One other item of note when using Salifert tests, make sure the liquid is at the 8.5 mark otherwise the test will be off slightly. Learned this from Salifert themselves.
Yes, you must fill the chamber containing the pump, then put the air line from the pump under water then turn the pump on. Once the water is flowing remove the air line to start the skimmer bubbles
"The more they overthink the plumbing the easier it is to stop up the drain." A quote by Scotty from a 40 year old movie. Star Trek III The Search For Spock. Gotta love engineers.🤣
@@jacksonsparrow8865 If I remember right, once the swing arm is "cured" it should work every time. If your budget allows, I highly recommend the Tropic Marin Precision Hydrometer, no calibration needed and it's always spot on, down side is that it's large and very brittle.
Surely contravariant vectors and covariant ones live in different vector spaces? That is, if the vector space containing the contravariant vectors is V, then the covariant vectors live in the dual space V*: they are really linear maps taking the vectors in V to the underlying field of scalars. There is symmetry because the dual space V** of the dual space V* is isomorphic (in a canonical way not depending on a choice of basis) to the original space V, so that V may be naturally considered the dual space of V* as well as V* being the dual space of V. But there is no such canonical isomorphism between V and V*. The upshot is that you cannot equate a vector in the original space with a vector in the dual space as you do at 2.20.
I've always wondered: If V is finite-dimensional with a basis B, why isn't the isomorphism to V* with a basis B* (such that b*_i(b_j) = δ_ij) considered canonical?
@@APaleDot Just because canonical *means* independent of a choice of basis. eg consider V = R² over the scalar field R. One basis is e_1 = (1,0), e_2 = (0,1), and then V*, the space of linear maps from V to R, has the dual basis E_1, E_2 defined by E_i(e_j) = δ_ij exactly as you say. And then K: e_i -> E_i is an isomorphism between V and V*, but not a canonical one. For example we can define another basis (f_i) for V by f_1 = (1,1), f_2 = (-1,1). Then eg f_1 = e_1 + e_2 while e_1 = 0.5f_1 - 0.5f_2. The new dual basis in V* corresponding to the f_i in V will be F_i defined by F_i(f_j) = δ_ij and this induces another isomorphism between V and V*, namely that given by L:f_i -> F_i. These isomorphisms (K and L) are not the same. Notice for example that the latter isomorphism L maps eg e_1 (= 0.5f_1 - 0.5f_2) to 0.5F_1 - 0.5F_2 (by linearity), and (again using linearity) this linear map (from V to R) maps e_1 to 0.5F_1(e_1) - 0.5F_2(e_1) = 0.5F_1(0.5f_1 - 0.5f_2) - 0.5F_2(0.5f_1 - 0.5f_2) = 0.25δ_11 - 0.25δ_12 - 0.25δ_21 + 0.25δ_22 = 0.25 + 0.25 = 0.5 and similarly maps e_2 to 0.5F_1(e_2) - 0.5F_2(e_2) = 0.5F_1(0.5f_1 + 0.5f_2) - 0.5F_2(0.5f_1 + 0.5f_2) = 0.25δ_11 + 0.25δ_12 - 0.25δ_21 - 0.25δ_22 = 0.25 - 0.25 = 0 In other words, while K(e_1) = E_1, L(e_1) = 0.5E_1 so the two isomorphisms K and L from V to V* are certainly not the same. All this illustrates that the basis we choose for V determines the induced isomorphism mapping V to V*.
It's possible he's mute, but it's also possible his muteness was a learned behavior; Scottish wildcats are completely mute as kittens, because they know that to cry and mew for their mothers will bring in predators looking for a meal.
@@lkapitan8232 Either way? Bless you for rescuing this lost little soul. If his muteness is learned, he will likely sing you the song of his people once he feels truly safe and at home 🥰 Be patient, though; trauma takes time to heal, for them, too~
I´ve kept 10 chromis in a 500 liter tank for more than 5 years now. I even added 2 more a couple of months ago without any problems. I strongly believe that an aquascape with lots of possibilities to hide increases the chance to keep a healthy, less aggressive school. I also believe that if you keep bigger fish they see as a potential threat it also increases the chance of them sticking together as a school. Moreover, I read that a bigger school results in a broader distribution of aggressive behaviour, meaning less stress for the ones being chased every now and then. But who knows, maybe I was just lucky.
That is the problem, it will not restart. Soon as power out it drains the overflow. What I now use are power heads with venturi nipples that keeps the air out.
@@lkapitan8232 Nope. I can always detect the primaries (sweet,sour,etc). Tabasco still burns though. (I occasionally like shots of Tabasco). I would say that my ability to discern the flavor of food to be at best 10-30 percent of what would be normal taste.
Crust around the edges is always the telltale sign on a leak. I had the same issue years ago with my 75 gallon. One thought, why not support the HOB filter on something in order to relieve the stress on the tank. Maybe Styrofoam, wood, or even books that you don't care about. That is if you have the room behind the tank to do that.
How was the spaghetti? Ever since watching this video I've REALLY been wanting spaghetti with meat sauce.🤤 Unfortunately ever since getting covid in January my sense of taste has been blown to smithereens. Frustrating.😫
@@lkapitan8232 I hope that it will return. I've heard of some that get taste back quickly, but I may be one of those "long covid" folks. Either way it still beats the alternative that could have come from getting sick.👍🏾
Hey i have a 60 gallon with 5 fish and 2 shrimp will this help my tank ? I have no skimmer at all. I dont have a sump so im running a canister fx4 filter full of seachem matrix and sponge.
It will certainly help, but I checked out your channel and some of those fish will get big, I would recommend the Aquamaxx HOB skimmer, just make sure it will fit over your rim.
Does your solenoid have a rubber stopper on it? The part I ordered didn’t come with the rubber stopper and now my gas tank just drains. Still can’t get it to stay started. Do you happen to know the part number for the solenoid? Thanks
Can't remember where I bought it, but here is the part number I found online, 846639 Fuel Shut-Off Solenoid for Briggs & Stratton Engine. To be double sure you can go to Repairclinic.com, type in your engine model and find the part.
1. 1:50, since metric components are defined to be dot products of basis vectors, I don't think you need another arbitrary vector r=xi+yj+zk. If you already have a coordinate system, just find the coordinate basis and take dot products, am I right? 2.4:20, to be precise, g^{km} means the components of the inverse matrix of the metric, which aren't guaranteed to be reciprocals of g_{km}. 3. 12:22, you used "a" for the radius when you first plugged in the spherical coordinates. So, what you have shown in the end is, up to a scalar, the scalar curvature of a sphere is inverse proportional to its radius squared, yes?
First of all, thanks for paying so much attention. 1. Not sure how to define r, theta, and phi if I don't project them onto a Cartesian frame. Would be interesting to learn. 2. You are correct, only because the off diagonals are zero can I get away with that, else I would have to take the proper tensor inverse. 3. Yes
Not sure I'm qualified to answer this hard question, but I will try. As I am sure you know, tensors were around long before relativity came along. Reimann used them in his development of differential geometry. In relativity, the first fundamental form is the metric tensor which is used to describe all of the components of the left side of the field equations, which has to do how space and time are curved by gravity. Did that help?
Thank you for doing that. It really does make me appreciate how complicated the equation is even though it is compactly written. I don't know the math at all except for what I've learned watching videos about GR. I thought the tensors are symmetrical thus the lower left triangular elements are redundant. Thus there are 10 sets of equations. I easily could be wrong about this. And it does not really change the conclusion that you presented that these are very complicated.
You're welcome. You are correct, these tensors are symmetric about the diagonal and I did not mention that, but as you stated it does not distract from the overall magnitude of the problem. Thanks for watching.
When Einstein first wrote the equations, he assumed no one would ever solve them. In his is calculation of the precession of mercury as well as the bending of light by the sun, he used perturbation theory and approximations. When Schwarzschild solved the equations, Einstein was shocked. Schwarzschild used symmetries to simplify them in his famous solution.
