The function α(t) is obtained explicitly in the case n=3 and parametrically for other n(≠2). The case n=2 is ... Leach, P. G. L - 《Journal of Mathematical Physics》 被引量: 73发表: 1985年 A Remark on Matrix Equation $x^{\\Delta}=A(t)x$ on Small TimeScales. In this ...
Let us prove that \(u^{\mu \nu }t_{\mu \nu }\ne 0\). Indeed, otherwise \((\varvec{u}\cdot \varvec{t})=0\), so let us consider the following matrix (similar to the Gram matrix, where, however, a different scalar product is used for complex vectors): $$\begin{aligned} ...
1. a) Verify that x=A cos (\omega t+\phi )+Bsin(\omega t+\phi) (for A and B arbitrary constants) is a solution to the differential equation: \ddot{x}=-\omega ^{2}x b) Show that this solution can be rewritten as x=C cos(\omega t+\phi ) and exp...
On the Functional Equation(Delta _{T_{1y} } Delta _{T_{2y} } f = 0)No Abstract available for this article.doi:10.1007/bf01832622Donald GirodBirkhäuser-VerlagAequationes MathematicaeGirod, D. (1973) On the functional equation Δ T1y ΔT2yf = 0. Aequationes Math. 9: pp. 157-...
because it can't determine if the argument is real: >>> (1-1/x**2).is_extended_real >>> x.is_real True Collaborator oscarbenjamin commented Nov 27, 2024 We need something else rather than is_real. The semantics of is_real are not right for this sort of distinction because it tr...
(t) = (ϕn + δn(t)) exp (iλt), and obtain a linear evolution equation forδn(t), where|{\delta }_{n}(t)|\ll |{\varphi }_{n}|. After decomposingδn(t) = xn(t) + iyn(t), and inserting into Eq. (1), one arrives at a set of coupled ...
(10)dV(L1,L2,L3,t)dt=A2ΔPμ(α(L1,L2,L3,t)cV(L1,L2,L3,t)+RmA) Here L1 and L2 are the two solid length directions and L3 is the counter for liquid length, which gets occluded into the solid crystals. V (L1, L2, L3, t) is filtrate volume, A is the filter surface area...
The blow-up time for solutions of nonlinear heat equations with small diffusion Consider a nonlinear heat equation ..mu../sub t/-epsilon..delta..=f(..mu..) in a cylinder /xelement of..cap omega.., t>0/, with ..mu.. vanishing on the lat......
What would be the delta in recoil between a firearm and a magnetic gun? List of "almost"-categories Getting a +5 V supply from a negative 48 V , non-isolated (Telecom) Get histogram of bytes in any set of files in Java - take II What is this strange microtransaction ...
In this paper we study the existence and multiplicity of solutions for the following nonlinear Choquard equation: $$\begin{aligned} -\Delta u+V(x)u=\bigl[ \vert x \vert ^{-\mu }\ast \vert u \vert ^{p}\bigr] \vert u \vert ^{p-2}u,\quad x \in \mathbb{R}^{N