Summation with Multiple Indices

If your question was specifically about simplifying this particular sum, see Elaqqad's answer for a combinatorial argument on what it is equal to. If your question is more about how to manually compute the sum and how to interpret the notation, then continue reading mine.Capital Sigma Notation can have several different ways of writing what the set of values you sum over are.

In this case, for the summation: $sumlimits_r,s,tgeq 0texts.t.rstn$, I interpret it as summing the expression over all possible $r,s,tinmathbbZ$ such that the following conditions hold:$$begincases rgeq 0 sgeq 0 tgeq 0 rstnendcases$$In particular, there will be $binomn2n$ summands (seen from stars&bars). It doesn't matter in what way you choose to add the terms together (since there are a finite number of terms and addition is commutative), though if you wanted to do it by hand I would recommend Lexicographic order (a.

k.

a. Dictionary Order).

You would do it as: $(0,0,n), (0,1,n-1), (0,2,n-2), dots, (0,n,0), (1,0,n-1), (1,1,n-2),dots, (n-1,0,1), (n-1,1,0), (n,0,0)$where you order the entries according to the the size of the earliest difference.For an explicit example, with $n2$ you would have$$binomm_10binomm_20binomm_32 binomm_10binomm_21binomm_31 binomm_10binomm_22binomm_30 binomm_11binomm_20binomm_31 binomm_11binomm_21binomm_30 binomm_12binomm_20binomm_30$$

How would the following summation work?

$sum_r,s,t ge 0_rstn binomm_1r binomm_2s binomm_3t$

How would you choose the value for the next integer in the series?

For example, for n2. Either r,s, or t 2. Or r 1 and s 1 (or any combination thereof)

I think the inclusion-exclusion principle would be used but I'm don't know how it would be applied.

Sorry if this is a duplicate question. I wasn't sure how to word it.

·OTHER ANSWER:

How would the following summation work?

$sum_r,s,t ge 0_rstn binomm_1r binomm_2s binomm_3t$

How would you choose the value for the next integer in the series?

For example, for n2. Either r,s, or t 2. Or r 1 and s 1 (or any combination thereof)

I think the inclusion-exclusion principle would be used but I'm don't know how it would be applied.

Sorry if this is a duplicate question. I wasn't sure how to word it.

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How Do I Stop a Widget From Displaying on Mobile Site?
The most obvious answers is to use WordPress plugin. You can check this plugin of mine : Widget Options for WordPress which is available for free on the repository : and easily hide widgets on mobile and other devices. You can check the screenshot below on how it's integrated.Alternatively, you can use custom CSS. Just make sure you know the Widget ID and add something like this on your style.cssOn my main site I have used the search widget in the sidebar.However, the mobile theme I am using (minileven) already has a search box built into its menu bar. This results in a second search box in the sidebar (which appears after the post content) due to the widget.How do I stop the search widget appearing on the mobile site?This is the code for sidebar.php from the mobile theme: Alternatively, would it be better not to use the search sidebar widget and have the search box hardcoded into the main site theme? Is it usual for WordPress themes to do that? (I am planning on publicly releasing the WordPress theme I have made).·OTHER ANSWER:On my main site I have used the search widget in the sidebar.However, the mobile theme I am using (minileven) already has a search box built into its menu bar. This results in a second search box in the sidebar (which appears after the post content) due to the widget.How do I stop the search widget appearing on the mobile site?This is the code for sidebar.php from the mobile theme: Alternatively, would it be better not to use the search sidebar widget and have the search box hardcoded into the main site theme? Is it usual for WordPress themes to do that? (I am planning on publicly releasing the WordPress theme I have made).
Use of Classes for Lua Extensions
The system that Supreme Commander uses is that you can subclass classes, then you define the class-specific functions and data like so:The way the code is set up, is all of the classes that have to be in C code are exposed to the lua environment for subclassing. The above method is much like your first, and i would recommend that you take it. It makes it quite usable for both programmers and modders (of which i'm both). I started out programming to this model, and while i didn't completely understand things, it worked perfectly well and made sense to meI'm asking about a very small domain. One-off extension scripts. IE, defining a new weapon for scorched earth.When providing and API for small extension I've seen two approaches.The API exposes classes that the extender then subclasses, overriding the needed methods.--# weapons/flame_missile.lua--#extender pulls in a predefined weapon base classrequire "weapon.missile"--# luabind syntax for classesclass "flame_missile" (missile)function flame_missile:__init() self.hotness 10 self:set_cost(42)endfunction flame_missile:on_hit( who ) who:take_damage(self.hotness) who:ignite()endIn the other approach the api just exposes accessors and sandboxes the script, re-executing the file with each new missile and using the globals as the instance's state.--# weapons/flame_missile.luahotness 10cost 42--# extender just knows that an on_hit function will be called--# when the missile hits something.function on_hit( who ) who:take_damage(hotness) who:ignite()endNOTE: in my example who's api is OO. I'm not interested in whether OO should be used in the extension API. I'm more interested if OO should be used to incorporate user extensions into the game.The first one feels more C-y. So I'm a little more comfortable with from a software engineering standpoint. However, one-off scripts don't need to fit together into a larger architecture. Further, they could be written by less proficient coders, so all the fancy OO might be lost on them.I really like how concise the sandbox approach is. But it's a little limiting (only one missile per file, inheriting behavior from another weapon is no longer possible. I'd really like to define my extension api like this but I'm a little wary as it's a radical departure from classic C programming style.Which method do you prefer?Have you had any bad experiences with one or the other?Is there an even better way to elegantly incorporate extensions into the game?·OTHER ANSWER:I'm asking about a very small domain. One-off extension scripts. IE, defining a new weapon for scorched earth.When providing and API for small extension I've seen two approaches.The API exposes classes that the extender then subclasses, overriding the needed methods.--# weapons/flame_missile.lua--#extender pulls in a predefined weapon base classrequire "weapon.missile"--# luabind syntax for classesclass "flame_missile" (missile)function flame_missile:__init() self.hotness 10 self:set_cost(42)endfunction flame_missile:on_hit( who ) who:take_damage(self.hotness) who:ignite()endIn the other approach the api just exposes accessors and sandboxes the script, re-executing the file with each new missile and using the globals as the instance's state.--# weapons/flame_missile.luahotness 10cost 42--# extender just knows that an on_hit function will be called--# when the missile hits something.function on_hit( who ) who:take_damage(hotness) who:ignite()endNOTE: in my example who's api is OO. I'm not interested in whether OO should be used in the extension API. I'm more interested if OO should be used to incorporate user extensions into the game.The first one feels more C-y. So I'm a little more comfortable with from a software engineering standpoint. However, one-off scripts don't need to fit together into a larger architecture. Further, they could be written by less proficient coders, so all the fancy OO might be lost on them.I really like how concise the sandbox approach is. But it's a little limiting (only one missile per file, inheriting behavior from another weapon is no longer possible. I'd really like to define my extension api like this but I'm a little wary as it's a radical departure from classic C programming style.Which method do you prefer?Have you had any bad experiences with one or the other?Is there an even better way to elegantly incorporate extensions into the game?
Definition by Recursion: Why Is the Existence Part Not (almost) Obvious?
In fact your proof is a circular argument. To prove something by induction you first have to have the something. To define something "inductively" (loose terminology) is definition by recursion.You can define a recursive function $f$ for a finite range of $ninmathbb N$, say $n le N$ by saying $f(1) e, f(2) k(e), ...... f(n) k^n-1(e)$ but why would this function exist for all values of $ninmathbb N$ ? - you can't write an infinite specification for the function. So, you have actually relied on the Theorem of Recursion (i.e. in one form, the statement you are trying to prove) when you assume the existence of $f$ for all $ninmathbb N$ (and you are then using induction to prove $f$ has the property you have assumed it to have).The longer proofs that you may have seen might in outline go as follows:(1) if $f$ exists it would be represnted as a subset of N x H, i.e. a set of ordered pairs where each $ninmathbb N$ is represented in exactly one ordered pair.(2) whatever values $f$ might take N x H contains them(3) the powerset of N x H, $mathscr P(N mathrm x H)$ contains all possible subsets of N x H(3) using specification, one can obtain a subset $mathscr D$ of $mathscr P(N mathrm x H)$ with the property that all the elements of $mathscr D$ (which are subsets of N x H) include $(1, e)$ , and if $(n, h)$ is in such an element of $mathscr D$ then so is $(n 1, k(h))$(4) The intersetion of all elements of $mathscr D$ is formed and shown to be a function and (by definition) to be recursive.(5) the function $f$ is then shown to be uniqueI saw the following statement.Let $H$ be a set, let $ein H$ and let $k:Hrightarrow H$ be a function. Then there is a unique function $f:mathbbNrightarrow H$ such that $f(1)e$, and that $fcirc skcirc f$.(where $s:mathbbNrightarrowmathbbN$ is the successor function)On the 'existence' part alone, my problem is that I can't see what the flaw is in my argument.We know $f(1)$, and if ,for some $ninmathbbN$, we are given $f(n)$ then we define $f(s(n)):k(f(n))$; so we know $ f(s(n))$ .By induction $f$ is defined on $mathbbN$.Maybe the "proof" is too informal. Some examples to illustrate may be helpful.Thanks
Title of Novel About Amateur Scientist Who Discovers Earth's Magnetic Field Changes Orientation
This is The HAB Theory, by Allan Eckert. Protagonist is Herbert Allan Boardman (HAB), an electrical engineer who discovers at age 94 that the Earth undergoes these magnetic reversals, and does stage a faux assassination attempt on the President to get attention for his theories.It was originally published in 1976, and while out of print for many years it has recently been re-released so should be available. Magnetic pole reversal is a known phenomenon, and while we are "overdue" for one, current theories think that it would not be a catastrophic event: NASA page on reversal.I'm looking for the title/author of a sci-fi book I read in the mid 90's but was probably at least 5-10 years older than that.The basic premise was of a older guy who as an amateur scientist had discovered that the Earth's magnetic field changed orientation every few thousand years, and was currently long overdue. One of the main things I can remember is that early on in the book he used an attempted assassination of the US President (using wax bullets instead of the real thing), in an attempt to get the attention of the authorities.There was a lot of other stuff about how this would explain the myths of Atlantis and the Egyptians & Mayans having such advanced technologies. In the end people bought into his theory, but we only just getting prepared when the lights went out...Any ideas?Thanks.·OTHER ANSWER:I'm looking for the title/author of a sci-fi book I read in the mid 90's but was probably at least 5-10 years older than that.The basic premise was of a older guy who as an amateur scientist had discovered that the Earth's magnetic field changed orientation every few thousand years, and was currently long overdue. One of the main things I can remember is that early on in the book he used an attempted assassination of the US President (using wax bullets instead of the real thing), in an attempt to get the attention of the authorities.There was a lot of other stuff about how this would explain the myths of Atlantis and the Egyptians & Mayans having such advanced technologies. In the end people bought into his theory, but we only just getting prepared when the lights went out...Any ideas?Thanks.
Apache Always Serving First Virtual Host
As for my experience this can happen in the following situation:firstsite.com has dns 1.2.3.4 and ip in vhost 1.2.3.4 or *secondsite.com has dns 1.2.3.4 and ip in vhost is 1.2.3.5.Both 1.2.3.4 and 1.2.3.5 are ips of the problematic server and apache is listening on both ips.BUT as for the few logs and details you provided it is hard to find if this is actually the case.I have seen this asked about few times, but surprisingly no solutions worked for me:Yes, I have used "sudo a2ensite com.secondwebsite.conf"Yes, I have used "sudo /etc/init.d/apache2 reload"Yes, I have used "sudo /etc/init.d/apache2 restart"Yes, I have tried putting both virtual hosts into one file (/etc/apache2/sites-available/default), adding "NameVirtualHost *:80" on top of it and removing it from "/etc/apache2/ports.conf"Yes, I have used "sudo chmod 777 /var/www/secondwebsite"Whatever I do, secondwebsite.com keeps showing firstwebsite.com. Does anyone have any idea what might be causing this?Here is my "/etc/apache2/sites-available/default" ServerAdmin admin@gmail.com ServerName firstwebsite.com ServerAlias www.firstwebsite.com DocumentRoot /var/www Options FollowSymLinks AllowOverride None Options Indexes FollowSymLinks MultiViews AllowOverride None Order allow,deny allow from all ScriptAlias /cgi-bin/ /usr/lib/cgi-bin/ AllowOverride None Options ExecCGI -MultiViews SymLinksIfOwnerMatch Order allow,deny Allow from all ErrorLog $APACHE_LOG_DIR/error.log # Possible values include: debug, info, notice, warn, error, crit, # alert, emerg. LogLevel warn CustomLog $APACHE_LOG_DIR/access.log combined Alias /static /home/user/firstwebsite/firstwebsite/static Order allow,deny Allow from all Alias /media /home/user/firstwebsite/firstwebsite/site_media/media Order allow,deny Allow from all Order allow,deny Allow from all WSGIDaemonProcess firstwebsite WSGIProcessGroup firstwebsite WSGIScriptAlias / /home/user/firstwebsite/firstwebsite/wsgi.py My "/etc/apache2/sites-available/com.secondwebsite.conf" ServerAdmin admin@gmail.com ServerName secondwebsite.com ServerAlias www.secondwebsite.com DocumentRoot /var/www/secondwebsite/public_html ErrorLog $APACHE_LOG_DIR/secondwebsite_error.log # Possible values include: debug, info, notice, warn, error, crit, # alert, emerg. LogLevel warn CustomLog $APACHE_LOG_DIR/access.log combined My "/etc/apache2/ports.conf" # If you just change the port or add more ports here, you will likely also # have to change the VirtualHost statement in # /etc/apache2/sites-enabled/000-default # This is also true if you have upgraded from before 2.2.9-3 (i.e. from # Debian etch). See /usr/share/doc/apache2.2-common/NEWS.Debian.gz and # README.Debian.gz NameVirtualHost *:80 Listen 80 # If you add NameVirtualHost *:443 here, you will also have to change # the VirtualHost statement in /etc/apache2/sites-available/default-ssl # to # Server Name Indication for SSL named virtual hosts is currently not # supported by MSIE on Windows XP. Listen 443 Listen 443 Result of sudo /usr/sbin/apache2ctl -S VirtualHost configuration: wildcard NameVirtualHosts and _default_ servers: *:80 is a NameVirtualHost default server firstwebsite.com (/etc/apache2/sites-enabled/000-default:1) port 80 namevhost firstwebsite.com (/etc/apache2/sites-enabled/000-default:1) port 80 namevhost secondwebsite.com (/etc/apache2/sites-enabled/com.secondwebsite.conf:1) Syntax OK·OTHER ANSWER:I have seen this asked about few times, but surprisingly no solutions worked for me:Yes, I have used "sudo a2ensite com.secondwebsite.conf"Yes, I have used "sudo /etc/init.d/apache2 reload"Yes, I have used "sudo /etc/init.d/apache2 restart"Yes, I have tried putting both virtual hosts into one file (/etc/apache2/sites-available/default), adding "NameVirtualHost *:80" on top of it and removing it from "/etc/apache2/ports.conf"Yes, I have used "sudo chmod 777 /var/www/secondwebsite"Whatever I do, secondwebsite.com keeps showing firstwebsite.com. Does anyone have any idea what might be causing this?Here is my "/etc/apache2/sites-available/default" ServerAdmin admin@gmail.com ServerName firstwebsite.com ServerAlias www.firstwebsite.com DocumentRoot /var/www Options FollowSymLinks AllowOverride None Options Indexes FollowSymLinks MultiViews AllowOverride None Order allow,deny allow from all ScriptAlias /cgi-bin/ /usr/lib/cgi-bin/ AllowOverride None Options ExecCGI -MultiViews SymLinksIfOwnerMatch Order allow,deny Allow from all ErrorLog $APACHE_LOG_DIR/error.log # Possible values include: debug, info, notice, warn, error, crit, # alert, emerg. LogLevel warn CustomLog $APACHE_LOG_DIR/access.log combined Alias /static /home/user/firstwebsite/firstwebsite/static Order allow,deny Allow from all Alias /media /home/user/firstwebsite/firstwebsite/site_media/media Order allow,deny Allow from all Order allow,deny Allow from all WSGIDaemonProcess firstwebsite WSGIProcessGroup firstwebsite WSGIScriptAlias / /home/user/firstwebsite/firstwebsite/wsgi.py My "/etc/apache2/sites-available/com.secondwebsite.conf" ServerAdmin admin@gmail.com ServerName secondwebsite.com ServerAlias www.secondwebsite.com DocumentRoot /var/www/secondwebsite/public_html ErrorLog $APACHE_LOG_DIR/secondwebsite_error.log # Possible values include: debug, info, notice, warn, error, crit, # alert, emerg. LogLevel warn CustomLog $APACHE_LOG_DIR/access.log combined My "/etc/apache2/ports.conf" # If you just change the port or add more ports here, you will likely also # have to change the VirtualHost statement in # /etc/apache2/sites-enabled/000-default # This is also true if you have upgraded from before 2.2.9-3 (i.e. from # Debian etch). See /usr/share/doc/apache2.2-common/NEWS.Debian.gz and # README.Debian.gz NameVirtualHost *:80 Listen 80 # If you add NameVirtualHost *:443 here, you will also have to change # the VirtualHost statement in /etc/apache2/sites-available/default-ssl # to # Server Name Indication for SSL named virtual hosts is currently not # supported by MSIE on Windows XP. Listen 443 Listen 443 Result of sudo /usr/sbin/apache2ctl -S VirtualHost configuration: wildcard NameVirtualHosts and _default_ servers: *:80 is a NameVirtualHost default server firstwebsite.com (/etc/apache2/sites-enabled/000-default:1) port 80 namevhost firstwebsite.com (/etc/apache2/sites-enabled/000-default:1) port 80 namevhost secondwebsite.com (/etc/apache2/sites-enabled/com.secondwebsite.conf:1) Syntax OK
Viscosity of Ideal Gas From Dimensional Analysis
Your intuition is wrong on this. Consider one-dimensional steady flow, say in the $x$-direction, with a velocity gradient in the $y$-direction. Thus the particles at a given level have average velocity $$barmathbf u(u(y), 0, 0)^T,$$ and fluctuating velocities $$mathbf u'(u', v', w')^T.$$ Let's consider particles that at time $t_0$ are located at $(x,y_0)^T$, which have velocities $mathbf u(u_0u', v', w')^T.$ These particles will, on average, travel a distance of the mean free path length $l$ at that velocity, before hitting other particles. The particles will thus have migrated to a different $y$ position, where the average particle velocity will be $$barmathbf u(y)(u(y_0)(y-y_0)fracpartial upartial y, 0, 0)^T.$$ Notice that the average difference in the $x$-component of the velocity of such particles will therefore be proportional to the mean free path $l$ times an integral $I$ over the distribution of $v'$ and $w'$ velocities which does not matter here: We have $y-y_0I,l$. The mean velocity difference for such particles is therefore just $barDelta uI,l,(partial u/partial y)$.Since the mean velocity is assumed to stay constant, such particles will have their velocity adjusted to the one at their new $y$-position. Viscous forces correspond to the work required to achieve this. These forces must therefore be proportional to the velocity gradient times the mean free path length.P.S.: Also see the derivation in the Wikipedia article on viscositySummaryFrom dimensional analysis I find that the dynamic viscosity of an ideal gas must depend on its pressure $p$, density $rho$ and mean molecular free path $l$ in this way:$$mu C sqrtrho p l.quad$$Here, $Cgeq0$ is a non-dimensional constant.However, I find it counter intuitive that the dynamic viscosity, the 'internal friction', of the fluid increases with an increasing mean free path. My intuition tells me that the internal friction is low if the molecules are widely separated.Have I missed some quantity that should enter the expression?Has my derivation failed in some other way?Is my intuitive picture wrong?The derivationIn an ideal gas, molecules are interacting only through ellastic collisions. The equation of state is:$$p rho R T. quad (1)$$The variables and their units are:$p$: Pressure [kg/(m s$^2$)]$rho$: Density [kg/(m$^3$)]$R$: Specific gas constant [m$^2$/(s$^2$ K)]$T$: Temperature [K]In general, these are field variables, so $p p(mathbfx,t)$, $rho rho(mathbfx,t)$ and $T T(mathbfx,t)$. In fluid dynamics, a common assumption is that each infinitesimally small volume is in thermodynamic equilibrium, so that (1) holds at every point in the fluid. I make this assumption. I also assume that the fluid is 'Newtonian', so that the viscous stress tensor is proportional to the rate of strain. The constant of proportionality is the dynamic viscosity, $mu$, whose unit is [kg/(m s)].The dynamic viscosity is a 'material property'; it is independent of the motion of the fluid. In general, it is varying over space, so that $mu mu(mathbfx,t)$. It's value is a property of the material and depends on its thermodynamic state.It seems impossible to find how $mu$ depends on the thermodynamic state from (1). Pressure has 'almost' the correct units, but I need to multiply the pressure by some time scale $tau$ [s]. This time scale must depend on the microscopic properties of the material, and the only way I find it possible to construct it is by using the $l$ [m] the mean free path of the molecules in the fluid. The time scale contructed is:$$tau sqrtfracrhop l.quad (2)$$Using (2) I find that the dynamic viscosity must depend on $p$, $rho$ and $l$ in this way:$$mu C sqrtrho p l,quad (3)$$where $Cgeq0$ is a non-dimensional constant.·OTHER ANSWER:SummaryFrom dimensional analysis I find that the dynamic viscosity of an ideal gas must depend on its pressure $p$, density $rho$ and mean molecular free path $l$ in this way:$$mu C sqrtrho p l.quad$$Here, $Cgeq0$ is a non-dimensional constant.However, I find it counter intuitive that the dynamic viscosity, the 'internal friction', of the fluid increases with an increasing mean free path. My intuition tells me that the internal friction is low if the molecules are widely separated.Have I missed some quantity that should enter the expression?Has my derivation failed in some other way?Is my intuitive picture wrong?The derivationIn an ideal gas, molecules are interacting only through ellastic collisions. The equation of state is:$$p rho R T. quad (1)$$The variables and their units are:$p$: Pressure [kg/(m s$^2$)]$rho$: Density [kg/(m$^3$)]$R$: Specific gas constant [m$^2$/(s$^2$ K)]$T$: Temperature [K]In general, these are field variables, so $p p(mathbfx,t)$, $rho rho(mathbfx,t)$ and $T T(mathbfx,t)$. In fluid dynamics, a common assumption is that each infinitesimally small volume is in thermodynamic equilibrium, so that (1) holds at every point in the fluid. I make this assumption. I also assume that the fluid is 'Newtonian', so that the viscous stress tensor is proportional to the rate of strain. The constant of proportionality is the dynamic viscosity, $mu$, whose unit is [kg/(m s)].The dynamic viscosity is a 'material property'; it is independent of the motion of the fluid. In general, it is varying over space, so that $mu mu(mathbfx,t)$. It's value is a property of the material and depends on its thermodynamic state.It seems impossible to find how $mu$ depends on the thermodynamic state from (1). Pressure has 'almost' the correct units, but I need to multiply the pressure by some time scale $tau$ [s]. This time scale must depend on the microscopic properties of the material, and the only way I find it possible to construct it is by using the $l$ [m] the mean free path of the molecules in the fluid. The time scale contructed is:$$tau sqrtfracrhop l.quad (2)$$Using (2) I find that the dynamic viscosity must depend on $p$, $rho$ and $l$ in this way:$$mu C sqrtrho p l,quad (3)$$where $Cgeq0$ is a non-dimensional constant.
70's/80's Sci-fi TV Movie with People Exploring an Island and Being Attacked by an Extremely Large M
I think the movie is the 1977 USA/Japanese co-production The Last Dinosaur. Rankin and Bass (of Rudolph, The Red Nosed Reindeer fame) financed it. Your description of the ship matches well the Polar-Borer that takes the explorers through the Earth's crust to a prehistoric land in the Artic. Did the ship look like the one in the pictures below? The dinosaur does attack their ship at the beach and carries it away in its mouth, stranding them on the island.The Last Dinosaur is a color movie. The effects are very much in the Toho style. The T-Rex is a very unconvincing man-in-a-suit. That is why you may associate the dinosaur with Godzilla. The movie never played in movie theaters in the states. I remember watching it repeatedly on network and local television in the late '70's and early '80's. It has a largely American cast, so the lead actors speak their own lines without dubbing.Richard Boone stars as an oil tycoon (and big game hunter) who finances a scientific expedition to explore a recently discovered prehistoric land at the North Pole. A very active volcano has kept the area a tropical paradise for millennia and it is inhabited by prehistoric creatures and cave people. Both attack the expedition. Boone becomes increasingly more savage and threatens the other team members. All he wants to do is hunt and kill the last T-Rex on Earth, while the others want to recover their ship and escape. Joan Van Arc (from television's Knots Landing) plays the lead scientist.The original, un-edited cut of the movie has been released on DVD. I found two good reviews of those DVDs here and hereThe movie has a group of people who either were exploring an island or another mysterious continent. At a point in the movie, I think their ship was damaged or was thrown around by either an extremely large monster/dinosaur (or maybe even Godzilla?) I think this scene happened on land or right by water. I remember that the ship was not that fancy. I don't think that it had the look of a submarine. It almost just looked like a silver tube. Almost like a cylinder. Maybe with a cone at one end. The ship may have just have sides dented. I don't think it was destroyed and the people may have still been able to escape in the ship.I would say that the movie was made between 1950 through the 1960's. I saw it on TV in the 70's or 80's. I remember it being in color but it could have been a black and white movie with a certain hue to it to make me think it was color.
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