Natural Definition and 1000 Threads

I was talking to my professor and she said that $(ln n)^a < n$ for all values of $a$. Is this true or was I misunderstanding?

I have this equality: $$ (\ln\left({n}\right))^4 < {n}^{\frac{1}{4}} $$ where $ n > 1$ Can I derive a law from this such that $$ (\ln\left({n}\right))^b < {n}^{\frac{1}{b}} $$ where $n > 1$ ?

I just finishedOn the Origin of Species. It seems Darwin is saying that characteristics that make it less likely for an organism to survive will drop out over time. But other scientists tell me that cancer has a genetic link, that suicide has a genetic predisposition, etc. Many diseases have...

If I have $\ln\left({a}\right) - \ln\left({b}\right)$ that would equal $\ln\left({\frac{a}{b}}\right)$ or $-(\ln\left({b}\right) - \ln\left({a}\right))$ which is also $- \ln\left({\frac{b}{a}}\right)$. So does this mean $\ln\left({\frac{a}{b}}\right)$ equals $- \ln\left({\frac{b}{a}}\right)$?

I have this sequence: $${a}_{n} = \ln \left(\frac{12n + 2}{-9 + 4n}\right)$$ I need to find the limit of this sequence. How can I go about this? Do I need to apply L'Hopitals rule? I'm unsure how to simplify this expression. If I use the rule $\ln(\frac{a}{b}) = \ln a - \ln b$ I get $\infty -...

Homework Statement Homework EquationsThe Attempt at a Solution I found this solution for the nature frequency but here it does not include the Ball weight and centrifugal force in the moment balance equation about the pivot (O), it is wrong answer...is not it? I tried to solve the problem...

I am trying to find the source of this diagram which came out of some old notes (not mine) I found uploaded on the web. the referencing is not clear. it seems a great diagram and I would like to find a similar one like it (or better graphics) if not the original, and some explanatory text. I...

I'm a (physical) chemistry major, middle of my undergrad but I didn't really get into it until very recently. After realizing that I was missing out, I started to self study physics and chemistry earlier last month pretty seriously. I have come to the conclusion that I have no natural talent...

Is there a term used to describe all number except the natural numbers?

i work at a cavern attraction and one of the parts in the speech we say is that a section of the cavern was once filled with a naturally occurring vacuum until it was punctured and destroyed. we explain in the speech that the vacuum was created when a river packed in that area with mud and clay...

Is Philosophiæ Naturalis Principia Mathematica by Sir Isaac Newton, one of the top 5 Physics-Maths books of all times?

Find all the natural numbers $a$ and $b$ such that $(a^2+1)(b^2+1)+45=2(2a+1)(3b+1)$.

Find the solutions in natural numbers for the following equation: $$\frac{10}{x+10}+\frac{10\cdot 9}{(x+10)(x+9)}+\cdots+\frac{10\cdot 9\cdot 8 \cdots\cdot 3 \cdot 2 \cdot 1}{(x+10)(x+9)(x+8)\cdots(x+3)(x+2)(x+1)}=5$$

Homework Statement In natural units, the inverse lifetime of the muon is given by ##\tau^{-1}=\frac{G_{F}^{2}m^{5}}{192 \pi^{3}}##, where ##m## is the muon mass, ##106\ \text{MeV}##. What is the dimension of ##G_{F}## in natural units? Put in the factors of ##\hbar## and ##c## so that the...

Hi! I am new in ansys. I am doing rotor dynamic study of a high speed rotating shaft. the shaft comprise of two discs and at the it ends the shaft is supported by the bearing I am facing problem in modelling stage please tell me how to model the bearing and disc briefly.I am uploading the image...

My brother is working on an LNG transporter and I would like to know how much energy there is in the LNG the ship is transporting, here is the info I got : Methane ISO6974 99.8518 mole% ethane 0.0137 mole% propane 0.0000 mole% i-butane 0.0000 mole% n-butane 0.0000 mole% i-Pentane 0.0000 mole%...

Hello everyone, I have a strange question. Can complete electrical circuits be found in nature? If so, can you give any examples? And what is necessarily required (besides electricity) for a complete electrical circuit to occur, naturally or unnaturally?

I am doing a project that relates to welding acrylic. I got the bottle today, and I can't use it because its flammable and has chemicals known by the state of California to cause cancer (makes you wonder why the hell they would market this crap). Are there any clean, non-flammable, and...

As far as I understand, a natural system of units is one in which the numerical values of ##c## and ##\hbar## are unity. However, they still have dimensions, indeed ##[c]=LT^{-1}## and ##[\hbar]=ML^{2}T^{-1}##. How is it the case then, that certain quantities, such as the action ##S##, can be...

Homework Statement Determine the corresponding natural frequencies M = [1 0 0 0;0 1 0 0;0 0 1 0;0 0 0 1]; C = [2 0 0 0;0 0 0 0;0 0 0 0; 0 0 0 0]; K = [10 -5 0 0;-5 10 -5 0;0 -5 10 -5;0 0 -5 10]; Homework Equations A = [zeros (4) eye(4); -M/K -M/C] [V,D] = eig(A) The Attempt at a Solution just...

How is it true that: Log[L+(Z^2+L^2)^(1/2)] - Log[-L+(Z^2+L^2)^(1/2)] = 2{Log[L+(Z^2+L^2)^(1/2)] - Log[Z]} ?

I read a very interesting article about this u235 deposit found in Africa. Everything I have read about it suggest that some of the components needed for this to naturally occur can not exist without human intervention. The water involved in the nuclear reaction must be extremely pure. Even a...

Explain how natural selection might have caused the changes in each of the following: -Size of horses -Foot structure of horses I'm quite sure as to why the size of horses needed, and I'm not quite sure why the structure of the foot needed to change.

Homework Statement Problem and work attached. It is mostly diagrams so I have just uploaded the pictures. I think what I did to determine the transfer function was correct. I'm not quite sure how to do the last section of part (a) where I need to determine the dampening, static gain, and...

Hello, At my exam I had to proof the title of this topic. I now know that it can easily be done by making a bijection between the two, but I still want to know why I didn't receive any points for my answer, or better stated, if there is still a way to proof the statement from my work. My work...

Greetings, I see that Indiana University East offers the new titular degree with a concentration in mathematics. Is anyone in this program? Is a B. A. degree worth having? Thanks, Gimblestitch

Hi, How and why set of natural numbers is closed?

So I just did a lab on resonant frequency, and have to find the error of the period: $$T = 2π\sqrt{m/k}$$ m and k were measured with an error of Δm and Δk. My teacher didn't explain well how to do errors, so I just want to know if I did this right. Prorogation of Error equations: $$y=x^n ⇒...

Homework Statement A block is fixed on the extremity of a mobile ideal spring that is horizontal and which has the other side of it fixed (Non mobile). When the length of the spring is 50 cm, the block has a force of 5 N on the right; When the length of the spring is 80 cm, the block has a...

Suppose I have an overhead tank that heats hot water by natural circulation via a thermosiphon (& a Heat Exchanger with some source of waste heat), is there a limitation on how tall this loop can be? e.g. Can there be an elevated tank at 30 feet with a heat exchanger at ground level that heats...

Homework Statement The problem is to sketch lines of constant u and v in the image plane for the function Log[(z+1)/(z-1)]. Homework Equations z=x+iy The Attempt at a Solution In order to do this I have to get the expression into u+iv form, so that I can read off and manipulate the u and v...

Homework Statement [/B] I'm working through a problem in Abott's Understanding Analysis, second edition, the statement of the problem being: "Fix a member n of the natural numbers and let An be the algebraic numbers obtained as roots of polynomials with integer coefficients that have degree n...

Homework Statement Find the natural frequency Homework Equations On picture The Attempt at a Solution Just need help with the equation of motion.

I'm studying a book on logic, and I'm having difficulties with the book's rules of natural deduction. ##P_1,P_2,\dots## are variables that represent propositions like ##x>0##. All variables and the symbols ##\top## and ##\bot## are formulas. For all formulas ##\varphi,\psi##, the following...

are they equal?

Homework Statement Derive the natural frequency f_n of the system composed of two homogeneous circular cylinders, each of mass M, and the connecting link \text{AB} of mass m. Assume small oscillations. Homework Equations The sum of the kinetic + potential energies in an isolated system...

I am writing story about Earth set 1000 years in future and I am looking for good example of living animals. So far I had wolves or dogs on my mind, how would they change in 1000 years?

If you pluck a guitar or cello string, the string vibrates at its fundamental and harmonic frequencies. Suppose the 3rd harmonic has the greatest vibrational amplitude out of all the other rung-out natural frequencies. Do we still associate the pitch with the fundamental, or will the pitch now...

Hello, I am wondering what will happen if I try to ventilate a room by natural ventilation through a single opening. In this opening there will be a ventilation grill. I already found a paper about counterflow through an open door by temperature differences...

Does there exist a closed form formula for in(x)?

Suppose a sound wave with multiple natural frequencies--a complex sound wave--strikes Object A. Some of those frequencies matches the natural frequencies of Object A. A) Will Object A vibrate at all the different frequencies or only to its natural frequencies? B) If Object A vibrates at all...

Why do most of the people like natural scenery (with varying degrees, of course)? Is it in our genes? Does it serve an evolutionary purpose? Any thoughts?

Hey! :o Action-at-a-distance forces are for example the gravity, the electromagnetic forces. They are reduced slowly in respect to the distance and are important even at distances comparable to the dimensions of the volume of the fluid. Is this correct?? (Wondering) Which is the natural...

Hi, As far as I know, every material has different sets of natural frequencies associated with it. For example, A simple one dimensional oscillator with stiffness "k" and mass "m" has a formula for calculating its natural frequency = 1/2pie*squareroot(k/m). I was wondering if there are...

haruspex submitted a new PF Insights post Frequently Made Errors in Probability - Conditionals in Natural Language Continue reading the Original PF Insights Post.

Hi, I've seen on on several sites that you can prove that nCr, where r<=n, is a natural number. I'm not sure how to do this by induction. So I need help on this proof. How do I write this as a mathematical statement at the start of the induction proof? Thank you

Find the partial derivatives of the following function: Q=(1/3)logeL+(2/3)logeK Any help would be much appreciated! Below is my working out so far: \frac{\partial Q}{\partial L}= \frac{\frac{1}{3}}{L} \frac{\partial Q}{\partial K}= \frac{\frac{2}{3}}{L} Are these correct?

I'm not a logician or mathematician but a philosopher (with dyscalculia) so please forgive me for skipping the technicalities... My question is this: Is there in the theory of non-well-founded sets (hypersets) something analogous to the set-theoretic construction of the natural numbers in ZF...

Homework Statement The problem is actually from chemical kinetics, but my problem is solving the differential equation obtained. (dx(t))/(dt) = -j*x^2-k*x+k*a ; x is a function of t, and j,k,a are all real positive constants. Homework Equations I know this is a Ricatti type equation. But this...

My Restricted (Natural) Cubic Spline Equation is Wrong ? I am trying to fit a restricted cubic spline (natural cubic spline) to toy data, attempting to follow Hastie, Tibshirani, Friedman 2nd ed. 5.2.1 p.144-146, Eqs 5.4 and 5.5. Data: Is basically a transposed ‘S’ shape. R-code is: n <© 100 x...