And what of that truth which more than anything else gives me confidence in Hong Kong? The truth is this. The qualities, the beliefs, the ideals that have made Hong Kong’s present will still be here to shape Hong Kong’s future.
Hong Kong, it seems to me, has always lived by the author, Jack London’s credo:
“I would rather be ashes than dust,
I would rather my spark should burn out in a brilliant blaze,
Than it should be stifled in dry rot.
I would rather be a superb meteor,
With every atom of me in magnificent glow,
Than a sleepy and permanent planet.”
Whatever the challenges ahead, nothing should bring this meteor crashing to earth, nothing should snuff out its glow. I hope that Hong Kong will take tomorrow by storm. And when it does, History will stand and cheer.
最能使我對香港信心十足的事實又是甚麼呢？那便是港人的優良特質、信念和理想，不僅為-香港奠下了今天的基業，而且必會繼續為香港開創美好明天。
在我看來，香港一直在生活中實踐作家傑克˙倫敦的信條：
「寧化飛灰，不作浮塵。
寧投熊熊烈火，光盡而滅；
不伴寂寂朽木，默然同腐。
寧為耀目流星，迸發萬丈光芒；
不羨永恒星體，悠悠沉睡終古。」
前路不管有何挑戰，都不會，我重複，都不會使這顆流星飛墜，光華從此消逝。我深願香港-能奮然而起，征服未來，那時候，歷史也必為之動容，起立喝采。
— Christopher Francis Patten
.
.
2019.10.13 Sunday ACHK
 = \int_{t_1}^{t_2} L \circ \Gamma[q]}](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle%7BS%5Bq%5D%28t_1%2C+t_2%29+%3D+%5Cint_%7Bt_1%7D%5E%7Bt_2%7D+L+%5Ccirc+%5CGamma%5Bq%5D%7D&bg=ffffff&fg=333333&s=0 "\displaystyle{S[q](t_1, t_2) = \int_{t_1}^{t_2} L \circ \Gamma[q]}")
![\displaystyle{h[q] = L \circ \Gamma[q]}](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle%7Bh%5Bq%5D+%3D+L+%5Ccirc+%5CGamma%5Bq%5D%7D&bg=ffffff&fg=333333&s=0 "\displaystyle{h[q] = L \circ \Gamma[q]}")
 = \int_{t_1}^{t_2} \delta_\eta h[q]}](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle%7B%5Cdelta_%5Ceta+S%5Bq%5D%28t_1%2C+t_2%29+%3D+%5Cint_%7Bt_1%7D%5E%7Bt_2%7D+%5Cdelta_%5Ceta+h%5Bq%5D%7D&bg=ffffff&fg=333333&s=0 "\displaystyle{\delta_\eta S[q](t_1, t_2) = \int_{t_1}^{t_2} \delta_\eta h[q]}")
be a path-independent function and 
be a path-dependent function; then![\displaystyle{\delta_\eta h[q] = \left( DF \circ g[q] \right) \delta_\eta g[q]~~~~~\text{with}~~~~~h[q] = F \circ g[q].~~~~~(1.26)}](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle%7B%5Cdelta_%5Ceta+h%5Bq%5D+%3D+%5Cleft%28+DF+%5Ccirc+g%5Bq%5D+%5Cright%29+%5Cdelta_%5Ceta+g%5Bq%5D%7E%7E%7E%7E%7E%5Ctext%7Bwith%7D%7E%7E%7E%7E%7Eh%5Bq%5D+%3D+F+%5Ccirc+g%5Bq%5D.%7E%7E%7E%7E%7E%281.26%29%7D&bg=ffffff&fg=333333&s=0 "\displaystyle{\delta_\eta h[q] = \left( DF \circ g[q] \right) \delta_\eta g[q]~~~~~\text{with}~~~~~h[q] = F \circ g[q].~~~~~(1.26)}")
![\displaystyle{\delta_\eta F \circ g[q] = \left( DF \circ g[q] \right) \delta_\eta g[q]}](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle%7B%5Cdelta_%5Ceta+F+%5Ccirc+g%5Bq%5D+%3D+%5Cleft%28+DF+%5Ccirc+g%5Bq%5D+%5Cright%29+%5Cdelta_%5Ceta+g%5Bq%5D%7D&bg=ffffff&fg=333333&s=0 "\displaystyle{\delta_\eta F \circ g[q] = \left( DF \circ g[q] \right) \delta_\eta g[q]}")
![\displaystyle{ \begin{aligned} &\delta_\eta S[q] (t_1, t_2) \\ &= \int_{t_1}^{t_2} \delta_\eta \left( L \circ \Gamma[q] \right) \\ \end{aligned}}](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle%7B+%5Cbegin%7Baligned%7D+%26%5Cdelta_%5Ceta+S%5Bq%5D+%28t_1%2C+t_2%29+%5C%5C+%26%3D+%5Cint_%7Bt_1%7D%5E%7Bt_2%7D+%5Cdelta_%5Ceta+%5Cleft%28+L+%5Ccirc+%5CGamma%5Bq%5D+%5Cright%29+%5C%5C++%5Cend%7Baligned%7D%7D&bg=ffffff&fg=333333&s=0 "\displaystyle{ \begin{aligned} &\delta_\eta S[q] (t_1, t_2) \\ &= \int_{t_1}^{t_2} \delta_\eta \left( L \circ \Gamma[q] \right) \\ \end{aligned}}")
is a path-independent function, so that we can use Eq. 1.26:![\displaystyle{ \begin{aligned} &= \int_{t_1}^{t_2} (D L \circ \Gamma[q]) \delta_\eta \Gamma[q] \\ \end{aligned}}](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle%7B+%5Cbegin%7Baligned%7D+%26%3D+%5Cint_%7Bt_1%7D%5E%7Bt_2%7D+%28D+L+%5Ccirc+%5CGamma%5Bq%5D%29+%5Cdelta_%5Ceta+%5CGamma%5Bq%5D+%5C%5C++%5Cend%7Baligned%7D%7D&bg=ffffff&fg=333333&s=0 "\displaystyle{ \begin{aligned} &= \int_{t_1}^{t_2} (D L \circ \Gamma[q]) \delta_\eta \Gamma[q] \\ \end{aligned}}")
![\displaystyle{ \begin{aligned} &= \int_{t_1}^{t_2} (D L \circ \Gamma[q]) (0, \eta(t), D\eta(t)) \\ &= \int_{t_1}^{t_2} (D L \left[ \Gamma[q] \right]) (0, \eta(t), D\eta(t)) \\ \end{aligned}}](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle%7B+%5Cbegin%7Baligned%7D+%26%3D+%5Cint_%7Bt_1%7D%5E%7Bt_2%7D+%28D+L+%5Ccirc+%5CGamma%5Bq%5D%29+%280%2C+%5Ceta%28t%29%2C+D%5Ceta%28t%29%29+%5C%5C++%26%3D+%5Cint_%7Bt_1%7D%5E%7Bt_2%7D+%28D+L+%5Cleft%5B+%5CGamma%5Bq%5D+%5Cright%5D%29+%280%2C+%5Ceta%28t%29%2C+D%5Ceta%28t%29%29+%5C%5C++%5Cend%7Baligned%7D%7D&bg=ffffff&fg=333333&s=0 "\displaystyle{ \begin{aligned} &= \int_{t_1}^{t_2} (D L \circ \Gamma[q]) (0, \eta(t), D\eta(t)) \\ &= \int_{t_1}^{t_2} (D L \left[ \Gamma[q] \right]) (0, \eta(t), D\eta(t)) \\ \end{aligned}}")
at that moment only, instead of depending on the whole path ![\displaystyle{ \begin{aligned} &= \int_{t_1}^{t_2} (D L (\Gamma[q])) (0, \eta(t), D\eta(t)) \\ &= \int_{t_1}^{t_2} (D L (t, q, v)) (0, \eta(t), D\eta(t)) \\ &= \int_{t_1}^{t_2} [\partial_0 L (t, q, v), \partial_1 L (t, q, v), \partial_2 L (t, q, v)] (0, \eta(t), D\eta(t)) \\ \end{aligned}}](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle%7B+%5Cbegin%7Baligned%7D+%26%3D+%5Cint_%7Bt_1%7D%5E%7Bt_2%7D+%28D+L+%28%5CGamma%5Bq%5D%29%29+%280%2C+%5Ceta%28t%29%2C+D%5Ceta%28t%29%29+%5C%5C++%26%3D+%5Cint_%7Bt_1%7D%5E%7Bt_2%7D+%28D+L+%28t%2C+q%2C+v%29%29+%280%2C+%5Ceta%28t%29%2C+D%5Ceta%28t%29%29+%5C%5C++%26%3D+%5Cint_%7Bt_1%7D%5E%7Bt_2%7D+%5B%5Cpartial_0+L+%28t%2C+q%2C+v%29%2C+%5Cpartial_1+L+%28t%2C+q%2C+v%29%2C+%5Cpartial_2+L+%28t%2C+q%2C+v%29%5D+%280%2C+%5Ceta%28t%29%2C+D%5Ceta%28t%29%29+%5C%5C++%5Cend%7Baligned%7D%7D&bg=ffffff&fg=333333&s=0 "\displaystyle{ \begin{aligned} &= \int_{t_1}^{t_2} (D L (\Gamma[q])) (0, \eta(t), D\eta(t)) \\ &= \int_{t_1}^{t_2} (D L (t, q, v)) (0, \eta(t), D\eta(t)) \\ &= \int_{t_1}^{t_2} [\partial_0 L (t, q, v), \partial_1 L (t, q, v), \partial_2 L (t, q, v)] (0, \eta(t), D\eta(t)) \\ \end{aligned}}")
![\displaystyle{ \begin{aligned} &= \int_{t_1}^{t_2} [\partial_1 L (t, q, v) \eta(t) + \partial_2 L (t, q, v) D\eta(t)] \\ \end{aligned}}](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle%7B+%5Cbegin%7Baligned%7D+%26%3D+%5Cint_%7Bt_1%7D%5E%7Bt_2%7D+%5B%5Cpartial_1+L+%28t%2C+q%2C+v%29+%5Ceta%28t%29+%2B+%5Cpartial_2+L+%28t%2C+q%2C+v%29+D%5Ceta%28t%29%5D+%5C%5C++%5Cend%7Baligned%7D%7D&bg=ffffff&fg=333333&s=0 "\displaystyle{ \begin{aligned} &= \int_{t_1}^{t_2} [\partial_1 L (t, q, v) \eta(t) + \partial_2 L (t, q, v) D\eta(t)] \\ \end{aligned}}")
, you end up with an ODE (viz. the Euler-Lagrange equation).
by a finite group, i.e. 
. In physics, the notion of an orbifold usually describes an object that can be globally written as an orbit space 
where 
is a manifold (or a theory), and 
is a group of its isometries (or symmetries) — not necessarily all of them. In string theory, these symmetries do not have to have a geometric interpretation.
-dimensional manifold has a neighborhood that is homeomorphic to the Euclidean space of dimension 
, as
, and ![\displaystyle{L \circ \Gamma[q]}](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle%7BL+%5Ccirc+%5CGamma%5Bq%5D%7D&bg=ffffff&fg=333333&s=0 "\displaystyle{L \circ \Gamma[q]}")
, which is a real-valued function of one real variable 
.
can be represented by a plane. A closed string at a fixed 
appears as a parameterized closed curve 
in this plane. Draw such an oriented closed string that lies fully in the first quadrant of the 
plane. Draw also the string 
.
