help me understand the operation of these circuit

Well, there is always the chance that the adapter is putting out more than 12v. Most of them do, and many of those only use half wave rectification or do not have a filter capacitor. Put a big (220uF - 1000uF) electrolytic capacitor across the adapter and measure this 'filtered' voltage. Be sure to observe the polarity and the voltage rating of the capacitor. The capacitor should be rated at more than 16v.

The delta V method varies depending on the internal resistance of the battery. It is most effective for large, low impedance batteries like those used in tools. Smaller, high impedance batteries, like those used in cordless phones and other low power electronics tend to float higher while charging and the delta V is not as sharp. Especially if the adapter you are using as a source has a low voltage. Remember, the diode and regulator are going to drop the input voltage by a minimum of 2.5 volts (and another 1.25V across the resistor, if you get things running), leaving you with only about 9.5 if indeed that adapter puts out only 12V. This is not enough to effectively charge your battery.

So, do the test I mentioned above and let us know what the resulting 'filtered' DC voltage of your adapter is.

You really do need at least 16V or this circuit will not work. If you can't get 16V, then I would recommend just using a resistor to limit current and cutting off the charge when the battery gets to 10.4V. The exact value of that resistor will not be known until we know the exact filtered output of your adapter.

Edit: By the way, I do not recommend you using a bridge, or anything else, to rectify the power coming out o the wall. What is the AC supply voltage in Malaysia? 240? Please don't try to power this thing off 240V directly. Very bad things will happen.

sorry for the late reply. quite busy with other projects. anyway, measured the filtered voltage of the adapter using a 1000uF 16v electrolytic capacitor by placing it between the output of the adapter..the value is 12.4v. the same as the unfiltered voltage. its hard to get a 16v adapter here. most of them are either 12v or selectable adapter up to 12v

Then the regulator is wasted. Just replace the regulator and 29 ohm resistor with a transistor and 50 or 60 ohm resistor. Turn off the charge (turn on Q2) when the battery gets to 10.4V

See attached schematic.

thanks.it works like a charm
anyway,im also planning on implementing a discharger with my system so i found this constant current sink

im planning to drain the battery at 100mA and then sending the data through serial comm which will later be analyzed by labview to produce a graph and the actual mAh of the battery.
I got the labview program running OK but cant find those mtp3055. Can anyone suggest other logic level n channel mosfet that is more common and can be applied to this constant current sink circuit?