I have had several business loans and understand that this is not by any means typical.  I noticed that for a year my payments were not decreasing the principal on the loan. When I asked the bank why, I found out that at some point my payments were getting applied to  principal only. Now I am paying interest off that was not paid for 6 months or so.  My banker states that he can change all the interest payments to principal payments. I am confused to why this would be. If I make all my principal payments first then would the bank lose a substantial amount of interest?  This has happened on 2 of the 3 loans I have looked at so far.  If they are willing to change all the payments to principal only,  would this be beneficial to paying less interest ultimately? I assume there would be an interest account accruing somewhere that would need to be paid off at the end of the loan.  I understand that typically you have a loan balance that would include interest and principal.  My balance owed did not change when I continued to make same payment? It gets applied to interest. The balance on the statement must not be a true balance. There must be interest owed above the balance showed but why would they do this to start with? They applied full payments to principle only first in order for interest to get to be more than several payments.
I have had several business loans and understand that this is not by any means typical.  I noticed that for a year my payments were not decreasing the principal on the loan. When I asked the bank why, I found out that at some point my payments were getting applied to principal only. Now I am paying interest off that was not paid for 6 months or so.  My banker states that he can change all the interest payments to principal payments. I am confused to why this would be. If I make all my principal payments first then would the bank lose a substantial amount of interest?  This has happened on 2 of the 3 loans I have looked at so far.  If they are willing to change all the payments to principal only, would this be beneficial to paying less interest ultimately? I assume there would be an interest account accruing somewhere that would need to be paid off at the end of the loan.  I understand that typically you have a loan balance that would include interest and principal. My balance owed did not change when I continued to make same payment? It gets applied to interest. The balance on the statement must not be a true balance. There must be interest owed above the balance showed but why would they do this to start with? They applied full payments to principle only first in order for interest to get to be more than several payments
What are the norms in Ito isometry? Itō isometry from :     Let $W : [0, T] \times \Omega \to \mathbb{R}$ denote the canonical   real-valued Wiener process defined up to time $T &gt; 0$, and let $X :  [0, T] \times \Omega \to \mathbb{R}$ be a stochastic process that is   adapted to the natural filtration $\mathcal{F}_{*}^{W}$ of the Wiener   process. Then $$      \mathbb{E} \left[ \left( \int_{0}^{T} X_{t} \, \mathrm{d} W_{t} \right)^{2} \right] = \mathbb{E} \left[ \int_{0}^{T} X_{t}^{2} \,  \mathrm{d} t \right], $$ where $\mathbb{E}$ denotes expectation with   respect to  $\gamma$. In other words, the Itō   stochastic integral, as a function, is an isometry of normed vector   spaces with respect to the norms induced by the inner products $$      ( X, Y )_{L^{2} (W)} := \mathbb{E} \left( \int_{0}^{T} X_{t} \, \mathrm{d} W_{t} \int_{0}^{T} Y_{t} \, \mathrm{d} W_{t} \right) =  \int_{\Omega} \left( \int_{0}^{T} X_{t} \, \mathrm{d} W_{t}  \int_{0}^{T} Y_{t} \, \mathrm{d} W_{t} \right) \, \mathrm{d} \gamma  (\omega) $$ and $$      ( A, B )_{L^{2} (\Omega)} := \mathbb{E} ( A B ) = \int_{\Omega} A(\omega) B(\omega) \, \mathrm{d} \gamma (\omega). $$   I was wondering what the two normed spaces are and what their norms are, so that the two normed spaces are isometric wrt their norms?  Thanks and regards! Consider a common proof of the uncountability of $(0,1]$, as presented  for example:  We assume that the reals can be arranged in a sequence $x_k$, represent every number in $x_k$ by its nonterminating decimal expansion, use the diagonal argument to create a sequence of decimal digits that differs from the nonterminating decimal expansion of each number in $x_k$ and then claim that this sequence of digits so generated must be the decimal expansion of some number not in $x_k$.  My problem is with this last step. Could it not be the case that the new sequence of digits is just the terminating decimal expansion of some number already in $x_k$?  Would it not be more correct to use the sequence $x_k$ to generate a sequence of all (both terminating and non-terminating) decimal expansion of all numbers in $[0,1)$ and then apply the diagonal argument? Because the default 'Profile Graph' tool was not sufficient, I wrote a custom VBA script that creates scaled and exaggerated profile cross-sections in ArcGIS but I need more features:   Visualize more than 1 surface Visualize vertical and directional boreholes Ability to symbolize / edit the output Linked with underlying data - changes in terrain (or profile 3D line) reflected in output   A few years ago I tested an extension by A-Prime software called 'CrossView For ArcGIS' but I am not sure if it is compatible with ArcGIS 10 (Contacted A-Prime but they have not yet responded)   Area there any alternatives? Other 3rd party software? A functioning script? that can do this? Greiner in his book "Field Quantization" page 173, eq.(7.11) did this calculation:     ${\mathcal L}^\prime=-\frac{1}{2}\partial_\mu A_\nu\partial^\mu A^\nu+\frac{1}{2}\partial_\mu A_\nu\partial^\nu A^\mu-\frac{1}{2}\partial_\mu A^\mu\partial_\nu A^\nu $   $\space\space\space\space=-\frac{1}{2}\partial_\mu A_\nu\partial^\mu A^\nu+\frac{1}{2}\partial_\mu[A_\nu(\partial^\nu A^\mu)-(\partial_\nu A^\nu) A^\mu]$        The last term is a four-divergence which has no influence on the field equations. Thus the dynamics of the electromagnetic field (in the Lorentz gauge) can be described by the simple Lagrangian        ${\mathcal L}^{\prime\prime}=-\frac{1}{2}\partial_\mu A_\nu\partial^\mu A^\nu$     Yes, if it is a four-divergence of a vector whose 0-component doesn't contain time derivatives of the field, indeed according to the variational principle this four-divergence will not influence the field equation.  And actually I calculated the time-derivative dependence of 0-component of $[A_\nu(\partial^\nu A^\mu)-(\partial_\nu A^\nu) A^\mu]$, in which only $[A_0(\partial^0 A^0)-(\partial_0 A^0) A^0]$ could possibly contain time-derivative, which vanishes fortunately, so whatever the general case it doesn't matter in this present case.  But how can he seem to claim that it holds for a general four-divergence term,The last term is a four-divergence which has no influence on the field equations?  EDIT: I only assumed the boundary condition to be $A^\mu=0$ at spatial infinity, not at time infinity. And the variation of the action $S = \int_{t_1}^{t_2}L \, dt$ is due to the variation of fields which vanish at time, $\delta A^\mu(\mathbf x,t_1)=\delta A^\mu(\mathbf x,t_2)=0$, not having the knowledge of $\delta \dot A^\mu(\mathbf x,t_1)$ and $\delta \dot A^\mu(\mathbf x,t_2)$, which don't vanish generally, so the four-divergence term will in general contribute to the action, $$\delta S_j=\delta \int_{t_1}^{t_2}dt\int d^3\mathbf x \partial_\mu j(A(x),\nabla A(x),\dot A(x))^\mu =\delta \int_{t_1}^{t_2}dt\int d^3\mathbf x \dot j^0 =\int d^3\mathbf x [\delta j(\mathbf x, t_2)^0-\delta j(\mathbf x, t_1)^0]$$ which does not vanish in general! What is the JavaScript >>> operator and how do you use it? Why can I only change my Stack Overflow name once every 30 days? Prove that for any positive integer $n$, $$2\sqrt{n + 1} − 2 \le 1 +\frac 1 {\sqrt 2}+\frac 1 {\sqrt 3}+ \dots +\frac 1 {\sqrt n} \le 2\sqrt n − 1$$ Progress I think Riemann sum should be used for the middle term. I got the limit as $n\to \infty$ of the function inside using Riemann sum but what I cannot get are the lower and upper bound. Emboss text onto curved surface I am fairly new to blender and I am trying to do something which I am assuming is fairly straight forward with no success. All I'm looking to do is emboss some text onto the curved part of a yogurt pot. Image attached below. What is the quickest and easiest way of doing this?  Thanks in advance Movie with "Where do the tubes go?" I'm trying to find a movie with an underground facility with people wearing white suits. The people have been affected such that they show no curiosity. There is one person that does and asks one of his co-workers where a tube leads to.      At the end there is an uprising where everyone gets to see the surface and sunlight.   What is the name of this movie? WP_query 'orderby=none' Problem I have another database which stores post's IDs and I want do display them using WP_query to use the WP default pagination. I'm using orderby => none to preserve the original order, but the result reorders them by IDs.  $ids = array (60, 23, 78, 46, 105, 130)  $args = array (     'posts_per_page' =&gt; -1,     'post__in' =&gt; $ids,     'orderby' =&gt; 'none' );  $query = new WP_Query ( $args );  while ( have_posts() ) : the_post();     echo '&lt;li&gt;';     the_title();     echo '&lt;/li&gt;'; endwhile;   Could anyone help me?  Thanks, Romulo De Lazzari How to reconnect a logically disconnected USB device? Repeat command n times? Is it possible to define a command, which repeats the following command n-times? Call it for example \Repeat, then   \Repeat[4] \command{...}    should be equivalent to   \command{...} \command{...} \command{...} \command{...} C non-blocking keyboard input I'm trying to write a program in C (on Linux) that loops until the user presses a key, but shouldn't require a keypress to continue each loop.  Is there a simple way to do this? I figure I could possibly do it with select() but that seems like a lot of work.  Alternatively, is there a way to catch a ctrl-c keypress to do cleanup before the program closes instead of non-blocking io? I have a header file  x.h which is included by more than one *.c source files. This header file has some structure variables defined.  I have put multiple inclusion prevention guard at the beginning of the header file as:  #ifndef X_H #define X_H ... .. //header file declarations and definitons.   #endif//X_H   On building I get linker errors related to multiple definitions. I understand the problem.   Won't a multiple inclusion prevention guard at the top of header file as I have, prevent multiple inclusions of the header file x.h and thereby avoid multiple definitions of the variables that are there in x.h? #pragma once does not work on this particular compiler, so what is the solution?  Someone had posted  answer to a similar question. It doesn't seem to work for me. How does this solution work? PDOException “could not find driver” Is it possible to dual boot two OS's at the same time? Is division of matrices possible? I came across the following problem in a book:  Give a combinatorial proof of  $$ {n \choose 0} + {n \choose 2} + {n \choose 4} + \, \, ... \, = {n \choose 1} + {n \choose 3} + {n \choose 5} + \, \, ...$$ using the "weirdo" method (i.e., where one of the elements is chosen as special and included-excluded -- I'm sure you get the idea).  After days of repeated effort, the proof has failed to strike me. Because every time one of the elements is excluded, the term would be ${n-1 \choose k}$ and not $ {n \choose k}$, which is not the case in either of the sides of the equation. I want to install Oracle's JRE and to update to the latest version with the Software Updater when they released. Is there a Ubuntu package that is provided by Canonical or Oracle?  Before release Java 7, I followed  to install Java 6.  But it doesn't work for Java 7. There is no package sun-java7-xxx. How can you install Java 7? The difference between sys.stdout.write and print?