If you are pondering over this question, “how to get back with my ex girlfriend” please understand that this is a very delicate situation. Feelings may be badly hurt on both ends and anything that you may do now or not do may cause even more hurt.
Read more on How to Get Back With My Ex Girlfriend – 5 Steps That Will Not Fail You…
The fact that you are asking this question, “can I get my ex girlfriend back?” shows that the breakup probably was not serious enough to negate the chances of reconciliation altogether. You also probably have the hope that she feels the same way about the relationship. If you have hurt her intentionally or unintentionally and you know it, it is time to say you are sorry. Being sorry and sincerely showing it is a very good first step to get back together with your ex girlfriend.
Read more on Can I Get My Ex Girlfriend Back By Being Sensitive Or By Making Her Jealous?…
The fact that you are asking this question, “can I get my ex girlfriend back?” shows that the breakup probably was not serious enough to negate the chances of reconciliation altogether. You also probably have the hope that she feels the same way about the relationship. If you have hurt her intentionally or unintentionally and you know it, it is time to say you are sorry. Being sorry and sincerely showing it is a very good first step to get back together with your ex girlfriend.
Read more on Can I Get My Ex Girlfriend Back By Being Sensitive Or By Making Her Jealous?…
There are times when your relationship suddenly falls apart and either one or both of you may doubt whether it is all over especially if the relationship is new. Some men simply cannot reconcile to the fact that their girlfriend dumped them and so they hope to get back with their girlfriend again. If you are asking, “How can I get back together with my ex girlfriend”, it is important to plan your moves ahead.
Read more on How Can I Get Back Together With My Ex Girlfriend – Nothing Is Impossible…
Recently from the Guangxi Sugar Association was informed by the extraordinary drought, 2009/2010 crop season in Guangxi is expected to drop by 50 million tons of sugar, but the head of Guangxi sugar Department told reporters that the heavy drought in Guangxi since the main West and Northwest regions, some areas seriously affected, the whole of Guangxi sugar 2009/2010 crop season limited.
March 31 Announcement of Guangxi, southern sugar claim, Guangxi persistent drought occurs once every hundred years, now, a severe drought occurs only in Guangxi, Guangxi, Baise Northwest, Hechi and other local areas, Nanning Sugar's sugarcane is not serious within the arid region, drought also Nanning Sugar Sugarcane had different effects. Farm sector, according to preliminary statistics, the company, this drought on the production and operation of Nanning Sugar does not cause too much impact.
April 1 of Guangxi sugar industry's largest sugar group, an executive at the South China reporter's telephone interview, also hold the same view. He said the 2009/2010 crop season in Guangxi Sugar cut is a foregone conclusion, but compared to Yunnan, the yield reduction is not, especially under the rain last night, very conducive to sugar cane cultivation and growth of drought on the 2010 / crop season of 2011 is too early to discuss.
March 30, the reporter's largest sugar-producing areas in Guangxi Chongzuo interview, understand that Chongzuo mobilize all levels of government forces, drought, helping farmers plant crops of sugarcane. Huang Ke Chongzuo mayor said, "now or Zhongzhe season, we must do everything possible to planted sugar cane. If you missed the season, will affect the income of farmers in the coming year." Chongzuo Municipal Agricultural Bureau, according to the person in charge, Chongzuo City currently has 20 acres of sugarcane to drought can not Zhongzhe.
Industry believes that the impact of drought on the next crop season will be highlighted. "Affected by the drought this year, we plan a new species of sugarcane area of 600 mu, as of mid-March and about 200 acres not planted, this is a big problem." Sugar Guangxi Agriculture Department Director Chung Kin said.
It is understood that the present annual output of Guangxi sugar industry in the nation for more than Liucheng, because two consecutive cut sugar crop season, the relative national annual consumption of 14 million tons of sugar, the 2009/2010 crop season is expected to 11 million tons of sugar producing country, there larger gap, since the mid to late this year 3, the spot sugar price index in China has 5,500 yuan / ton to run, almost equal to 2006, Sugar City "fever" of 5551.22 yuan / ton record high.
Read more on Guangxi sugar industry this year of drought have limited impact…
Relationships are delicate and need to be nurtured with loving dedication to make them grow strong. Sadly, everything is not as rosy as we would like it to be. When relationships are broken, they drain us of all our emotions, feelings, ability to think clearly and in acute cases, even our physical well being.
Read more on Get Back at Your Ex – 5 Ideas…
Have you just gone through a break up? Are you thinking how to get an ex back? Many people experience some sort of a break up but most of them just concentrate on moving on rather than searching for a way to get an ex back. If you are not a part of that league and you want to work towards how to get an ex back, then here are some tips for you. Does a break up mean that there are no chances of getting back together with your ex?
Read more on How To Get An Ex Back – Know What You Are Doing…
Education marketers tell us Canada is involved in a four-way battle for international students along with Australia, the United Kingdom and the United States – and the good news is Canada may be gaining the upper hand.
Read more on Canada – A Place for Prosperity and Warmth…
As we get older, joint pain becomes more of an issue. This can mainly be due to the thinning of the cartilage and as a result arthitis begins to take a hold. Sure enough, we crave natural joint pain relief and strive to find that perfect solution that will allow us to carry on with our lives pain free. Below are some strategies to bring you that desired pain relief.
Hutuo River Bridge construction site 31 SR360 auger drill under construction ( HC Engineering Machinery Network distribution map )
HC Engineering Machinery Network Recently Ben Wang noted that Asia's first National Taiwan University diameter, deep foundation Rotary Drilling Rig Beijing 31 SR360 Rotary drilling is Shijiazhuang Hutuohe bridge construction. Poor understanding of local geological conditions, Rotary Rig out of pebbles up to 50-60 cm in diameter. This undoubtedly is the second Shaanxi Zhao River Bridge, the right for large-diameter, deep foundation construction of the Beijing 31 SR360 rotary drilling rig yet another test. Beijing 31 of SR360 device performance then? July 13, Ben Wang edit to Shijiazhuang, the project site Hutuo Bridge glimpse 31 SR360 rotary drilling rig's style.
Project description Hutuo Bridge Engineering ( HC Engineering Machinery Network distribution map )
Hutuohe Highway Bridge is located in Chang Zhengding County, Shijiazhuang section, starting mileage for the K4 +375.1, end mileage k6 +942.5, length 2.571km. Full width of the bridge was 44.5 meters, and the line direction was 110 degrees, formed by the main bridge and approach spans. The main bridge 40 +200 +40 m in the basket bridge deck structures, the arch ribs with steel pipe arch, arch main span between the use of steel beams. Approach the south bank of a 20 * 40 +30 +16 +40 +30 meters north of 30 +19 * 40 meters using prestressed concrete continuous T beam structure, with all Bridge of pier column, ribs Taiwan, pile foundation.
Project Difficulty: pebble diameter of 50-60 cm, geological strength of 1200 kPa
Hutuohe Bridge the main bridge spanning 200 meters, the "First North Cross," said. 2 m diameter pile requirements, the average pile depth is 65 meters, another underground gravel higher density on the basis of construction caused some difficulty. 31 SR360 Rotary drilling commitment is the main bridge pile foundation construction, the project required the Department of Construction, the main bridge pile cap required for each play eight holes, each hole diameter of 2 meters and 71 meters deep.
Due within 20 meters of underground geological soft, Rotary Drilling with the high construction cost, the construction of choice within 20 meters of artificial underground mining, underground 20 meters to 70 meters underground part by Rotary Rig.
31 service personnel told us: "Bridge Engineering Geology Hutuo very bad, both sand and gravel underground, large sandstone formation changes, location of each hole there is quite different in the gravel, increased difficulty of construction . In addition to pebble the size of a large, high hardness, especially good to play. we play the largest pebbles are more than 50 cm, geological strength of 1200 kPa. "
In Hutuohe bridge construction site, we see 31 SR360 play the part of the Rotary Drilling pebbles ( HC Engineering Machinery Network distribution map )
31 of the SR360 bridge auger drilling in the main cap 39 # A-4 position to lay four holes, A-5 lay five holes, played nine holes total. It is worth mentioning that the cap at 39 # A-4 position, the construction is very difficult. On the one hand is the engineering requirements aperture large, deep pile, need to use a large auger drill, some medium and small models could not do Rotary drilling; the other hand, engineering geology great loss of equipment, geological drilling too hard on the tooth loss very serious, some of the larger equipment will not do that. Tooth loss from the drilling, we can feel the hardness of the geological situation. 31 service personnel, said: "As 31 of the original drilling teeth other than domestic drilling more expensive gear, the user selects the other domestic drilling teeth, cheap, but quality good as 31 accessories. Hit a hole almost destroy a set of drill teeth, the cost of the million or so. "
User rating: 31 of SR360 Rotary drilling equipment, in our minds is quite satisfactory
The construction unit, Beijing, 31 new users based construction company, Zhejiang European power construction experience, have used the Italian meaning horse, Yutong, Roth Rui, Xu workers and other brands of rotary drilling rig.
Head of the construction site of the European force of Zhejiang Wang said: "Zhejiang European power companies have set up six years, and our wider work area, from Guangxi, Zhejiang, there are basically some of the projects involved the construction of the bridge pile, the Housing pile, rail pile more we fight. We feel that playing more and more large piles, but fewer large domestic equipment. In recent years the development of rotary drilling rig market, the pile foundation construction market on a small pile of ordinary profits dropping, and more difficult to fight the general pile more money, so we consider the purchase of large equipment. In contrast, high price of imported equipment, the maintenance side is also too much trouble to find parts, find parts of a find that one month, so we consider buying a domestic product. learned 31 large equipment, the service was excellent from the start we plan to purchase 31 in Beijing BICES 2009 exhibition on display at the new SR400-type auger drilling, but more time for the duration of this site, so we buy them in 2008 off the assembly line of the SR360 Rotary Drilling. "
About 31 devices on the bridge construction site in Hutuohe performance, Zhejiang Province Wang heartfelt European force, said: "This is our first time with 31 Cooperation , 31 of SR360 Rotary drilling equipment, in our minds is quite satisfactory. Construction of the models in this site are basically 260's, our equipment is 31 360, from power equipment such as no other way than with us. At this site, people can not get the post, we can get, compare the time not very long, in general, also. We selected the intention of this equipment is here. "
Mr. Wang said that after the purchase of equipment directly to the site Hutuohe Bridge, after testing machine after the machine and transported from the site will return to Beijing 31 back to the rectification works, the problems identified for the construction site and the special needs of customers, Beijing 31 are adjusted to customer needs will change, so that the use safer, more assured. For services to Beijing on March 1, Wang praise, he said: "Beijing 31 360 this device with our after sales staff are on site 24 hours standby, the service was good."
For 31 SR360 auger drilling performance of the site, the project head of the Department of Construction of Pile Foundation, said: "just when entering the site, 31 SR360 equipment because of new products into the site, are the experimental stage, there are some does not match, but after they adjusted quickly can work, and current performance can be. not
Read more on Hutuohe Bridge again witnessed the 31 SR360 Rotary Drilling…
HC HVAC & R Network Recent sudden temperature drop, the people are reflected in Heating Issue has sharply increased.
Hotline 1: Substandard maintenance temperature to collect the money Public Wang is an Urban Garden District resident, he told reporters: Urban Garden District so that people in residential heating has been very satisfied, first, heating time to start late, end early, close in December this year started within the district heating, heating than the specified date later than 20 days, and even during the heating is intermittent, the indoor temperature was maintained at 12 degrees, 16 degrees not reach the required standards. Mr. Wang told reporters, "Since the beginning central heating, residents home Radiator Have been only a warm, our family's radiator four of them two hot pretty good, last Friday it stopped heating, up to now has not brought gas, too cold outside, cold in the family, the elderly have children at home could not stay. "Reporter in the interview the residents within the district learned that, in addition to temperature and heating time is not compliance, the residential property management within the residents are very unhappy living in the district of a woman told reporters that people in residential homes The heating is broken, call to find the property to repair, maintenance workers actually to impose a time charge for each hour and 15 yuan to 30 yuan range, and public channels Valve Bad, to find the property to repair, maintenance man's asking price is 30 yuan, while the market such Valve Gate prices are less than even 20 yuan. "We have paid property management fees, hours of work may be why charge fees, but also a pipeline valve replacement when the residents refused to Delivery, the property's maintenance man actually would have been installed on the valve then unloaded down and closed Heating Pipeline, making the residents of the upstairs heating unit affected. "
Mr. Wang told reporters: heating temperature is not up to the residents home, people sit still cold, full of complaints of property management for residents, while the heating and property fees, charges and usual, in charge of the district heating units and heat Community property sector should explain?
Hotline: Hot and cold when Heating Heating units and property Who is responsible?
Owner who lives in a bright cell phone as she had got to reporters, saying the situation in the district heating within the cell so that the residents were very dissatisfied.
Yesterday afternoon, reporters came to light district. Area residents told a reporter from the heating start date, home heating has been intermittent, and each winter to warm radiator is almost on it a few days. She said: Each year we pay for heating costs, home heating, but never too hot, the annual winter is about 13 degrees inside the compound's residents great views of the property, and in most cases the year before serious, residents hand in the money, the city has begun rapidly heating a month until our district heating, and had stopped shortly after the gas a year, and stopped earlier than other communities more than a month. This year's heating conditions for the residents within the district was very angry last year when they collectively refused to pay heating costs, then the residents self-organized communities and residential property management company coordinating committee this year, after payment of fees to continue heating the property , but did not take long remained intermittent.
To this end, the residents within the district once again found a property company, property company explained that because the pressure is not enough heat transmission company, while the heat is a district of the company confirmed that the thermal conversion facility problems. In the end the problem where residents who give the cold a reasonable argument?
Inhibition of overcapacity in some industries and duplication of the heavy fist to pound the building materials industry. Yesterday, the National Development and Reform Commission issued "on the cement, plate glass construction project clean-up work-related Issues" (hereinafter referred to as "Notice"),
Thus beginning the building materials industry, the project cleared off. "Notice" requirement, with immediate effect on the end of September has not started the project before the full stop the clean-up, re-examine the decision be retained after the clean-up work to be completed before the end of this year.
Cement and flat glass production capacity significantly excess
"Notice" clearly points out the clean-up range, which cement this year on Sept. 30 projects under construction have not yet put into operation, has approved the project has not started (and closed circuit grinding with cement clinker line); flat this year on September 30 not fire in the building project, has not started the project record.
"Cement industry as an example, the clean-up project involving not only the cement itself, but also including clinker line and grinding stations, see the relevant departments to check their excess capacity determination and strength." Senior cement expert, president of Digital Cement net Liu Zuoyi said.
Reporter noted that after the State Council has issued a suppression part of the industry overcapacity and duplication in its notice that the country presently under construction, cement production line 418, capacity 620 million tons, in addition to the approved have not yet started the production line 147, capacity 210 000 000 tons. After the completion of the production, cement production capacity will reach 2.7 billion tons, the market demand was only 16 million tons of excess production capacity severely. The notice also pointed out that all over the country there are more than 30 articles in and construction of the proposed float glass production line, flat glass production capacity of more than 800 million weight boxes, excess production capacity significantly.
"From the above data, the NDRC notice required clean-up project involves large scale production, is no small effort." Liu Zuoyi respect, the current implementation depends on the specific situation.
Are very strict approach
According to "notice" requirement, the clean-up includes: the construction of the project focused on review of compliance with industrial policies, the approval process is complete, construction of the content is consistent with the declared content.
At the same time, provinces and autonomous regions have approved the project has not started to clean-up "compliance with national and regional planning and layout requirements, compliance with industrial policies, whether to obtain land use permits, environmental impact assessment report, the Bank approved the loan commitment and other necessary items related materials. "
"Notice" also requires clean up, the cement to be submitted to limestone mining permit; flat glass items should be consistent with Development and Reform Commission and other six ministries and flat file access requirements.
It is noteworthy that the clean-up project approach is quite strict.
"The provinces and autonomous regions not started and the cement of approved projects have been started in the flat glass items are not filed, shall be allowed to start construction. Really necessary to build the project, subject to verification and approval of the Organization. For all of the proposed cement, plate glass project provinces, autonomous regions and municipalities are not allowed to approve or record. subject to the investment management regulations and procedures, by the provincial, district and municipal investment department in charge of Development and Reform Commission and approval of proof. on flat glass in the construction project, you must file by six ministries and access only after the requirements of recognized fire. "" notice ", said.
Read more on NDRC: 9 months ago has not started the project of cement and flat glass can not start…
"First Financial Daily" from the source was informed, as the bidding of drugs, "national standard" and "medical institutions Centralized Bidding Procurement Standards" (hereinafter "Standards") has just completed six departments will, and will be formally within two weeks release.
It is worth noting that the document does not involve the countries currently most concerned about the tender part of the essential drugs.
"" Standard "has been approved in principle by the Ministry of Inter, is now a final word processing." Yesterday, a close to the Ministry of Health told us that, "Not surprisingly, then, can be released before the end of this month."
Reporter was informed that as a "standard" concrete implementation of the document, "Medical institutions Centralized Bidding Procurement Regulations" will also be released simultaneously.
Had "standard" has been closed in a small area to seek advice, including domestic production and business operations of several large corporate representative had attended at the Ministry of Health on "norms" of non-public discussion.
But told the newspaper after the delegates, as their corporate identity, market share and their status is different in the actual bidding in the problems and situation are different, therefore, even in the already reduced to a median business discussion, "many provisions of the current tender and still there is considerable disagreement."
"This document does not take the form of online direct comments, but the draft to all provinces and industry associations, considered the country to seek their views." Solicit the views of a person involved told reporters.
Ministry of Planning and Finance, Deputy Director Wang Xun, has also publicly said: "We have listened to the views of all aspects, the two documents recently again been revised to put across the voice of this paper is relatively high, so We want to speed up the process is released, as soon as possible to introduce. "
Newspaper learned that because of the medical reform policies throughout the drug tender "quality first, price reasonable" requests the Executive is not in place, businesses reflect the views of more "standard" key in Chapter VIII of the Drug Quality Assessment made detailed provisions.
At the same time, how the province as a unit throughout the tendering procurement experts in library science to play a role in the specific procurement, evaluation, strengthening of the management of experts, "norms" are also put forward a specific request.
Wang Xun said, the health sector this year, a key aspect in the drug tender the work is to understand the situation in a timely manner, found the problem around the same time, in a timely manner to carry out a number of key local supervision and inspection. Although the content of the final version
refused to reveal more, but above the industry said, and compared to previous draft newspaper reported, "" normative "framework has not changed, but for some controversial issues do not rule out further there might be revised. "
"Some of the content, as long as the modification of a word, has a significant impact on the enterprise." He emphasizes.
Read more on Drug Bidding national standards published or does not involve months of basic drugs…
Just concluded 23rd World University Games men's 100 meters champion of Qingdao University student membership Kai Hu rewarding experience. Stop celebration last night drinking wine, "glasses Chivalry" pleased to accept the reporter an exclusive telephone interview. He excitedly said: thank the people of my hometown attention and support, as the Qingdao people, whether I go anywhere in the country or the world, are proud of. I love Qingdao??? My beautiful hometown.
Hu Kai rewarding experience Future: knowledge is for life In the future, he will continue to be school-based or will invest more effort in training go? Hu Kaiming really told reporters, school is good enough to let all his life, while training and performance are just a few years to do. Therefore not affect the school's case, he will train as a phased thing to treat.
For the news hope he went to the 2008 Olympic Games, to participate in China's men's 4 × 100 meter relay race to achieve good results, the Hu Kai, that for an athlete to participate in the Olympic Games on behalf of the motherland is the greatest dream, he hopes his Status and results can be maintained until then, let him also fulfill an Olympic dream.
Whole operation: on behalf of Chongqing Shizhuwunai
Be held at the Tenth National Games in Nanjing, Chongqing, Hu Kai, will represent and not participating in Shandong. Hu Kai Helpless to give this explanation: In accordance with the provisions of the State Sports General Administration, university training, athletes can participate in the competition on behalf of any provinces, who will depend on the specific representatives of schools and where to sign. As Shandong Province, Qingdao, he naturally wanted to participate in the Games on behalf of Shandong, but early last year, and Chongqing area Tsinghua signed on to identify several other members of his National Games on behalf of Chongqing game. The contract will end after the Games, but then can participate in the competition on behalf of Shandong Province, Hu Kai said he did not have discretion to look at the attitude of schools.
Junior: clamoring to play Hu Kai told reporters that he had a habit of sports, especially football. In junior high school was clamoring to go play. There is no way that his father had asked a friend found him an amateur football club, but after a few days in the training, coach said he was not fit to play. So he had to go back to peace of mind to learn. So until the Middle School was discovered to have Sprint, have today "glasses night" outstanding performance. Hu Kai, joked that it might make China less of a speed of football players.
Aspirations: to be proud of Qingdao
Listening to reporters after talking about his win after the reaction caused in Qingdao, Hu Kai was very very excited. "As a person I both went to Qingdao, China or anywhere in the world are proud of for the home." Hu Kai
listening to pure Mandarin, the reporter asked him if he has forgotten how to say the words, Qingdao, Hu Kai, told reporters his words well, Qingdao lot, actually, every time and his family, said relatives would exchange words in Qingdao. But the plane from the beginning, the welcoming ceremony, leadership dinner, return to school, interview, Hu Kai no time to have a chat with their parents do. The next Shanghai, Nanjing, Macau, race one after he has not time to reunite with their parents back to Qingdao. It seems only time he was over the phone and talk to their parents, had been said that if the addiction of Qingdao. Reporter Ma Hongwen
Concern glasses Xia Experience: did not expect such a sensation
23-year-old Hu Kai, is to follow the delegation of Chinese university students from Turkey, returned yesterday afternoon in Beijing. In the Capital Airport Kai Hu and his delegation were warmly welcomed. Such a grand welcome for the scene, Hu khaitan statement did not expect. But this scene also made him realize that, as long as the representative of the motherland and win honor for the motherland, the motherland and the people will be so welcome their return.
Talking about race just ended, Hu Kai said he did not expect this title to produce their own such a big influence. Men's 100 meters, after all, the competition level is not high. He was satisfied with his performance, but win really did not expect.
Goal: breaking ten seconds of 27
Ran 10 seconds for 30 meters master of domestic, Hu Kai, he told reporters following the game there are many, from September's Shanghai Golden Grand Prix, to 10 months of National Games, as well as the subsequent East Asia Games. National men's 100 meters has entered the ranks of elite athletes, said Hu Kai, a real higher education by accepting his deeper understanding of movement itself, such as competitions and training and the dialectical relationship, and how to control the tempo pace is to improve the performance go a long way. Therefore, the next goal is to break 10 seconds, a personal best of 27, not ranking. Of course, he wanted to win the title the better. However, world experts gathered in Shanghai Grand Prix, that he should be a good opportunity to learn. The National Games is fierce competition for sure he was not opposed to title, but have to run good result Caixing.
Vice President of Tsinghua University in person to enjoy the airport Hu Kai Liu General Treatment
In the World Series win in the Sprint, in addition to Liu Xiang, China, Chongqing is the team's Hu Kai, a real second person. Therefore, 23 Capital Airport, Hu Kai indeed become the Universiade delegation hottest athlete. Flowers, applause, not only his name into the airport's most resounding slogans health and happiness, and his return also "alerted" the deputy party secretary of Tsinghua University, who's Da Jia Yang Zhenbin even Chongqing Luoan Ming were not far behind track and field team from Chongqing went to Beijing to pick you up.
But half a day after 23 become an unbearable burden for Hu Kai, which is a "Liu Xiang second" price. According to Luo Anming introduction, from the plane to go to bed at night, almost without interruption entertainment Hu Kai, an interview, attend the celebration dinner, etc., yesterday morning, Hu Kai, and also with the Universiade delegation of the Minister of Education accepted the interview, Hu Kai they Tsinghua University, also participated in this evening within the school leadership meeting will be organized. Hu Kai outside to the impact is obvious, Hu Kai in the National Games in order to ensure the proper training before, Luoan Ming and Hu Kai, a coach at Tsinghua University to exchange views, Hu Kai decided to decline all interviews in the near future, peace of mind preparing for 10 the Games.
Explanation
In Reverse Polish notation the operators follow their operands; for instance, to add three and four, one would write “3 4 +” rather than “3 + 4″. If there are multiple operations, the operator is given immediately after its second operand; so the expression written “3 4 + 5″ in conventional infix notation would be written “3 4 5 +” in RPN: first subtract 4 from 3, then add 5 to that. An advantage of RPN is that it obviates the need for parentheses that are required by infix. While “3 4 * 5″ can also be written “3 (4 * 5)”, that means something quite different from “(3 4) * 5″. In postfix, the former would be written “3 4 5 * “, which unambiguously means “3 (4 5 *) ” which of course reduces to “3 20 -”.
Interpreters of Reverse Polish notation are often stack-based; that is, operands are pushed onto a stack, and when an operation is performed, its operands are popped from a stack and its result pushed back on. So the value of postfix expression is on the top of the stack. Stacks, and therefore RPN, have the advantage of being easy to implement and very fast.
Note that, despite the name, reverse Polish notation is not exactly the reverse of Polish notation, as the operands of non-commutative operations are still written in the conventional order (e.g. “/ 6 3″ in Polish notation corresponds to “6 3 /” in reverse Polish, both evaluating to 2, whereas “3 6 /” would evaluate to 0.5).
Practical implications
This section is in a list format that may be better presented using prose. You can help by converting this section to prose, if appropriate. Editing help is available. (May 2009)
Calculations occur as soon as an operator is specified. Thus, expressions are not entered wholesale from right to left but calculated one piece at a time, most efficiently from the center outwards. Some claim this results in fewer operator errors when performing complex calculations.[citation needed]
The automatic stack permits the automatic storage of intermediate results for use later: this key feature is what permits RPN calculators to easily evaluate expressions of arbitrary complexity: they do not have limits on the complexity of expression they can calculate, unlike algebraic calculators.
Brackets and parentheses are unnecessary: the user simply performs calculations in the order that is required, letting the automatic stack store intermediate results on the fly for later use. Likewise, there is no requirement for the precedence rules required in infix notation.
In RPN calculators, no equals key is required to force computation to occur.
RPN calculators do, however, require an enter key to separate two adjacent numeric operands.
The machine state is always a stack of values awaiting operation; it is impossible to enter an operator onto the stack. This makes use conceptually easy compared to more complex entry methods.
Educationally, RPN calculators have the advantage that the user must understand the expression being calculated: it is not possible to simply copy the expression from paper into the machine and read off the answer without understanding. One must calculate from the middle of the expression, which is only meaningful if the user understands what they are doing.
Reverse Polish notation also reflects the way calculations are done on pen and paper. One first writes the numbers down and then performs the calculation. Thus the concept is easy to teach.
The widespread use of electronic calculators using infix in educational systems can make RPN impractical at times, not conforming to standard teaching methods. The fact that RPN has no use for parentheses means it is faster and easier to calculate expressions, particularly the more complex ones, than with an infix calculator, owing to fewer keystrokes and greater visibility of intermediate results. It is also easy for a computer to convert infix notation to postfix, most notably via Dijkstra’s shunting-yard algorithm see converting from infix notation below.
Users must know the size of the stack, since practical implementations of RPN use different sizes for the stack. For example, the algebraic expression , if performed with a stack size of 4 and executed from left to right, would exhaust the stack. The answer might be given as an erroneous imaginary number instead of approximately 0.5 as a real number.
When writing RPN on paper (something which even some users of RPN may not do) adjacent numbers need a separator between them. Using a space is not good practice because it requires clear handwriting to prevent confusion. For example, 12 34 + could look like 123 4 + but in a monospace font it is quite clear, while something like 12, 34 + is straightforward. The comma becomes a virtual Space key.
RPN is very easy to write and makes practical sense when it is adopted. The “learning” process to adopt RPN in writing usually comes later than adopting RPN on a calculator so that one may communicate more easily with non-RPN users.
The postfix algorithm
The algorithm for evaluating any postfix expression is fairly straightforward:
While there are input tokens left
Read the next token from input.
If the token is a value
Push it onto the stack.
Otherwise, the token is an operator (operator here includes both operators, and functions).
It is known a priori that the operator takes n arguments.
If there are fewer than n values on the stack
(Error) The user has not input sufficient values in the expression.
Else, Pop the top n values from the stack.
Evaluate the operator, with the values as arguments.
Push the returned results, if any, back onto the stack.
If there is only one value in the stack
That value is the result of the calculation.
If there are more values in the stack
(Error) The user input has too many values.
Example
The infix expression “5 + ((1 + 2) * 4) 3″ can be written down like this in RPN:
5 1 2 + 4 * + 3
The expression is evaluated left-to-right, with the inputs interpreted as shown in the following table (the Stack is the list of values the algorithm is “keeping track of” after the Operation given in the middle column has taken place):
Input
Operation
Stack
Comment
5
Push operand
5
1
Push operand
5, 1
2
Push operand
5, 1, 2
+
Add
5, 3
Pop two values (1, 2) and push result (3)
4
Push operand
5, 3, 4
*
Multiply
5, 12
Pop two values (3, 4) and push result (12)
+
Add
17
Pop two values (5, 12) and push result (17)
3
Push operand
17, 3
Subtract
14
Pop two values (17, 3) and push result (14)
When a computation is finished, its result remains as the top (and only) value in the stack; in this case, 14.
The above example could be rewritten by following the “chain calculation” method described by HP for their series of RPN calculators:
As was demonstrated in the Algebraic mode, it is usually easier (fewer keystrokes) in working a problem like this to begin with the arithmetic operations inside the parentheses first.
1 2 + 4 * 5 + 3
Converting from infix notation
Main article: Shunting-yard algorithm
Edsger Dijkstra invented the Shunting-yard algorithm to convert infix expressions to postfix (RPN), so named because its operation resembles that of a railroad shunting yard.
There are other ways of producing postfix expressions from infix notation. Most Operator-precedence parsers can be modified to produce postfix expressions; in particular, once an abstract syntax tree has been constructed, the corresponding postfix expression is given by a simple post-order traversal of that tree.
Implementations
History of implementations
The first computers to implement architectures enabling RPN were the English Electric Company’s KDF9 machine, which was announced in 1960 and delivered (i.e. made available commercially) in 1963, and the American Burroughs B5000, announced in 1961 and also delivered in 1963. One of the designers of the B5000, Robert S. Barton, later wrote that he developed RPN independently of Hamblin, sometime in 1958 while reading a textbook on symbolic logic, and before he was aware of Hamblin’s work.
RPN in Hewlett-Packard
Friden introduced RPN to the desktop calculator market with the EC-130 in June 1963. Hewlett-Packard (HP) engineers designed the 9100A Desktop Calculator in 1968 with RPN. This calculator popularized RPN among the scientific and engineering communities, even though early advertisements for the 9100A failed to mention RPN. The HP-35, the world’s first handheld scientific calculator, used RPN in 1972. HP used RPN on every handheld calculator it sold, whether scientific, financial, or programmable, until it introduced an adding machine-style calculator, the HP-10A. HP introduced an LCD-based line of calculators in the early 1980s that used RPN, such as the HP-10C, HP-11C, HP-15C, HP-16C, and the famous financial calculator, the HP-12C. When Hewlett-Packard introduced a later business calculator, the HP-19B, without RPN, feedback from financiers and others used to the 12-C compelled them to release the HP-19BII, which gave users the option of using algebraic notation or RPN. From 1990 to 2003 HP manufactured the HP-48 series of graphing RPN calculators and in 2006 introduced the HP-50g with a 131×80 LCD and a 75 MHz ARM CPU that emulates the Saturn CPU of the HP-48 series.
RPN in Soviet Union
Soviet programmable calculators (MK-52, MK-61, B3-34 and earlier B3-21 models) used RPN for both automatic mode and programming. Modern Russian calculators MK-161 and MK-152, designed and manufactured in Novosibirsk since 2007, are backward compatible with them. Their extended architecture is also based on Reverse Polish notation.
Current RPN implementations
Existing implementations using Reverse Polish notation include:
Any Stack-oriented programming language, such as:
Forth
Factor
PostScript page description language
Ambi
Befunge
RPN Scientific Calculator for Mac OS X
RPN calculator for Microsoft Windows
XCALC for Microsoft Windows
Open Source RPN Calculator for Microsoft Windows
RPN Alchemy Arbitrary Precision RPN Calculator for Microsoft Windows and Linux
Microsoft PowerToy calculator for Microsoft Windows XP
RPN calculator for cellular phones, in open source Java
RPN calculator for Palm PDAs
RPN Financial Calculator for Android smartphones
Mac OS X Calculator
RPN calculator for Mac OS X and iPhone
Some Hewlett-Packard science/engineering and business/finance calculators
Unix system calculator program dc
MAcalc for the iPhone
Interactive JavaScript RPN calculator
JavaScript RPN calculator with keyboard-based user interface, more like HP calculators
Mouseless online RPN calculator
Linux IpTables “Rope” programming language
b:Ada Programming/Mathematical calculations (RPN calculator implemented in Ada)
Emacs lisp library package: calc
Sinclair calculators
Open source GTK+ based galculator
Infix to Postfix Conversion / Postfix Evaluator / Postfix to Infix Conversion
Simple XUL RPN Calculator
Programmable JavaScript RPN calculator
Basic JavaScript keyboard-centric RPN calculator you can copy and customize
Custom Function for FileMaker Pro Advance
RPNParser class in Ruby
The RPN/RPL Implementations web page, also posted as a USENET FAQ
HC – Open Source calculator – Open Source calculator for almost any system (precompiled versions exist for *NIX and Windows) which supports both infix and postfix (RPN) notation
A Postfix evaluator implemented in Python
import operator
OPERATORS = {
‘+’: operator.add,
‘-’: operator.sub,
‘*’: operator.mul,
‘/’: operator.truediv,
‘^’: operator.pow,
‘%’: operator.mod,
}
def evaluate_rpn(expression, stack):
try:
for token in expression.split():
try:
result = float(token)
except ValueError:
result = OPERATORS[token](stack.pop(-2), stack.pop())
stack.append(result)
except KeyError:
print “Invalid input”, repr(token)
except IndexError:
print “The stack is too small to apply the operator”, repr(token)
if __name__ == “__main__”:
print “RPN.py – Press Control-D to exit.”
stack = []
try:
while True:
evaluate_rpn(raw_input(‘%s> ‘ % stack), stack)
except (KeyboardInterrupt, EOFError):
See also
Calculator input methods
Factor programming language
Formula calculator
Forth (programming language)
HP calculators
Joy Programming Language
LIFO (computing)
Object Subject Verb
Orpie, an RPN calculator
PostScript
Stack machine
Subject Object Verb
References
^ “An Analysis of a Logical Machine Using Parenthesis-Free Notation,” by Arthur W. Burks, Don W. Warren and Jesse B. Wright, 1954
^ “Charles L. Hamblin and his work” by Peter McBurney
^ “Charles L. Hamblin: Computer Pioneer” by Peter McBurney, July 27, 2008. “Hamblin soon became aware of the problems of (a) computing mathematical formulae containing brackets, and (b) the memory overhead in having dealing with memory stores each of which had its own name. One solution to the first problem was Jan Lukasiewicz’s Polish notation, which enables a writer of mathematical notation to instruct a reader the order in which to execute the operations (e.g. addition, multiplication, etc) without using brackets. Polish notation achieves this by having an operator (+, *, etc) precede the operands to which it applies, e.g., +ab, instead of the usual, a+b. Hamblin, with his training in formal logic, knew of Lukasiewicz’s work.”
^ http://h20219.www2.hp.com/Hpsub/downloads/17b2pChain.pdf
^ Elektronika B3-21 page on RSkey.org
^ Elektronika MK-161 page on RSkey.org
^ MK-152: Old Russian Motive in a New Space Age.
External links
RPN or DAL? A brief analysis of Reverse Polish Notation against Direct Algebraic Logic By James Redin
Postfix Notation Mini-Lecture By Bob Brown
Fith: An Alien Conlang With A LIFO Grammar By Jeffrey Henning
Good Ideas, Through the Looking Glass by Niklaus Wirth
Ambi browser-based extensible RPN calculator By David Pratten
Categories: Calculators | Mathematical notation | Articles with example Python code | Polish inventions | Science and technology in PolandHidden categories: Articles needing cleanup from May 2009 | All pages needing cleanup | Articles with sections that need to be turned into prose from May 2009 | All articles with unsourced statements | Articles with unsourced statements from June 2008
Read more on Reverse Polish notation…
