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Let $0<x_1leqdotsleq x_m<1$, I denote$$a=sum_{i=1}^mx_i,qquad b=sum_{i=1}^mfrac{1}{x_i},qquad c=sum_{i=1}^mfrac{x_i}{1-x_i}.$$Im trying to prove that$$(b-m)(c+1-frac{c}{a})geq m(m-1).$$I did prove it for the case of $ageq 1$ using...
Asked on 02/01/2021 by nizar
2 answerLet $G$ be a planar (and connected) graph on $n geq 3$ vertices. Show that the number of faces of $G$ is bounded from above by ...
Asked on 02/01/2021 by Carl J.
1 answerI am not sure of the meaning of the notation C<<...>> used to define a commutative algebra A and non commutative algebra A^ in the image attached. I do understand...
Asked on 02/01/2021 by theoreticalphysics
1 answerGiven is the function $f : mathbb{R}^p to mathbb{R}$ with $$f(x) = q(x)^{top} G^{-1} q(x)$$ where $G = A + x_1 B_1 + ldots +...
Asked on 02/01/2021 by Ronaldinho
1 answerQuestion: The time gap between the two instants, one before and one after $12:00$ noon, when the angle between the hour hand and the minute hand is $66^°$...
Asked on 02/01/2021 by nmasanta
1 answerI want to approximate $$ f(x) = left(1+frac{2}{4x-1}right)^{x} $$ I begin with the Stirling Approximation $$ n! sim sqrt{2 pi n} left(frac{n}{e}right)^{n}$$ Raise both sides to the power...
Asked on 02/01/2021 by No-one Important
4 answerI have a Weiner process ${W(t)}_{tge0}$ with $sigma^2=text{Var}(W(1))=1$. For a real constant $epsilon>0$ consider the differential ratio process $Delta_epsilon={Delta_epsilon(t)}_{r>0}$ given bybegin{equation}Delta_epsilon(t) = frac{W(t+epsilon)-W(t)}{epsilon},...
Asked on 02/01/2021 by Parseval
1 answerMy question revolves around the polynomial$$x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1$$I know that it can be factorised into$$(x^2+x+1)(x^6+x^3+1)$$but what method can we employ to obtain this result in the...
Asked on 01/31/2021 by A-Level Student
2 answerConsider a manifold $zeta:={varphi_S}cap{varphi_T}$ as the non-empty transversal intersection between two Lorentzian manifolds, s.t. all three manifolds have dimension $D=3+1.$ Is $zeta$ also a Lorentzian manifold? I...
Asked on 01/31/2021 by Jack Zimmerman
0 answerProve that if G is isomorphic to H, then $alpha(G) = alpha(H)$ Considering that $alpha(G)$ is the independence number of a graph G, how can I prove if...
Asked on 01/31/2021 by Marconian
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