alejandrito20

the problem says: "show that the zero solution is nonlinear stable. For this, find the change of variable that transforms this system in a linear system" [math] \frac{dx}{dt}=-x + \beta (x^2+ y^2) [/math] [math] \frac{dy}{dt}=-2y + \gamma x y [/math] i tried with the method of eigenvalues of Jacobian matrix, and both eigenvalues are negatives, but my teacher says that this method is incorrect. Help please

in the text (http://arxiv.org/PS_cache/hep-th/pdf/0011/0011225v2.pdf eq2.13) says: "in a compact internal space without boundary, the integral vanishes" the inicial space is [math] z \in -\infty, \infty[/math], but [math] z = r \phi [/math] , whit r radio konstant

yes , is discontinuous in A' your says [math]\int_1^{1+2\pi} dy (A' exp(A))' [/math]????? (A' exp(A))' there is Not exist in -pi,0,pi

i need to evaluate the follows integral: [math]\oint dy (A' e^{A})' [/math] where ' is derivation respect [math]y[/math] and [math]A(y)=A(y+2\pi)[/math] and too [math]A(y)'=A(y+2\pi)'[/math] where [math]y \in (-\pi,\pi)[/math] ia a angular coordinate , and [math]A' [/math] is discontinuous in [math]-\pi,0,\pi[/math] the result is zero, but i think that is NOT CORRECT to say: [math]\oint dy (A' e^{A})' = A' (\pi)e^{A(\pi)}- A' (-\pi)e^{A(-\pi)} =0 [/math], since [math]A' [/math] is discontinuous in -pi and pi

In a space time [math]5D[/math], the action for the brane [math]4D[/math] is: [math] \int dx^4 \sqrt{-h}[/math] In the Randall Sundrum the action for the hidden brane is: [math] V_0\int dx^4 \sqrt{-h}[/math], where [math]V_0[/math] is the tension on the brane hidden. follow the stress energy tensor [math] T_{MN}= V_0 h_{uv} \delta^u_M \delta^v_N \delta(\phi)[/math], where [math]\phi[/math] is the extra dimention. In other paper, where [math]T_{MN}[/math], for example in the friedman equation in http://arxiv.org/abs/hep-th/0303095v1 (page 6)... [math] T_{00}= -\rho \delta(\phi)[/math] [math] T_{ii}= p \delta(\phi)[/math] the other component are zero. I understand thar [math]\rho , p[/math] are energy density and presion If , i use other embedding my energy stress tensor is [math] T_{00}= - \delta(\phi)[/math] [math] T_{ii}= \delta(\phi)[/math] [math] T_{0 \phi}= \delta(\phi)[/math] [math] T_{\phi \phi}= \delta(\phi)[/math] ¿can i to multiply the each component of the stress tensor by differents constants???...for example: [math] T_{00}= - k_1 \delta(\phi)[/math] [math] T_{ii}= k_2 \delta(\phi)[/math] [math] T_{0 \phi}= k_3 \delta(\phi)[/math] [math] T_{\phi \phi}= k_4 \delta(\phi)[/math]

In the serie [math] \sum_0^{\infty} a_n (x - c)^n [/math], the radius of convergency is: [math]R= \lim_{n \to \infty } |\frac{a_n}{a_{n+1}}|[/math]. My problem is : Find the radius of convergency when: [math] \sum_0^{\infty} \frac{(-1)^n}{(2n+1)!} \cdot x^{2n+1} [/math] i don't understand mainly who is [math]a_n[/math]. The answer is [math]R= \infty[/math]

thanks :=)

groups, singer, or instrumen, in particular, of music listen to you, when you doing calculus of theoretical physics? sorry, but I dont speack english very good.

Hello The problem is find the value of [math]\lambda[/math] for [math]\lim_{n \to \infty} \frac{a_{n+1}}{a_n} \nonumber\ [/math] < 1, where [math] a_n= \frac{(\lambda^nn!)^2}{(2n+1)!} \nonumber\ [/math] con [math]\lambda >0 [/math] I tried to do: [math]\frac{a_{n+1}}{a_n}=\frac{(\lambda^{n+1}(n+1)!)^2}{(2n+3)!}\cdot \frac{(2n+1)!}{(\lambda^nn!)^2}[/math] [math]=( \frac{\lambda^{n+1}}{\lambda^n}\frac{(n+1)!}{n!})^2\frac{(2n+1)!}{(2n+3)!} [/math] [math]\frac{(2n+1)!}{(2n+3)!}= \frac{3 \cdot 5 \cdot 7........(2n+1)}{5 \cdot 7 ........(2n+1) \cdot (2n+3)}[/math] [math]= ( \lambda (n+1))^2\frac{3}{(2n+3)} [/math] but the Answer is [math]\lambda \in {0,2}[/math]

in a pipe , open and closed at the ends, the frecuency is [math]f=(2n-1)\frac{v}{4L}[/math], if [math]L[/math] decreases, then [math]f[/math] increasses. I don't understand why in a text of physics of music (in spanish) says: "in a pipe, closed in the vocal fold, and open in lips....in the lips there is antinodes of velocity... if the lips widen, then frecuency increasses" someone tell me the mathematics asociated to this afirmation?

i need examplees of spacetimes where the ricci scalar is constant but nonzero . Particulary i search examples of line element.

there is correct the expresion [math]\int^{-\pi+\epsilon}_{\pi-\epsilon} d\theta[/math]....where [math]\theta[/math] is a angular coordinate between [math](-\pi,\pi)[/math]....¿what means this?... i believe that this mean that the angular coordinate theta runs from [math]\pi-\epsilon[/math] to [math]-\pi+\epsilon[/math] in the sense anti clock (figure)

If the brane tension in RS is [math]T=24M^3_5 \sqrt{\frac{-\Lambda}{24M^3_5}}[/math] eq1 ¿whats units have the tension of brane??? and , ¿whats units have the cosmological constant and planck scale [math]M_5[/math]?? I have tried with units of [math]\Lambda =\frac{1}{L^2}[/math] (L lenght), but if E have units of (E=energy), then en eq1 units of T is [math]\sqrt {\frac{E^3}{L^2}}[/math]

In the einstein equation [math]R_{uv}-0,5 R g_{uv}+ \Lambda g_{uv} = \frac{8\pi G}{c^4}T_{uv}[/tex][/math] i understand that units of [math]g_{uv}=L^2[/math] and then [math]R=\Lambda=\frac{1}{L^2}[/math] ¿[math]R_{uv}[/math] is dimensional less?? [math]G=\frac{L^3}{T^2 M}[/math] and [math]\frac{G}{c^4}=\frac{T^2}{M}[/math] then ¿¿¿[math]T_{uv}=\frac{M}{T^2}[/math]?????

yes [math]t =x^{0} [/math] , [math]f(t=0)=\infty[/math],[math]f(t=\infty)=0[/math], f(t) is positive. the metric in t= 0 is [math]\infty \eta_{uv}dx^u dx^v[/math], in [math]t=\infty[/math] is [math]0\eta_{uv}dx^u dx^v[/math]..... physically....¿what would mean this???