1. The world we live in today is full of mysteries unsolved even by today’s advanced science and technology.
我们生活的世界里充满了谜团, 这些谜团即使是当今发达的科学技术也无法解开。
过去分词短语unsolved even by today’s advanced science and technology是mysteries的定语，它的作用相当于定语从句which are unsolved even by today’s advanced science and technology。当定语从句是由关系代词＋be动词＋过去分词或现在分词短语构成时，关系代词和be动词可以省略。例如：
Stories (which were) made up by him didn’t sound very convincing.
People (who are) living in these areas believe in ghosts.
Advanced 先进的、发达的。

2. Police in America have stepped up their search for a fifteen-year-old boy who went missing in Dover, New Hampshire.
美国警方现已加紧对一名15岁失踪男孩的搜索，该男孩于两天前在新罕布什尔州的多佛市失踪。
step up加紧，如: step up production, step up the campaign, step up the lobby(加紧游说)
search在句中作名词，常见词组有one’s/the search for（对…的搜索、探求），in search of(为了寻求)。例如：
His search for truth has led to one discovery after another.
He risked his life in search of truth.
Police是集体名词，形式上永远是单数，和复数动词连用。

3. People have shown great interest in his disappearance due to sighting of puzzling lights in the sky and reports of alien visits around the time of his disappearance.
公众对男孩的失踪表现出极大的兴趣，原因是在他失踪前后有人声称看到天空中出现令人迷惑不解的亮光，还有关于外星人造访地球的报道。

4. Standing inside were lots of white-skinned, strange-looking creatures with large black eyes.
（飞碟）里面站着许多白皮肤、样子奇怪、长着黑色大眼睛的生物。
这是个倒装句，这句话的正常语序是：Lots of white-skinned, strange-looking creatures with large black eyes were standing inside. 当句子的主语部分太长，或说话人想要强调对动作的描写时，可以把现在分词短语和主语部分的位置交换，形成“现在分词短语＋be动词＋主语部分”的倒装结构。例如：
Lying there was a thin, black woman with untidy hair and stony face.
Coming up is a talk show by our famous host Peter Pan.
white-skinned白皮肤的，这是一个由形容词＋名词＋ed构成的复合形容词，中学阶段常见的还有: kind-hearted, bold-faced, ill-tempered等。
strange-looking样子奇怪的。形容词/副词＋动词＋ing也可以构成的复合形容词，例如：good-looking, easy-going(好相处的), never-ending, ever-lasting.

5. believe和believe in
believe+sb表示“相信某人的话”，believe+sth表示“相信某事的真实性”。例如：
I believe George, he has never told a lie.
Do you believe his story?
Believe in+sb表示“信任某人”，believe in+sth表示“相信某事的存在、信仰某种学说或宗教”。例如：
I believe in Ed, he will never let me down (让我失望).
I don’t believe in UFO.
He believes in Maxism.