第一篇：情人节携手爱人看世上最美风景
情人节携手爱人看世上最美风景
2月14日是情人节，想携手爱人来趟浪漫之旅吗？情人节不可错过的是世界上那些极致浪漫的爱情胜地，例如澳大利亚的大碉堡、挪威深邃的森林、芬兰独特的冰雪酒店……情人节，留住时光，把握浪漫。
情人节在向我们招手，想携手出游的情侣们该为这浪漫的日子做些计划了，在那些如画的风光中深刻体验极致的浪漫。
马尔代夫被评为世界十大热恋天堂之一。瓦宾法鲁岛中央是绿色，四周是白色，近岸十数米处的透明浅海呈澄亮的浅蓝，再远些的海水则是碧如翡翠般的孔雀蓝，而深海就是深邃的幽蓝。没有亲眼看到过的人真是很难相信这样的色彩竟然是真实的。纯木制别墅清爽舒适，外面宽阔的露台面对大海，躺在有幔帐的大床上，侧身就能看到大海。在这样的环境里，不放下一切尘世琐事尽情享受，简直是暴殄天物。洁白沙滩、无边海景，啜一口冰凉饮品，让舒爽的感觉在心底蔓延。
第二篇：世上最美英文
《CAPTURE YOUR SOUL》-FIVE MINUTES TO SPARE
No matter how busy you are ,you could spend five minutes:
To answer the telephone
To read the morning paper
To talk with a neighbor
To dispute with the laundryman about a mistake
To watch new furniture being unloaded next door
To chat with a salesman
To read a trivial letter
Or to write one
It takes only five minutes:
To say a prayer for the suffering friend
To stop and think of God's daily gift of mercy
To remember the cross
To make an act of faith, hope, and love
To whisper an“our Father” or “Hail Mary” for someone in need
To say a decade of the Rosary for the pour souls
To vist the little statue or picture on the mantle place and tell the Savior how much you love him
To make a spiritual communion
Which is the better way to spend five minutes?
LIFE IS A DO-IT-YOURSELF PROJECT 生活是一个自己动手的项目
An elderly carpenter was ready to retire.he told his employer contractor of his plans to leave the house building business and live a more leisurely life with his wife enjoying his extended family.He would miss the paycheck,but he needed to retire.They could get by.The contractor was sorry to see his good worker go and asked if he could build just one more house as a personal favor.The carpenter said yes,but in time it was easy to see that his heart was not in his work.He resorted to shooddy workmanship and used inferior materials.It was an unfortunate way to end his career.When the carpenter finished his work and the builder came to inspect the house,the contractor handed the front door key to the carpenter.“This is your house,”he said,“my gift to you.”
What a shock!
What a shame!
If he had only known he was building his own house,he would have done it all so differently.Now he had to live in the home he had built none too well.So it is with us.We build our lives in a distracted way,reacting rather than acting,willing to put up less than the best.At important points we do not give the job our best effort.Then with a shock we look at the situation we have created and find that we are now living in the house we have built.If we had realized that we would have done it differently.Think of yourself as the carpenter.Think about your house.Each day you hammer a nail,place a board or erect a wall.Build wisely.It is the only life you will ever build.Even if you live it for day more that day deserves to be lived graciously and with dignity.The plaque on the wall says,“Life is a do-it-yourself project.”
Who could say it more clearly?Your life today is the result of your attitudes and choices in the past.Your life tommorrow will be the result of your attitudes and choices you make today.Parenthood 为人父母
If it was going to be easy, it never would have started with something called labor!
Shouting to make your children obey is like using the horn to steer your car, and you get about the same results.To be in your children’s memories tomorrow, you have to be in their lives today.The smartest advice on raising children is to enjoy them while they are still on your side.The best way to keep kids at home is to give it a loving atmospherehandy to have around and easily wrapped around the fingers of grandchildren.A child outgrows your lap, but never outgrows your heart.God gave you two ears and one mouth....so you should listen twice as much as you talk.There are three ways to get something done: Do it yourself, hire someone to do it, or forbid your children to do it.Adolescence is the age when children try to bring up their parents.Cleaning your house while your kids are at home is like trying to shovel the driveway during a snowstorm.Oh, to be only half as wonderful as my child thought I was when he was small, and half as stupid as my teenager now thinks I am.There are only two things a child will share willingly: communicable diseases and his mother’s age.Money isn’t everything, but it sure keeps the kids in touch.Adolescence is the age at which children stop asking questions because they know all the answers.A alarm clock is a device for awakening people who don’t have small children.No wonder kids are confused today.Half the adults tell them to find themselves;the other half tell them to get lost.People hardest to convince that it’s time for retirement are children at bedtime.Kids really brighten a household;they never turn off any lights.A Smile is A Gift That Anyone Can Give
It costs noting, but saves much.微笑不需要花费你一分钱,但却能带来很多.It enriches those who receive,without impovershing those who give.它使那些得到它的人富有,却不会使付出它的人贫穷.It happens in a flash , and the memory of it sometimes lasts forever.它发生在一瞬间,但它的记忆有时却是永恒的.None is so rich that he can get along without it;none so poor that he is not enriched by it.如果人们可以没有微笑,那么,无论拥有什么都会觉得贫穷.如果人们无法因此而丰富,那么就没有什么比这更贫穷了.It creates happiness in the home, fosters goodwill in business,and is the countersign of friends.微笑为家庭到来欢笑,为工作增添善意,是友谊的象征.It is rest to the weary, daylight to the discouraged, sunshine to the sick, and Nature's best antidote for trouble.它是缓解疲劳的良药,是征服气馁的日光,是治疗疾病的阳光,是自然界中战胜困难的灵丹妙药.It cannot be bought, borrowed, or stolen, for it is no earthly good to anyone until it is given away.它不能买,不能借,也不能偷,因为在它被给予他人之前是毫无用处的.If you meet someone too burdened with grief or worry to smile, just give him one of yours.如果你遇见某人被悲伤和焦虑压得喘不过气来,只要给他一个微笑就行.For nobody needs a smile so much as he who has none left to give.因为当一个人无法再给予微笑的时候,他也就不那么需要微笑了!
Wealth,Success&Love财富，成功和爱
A woman came out of her house and saw three old men
with long white beards sitting in her front yard.She did not recognize them.一个妇人出门看到3位白须飘然的老者坐在她家前院。妇人与他们素不相识。
She said “I don't think I know you, but you must be hungry.Please come in and have something to eat.”
她上前同他们打招呼：“你们一定饿了，进屋吃点东西吧?”
“Is the man of the house home?”, they asked.“No”, she replied.“He's out.”
“Then we cannot come in”, they replied.“你们家男主人在吗?”老人们问。
妇人回答： “他出去了。”
“他不在，我们就不进去。”老人们回答。
In the evening when her husband came home，she told him what had happened.“Go tell them I am home and invite them in!”
晚上，丈夫回家了，妇人将遇到的事告诉了他。
“快去告诉他们我回来了，请他们进来!”
The woman went out and invited the men in.“We do not go into a house together,” they replied.“Why is that?” she asked.于是妇人出去邀老人们进屋。
“我们不能一同进屋。”老人们说。
“那是为什么?”妇人感到疑惑。
One of the old men explained: “His name is Wealth,”
he said pointing to one of his friends，and said pointing to another one, “He is Success, and I am Love.”
一个老人指着一个同伴说：“他名叫财富。”
指向另一个同伴说：“他叫成功，我是爱。”
Then he added, “Now go in and discuss with your husband
which one of us you want in your home.”
他接着说：“你现在进去和丈夫商量，看你们家需要我们中哪一个。”
The woman went in and told her husband what was said.Her husband was overjoyed.“How nice！”, he said.“Since that is the case, let us invite Wealth.Let him come and fill our home with wealth!”
His wife disagreed.“My dear, why don't we invite Success?”
妇人把老人的话告诉丈夫。丈夫十分惊喜，说：“既然如此，我们就邀请财富老人吧，让他进来，把我们的房子装满财富!”
妻子不同意，说：“亲爱的，为什么不邀请成功呢?”
Their daughter-in-law was listening from the other corner of the house.She jumped in with her own suggestion: “Would it not be better to invite Love?
Our home will then be filled with love!”
他们的儿媳妇在屋子的另一头听到这些话，建议道：“邀请爱进来不是更好吗?我们家将会充满爱。”
“Let us heed our daughter-in-law's advice,” said the husband to his wife.“Go out and invite Love to be our guest.”
The woman went out and asked the three old men，“Which one of you is Love? Please come in and be our guest.”
“我们接受儿媳的建议吧，” 丈夫对妻子说，“去吧爱请进来坐我们的客人吧。”
这位妇人走出门问3个老人：“你们之中哪位是爱?请进来做客。”
Love got up and started walking toward the house.The other two also got up and followed him.Surprised, the lady asked Wealth and Success:
“I only invited Love, Why are you coming in?”
爱老人起身朝房子走去，另外两位也起身跟着走了进去。
这位妇人吃惊地问道：“我邀请的是爱，你们两位怎么也跟进来?”
The old men replied together: “If you had invited Wealth or Success，the other two of us would've stayed out，but you invited Love, and wherever he goes, we go also.Wherever there is Love, there is also Wealth and Success!”
Yesterday...Today...AND Tomorrow 昨天，今天，还有明天
There are two days in every week that we should not worry about，two days that should be kept free from fear and apprehension.One is Yesterday, with its mistakes and cares, its faults and
blunders, its aches and pains.Yesterday has passed, forever beyond our control.All the money in the world cannot bring back Yesterday.We cannot undo a single act we performed.Nor can we erase a single word we saidbut it will rise.Until it does, we have no stake in Tomorrow, for it is yet unborn.This leaves only one day
It is remorse or bitterness for something which happened Yesterday, and the dread of what Tomorrow may bring.Let us, therefore, live One Day at a Time!
SAND OR STONE 写在沙子或者石头上的话
A story tells that two friends were walking through the desert.In a specific point of the journey they had an argument, and one friend slapped the other one in the face.The one who got slapped was hurt, but without saying anything, wrote in the sand: TODAY MY BEST FRIEND SLAPPED ME IN THE FACE.They kept on walking until they found an oasis, where they
decided to take a bath.The one who had been slapped got stuck in the mire and started drowning, but the friend saved him.After he recovered from the near drowning, he wrote on a stone:
TODAY MY BEST FRIEND SAVED MY LIFE.The friend who had slapped and saved his best friend asked him，“After I hurt you, you wrote in the sand and now, you write on a stone, why?”
The other friend replied “When someone hurts us we should write it down in sand where winds of forgiveness can erase it away.But, when someone does something good for us, we must engrave it in stone where no wind can ever erase it.”
LEARN TO WRITE YOUR HURTS IN THE SAND
AND TO CARVE YOUR BENEFITS IN STONE.Advice from Mother Teresa 特蕾纱修女的忠告
People are often unreasonable,illogical,and self-centered；
Forgive then anyway.If you are kind,people may accuse you of selfish,ulterior motives；
Be kind anyway.If you are successful, you will win some false friends and some true enemies；
Succeed anyway.If you are honest and frank, people may cheat you；
Be honest and frank anyway.What you spend years building,someone could destroy overnight；
Build anyway.If you find serenity and happiness,they may be jealous；
Be happy anyway.The good you do today,people will often forget tomorrow；
Do good anyway.Give the world the best you have,and it may never be enough；
Give the world the best you've got anyway.You see, in the final analysis,it is between you and God:
It was never between you and them anyway.A Spiritual Message to America
As we stand before the dawn of a new millennium,we pray for America's survival,our survival.We pray that we will be given strength by the Creator to follow the footsteps of our forefathers to share our love,respect and compassion for one another.There is good in everyone because the Creator has put a little of Himself in all of us.We pray for forgiveness for the pain and suffering we have caused one another.We pray that our children will not repeat our mistakes.We pray that we can respect the diversity of America;all life is sacred.Every child born is a precious gift of our Creator.It is our sacred trust to embrace children from all walks of life because we are part of the same family.We pray that our children will honor and respect their elders--that is where the wisdom comes from.This respect will not only allowed forgotten elders.We are all equal,with each having our own special gift to contribute.These values allow our youth to become leaders and workers in our society.Children,you are our future and our hope for the people.Stand and be courageous.We pray to learn and use the wisdom of all that has come before us,to achieve personal successes and to contribute to those of others.Only when our young ones learn respect for everything can they evolve.Earth
We pray for respect and love of Mother Earth because she is the foundation of human survival and we must keep her pollution-free for those who will travel after us.Protect her water,air,soil,trees,forests,plants and animals.Do not just take and waste resources.Make it a priority to conserve.The land is given to us by the Creator to care for,not to own.If we take care of the land,the land will take care of us.Unity
We should have respect for each other.We pray for commitment and responsible behavior in order to help those in need and to give them support and friendship.Be an example in life that others may follow;serve people,community and country.We should all strive to be leaders and contributors.Do not sit back and let others plan and do all the thinking.Let us unite together so that we may have the strength to protect our future.Strength comes from working through trials and tribulations.Health
Spiritual health is the key to holistic health.We pray to have the discipline to set healthy examples for our children to follow.Respecting everyone and everything in the universe starts with self-respect.Take time to listen and take care of your body and spirit.Family and Youth
Family is important and precious.Always let them know that they are loved.Let our children and grandchildren know you are always there to love and support them and that they mean the world to you no matter what they do or say.Children are of infinite value.Live what you teach.Spiritual values,honesty,and integrity start in the home.We pray for the youth.We must teach the youth to work together and respect all that is living on our Mother Earth.We need to convey to our younger generations that the survival of our people lies in spirituality.Peace
We pray to learn ways to settle differences peacefully.Teach respect for each other's ideas.Value honesty on all levels,from children to parents to community to governments.We will be happy when we create peace with each other.To the 7th Generation
-Survive
-Keep hopes and dreams
-Take care of yourself
-Remember your spirit
-Be there for each other
-Respect courage
-Share knowledge
-Always keep learning
-Remember your true values
Confidence
Every day is a new day in our life.There is much to do today.The early morning sun inspires us to start things freshly and put back our past.Only a handful of us make use of this fresh bunch of energy.In various walis of life this affects the way we behave and our confidence level.Confidence is a key to survive in this world.It is the only key tool to win the rat race in every walk of life.Confidence in ones owns capabilities combined with sincere efforts help one to achieve unthinkable heights.But many times we see that this basic element of confidence is missing in us.As a result of lack of confidence we perform well below our caliber.Be it in a public speech, proposing your beloved, visas for your college or in an interview or say even on the eve before your exams.This can be due to fear of being rejected or any other reason.If we look into our hearts and think, we will come to know that fear inside us I going to get us nowhere.The confidence inside us is going to take us places.This is because with confidence we can put our thoughts into words in a better and pleasing way.So we have to get out of that shell where we think whether people will accept us as we are?
Instead of living in these unending moments of fear and thoughtless analysis, it is better if we project ourselves with the skills we have with the gloss of confidence.With confidence we can portray the finer points of our personality in such a way that the places where we do lack are never highlighted.Confidence should glow in us only till the point where our personality is boosted.Above this it leads to over-confidence that is harmful.Over-confidence results in unsatisfied performance levels as the seed of ego grows into a plant into our mind.We then imagine and make big talks just to maintain our ego.So guys don’t let the seed of ego to germinate in your mind, as this seed should be used only for you to live up to your expectations.Confidence is all about being cool, calm and composed.So guys do you have it in you?
If you think you don't,boost up yourselves as your mind is your greatest mentor.You are your greatest helper.
第三篇：世上最美莫过于夕阳红
世上最美莫过于夕阳红
世间情爱诸多情形，诸般滋味。但最美莫过于夕阳红。两个人从青葱岁月到苍颜白发，其间的苦辣酸甜一起走过，人生的沟沟坎坎一起迈过。人生的千回百转到头来走成了夕阳红。那才是一种不离不弃的相守，那才是过尽千帆的风平浪静。人生最幸福的事情莫过于有人陪你一起慢慢数着平淡的流年，然后陪你一起慢慢变老。那是被岁月过滤后的一碗浓而后淡的高汤。你中有我，我中有你。记得前几日和女儿母亲一起去泽园，一路上花红柳绿，似乎春的气息都在花叶间流淌。突然一位年过六十的老爷爷推着一个坐在轮椅上的老奶奶慢慢的走在泽园的小路上。老人静静的推着轮椅，嘴里不住的嘟囔着：‘你看，花开的多好看，你也该出来晒晒太阳了。“轮椅的速度不急不缓，渐渐的老人把轮椅推到了太极盘旁，老奶奶极默契的在老爷爷的搀扶下慢慢站起，用一个手极其缓慢的把弄着转盘，老爷爷也在另一个转盘旁边用两手转动着。约摸五分钟过去了，老爷爷轻轻的走到老奶奶的旁边，俯下身子不晓得对老奶奶耳语了几句什么，老奶奶极其缓慢的又坐回了轮椅上，推着继续往小路的深处走去了。望着他们渐行渐远的背影，我忽然感觉这才是人世间最美、最有福气的风景。有人说一个人的孤独源于爱上一个人，老人最大孤独的莫过于没有了自己的另一半。在我们楼下小区有一对八十岁的老夫妻，天天老大爷牵着老大娘的手，围着小区的广场绕圈圈，绕累了他们就一起坐在椅子上看行人。老大娘的手不住的颤抖。有时老大爷会极其认真的看着自己的老伴说，你没呆够吧，就呆着吧，一会我来接你。周围有爱逗笑话的人就说：“怎么接呀，开车还是抬轿。”老大爷会笑呵呵的说：“骑路。”逗得周围的人一阵哄笑。然后老大爷还会补充一句，她不会开门。
走在大街上，看到那些青年男女手挽手一起说笑着从身旁走过，我总是看不出美感，相反有点让人感觉不雅。但看着一对老年夫妻能这样携手从身旁走过，我总是心怀一份祝福与感动，这才是人世间绝佳的风景。世上最美莫过于夕阳红。
第四篇：情人节对爱人说说
情人节到了，给另一半送上温馨的祝福吧。下面小编带来的是情人节对爱人说说，希望对你有帮助。
1、茫茫世界，想要遇到一个知心的人，确实很难。芸芸众生，想要遇到一份难得的爱，确实也很难。但我是幸运的，因为我遇到了你，愿你因我而幸福！
2、如果青蛙没有变成王子，如果公主没有醒来，如果小人鱼没有化作泡沫，我还会相信爱情吗？相信。因为还有你在我的身边！
3、情人节，我愿做一条鱼，任你红烧白煮清蒸，然后躺在你温柔的胃里。
4、有你在我的身边真好。茫茫人海，凭你的名字导航。凄凄寒夜，握你的名字取暖。漫漫人生，携你的名字同游。
5、没有你的世界，我感觉天都黑压压的一片。没有谁进的了我心，只要有，只会是你。那个我最爱的你！
6、只要你还在远处看着我，就不会有别人走进我的心里，一颗心永远为你而跳动。
7、爱是缘分，爱是感动，爱是习惯，爱是宽容，爱是牺牲，爱是体谅，爱是一辈子的承诺。
8、怀念你想念你，季节匆匆地走过，岁月带来了变化，却为什么总抚不去对你的思念。一颗久久悬着的心，总在怀念你。
9、从见你的第一眼开始，我就发现终于找到我的另一半了！我要给她一生的幸福！从未动摇过！我坚信一生不动摇！
10、我爱你，你感觉到吗？爱是美丽动人的，爱是温馨浪漫的，我多么希望你能一一感受。特别是我爱你！
11、宝贝：最近我牙齿痛，因为常常晚上想你，那感觉太甜蜜了，会蛀牙。
12、我们不一定形影不离，但一定心心相惜。不一定锦上添花，但一定雪中送炭。不一定常常联络，但一定时时牵挂！
13、我无法保证无法向你承诺什么，但我会做到：如果有一天你有饥饿的感觉，那时你定会看到，我已含笑饿死在你的怀抱中。
14、如果说下雨的日子里，人们最先想起来，要去找的东西是雨伞的话，那么你在难过和疲倦时，最先想起来去找的东西，就是我。
15、心动是等你的留言，渴望是常和你见面，甜蜜是和你小路流连，温馨是看着你清澈的双眼，爱你的感觉真的妙不可言！
16、征婚启事：男，本科，只差几分。在跨国机构上班，麦当劳擦桌子。有房，多人拥有。有车，非机动。觅貌美女青年共赴黄泉，若干年后。
17、月缺时我想你，月圆时我念你，无论月圆月缺，我的心如那恒古不变的月光，默默地追随着你！情人节快乐！
18、假如无一地，我有法持续吸呼，这只非阐明，人的世界缺乏了空气，或许，短长了你。所以收个欠疑给您，标明你的主要性！
19、在这个与众不同的情人节里，我把誓言一生一世戴在你的手指上，纵然一生平平淡淡，同尝甘苦，我愿永远为你挡风遮雨共度朝朝暮暮。
20、我一生中最幸运的两件事：一件是时间终于将我对你的爱消耗殆尽。一件是很久很久以前有一天，我遇见你。
21、爱你一万年，夸张。爱你五千年，无望。爱你一千年，荒唐。爱你一百年，太长。接连爱你年，只要我身体健康，这是我的强项！
22、如果世界只剩分钟，我会和你一同回忆走过的风雨，如果世界只剩分钟，我会深深吻你次，如果世界只剩分钟，我会说次我爱你！给我最爱的丫头。
23、最难忘的是你的微笑，当它绽开在你的脸上时，我仿佛感到拂过一阵春风，暖融融的，把我的心都溶化了。
24、月光下你温柔的笑容，将我融化在你心中，带着无边的爱恋幸福走来，将你轻拥在怀，生生世世，此情惟你独钟。
25、每次见到你我都会有一种莫名的冲动，聆听你的呼吸，亲吻你的朱唇。用心去守侯，用一生做赌注，情人节这天我要对你说一句“我爱你”。
26、岁月流转，流年偷换，青春离我们渐行渐远。伴着我的痴情一片，去触摸爱的标签，辗转在你的温柔里是我无尽的爱恋。
27、亲爱的，我宁愿做过了后悔，也不要错过了后悔。请不要怀疑，我是那么地在乎你，这一辈子，我们相偕到老！
28、左手刻着我，右手写着你，心中充满爱，当我们掌心相对，心心相印时，所有的人都会看到我爱你！
29、如果你流泪，我愿是你手里的手纸。如果你醒来，我愿是你眼中的眼屎。如果你热死了，我愿是你身上仅剩的布三尺。
30、牵挂是一颗心对另一颗心的深情惦记，一缕相思一种幸福一份温情，醉了两人的心扉，绽放了两朵心花。牵挂是刻骨铭心的思念，就象我漫长的等待。
31、当你看到这条短信息时，你已经中了猛烈无比的爱毒，唯一的解药就是嫁给我，不用考虑了，咱们结婚吧！
32、你爱我吗？如果是，请承担一切爱情义务，即每天想我多一点，每天爱我多一点，每天关心多一点，每天联系多一点，一定要完成哟！
33、我将把你紧紧地搂在怀中，吻你亿万次，像在赤道上面那样炽烈的吻。
34、一句承诺一世情，一生守候一颗心，一声问候一天暖，一份思念永延绵，一个想念你的我，在等着你的回信，愿我的存在，让你更加快乐幸福！
35、你心我心，爱上了你，一生痴心。君心我心，见不到你，只有伤心。你心他心，旁若无人，请你放心。以心换心，即便万箭穿心，也不变心！
36、你的美丽吸引着我，你的笑容像是雨后的甘露那样清甜，但每当我向你表白的时候，你沉思了。
37、片片尘埃铺展在撕碎的欢乐上，你长袖轻舞，就能扫去尘埃，重聚往日的欢乐，思念，若说这是梦，我愿是不醒的梦，因梦中有您，梦里有情！情人节快乐！
38、去了秋叶，来了冬雪，当年轮再到今日时，希望别是用信函说声再见，请接受我的思念，让我们携手度过以后的每一个情人节！
39、真希望小路没有尽头，就这样手拉手一直走下去，让我们共同走完以后生命的每一个情人节，祝节日快乐！
40、他如同水中遨游的鱼儿，悠闲，清爽，浪漫，他与人类灵魂的最终处深深相连。他行出的直觉引导人们远离孤独寂。
41、我习气你的庇护，习气你的调皮，习性你的温顺，习性你的笑颜，习性你的声响，你就是我饿饥外的里包，乌明外的灯泡，你就是我独一的独一。
42、飞跃的是思念，飞舞的是爱恋，飞动的是祝福，飞向的是你心中。对你的爱飞一般的蔓延，好想飞到你身边。
43、你笑了，我的天空放晴。你恼了，我的天空多云。你的一举一动，左右我的心情。亲爱的，我在蜜罐里思念着你！
44、有了太阳地球才回转，有了地球月亮才回转，有了月亮星光才如此灿烂，有了你我的世界才如此丰富浪漫。
45、一枚水晶之恋，映出世界的美丽：草的青花的香，流水的殷勤，鸟的歌唱，神妙的春信，还有，美丽的恋人。情人节快乐。
46、星月不误，因为你已离去。清风不语，因为我在哭泣。我也不语，因为还在想你。
47、你是幸福的，我就是快乐的，为你付出的再多我也值得。与你是同路的，我就是幸运的，我幸福走过的是你搀扶的。
48、茶，要喝浓的，直到淡而无味。酒，要喝醉的，永远不想醒来。人，要深爱的，要下辈子还要接着爱的那种。
49、自己买玫瑰，算了，会被人笑的。买巧克力，算了，会胖。点上蜡烛，算了，没有情人。情人节，愿没有情人的你和我一起度过快乐情人节！
50、当阳光还没爬上布满蔓藤的篱笆。我的迫不及待的红玫瑰早已缀满了你的窗台。让它带给你我最真挚的祝福：祝你情人节快乐！
第五篇：看风景（模版）
利用MATLAB求解线性方程组
（姓名 郭亚兰 12010245331 2010 级通信一班）
【摘要】线性代数是数学的一个分支，它的研究对象是向量，向量空间（或称线性空间），线性变换和有限维的线性方程组。因而，线性代数被广泛地应用于抽象代数和泛函分析中；由于科学研究中的非线性模型通常可以被近似为线性模型，使得线性代数被广泛地应用于自然科学和社会科学中。
在研究线性方程组，因式化简，方程求根，高维几何，多元积分方面都有广泛的应用。
线性代数是讨论矩阵理论、与矩阵结合的有限维向量空间及其线性变换理论的一门学科。
随着科学的发展，我们不仅要研究单个变量之间的关系，还要进一步研究多个变量之间的关系，各种实际问题在大多数情况下可以线性化，而由于计算机的发展，线性化了的问题又可以计算出来，线性代数正是解决这些问题的有力工具。
【关键字】线性代数
MATLAB语言
秩
矩阵
解
一：基本理论
1，N级行列式A：A等于所有取自不同性不同列的n个元素的积的代数和。2，矩阵B：矩阵的概念是很直观的，可以说是一张表。
3，线性无关：一向量组（a1,a2,„,an）不线性相关，既没有不全为零的数k1,k2,„„„kn使得：k1*a1+k2*a2+„„„+kn*an=0 4，秩：向量组的极在线性无关组所含向量的个数成为这个向量组的秩。5，矩阵B的秩：行秩，指矩阵的行向量组的秩；列秩类似。记：R(B)6，一般线性方程组是指形式： {a11*x1+a12*x2„„+a1n*xn=b1 a21*x1+a22*x2+„„+a2n*xn=b2 „„
as1*x1+as2*x2+„„„+asn*xn=bn
二：基本理论 三种基本变换：1，用一非零的数乘某一方程；2，把一个方程的倍数加到另一方程；3，互换两个方程的位置。以上称出等变换。
消元法
首先用初等变换化线性方程组为阶梯形方程组：1，如果剩下的方程当中最后的一个等式等于一非零数，那么方程组无解；否则有解；2，如果阶梯形方程组中方程的个数r等于未知量的个数，那么方程组有唯一的解；3，如果阶梯形方程组中方程的个数r小于未知量的个数，那么方程组就有无穷个解。定理1：线性方程组有解的充要条件为：R(A)=R(A,b)线性方程组解的结构：
1：对齐次线性方程组，a:两个解的和还是方程组的解；b:一个解的倍数还是方程组的解。定义：齐次线性方程组的一组解u1,u2,„ui称为齐次线性方程组的一个基础解系，如果：齐次线性方程组的任一解都表成u1,u2,„ui的线性组合，且u1,u2,„ui线性无关。
2：对非齐次线性方程组（I）（II）方程组（1）的两个解的差是（2）的解。
方程组（1）的一个解与（2）的一个解之和还是（1）的解。
定理2 如果R0是方程组（1）的一个特解，那么方程组（1）的任一个解R都可以表成;R=R0+V„.(3)其中V是（2）的一个解，因此，对方称（1）的任一特解R0，当v取遍它的全部解时，（3）就给出了(1)全部解。
三：基本思路
线性方程的求解分为两类：一类是方程求唯一解或求特解；一类是方程组求无穷解即通解。
（I）判断方程组解的情况。1:当R(A)=R(B)时，有解（R(A)=R(A，b)）》=n唯一解，R(A)=R(A,b)(n,有无穷解)；2：当R(B)+1=R(A，b)时无解。
（II）求特解；
（III）求通解（无穷解），线性方程组的无穷解=对应齐次方程组的通解+非齐次方程组的一个特解； 注：以上针对非齐次线性方程组，对齐次线性方程组，主要使用到（I）,(II)步！
四：基本方法
基本思路将在解题的过程中得到体现。
1，（求线性方程组的唯一解或特解），这类问题的求法分为两类：一类主要用于解低阶稠密矩阵——直接法；一类是解大型稀疏矩阵——迭代法。2，I利用矩阵除法求线性方程组的特解（或一个解）方程：AX=b,解法：X=Ab，（注意此处’’不是’/’）例 求方程组{2x1-x2-x3+ x4=2 x1+ x2-2x3+ x4=4 4x1-6x2+2x3-2x4=4 3x1+6x2-9x3+7x4=9 命令如下：
A=[2，-1，-1,1；1,1，-2,1；4，-6,2，-2；3,6，-9,7];%产生4x4阶
系数矩阵
b=[2；4；4；9]’;%对矩阵进行转置 x=Ab %进行左初运算 x= 曾介绍过利用矩阵求逆来解线性方程组，即其结果于使用左除是相同的。2，利用矩阵的分解求线性方程组
矩阵分解是指根据一定的原理用某种运算将一个矩阵分解成若干个矩阵的乘积。常见矩阵分解如，LU,QR和Cholesky分解求方程组的解，这三种分解，再求大型方程组是很有用。其优点是运算速度快，可以节省磁盘空间，节省内存。（I）LU分解又称Gauss 消去分解，可把任意方阵分解为下三角矩阵的基本变换形式（行变换）和上三角矩阵的乘积。即A=LU,L为下三角阵,U为上三角阵。
则：A*X=b 变成L*U*X=b 所以X=U(Lb)这样可以大大提高运算速度。命令[L,U]=lu(A)在matlab中可以编如下通用m文件； 在MATLAB建立M文件如下 % exp1.m A;b;[L,U]=lu(A);%产生一个三角矩阵A和一个变换形式的下三叫矩阵L（交
换行），使之满足X=LU X=U(Lb)%L右乘b的结果再右乘U得到x的值 例 求方程组{ x1+ x2-x3-x4=1, 2x1-5x2+3x3+2x4=3, 7x1-7x2+3x3+ x4=6 命令如下：
A=[1,1，-1，-1；2，-5,3,2；7，-7,3,1]；%产生3x4阶系数矩阵 b=[1；3；6]’ %对矩阵进行转置
[L,U]=lu(A);%产生一个三角矩阵A和一个变换形式的下三叫矩阵
L（交换行），使之满足X=LU x=U(Lb)%L右乘b的结果再右乘U得到x的值 x= 采用第二种格式分解，在MATLAB建立M文件如下 %exp1.m A;b;[L,U,P]=lu(A);X=U(LP*b)例 求方程组{ x1+ x2-x3-x4=1, 2x1-5x2+3x3+2x4=3, 7x1-7x2+3x3+ x4=7 命令如下：
A=[1,1，-1，-1；2，-5,3,2；7，-7,3,1]； %产生3x4阶矩阵 b=[1;3;7]’;%对矩阵进行转置 [L,U,P]=lu(A);%产生一个三角矩阵A和一个下三角阵L以及一个
置换矩阵P,使之满足PX=LU x=U(LP*b)%x的值 x=(II)Cholesky分解
若A为对成正定矩阵，则Cholesky分解可将矩阵A分解成上三角矩阵和其转置的乘积，即:A=R’*R 其中R为上三角矩阵。
方程 A*X=b 变成 R’*R*X=b 所以 X=R(R’b)在MATLAB中建立M文件如下 %exp2.m A;b;[R’,R]=chol(A);%产生一个上三角矩阵R，使R’R=x X=R(R’b)%x的值
例 求方程组{x1-x2-x3+ x4=0, x1-x2+ x3-3x4=1, x1-x2-2x3+3x4=-0.5 命令如下：
A=[1，-1，-1,1；1，-1,1，-3；1，-1，-2.3]； %产生3x4阶的矩阵 b=[0；1；-0.5]’； %对矩阵进行转置
[R,P]=chol(A);%产生一个上三角矩阵R，使R’R=x x=P(Rb)%x的值 x= 命令执行时，此格式将不出现错误信息。当A为对称正定时，则p=0；否则p为一个正整数。如果X未满秩矩阵，则R为一个阶数为q=p-1的上三角阵，且满足R’R=X(1：q,1:q)。（III)QR分解
对于任何长方矩阵A,都可以进行QR分解，其中Q为正交矩阵，R为上三角矩阵的初等变换形式，即：A=QR 方程 A*X=b 变形成 QRX=b 所以 X=R(Qb)上例中 [Q,R]=qr(A)%产生一个正交矩阵Q和一个上三角矩阵R，使之
X=QR X=R(QB)%x的值
在MATLAB中建立M文件如下
%exp3.m A;b;[Q,R]=qr(A);X=R(Qb)例 求方程组{4x1+2x2-x3=2, 3x1-x2+2x3=10, 11x1+3x2 =8 命令如下：
A=[4,2，-1；3，-1,2；11,3,0]；%产生3x3阶的矩阵 b=[2;10;8]’;%对矩阵进行转置
[Q,R]=qr(A);%产生一个正交矩阵Q和一个上三角矩阵R，使之满足
X=QR x=R（Qb）%x的值 x= 除了用直接方法求解线性方程组的解之外，还可以用迭代法求解。迭代法适合求解大型系数矩阵的方程组。它主要包括Jacobi迭代法，Gauss-Serdel迭代法，超松驰迭代法和两步迭代法。在此只讨论Jacobi与Gauss-Serdel迭代法。1’ Jacobi迭代法
例：用Jacobi迭代法求解下列线性方程组，迭代初值为0，迭代精度为10e-6。jacobi函数文件：function[y,n]=jacobi（A，b,x0,eps）if nargin==3 eps=1.0-6 %精确度为10e-6 elseif nargin<3 error %错误 reture %结束该函数的执行 end D=diag(diag(A));%求A的对角矩阵 L=-tril(A,-1);%求A的下三角阵 U=-tirl(A,1);% 求A的上三角阵 B=D(L+U);f=Db；
y=B*x0+f ； %y的值 n=1； %迭代次数 例 求解方程组{ x1+2x2+x3-x4=1, 3x1+6x2-x3-3x4=5, 5x1+10x2+x3-5x4=3 在命令中调用该文件jacobi.m, 程序如下：
A=[1,2,1，-1;3,6，-1，-3;5,10,1，-5];%产生3x4阶的矩阵 b=[1；5；3]’;%对矩阵进行转置
[x,n]=Jacobi(A,b,[0,0,0]’,1.0e-6)%调用jacobi函数
x= n= 2，求线性齐次方程组的通解（A*X=0）
在MATLAB中，函数null用来求解零空间，即满足A*X=0的解空间，实际上是求出解空间的一组基（基础解析）。
在MATAB中建立一个函数文件line_solution.m如下 Function[x,y]=line_solution{A,b} [m,n]=size(A);y=[]；
if norm(b)>0 %非齐次方程组 if rank(A)==rank([A,b])if rank(A)==n %有唯一解 disp(‘原方程组有唯一解x’);x=Ab;else %方程组有无穷多个解，基础解系
disp(‘原方程组有无穷个解，特解为x, 其齐次方程组的基础解系为y’);x=Ab;y=null(A,‘r’)； end else disp(‘原方程组无解‘)； %原方程组无解 x=[];end else %齐次方程组 disp(‘原方程组有零解x’);x=zeros(n,1);%0解 if rank(A) A=[1,1,-3,-1;3,-1,-3,4;1,5,-9,-8];%产生3x4阶的矩阵 b=[1；4；0]’； %对矩阵进行转置 [x,y]=line_solution(A,b)%调用line_solution函数 x,y format rat %恢复默认的短格式输出 输出结果为： 五：总结 Matlab语言运算以矩阵运算为基础，可视化，程序设计有机的融合到一个简单易行的互换式工作环境中，有出色的数值计算功能和强大的图形处理功能，而且简单易学，代码短小高效。线性代数是数学中的一个重要分支，很多理论问题和实际问题都需要借助于线性代数的理论工具来分析解决，而且随着计算机的普及，线性代数被广泛应用于科学，经济，工程和管理等各个领域，同时线性代数也成为高校理工科和经济管理类各专业的一门公共基础课。线性代数课程是由方程Ax=b发展起来的，主要研究线性方程组和二次型，对线性方程组的研究引入了行列式，矩阵，向量。这三块内容是研究线性方程组的三大工具。学习线性代数有两大难点：一是概念，理论抽象，二是计算量大。不过利用Matlab语言，就可以轻松快捷的解决很多线性代数问题。比如说求方阵的逆和行列式，线性方程组中论述的求方阵的逆运算和行列式比较复杂，而在Matlab中，方阵的逆运算只需用函数“inv”即可„ 六：心得体会 1.通过写本次的论文，我受益匪浅，才发现原来论文的书写格式要求这么严格，以前也没怎么注意格式。由于学的不精，在Matlab软件中编程时出现了好多好多问题，格式上的，大小写，还有软件中的一些特殊用法等等。在多次的修改后才勉强完成这次论文。在学习Matlab的时候，我感觉这个语言要比我们在大一时学的C语言更加方便，实用，虽然各有各的特点。比如在求解不等式问题上，C语言需要运用if,else,for等多条语句才能完成不等式的求解，然Matlab则只需几个简单的语句就可运行出结果。这样就可以是工作量大大减少。在学完该课程后，我发现利用Matlab作为后继课程的解题工具，可以使我们从繁杂的计算中解放出来，同时将计算机与其他课程结合起来，大大提高了学习效率。 参考文献： 1.《高等代数》，北京大学数学系编，1978 2.《Matlab6.0数学手册》，蒲俊，吉家峰，伊良忠编著，2002 3.《MATLAB程序设计与应用》第二版，刘卫国主编[M].北京：高等教育出版社，2006.
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