Stable Definition and 277 Threads

Is exponential function e to the power x[t] stable? My book uses BIBO and says its stable but for -x[t] it says its not stable. Is my book wrong?

I'm not sure why Chromium(VI) is reducing and Tungsten(VI) isn't. I also noticed their radius is quite similar. Is that related?

I'm an oldie and not well-versed in the modern formalism used in stochastic calculus, so please bear with me. I'm aware of Levy's characteristic function for stable distributions, though not well-versed in its practicalities. I have read that for alpha=2 the stable distribution is Gaussian...

Hi, I wondered if an isolated singly negatively ionized hydrogen atom (1 proton, 2 electrons) would be stable. In the corresponding wikipedia article it states: "H− is unusual because, in its free form, it has no bound excited states, as was finally proven in 1977 (Hill 1977)." - does this...

Hi, aside from nucleons is there any other stable (metastable doesn't count in this question) hadronic matter that could form 'exotic atoms' in a way? Thanks for any help.

Latches and flip flops - how is "stable state" defined? My textbook and professor both make numerous references to "stable state" of a latch of flip-flop, but never actually define it. It's not intuitive. For instance, if the present output Q is 0, and we input S=1 and R =0, the circuit's...

I am a high school student.. I have come across so many times that lower energy state of matter is more stable than higher energy states .. I can't understand why. Someone help me out.. Thanks.

Background: I've derived the equation of motion of the bead shown in the picture below using the Lagrangian \omega^2Rsin(\theta)+r\ddot{\theta}=0 The equilibrium points are at θ=0 and π. I'm now to show that only one of these points is stable. Homework Statement Show that only one of the...

What is the physical meaning of an object to be in stable equilibrium? Would it make sense to say that the object wants to stay at that position and any movement will cause the restoring force to move the object back to equilibrium?

Sodium carbonate will not decompose in the presence of heat. This is because sodium is a very reactive metal, and hence forms very strong bond with the carbonate ion. In contrast, aluminium is not as reactive as sodium. Hence the bond by aluminium is weaker, and aluminium carbonate will...

I've always heard that when atoms make ions or create chemical blonde, thru try to make their electron configurations the same as that of a noble thereby filling their electron shells and making them stable. Why then, are noble gas election configurations considered stable?

Hello, I made this video from Celestia showing the orbits of the 6 stars that comprise of the Castor system: http://www.youtube.com/watch?v=wIWdfFG7eKw&feature=youtu.be However, I noticed that when Castor C (the barycenter of Castor-Ca and Castor-Cb) enters the fastest part of its orbit...

Hi : according to :https://en.wikipedia.org/wiki/Gear#Helicalthe stable configuration is when the cave in one of the gear's "V" teeth drives the arrow of the other "V".where unstable configuration is when the arrow part of V drives the cave of the other Vso assuming the direction of motion is...

Hi, Let f be a linear transformation over some finite field, and denote f^{n} := f \circ f \circ \cdots \circ f, n times. What do we know about the linear maps f such that there exist an integer n for which f^{N} = f^n for all N \geq n? Also, how about linear maps g satisfying g = g \circ f^i...

Homework Statement In the Kiliani-Fischer synthesis of aldopentose, why a γ lactone is formed when there is a possibility of δ lactone? Homework Equations The Attempt at a Solution I think δ lactone should be more stable as it is a six-membered ring.

Consider the system $$x' = -x,$$ $$y' = y + g(x),$$ where $g$ is a class $C^1$ function with $g(0) = 0$. Compute the stable manifold $W^s (\mathbf{0}).$ Using $g(x) = x^n (n \geq 1)$, compute $W^s (\mathbf{0})$ and $W^u (\mathbf{0})$. The other was an exercise I found, this is an actual...

Consider the system of differential equations $$x' = 2x - e^y (2+y),$$ $$y' = -y.$$ Find the stable and unstable manifolds near the rest point. I know that the stable manifold $W^s$ is a immersed surface in $\mathbb{R}^2$ with tangent space $E^s$ (the stable linear subspace). How can I...

Homework Statement Discuss the stability of the equilibrium solutionsHomework Equations dy/dx = cos^2(y) between 0<=y<=2pi y(0)=0 y(0)=pi/2 y(0)=piThe Attempt at a Solution Found the equilibrium solutions to be pi/2 and 3pi/2. Rough graphed y(x) which was a y vs x graph with horizontal lines...

Hi everyone, Today I noticed something curious while I was drying a blanket in a dryer. The dryer was turning and the blanket was jumbling around as usual, but then I realized the motion was approximately periodic. This periodic motion was strange to me. Of course, the dryer is driven on a...

Homework Statement Hi all, I have a HW question which is about a simple beam the beam carries a uniform load across its whole length and has two concentrated loads. The beam looks something like this: O____________I____________________I_________________X...

Hi , not sure if this is the best place to set this question, if not please tell me where.. me and my friend are arguing about the best way to set a table, we have a rectangular plank and four legs in 'L' shape, how do we put the legs so they sustain the plank better? like this : L or ¬ ? and...

The will be a G2v star with the sam mass, radius and luminousity of our sun Planet 1: 0.5 Earth masses orbiting at 0.51 au Planet 2: 1 Earth masses orbiting at 0.63 au planet 3: 2 Earth masses orbiting at 0.78 au planet 4: 0.2 Earth masses orbiting at 0.85 au planet 5: 4 Earth masses...

Homework Statement i meet problem below in control system : G(s)= K(s+4)/s(s+1)(s+2) its a unity feedback system. 1. determine the range of K that keeps the system stable. 2. determine the range of K that makes the system oscillate 3. calculate the frequency of oscillation when the...

Hi, i need a real world example of an asymptotically stable node, is there such a thing as asymptotically unstable node?

Homework Statement We know that the average kinetic energy of an ideal gas atom or molecule at Kelvin temperature T is (3/2)kbT. For what temperature T_He does the average kinetic energy of an ideal gas atom or molecule equal the bond energy of the van der Waals bond in He_2 7.9*10^-4 ev...

The title says it all. I'm contrasting "stable matter" with short-lived particles that quickly decay into something else. (The E=mc2 equation implies that it's possible, but in terms of stable matter, I'm familiar only with it being destroyed, say, in nuclear explosions.) Are ordinary...

Is it possible to make an alloy with all possible stable (non-radioactive) metals? I've googled around, and I couldn't find one, and also couldn't find a reason why it hasn't been made. If its not possible, what is the reason behind it?

I probably knew the textbook answer to this at one time, but I don't recall. Feynman states in the beginning of Vol II of the FLP that electrons don't collide into the nucleus due to the uncertainty principle. But an electron positron pair will mutually annihilate. I suspect the answer has...

Homework Statement A uniform rod AB of weight 20N is hinged at a fixed point A. A force acts at B holding it in equilibrium at 30 degrees to the vertical through A. calculate force acting at B if it is perpendicular to the rod. The Attempt at a Solution I figured that the angle between...

Hello Physicsforums, I'm curious to know what stability hydrogen receives through adding one more electron to its 1s sublevel level. The whole sublevel is at the same energy state, so why must it fill that one more space to attain stability? What does a full 1s orbital do to make it...

What is meant by "Early atomic models predicted...noble gas...stable" Hello, I am troubled by the following statement "Early models of atomic structure predicted that atoms and ions with noble gas electron arrangements should be stable" Is this referring to the Niels Bohr model or am I...

At my fixed point of (1,1), I should have a stable spiral but I keep getting analytically that it is a saddle. $$ \begin{cases} \dot{x} = x(3 - 2x - y)\\ \dot{y} = y(-5 + 5x) \end{cases} $$ The fixed points are $(0,0)$, $\left(\frac{3}{2},0\right)$, and $\left(1,1\right)$. Also, the Jacobian...

Hey guys. I made myself a pulse circuit but my power supply failed. Now I need a way to use a 12v magneto as a power supply. But a magneto puts out pulses. Can I put a capacitor or a diode there to make it a steady stream of dc current? This is for my go kart 5hp briggs. for turn signal...

This probably seems naiive, but why? My main question being that why isn't hydrogen the most stable. It is the simplest and should be, right? If everything wants to arrive at the lowest possible energy state, why do nuclei want to arrive at iron? I can understand splitting atoms (fission)...

It is said that a soap film will find the surface with the minimum area. If the two interfaces between the soap and the air meet, the soap film can effectively reduce its area by bursting. You would think that if you simply hold a soap film up vertically, all the liquid would want to go to the...

I know that an electron can be brought to a higher energy level when hit by a photon, but if it is hit by several photons, is it possible that it will become no longer attached to the particle? This may be a stupid question, I'm not a scientist.

Hi. I would appreciate if some one could help me with my question. But first some background: There is a classical problem of inverted pendulum under control. Pendulum can be put to UNSTABLE equlibrium and (if no control applied) it can put itself to STABLE equlibrium. So system under...

If the free neutron decays in only 15 minutes, why are neutrons in the nucleus attached to protons stable? This has always bewildered me. Just a side question, are 'tetraneutrons' stable or even possible?

in a chunk of a pure element like iron-would the outside diameter of the the last electron shell ever naturally change from picosecond to picosecond?

Homework Statement A negative charge placed at point A is a)in stable equilibrium along x-axis b)in unstable equilibrium along y-axis c)in stable equilibrium along y-axis d)in unstable equilibrium along x-axis (There can be more than one answers) Homework Equations The Attempt at a Solution...

I am trying to power 230x Laser diodes at 30mA each. Applying 5V to each would accomplish this. However, I've converted two PC Power Supplies to general purpose power supplies and neither of them were able to support the required current. They would drop from 5V to maybe 3.5V at around...

The normal distribution has the property that if X and Y are i.i.d. and are both normally distributed, then X + Y will also be normally distributed. My question is about directional statistics. Consider probability distributions on the unit circle, where all points can be parametrized by angle...

We always get to know that there could be other 'multiverses' with completely different physical constants, but I'm wondering in particular if it is possible to re-adjust the natural constants in order to obtain stable atoms? That should not be too difficult to estimate, isn't it? Did someone...

So, watching the chart of isotopes (or nuclides), where I have isotopes put according to how stable they are, I have seen that the stable elements have more neutrons than protons. And I wonder why that is? Is it because neutrons are responsible for binding the nucleus with nuclear force...

Is it possible to replace one of the electrons in a heavy atom like uranium with an Antiproton and form a stable atom?

Homework Statement A particle of mass moving in one dimension has potential energy ##U(x)=U_0[2(x/a)^2-(x/a)^4]##, where #U_0# and ##a## are positive constants. (i)What is the angular frequency ##w## of oscillations about the point of stable equilibrium? (ii)What is the minimum speed the...

Hi guys, I am currently writing my dissertation on Graphene and I am investigateing how graphene remains stable, contradicting existing well established theory which states 2D materials cannot exist independently. With the main area of investigation looking at possible lattice distortions...

I'm halfway through the Selfish Gene, and was intrigued by his talk of strategies. Are there any good books that talk about this development in human behavior?

Hi all, Typically, we know that the surface tension for water is about 72mN/m at RT. so do this mean that the surface tension over the whole droplet is exactly the same? Moreover, we know that the Laplace pressure may be different over the whole droplet as the curvature in different parts...

When do they emit α, β+ or β- particle to become more stable? From what I've seen in the textbook, β- is emitted when there is an excess neutrons and β+ is emitted when there is a short of neutrons. Then when does an α-particle emitted?