Injection Definition and 93 Threads

I got my first COVID infection sometime last weekend (best guess). Mild symptoms kicked in Monday evening (in retrospect). Spent most of yesterday in bed with fever chills, a bit worse and longer-lasting than the aftereffects of the earlier COVID vaccinations. Test this morning confirmed COVID...

My attempt: ## ( \rightarrow ) ## Suppose G is injective. Let ## y \in Y ## be arbitrary, denote A = ## \{ y \} ## so that ## G(A) = G(\{ y \}) = f^{-1}[\{ y \}] = \{ x \in X | f(x) \in \{ y \} \} =\{ x \in X | f(x)= y \} ##. [ However, now I am stuck because I don't know if ## G(A)=...

Hi all, Sorry to post an open ended question, but I'm struggling because I don't know the right terms I need to do a literature search on my own. Any kind of feedback here is helpful! I'm interested in the dyanmics of a class of device I've heard described as a "jet injector". I know of two...

My first thought was S = {1,2,3,...}. However, if I define R = { (x,y) | y = 1/x }, I have a total injective relation, so this doesn't work. The second thought was to try S = {...,-3,-2,-1,0,1,2,3,...}. However, a total injective relation can also be found here. For example, if I do something...

Currently there is an operation scenario at one of our plant which directly injecting steam into cooling water line at pump suction in order to generate hot water at 60 deg C for circulation, by doing this its generate vapor at pump suction and lead to cavitation which ultimately damage pump and...

Is the following (or, the following after any minor errors are corrected) a bijection from the unit square S=[0,1]X[0,1] to the line L=[0,1], or only an injection? If only an injection, are the excluded points in L countable? [1] Let L be identified with the set of real numbers r, 0 ≤ r ≤ 1...

I am trying to find peak pressure of a diesel engine injection pump.. It doesn't have to be exact but +/- 1000psi would be fine. The basic principle is the same as an engine. Piston goes up and covers a fill hole, once it is covered the only way it can flow fuel is through the injector, so...

Hello everybody, I'm designing a gas pressure feed system for a hydrogen peroxide - ethanol rocket engine, and after analyzing the devised injection plate, I noticed it is very sensitive to the propellants' pressure drops and discharge coefficients. Once the plate is manufactured, the only...

I have been researching the Rankine cycle. I know that it consists of two adiabatic and two isobaric processes. However, I'm not entirely sure why we ignore the work done during the isobaric processes (this seems to be the case in the analysis I'm looking at). Is that because the work done there...

Im currently trying to calculate the pressure inside an injection mold. Does anyone have experience with similar problems? I need to use coeficient of Thermal expansion and volume. please help .

Just wondering if anyone could help me get in the right direction with these questions and/or point me to some material that will help me better understand how to approach these questions In what follows I will denote the identity function; i.e. I(x) = x for all x ∈ R. (a) Show that a function...

1.Prove f(A⋂B) ⊂ f(A) ⋂ f(B) 2.Prove f(A) ⋂ f(B) ⊂ f(A⋂B) ⟺ f is an injection I've solved the first question , as for the second I started with f(A) ⋂ f(B) ⊂ f(A⋂B) ⇒ f is an injection this way : Let's suppose f(a) = f(b) = p If we consider A = {a} and B = {b} then f(A) = f(B) = p then f(A) ⋂...

Hello, I have a problem Basically, in theory -- a damaged 1220mm dia pipeline sub-sea (-8msw) with a 500mm hole in the 12oclock position 600mm. Pipeline resting on the seabed The goal of the problem is to flush the pipeline of its contents in both directions. The idea - have a containment...

Homework Statement Prove that ##f: \mathbb{R}\to\mathbb{R}, f(x) = x^2## is not injective. Homework Equations Definition of an injection: function ##f:A\to B## is an injection if and only if ##\forall a,b \in A, f(a) = f(b) \Rightarrow a = b##. The Attempt at a Solution ##f...

According to NFPA 11, subsurface foam injection can't be used on IFR tanks with fixed/covered roof. However, this has been done for a long time by various companies and there doesn't seem to be any issues with that. Can anyone give their opinion based on knowledge/experience why this should not...

Hello guys :cool: Imagine that we have got a rat and we administer a certain dose (let it be 4.0 µl of a 0.052 M solution) of some (let’s say Propionic Acid - PPA) drug in a intracerebroventricular way – directly in rat’s brain. Now imagine that we administer the same drug in intraperitoneal...

Homework Statement Proof that: f has an inverse ##\iff## f is a bijection Homework Equations /definitions[/B] A) ##f: X \rightarrow Y## If there is a function ##g: Y \rightarrow X## for which ##f \circ g = f(g(x)) = i_Y## and ##g \circ f = g(f(x)) = i_X##, then ##g## is the inverse...

http://www.fluidmechanics.co.uk/ I have found this by searching net. The inventor claimed that by using a new kind of piston fitted with fins, he achieved almost isothermal compression and greatly reduced the power consumption process. I want to know how much theoretically sound it is.

Hello, I am currently working on a storage project which allows me to decouple the compressor from the expander of a gas turbine. (see image link below) The reason I use a gas turbine is to reheat the air which was cooled after being compressed. As you can imagine there is a efficiency loss...

What are the benefits of carburetors over fuel injection methods in engines? I have started working on motorcycles and have noticed that even modern motorcycles are carb'ed rather than fuel inject. Is it because of the cost of adding a computer? Or is there something else to it? I know that...

This is a rather simple question, so it has been rattling my brain recently. Consider a surjective map ## f : S \rightarrow T ## where both ## S ## and ## T ## are finite sets of equal cardinality. Then is ## f ## necessarily injective? I proved the converse, which turned out to be quite...

How does start of injection effected by speed of the engine? According to data, it seems for higher engine speed, the SOI (in terms of degree BTC) is higher.

Hey I've been thinking of this idea for a while, If I had a small boat with a home made gas turbine engine on it to power it solely with thrust. If I put an afterburner on it and nozzle; and had a small intake for water that filtered out all of the crud. Would it be possible to generate more...

Homework Statement Let ##G## be a group. I need to find a set ##X## and an injective function from ##G## into ##Sym(X)## Homework EquationsThe Attempt at a Solution I am having difficulty with this problem, and I want to make sure I understand exactly what it is asking. If I understand the...

Hello, I am making an injection molding machine for fun. There is a lack of available information regarding the details of how the process works. There is something call the Lyman extruder that uses a wood auger bit as the injection screw. This auger is shaped much differently than the...

see attached. the main 10" header is water, and the 1/2" chemical injection is polymer feed (not sure how much by volume, we go by pump strokes). problem is during winter, the polymer becomes viscous, and the pump has a hard time pumping the stuff all the way to the header. So we're thinking...

I was looking up plastic injection molders for a project, and I noticed that while benchtop injection molders can be very small, industrial ones weigh several tons and take up an entire room! What accounts for this difference in size? Is it simply the capability to apply more pressure, or is it...

Hello, Actually i want to make use of Clamping Force of Injection Moulding Toggle System to produce Electricity by making use of Piezoelectric effect. For example, if we place a quartz crystal (or any other piezoelectric material) on either side of the platen, then on each machine cycle, when...

In Science 4 July 2014, there is an item that I saw summarised online: Injection wells blamed in Oklahoma earthquakes. ...The pressure can reduce forces acting to keep faults locked and trigger earthquakes... Now, I don't know how likely this is, and the discussion was commendably...

Sorry it's been a while since I posed here. I'm working on a project for school that will involve sending a synchronizing signal to an oscillator on a reciever, which I know often uses a phase-lock-loop. However, I was doing some reading on injection-locking, and it seems that it would be...

I work at a company that manufactures TPU screen filters for the mining industry. I've got a test to do to inspect whether the qaulity of the TPU is affected by time in the heated barrel of the injection moulding machine. The TPU material sits in the barrel due to tea and lunch breaks (15 - 30...

Homework Statement The Attempt at a Solution Can someone please check my work?

Why is Safety Injection used during Main Steam Line Break? All that I can find is that it brings water back to the cold leg to compensate for the loss during the break.

Homework Statement Let A and B be two sets. Homework Equations Prove that there exists a injection from A to B if and only if there exists a surjection from B to A The Attempt at a Solution I did one implication which is we suppose that f: B→A is a surjection. Then by definition of a...

Can anyone explain to me how to do these types of questions? I have the answers but I don't understand it. The function f: N -> N, f(n) = n+1 is (a) Surjection but not an injection (B) Injection but not a surjection (c) A Bijection (d) Neither surjection not injection The answer is B...

Hi, I was just curious, I needed verification, I am reading up on PIM process and I see they use "binders" to keep the shape of the powders before sintering, anyways as I've been reading the binder consists of a surfactant, a filler and a backbone, I was just curious as to what ratios are there...

Homework Statement Is it possible to create an injection from {a^2+b^2 l a,b\inQ} to {{a+b l a,b\inQ} Homework Equations I am not sure about this. The problem is that many combinations of a,b can yield the same number, so how do I tackle this obstacle? The Attempt at a Solution

I just want to ask. For the set {a^2+b^2 , a,b \in Q}. Am i then right in saying that the map: f(a^2+b^2)=(lal,lbl) is an injection on QxQ (the absolute values are there to make sure f is well-defined)? And is this how you write a thing like this formally.

Homework Statement Let X be a set and let A be a subset of X. Suppose there is an injection $f: X \rightarrow A$. Show that the cardinalities of A and X are equal. Homework Equations The Attempt at a Solution I tried proving this for hours but couldn't really get anywhere. So...

Homework Statement Suppose that f is an injection. Show that f-1(f(x)) = x for all x in D(f). Homework Equations The Attempt at a Solution Let z be in f-1(f(x)). Then f(z) is in f(x) by definition of inverse functions. Since f is injective, z = x for some x in D(f). Thus...

hi I would like to ask, what is all about a "signal injection test" ? How is it done and what one expects to see ? I ve read about it in some Higgs study/plots CERN has published thanks Alex

Attached is a picture of IIL (integrated injection logic) cell. I understand the operation of the second (bottom-most) transistor, and analysis of digital circuits is adequate only understanding the operation of this transistor. I do not understand the operation of the transistor with...

This is a question that comes from my research. I know next to nothing about topology, so I'm not able to assure myself of the answer. The problem is this: I'm watching an animal move in two dimensions. At three successive points in time I have three positions, (x1,y1), (x2,y2), (x3,y3). But...

Hi, I have this report to do on "Charge injection in heterostructures". I have been searching and reading but I still have some trouble with the basics, i.e. defining the concept. As far as I understood a heterostructure is a junction between two or more different semiconductors and the...

Hello, and thank you kindly for considering my question. Background: Medical needles come in gauges such that a smaller gauge represents a larger needle. Scenario: Doctor Jack says "18 gauge needles are best for this procedure", but Doctor Jane says "27 gauge needles are best because...

trying to learn how to do proofs. So I have A=> B which is injective and E \subseteq B then prove f^-1(f(E)) = E. So let x \in f^-1(f(E)) => thus f(x) \in f(E) => x\in E So I have proved that x is a point within E, a subset of A, to me I think I am missing something and have not proved...

Hi, Can I get some learning material or guidance on how to build equipment for generating specific waveforms of DO-160 section 22? Thanks

For any set S, the natural numbers N and function f, if f : S → N is injective but not surjective, is S finite?

Homework Statement Let f: A --> B be an injection and suppose that the set A is countably infinite; how can I prove that there is an injection from B to A if and only if B is countably infinite? Also, if we would suppose that A is uncountable, can B be countable? Homework Equations...

I have been geting confused with injection moulding, could somebody please help me.