the end of a long rest, you can touch one nonmagical object that is a suit of armor or a simple or martial weapon. Until the end of your next long rest or until you die, the object becomes a magic item, granting a +1 bonus to AC if it’s armor or a +1 bonus to attack and damage rolls if it’s a weapon.

Is there anything a +1 chain shirt has that a mundane breastplate doesn’t have?

Footer ubicado solo en la parte inferior de la página sin espacios de alto y ancho en

Estoy creando una app en ASP.NET y para acomodar el footer abajo se me esta complicando al igual que poner el ancho del 100% de la página, cosa que no se quiere aplicar y se mantiene centrada, por cierto estoy usando libreria de estilos de Bootstrap. Este es el código html / aspx del footer de la página maestra:

<footer class="page-footer font-small bg-dark" style="padding: 0; margin: 0; width: 100%; bottom: 0;">                 <!-- Footer Links -->                 <div class="container-fluid text-center text-md-left">                     <!-- Grid row -->                     <div class="row">                         <!-- Grid column -->                         <div class="col-md-6 mt-md-0 mt-3">                             <!-- Content -->                             <h3 style="color: white;">Acerca de Nosotros</h3>                             <p class="lead" style="color: white;">Texto</p>                             <p style="color: white;">Esta es nuestra ubicación</p>                             <iframe src="!1m18!1m12!1m3!1d3965.716385745309!2d-75.57092518517804!3d6.300947927458416!2m3!1f0!2f0!3f0!3m2!1i1024!2i768!4f13.1!3m3!1m2!1s0x8e442f25d6670d4d%3A0x8043999e5e767b96!2sSENA%20-%20Centro%20de%20Tecnolog%C3%ADa%20de%20la%20Manufactura%20Avanzada!5e0!3m2!1ses!2sco!4v1570754942399!5m2!1ses!2sco" width="400" height="100" style="border: 0;"></iframe>                         </div>                         <!-- Grid column -->                         <hr class="clearfix w-100 d-md-none pb-3">                         <!-- Grid column -->                         <div class="col-md-3 mb-md-0 mb-3">                             <!-- Links -->                             <p class="lead" style="color: white;">¿Necesitas ayuda?</p>                             <ul class="list-unstyled">                                 <li>                                     <a style="color: white;">Contactenos</a>                                 </li>                             </ul>                         </div>                         <!-- Grid column -->                     </div>                     <!-- Grid row -->                 </div>                 <!-- Copyright -->                 <div class="footer-copyright text-center py-1 blue" style="color: white;">© 2019 Derechos Reservados de Jose Quintero</div>             </footer> 

AdMobs/ AdView – Anuncio na parte inferior

adicionei o anúncio conforme abaixo. Porém esta centralizado no meio da tela, gostaria de adicionar na parte de baixo. Já adicionei o android:layout_alignParentBottom=”true” mas nada:

<?xml version="1.0" encoding="utf-8"?> 

<include     layout="@layout/app_bar"     android:layout_width="match_parent"     android:layout_height="match_parent" />  <     android:id="@+id/nav_view"     android:layout_width="wrap_content"     android:layout_height="match_parent"     android:layout_gravity="start"     android:fitsSystemWindows="true"     app:headerLayout="@layout/header_main"     app:menu="@menu/activity_main_drawer"     android:background="@color/colorBlue"     app:itemTextColor="@drawable/drawer_item"     app:itemBackground="@drawable/selector_menu"     app:itemTextAppearance="@style/MenuItem"     app:paddingStart="@dimen/space8"/> < xmlns:ads=""     android:id="@+id/adView"     android:layout_width="wrap_content"     android:layout_height="wrap_content"     android:layout_alignParentBottom="true"     android:layout_marginBottom="681dp"     ads:adSize="BANNER"     ads:adUnitId="xxxxxx"></> 

Limit superior and inferior when one part diverges

How can I find the limit superior and inferior of given sequence: $ x_n = (1 + \frac{1}{2n})\cos{\frac{n\pi }{3}}$ as $ n \in \mathbb N $

I did the following: since $ \lim_{n\to\infty}(1 + \frac{1}{2n}) = 1$ and the second term’ limit oscillates between -1 and 1, I decided that the supremum should be $ 1$ and infimum should be $ -1$ . But this is incorrect answer.

What I do wrong? Thank you.

Limit inferior of $\mathbb{E}_x [f(X_T)]/T$

Assume that for a one dimensional diffusion process with natural boundaries we have that $ $ \liminf_{T \to \infty} X_T \leq y$ $ where $ y$ is a constant. Can we prove that for every $ f \in C^2$ we have $ $ \liminf_{T \to \infty} \frac{1}{T} \mathbb{E}_x \left[ f(X_T)\right]=0.$ $ If not, what should we assume more for the diffusion or $ f$ ? My first thoughts were to use some kind of convergence theorem to change the order of limit and the integral..