日益的英文：
day by day
more and more
increasingly
more and more with each passing day

参考例句：

The revolutionary struggles of the world people are rising and surging ahead every day.
世界人民革命斗争方兴未艾，日益高涨。

He became a broken man when his wife died.
妻子过世后，他日益颓废。

His passion for peace grew in intensity and profundity
他对和平的热情日益强烈和深厚。

managerial economics is becoming a sophisticated art.
企业经营经济学正在日益成为一门高深的学问。

New Hello Kitty products will reflect the growth in pet ownership in Japan, with Kitty getting her own hamster.
在新一代Hello Kitty的产品中,Kitty也有了自己的仓鼠,这反映出了日本养宠物的人日益增多。

Increasingly expanded every day
日益增广

The morale of the enemy troops is sinking lower every day.
敌军士气日益低落。

The lives of the working people are improving every day.
劳动人民的生活水平日益提高。

The government's popularity is on the wane.
政府的声望日益低落。

A growing trend towards smaller families
家庭日益小型化的趋势

day是什么意思：
n. 一天；白昼，白天；工作日；时代，时期

Things go on day by day.
事情逐日进行着。

Day by day the situation is improving.
情况在一天天地好转。

Like this, day after day.
就这样，日复一日。

more是什么意思：
adv. 更多；此外；更大程度地
adj. 更多的；附加的
pron. 更多的数量
n. 更多；附加

The rainstorm is more and more more fierce.
暴风雨越来越猛烈。

The more illumination, the more temptation.
道高一尺，魔高一丈。

There are more and more gossipers.
现在传闲话的人越一越多了。

increasingly是什么意思：
adv. 越来越多地，不断增加地

The foreign market was increasingly crucial.
国外市场越来越重要了。

She is increasingly paranoid and secretive.
她是越来越害怕和秘密的。

Ownership of the large estates is increasingly fragmented.
这一大笔地产的所有权逐渐地四分五裂了。