1. alone， lone 和 lonely
alone 作形容词和副词用,是“独自一人”（by oneself） 或“只有,仅有”（and no other）;作 形容词用通常只作表语:
I'm all alone here at present. 我现在孤单一人在这里。
It was dreadful to find oneself alone in such a place.孤独一人在这么一个地方是很可怕的。
I am anxious about leaving Jimmy alone in the house. 让吉米一人留在房子里,我很担心。
You are hardly fit to travel alone at present. 照目前的情况,你不宜单独旅行。
我们不说* He is the alone person who knows it. 该说:He is the only person who knows it. (他是唯一知道此事的人。)
lone 是形容词,只作定语,是“孤零零的一个”:
In the cloudy sky only one lone star could be seen. 在多云的天空,只看见孤零零的一颗星。
There's a lone tree in the garden. 花园里孤零零地有一棵树。
lonely 作形容词用,带有浓厚的感情色彩,是“孤单,寂寞;荒凉”的意思:
I shall have a companion in the house after these lonely years.在多年寂寞生活之后,我将在家中有个伴了。
The house was built in the lonely spot. 房子建在一个荒凉的地方。
I was alone， but not lonely. 我孤单一人,但不寂寞。
2. ability， capacity， competence， talent ability 是“ power and skill， esp. to do， think， act” 。即“(做、思考、行动、制造方面的)能力和技能”。例:ability to make a boat （制造一艘船的能力）,musical ability （音乐方面的才能）,ability in diploma-cy （外交才能）,remarkable ability （杰出的才能）。
capacity 也作 ability 讲,例:They recognized his capacities / abilities as a man of business. 人们承认他具有企业家的才干。
但 capacity 的更常用意义是“容纳力、容量,”（ability to hold, contain ，get sth. ）,例:The cinema has a capacity of 1000.该影剧院能容纳1000人。
It is a leading enterprise in this country with a production capacity of ten million cars a year. 这是该国一家大型企业,具有年生产一千万辆汽车的能力。
ability 后接to不定式,for或in 短语,但不接of 短语;而capacity可后接to不定式或of doing sth. :
Most of the students of our college have the ability to speak English. 我们学校大多数学生都具有说英语的能力。
He showed considerable ability in / for organization when he was a child. 他从小就表现出非凡的组织能力。
The scientist has the capacity of doing/to do important research. 这位科学家有能力进行重要的科学研究。
competence 除了作“能力”讲外,还作“ 财力、胜任、资格、权限”讲:
He has wisely resolved to defer the ceremony until he has saved the competence necessary to support a family .他已经明智地作出决定,把婚礼推迟,直到他的储蓄足以维持一家人生活时才举行。
This case is beyond this court's competence . 这项诉讼超出该法庭的权限。
talent是 special natural or learnt ability or skill， esp.of a high quality,即“天才,某方面的特殊才能 ”,也指“有才能的人、人才”:
He showed an unusual talent for organization in primary school. 他小学时就表现出非凡的才能。
The boy is a real mathematics talent . 那男孩是个真正的数学天才。
“数学才能”可以是:ability/capacity/talent for mathematics。
