In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems. Algorithms can perform calculation, data processing, automated reasoning, other tasks; as an effective method, an algorithm can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. Starting from an initial state and initial input, the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states producing "output" and terminating at a final ending state; the transition from one state to the next is not deterministic. The concept of algorithm has existed for centuries. Greek mathematicians used algorithms in the sieve of Eratosthenes for finding prime numbers, the Euclidean algorithm for finding the greatest common divisor of two numbers; the word algorithm itself is derived from the 9th century mathematician Muḥammad ibn Mūsā al-Khwārizmī, Latinized Algoritmi.
A partial formalization of what would become the modern concept of algorithm began with attempts to solve the Entscheidungsproblem posed by David Hilbert in 1928. Formalizations were framed as attempts to define "effective calculability" or "effective method"; those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's Formulation 1 of 1936, Alan Turing's Turing machines of 1936–37 and 1939. The word'algorithm' has its roots in Latinizing the name of Muhammad ibn Musa al-Khwarizmi in a first step to algorismus. Al-Khwārizmī was a Persian mathematician, astronomer and scholar in the House of Wisdom in Baghdad, whose name means'the native of Khwarazm', a region, part of Greater Iran and is now in Uzbekistan. About 825, al-Khwarizmi wrote an Arabic language treatise on the Hindu–Arabic numeral system, translated into Latin during the 12th century under the title Algoritmi de numero Indorum; this title means "Algoritmi on the numbers of the Indians", where "Algoritmi" was the translator's Latinization of Al-Khwarizmi's name.
Al-Khwarizmi was the most read mathematician in Europe in the late Middle Ages through another of his books, the Algebra. In late medieval Latin, English'algorism', the corruption of his name meant the "decimal number system". In the 15th century, under the influence of the Greek word ἀριθμός'number', the Latin word was altered to algorithmus, the corresponding English term'algorithm' is first attested in the 17th century. In English, it was first used in about 1230 and by Chaucer in 1391. English adopted the French term, but it wasn't until the late 19th century that "algorithm" took on the meaning that it has in modern English. Another early use of the word is from 1240, in a manual titled Carmen de Algorismo composed by Alexandre de Villedieu, it begins thus: Haec algorismus ars praesens dicitur, in qua / Talibus Indorum fruimur bis quinque figuris. Which translates as: Algorism is the art by which at present we use those Indian figures, which number two times five; the poem is a few hundred lines long and summarizes the art of calculating with the new style of Indian dice, or Talibus Indorum, or Hindu numerals.
An informal definition could be "a set of rules that defines a sequence of operations". Which would include all computer programs, including programs that do not perform numeric calculations. A program is only an algorithm if it stops eventually. A prototypical example of an algorithm is the Euclidean algorithm to determine the maximum common divisor of two integers. Boolos, Jeffrey & 1974, 1999 offer an informal meaning of the word in the following quotation: No human being can write fast enough, or long enough, or small enough† to list all members of an enumerably infinite set by writing out their names, one after another, in some notation, but humans can do something useful, in the case of certain enumerably infinite sets: They can give explicit instructions for determining the nth member of the set, for arbitrary finite n. Such instructions are to be given quite explicitly, in a form in which they could be followed by a computing machine, or by a human, capable of carrying out only elementary operations on symbols.
An "enumerably infinite set" is one whose elements can be put into one-to-one correspondence with the integers. Thus and Jeffrey are saying that an algorithm implies instructions for a process that "creates" output integers from an arbitrary "input" integer or integers that, in theory, can be arbitrarily large, thus an algorithm can be an algebraic equation such as y = m + n – two arbitrary "input variables" m and n that produce an output y. But various authors' attempts to define the notion indicate that the word implies much more than this, something on the order of: Precise instructions for a fast, efficient, "good" process that specifies the "moves" of "the computer" to find and process arbitrary input integers/symbols m and n, symbols + and =... and "effectively" produce, in a "reasonable" time, output-integer y at a specified place and in a specified format
A database is an organized collection of data stored and accessed electronically from a computer system. Where databases are more complex they are developed using formal design and modeling techniques; the database management system is the software that interacts with end users and the database itself to capture and analyze the data. The DBMS software additionally encompasses; the sum total of the database, the DBMS and the associated applications can be referred to as a "database system". The term "database" is used to loosely refer to any of the DBMS, the database system or an application associated with the database. Computer scientists may classify database-management systems according to the database models that they support. Relational databases became dominant in the 1980s; these model data as rows and columns in a series of tables, the vast majority use SQL for writing and querying data. In the 2000s, non-relational databases became popular, referred to as NoSQL because they use different query languages.
Formally, a "database" refers to the way it is organized. Access to this data is provided by a "database management system" consisting of an integrated set of computer software that allows users to interact with one or more databases and provides access to all of the data contained in the database; the DBMS provides various functions that allow entry and retrieval of large quantities of information and provides ways to manage how that information is organized. Because of the close relationship between them, the term "database" is used casually to refer to both a database and the DBMS used to manipulate it. Outside the world of professional information technology, the term database is used to refer to any collection of related data as size and usage requirements necessitate use of a database management system. Existing DBMSs provide various functions that allow management of a database and its data which can be classified into four main functional groups: Data definition – Creation and removal of definitions that define the organization of the data.
Update – Insertion and deletion of the actual data. Retrieval – Providing information in a form directly usable or for further processing by other applications; the retrieved data may be made available in a form the same as it is stored in the database or in a new form obtained by altering or combining existing data from the database. Administration – Registering and monitoring users, enforcing data security, monitoring performance, maintaining data integrity, dealing with concurrency control, recovering information, corrupted by some event such as an unexpected system failure. Both a database and its DBMS conform to the principles of a particular database model. "Database system" refers collectively to the database model, database management system, database. Physically, database servers are dedicated computers that hold the actual databases and run only the DBMS and related software. Database servers are multiprocessor computers, with generous memory and RAID disk arrays used for stable storage.
RAID is used for recovery of data. Hardware database accelerators, connected to one or more servers via a high-speed channel, are used in large volume transaction processing environments. DBMSs are found at the heart of most database applications. DBMSs may be built around a custom multitasking kernel with built-in networking support, but modern DBMSs rely on a standard operating system to provide these functions. Since DBMSs comprise a significant market and storage vendors take into account DBMS requirements in their own development plans. Databases and DBMSs can be categorized according to the database model that they support, the type of computer they run on, the query language used to access the database, their internal engineering, which affects performance, scalability and security; the sizes and performance of databases and their respective DBMSs have grown in orders of magnitude. These performance increases were enabled by the technology progress in the areas of processors, computer memory, computer storage, computer networks.
The development of database technology can be divided into three eras based on data model or structure: navigational, SQL/relational, post-relational. The two main early navigational data models were the hierarchical model and the CODASYL model The relational model, first proposed in 1970 by Edgar F. Codd, departed from this tradition by insisting that applications should search for data by content, rather than by following links; the relational model employs sets of ledger-style tables, each used for a different type of entity. Only in the mid-1980s did computing hardware become powerful enough to allow the wide deployment of relational systems. By the early 1990s, relational systems dominated in all large-scale data processing applications, as of 2018 they remain dominant: IBM DB2, Oracle, MySQL, Microsoft SQL Server are the most searched DBMS; the dominant database language, standardised SQL for the relational model, has influenced database languages for other data models. Object databases were developed in the 1980s to overcome the inconvenience of object-relational impedance mismatch, which led to the coining of the term "post-relational" and the development of hybrid object-relational databas
Relational database management system
A relational database management system is a database management system based on the relational model of data. Most databases in widespread use today are based on this model. RDBMSs have been a common option for the storage of information in databases used for financial records and logistical information, personnel data, other applications since the 1980s. Relational databases have replaced legacy hierarchical databases and network databases, because RDBMS were easier to implement and administer. Nonetheless, relational databases received continued, unsuccessful challenges by object database management systems in the 1980s and 1990s, as well as by XML database management systems in the 1990s. However, due to the expanse of technologies, such as horizontal scaling of computer clusters, NoSQL databases have become popular as an alternative to RDBMS databases. According to DB-Engines, in June 2018, the most used systems were Oracle, MySQL, Microsoft SQL Server, PostgreSQL, IBM DB2, Microsoft Access, SQLite.
According to research company Gartner, in 2011, the five leading Proprietary software relational database vendors by revenue were Oracle, IBM, Microsoft, SAP including Sybase, Teradata. In 1974, IBM began developing System R, a research project to develop a prototype RDBMS. However, the first commercially available RDBMS was Oracle, released in 1979 by Relational Software, now Oracle Corporation. Other examples of an RDBMS include DB2, SAP Sybase ASE, Informix. In 1984, the first RDBMS for Macintosh began being developed, code-named Silver Surfer, it was released in 1987 as 4th Dimension and known today as 4D; the term "relational database" was invented by E. F. Codd at IBM in 1970. Codd introduced the term in his research paper "A Relational Model of Data for Large Shared Data Banks". In this paper and papers, he defined what he meant by "relational". One well-known definition of what constitutes a relational database system is composed of Codd's 12 rules. However, no commercial implementations of the relational model conform to all of Codd's rules, so the term has come to describe a broader class of database systems, which at a minimum: Present the data to the user as relations.
The first systems that were faithful implementations of the relational model were from: University of Michigan -- Micro DBMS Massachusetts Institute of Technology IBM UK Scientific Centre at Peterlee -- IS1 and its successor, PRTV The first system sold as an RDBMS was Multics Relational Data Store. Ingres and IBM BS12 followed; the most definition of an RDBMS is a product that presents a view of data as a collection of rows and columns if it is not based upon relational theory. By this definition, RDBMS products implement some but not all of Codd's 12 rules. A second school of thought argues that if a database does not implement all of Codd's rules, it is not relational; this view, shared by many theorists and other strict adherents to Codd's principles, would disqualify most DBMSs as not relational. For clarification, they refer to some RDBMSs as truly-relational database management systems, naming others pseudo-relational database management systems; as of 2009, most commercial relational DBMSs employ SQL as their query language.
Alternative query languages have been proposed and implemented, notably the pre-1996 implementation of Ingres QUEL. SQL Object database Online analytical processing and ROLAP Data warehouse Star schema Snowflake schema List of relational database management systems Comparison of relational database management systems
IBM Research - Almaden
IBM Research - Almaden is in Almaden Valley, San Jose, is one of IBM's twelve worldwide research labs that form IBM Research. Its scientists perform basic and applied research in computer science, storage systems, physical sciences, materials science and technology; the center opened in 1986, continues the research started in San Jose more than fifty years ago. Nearly all of Almaden’s 500 research employees are in technical functions and more than half of these hold Ph. D.s. The lab is home to ten IBM Fellows, ten IBM Distinguished Engineers, nine IBM Master Inventors and seventeen members of the IBM Academy of Technology. Almaden occupies part of a site owned by IBM at 650 Harry Road on nearly 700 acres of land in the hills above Silicon Valley; the site, built in 1985 for the research center, was chosen because of its close proximity to Stanford University, UC Santa Cruz, UC Berkeley and other collaborative academic institutions. Today, the research division is still the largest tenant of the site, but the majority of occupants work for other divisions of IBM.
IBM opened its first West Coast research centre, the San Jose Research Laboratory in 1952, managed by Reynold B. Johnson. Amongst its first developments was the IBM 350, the first commercial moving head hard disk drive. Launched in 1956, this saw use in the IBM 305 RAMAC computer system. Subdivisions included the Advanced Systems Development Division. Directors of the center include hard disc drive developer Jack Harker. Prompted by a need for additional space, the center moved to its present Almaden location in 1986. Scientists at IBM Almaden have contributed to several scientific discoveries such as the development of photoresists and the quantum mirage effect; the following are some of the famous scientists who have worked in the past or are working in this laboratory: Rakesh Agrawal, John Backus, Raymond F. Boyce, Donald D. Chamberlin, Ashok K. Chandra, Edgar F. Codd, Mark Dean, Cynthia Dwork, Don Eigler, Ronald Fagin, Jim Gray, Laura M. Haas, Joseph Halpern, Andreas J. Heinrich, Reynold B.
Johnson, Maria Klawe, Jaishankar Menon, Dharmendra Modha, William E. Moerner, C. Mohan, Stuart Parkin, Nick Pippenger, Patricia Selinger, Ted Selker, Barbara Simons, Ramakrishnan Srikant, Larry Stockmeyer, Moshe Vardi, Jennifer Widom. Official website
International Business Machines Corporation is an American multinational information technology company headquartered in Armonk, New York, with operations in over 170 countries. The company began in 1911, founded in Endicott, New York, as the Computing-Tabulating-Recording Company and was renamed "International Business Machines" in 1924. IBM produces and sells computer hardware and software, provides hosting and consulting services in areas ranging from mainframe computers to nanotechnology. IBM is a major research organization, holding the record for most U. S. patents generated by a business for 26 consecutive years. Inventions by IBM include the automated teller machine, the floppy disk, the hard disk drive, the magnetic stripe card, the relational database, the SQL programming language, the UPC barcode, dynamic random-access memory; the IBM mainframe, exemplified by the System/360, was the dominant computing platform during the 1960s and 1970s. IBM has continually shifted business operations by focusing on higher-value, more profitable markets.
This includes spinning off printer manufacturer Lexmark in 1991 and the sale of personal computer and x86-based server businesses to Lenovo, acquiring companies such as PwC Consulting, SPSS, The Weather Company, Red Hat. In 2014, IBM announced that it would go "fabless", continuing to design semiconductors, but offloading manufacturing to GlobalFoundries. Nicknamed Big Blue, IBM is one of 30 companies included in the Dow Jones Industrial Average and one of the world's largest employers, with over 380,000 employees, known as "IBMers". At least 70% of IBMers are based outside the United States, the country with the largest number of IBMers is India. IBM employees have been awarded five Nobel Prizes, six Turing Awards, ten National Medals of Technology and five National Medals of Science. In the 1880s, technologies emerged that would form the core of International Business Machines. Julius E. Pitrap patented the computing scale in 1885. On June 16, 1911, their four companies were amalgamated in New York State by Charles Ranlett Flint forming a fifth company, the Computing-Tabulating-Recording Company based in Endicott, New York.
The five companies had offices and plants in Endicott and Binghamton, New York. C.. They manufactured machinery for sale and lease, ranging from commercial scales and industrial time recorders and cheese slicers, to tabulators and punched cards. Thomas J. Watson, Sr. fired from the National Cash Register Company by John Henry Patterson, called on Flint and, in 1914, was offered a position at CTR. Watson joined CTR as General Manager 11 months was made President when court cases relating to his time at NCR were resolved. Having learned Patterson's pioneering business practices, Watson proceeded to put the stamp of NCR onto CTR's companies, he implemented sales conventions, "generous sales incentives, a focus on customer service, an insistence on well-groomed, dark-suited salesmen and had an evangelical fervor for instilling company pride and loyalty in every worker". His favorite slogan, "THINK", became a mantra for each company's employees. During Watson's first four years, revenues reached $9 million and the company's operations expanded to Europe, South America and Australia.
Watson never liked the clumsy hyphenated name "Computing-Tabulating-Recording Company" and on February 14, 1924 chose to replace it with the more expansive title "International Business Machines". By 1933 most of the subsidiaries had been merged into one company, IBM. In 1937, IBM's tabulating equipment enabled organizations to process unprecedented amounts of data, its clients including the U. S. Government, during its first effort to maintain the employment records for 26 million people pursuant to the Social Security Act, the tracking of persecuted groups by Hitler's Third Reich through the German subsidiary Dehomag. In 1949, Thomas Watson, Sr. created IBM World Trade Corporation, a subsidiary of IBM focused on foreign operations. In 1952, he stepped down after 40 years at the company helm, his son Thomas Watson, Jr. was named president. In 1956, the company demonstrated the first practical example of artificial intelligence when Arthur L. Samuel of IBM's Poughkeepsie, New York, laboratory programmed an IBM 704 not to play checkers but "learn" from its own experience.
In 1957, the FORTRAN scientific programming language was developed. In 1961, IBM developed the SABRE reservation system for American Airlines and introduced the successful Selectric typewriter. In 1963, IBM employees and computers helped. A year it moved its corporate headquarters from New York City to Armonk, New York; the latter half of the 1960s saw IBM continue its support of space exploration, participating in the 1965 Gemini flights, 1966 Saturn flights and 1969 lunar mission. On April 7, 1964, IBM announced the first computer system family, the IBM System/360, it spanned the complete range of commercial and scientific applications from large to small, allowing companies for the first time to upgrade to models with greater computing capability without having to rewrite their applications. It was followed by the IBM System/370 in 1970. Together the
The System/38 was a minicomputer and midrange computer server platform manufactured and sold by the IBM Corporation. The system offered a number of innovative features, was the brainchild of Frank Soltis and Glenn Henry. IBM announced the System/38 in 1978. Developed under the code-name "Pacific", it was made commercially available in August 1979; the System/38 was oriented toward a multi-user system environment. The typical system handled from a dozen to several dozen terminals; the midrange predecessors to the System/38 included the System/3, System/32, System/34. The System/38 offered more capacity than the previous System/34; the System/38 chronologically preceded the System/36, a successor to the System/34. The System/38 was nearly called the System/380, the AS/400 was nearly called the System/40; the System/38 was superseded by the AS/400. The AS/400 was a re-marketing of the System/38, with some updates to the operating system, including the luxurious non-trivial expansion of source and object names from 8 to a new 10 characters maximum.
S/38 programs with'observability' intact, source code embedded within the compiled binary executive at the expense of larger compiled object sizes, can still run on the AS/400 and successor systems as the restore option incorporates a recompile for the back-version source. However, most proprietary vendor application libraries of objects were compiled without such'observability' and required original vendor replacement and consequent expense when upgrading to an AS/400. Pricing at the time was tiered, the same exact software, but priced based upon the model, its speed and capacity, of the system to be installed upon; the AS/400 evolved into the iSeries. The System/38 legacy lives on in the enterprise-class IBM Power Systems series, which superseded System i in 2008, which can run IBM i as well as AIX and Linux. By contrast, competing proprietary computing architectures from the early 1980s such as Wang VS and Hewlett Packard's HP 3000 have long been discontinued without a compatible upgrade path.
In hindsight, the System/38's architecture was too demanding of the hardware of the era. When first launched, it struggled under the overhead of the software and operating system, which consumed 60 MB on disk, a vast sum at the time, leading some wags to suggest that the pre-announce code name for the series, PACIFIC, was an acronym meaning "Performance Ain't Critical If Function Is Complete." Decades the same software dismissed by some critics as a momentary aberration, runs better than on many thousands of modern iSeries and IBM/i systems within commercial and government enterprises of all types and sizes. The IBM 5381 System Unit contained processor, main memory, disk storage, a diskette magazine drive, a system console with keyboard and a display. 5381 was available in Model 100 and Model 200. The IBM 5382 System Unit was physically identical to 5381, but had more powerful processors, more memory, more disk storage. 5382 was available in Models 300, 400, 500, 600, 700. The system included a central processing unit with 512K, 768K, 1024K, 1280K, or 1536K bytes of main storage, It included a memory management unit supporting demand paging, used by the system software to implement a single-level store architecture.
The System/38 console included a keyboard and a display screen with 16 lines of 64 characters, inconsistent with the locally attached 5250 terminals, which were either 12x40 or 24x80, depending on model. The keyboard was used by the system operator; the diskette magazine drive was standard on all models. The operating system of the System/38 was called CPF, for "Control Program Facility". CPF is not related to SSP, the operating system of the IBM System/34 and System/36. CPF objects are files, message queues, user profiles, libraries; the System/38 has the distinction of being the first commercially available IBM Midrange computer to have a database management system integrated into the operating system. The operational control language of the System/38 was called CL, for "Control Language". CL programs, similar in concept to shell scripts, could be executed natively; the System/38 had 48-bit addressing, unique for the time, a novel integrated database system. The System/38 had security built in as part of its architecture.
Each object or library could have access controlled on a user-by-user basis. This has been expanded throughout the AS/400 and iSeries computer lines; the System/38 and its descendants are the only commercial computers to use a machine interface architecture to isolate the application software and most of the operating system from hardware dependencies, including such details as address size and register size. Compilers for System/38 and its successors generate code in a high-level instruction set. MI/TIMI is a virtual instruction set. Unlike some other virtual-machine architectures in which the virtual instructions are interpreted at runtime, MI/TIMI instructions are never interpreted, they constitute an intermediate compile time step and are translated into the processor's instruction set as the final compilation step. The MI/TIMI instructions are stored within the
Pratt & Whitney
Pratt & Whitney is an American aerospace manufacturer with global service operations. It is a subsidiary of United Technologies. Pratt & Whitney's aircraft engines are used in both civil aviation and military aviation, its headquarters are in Connecticut. As one of the "big three" aero-engine manufacturers, it competes with General Electric and Rolls-Royce, although it has formed joint ventures with both of these companies. In addition to aircraft engines, Pratt & Whitney manufactures gas turbines for industrial and power generation, marine turbines; as of 2014, the company reported having 31,500 employees supporting more than 11,000 customers in 180 countries around the world. In 2013, Pratt & Whitney's revenue totaled $14.5 billion. In April 1925, Frederick Rentschler, an Ohio native and former executive at Wright Aeronautical, was determined to start an aviation-related business of his own, his social network included Edward Deeds, another prominent Ohioan of the early aviation industry, Frederick's brother Gordon Rentschler, both of whom were on the board of Niles Bement Pond one of the largest machine tool corporations in the world.
Frederick Rentschler approached these men. Deeds and G. Rentschler persuaded the board of Niles Bement Pond that their Pratt & Whitney Machine Tool subsidiary of Hartford, should provide the funding and location to build a new aircraft engine being developed by Rentschler, George J. Mead, colleagues, all of Wright Aeronautical. Conceived and designed by Mead, the new engine would be a air-cooled, radial design. Pratt & Whitney Machine Tool was going through a period of self-revision at the time to prepare itself for the post-Great War era, discontinuing old product lines and incubating new ones; the Great War had been profitable to P&WMT, but the peace brought a predictable glut to the machine tool market, as contracts with governments were canceled and the market in used built tools competed against new ones. P&WMT's future growth would depend on innovation. Having idle factory space and capital available at this historical moment, to be invested wherever good return seemed available, P&WMT saw the postwar aviation industry, both military and civil, as one with some of the greatest growth and development potential available anywhere for the next few decades.
It lent Rentschler $250,000, the use of the Pratt & Whitney name, space in their building. This was the beginning of the Whitney Aircraft Company. Pratt & Whitney Aircraft's first engine, the 425 horsepower R-1340 Wasp, was completed on Christmas Eve 1925. On its third test run it passed the Navy qualification test in March 1926; the Wasp exhibited reliability that revolutionized American aviation. The R-1340 powered the aircraft of Wiley Post, Amelia Earhart, many other record flights; the R-1340 was followed by another successful engine, the R-985 Wasp Junior. A whole Wasp series was developed. Both engines are still in use in agricultural aircraft around the world and produce more power than their original design criteria. George Mead soon led the next step in the field of large, state-of-the-art, air-cooled, radial aircraft engines when Pratt & Whitney released its R-1690 Hornet, it was "a bigger Wasp". In 1929, Rentschler ended his association with Pratt & Whitney Machine Tool and merged Pratt & Whitney Aircraft with Boeing and other companies to form the United Aircraft and Transport Corporation.
His agreement allowed him to carry the Whitney name with him to his new corporation. In October 2014, Pratt & Whitney was awarded a $592 million contract with US Defense Department to supply 36 F135 engines for the F-35 fighter. In January 2017, 10 employees left the company, including the head of the F135 engine program. Incurred expenses used to transport South Korean officials to the company's West Palm Beach facility in 2012 were deemed unethical, which led to the departure of the employees. Pratt & Whitney is headquartered in East Hartford and has plants in Springdale, Arkansas; the home stadium for the University of Connecticut Huskies football team, Rentschler Field, is located adjacent to Pratt & Whitney's East Hartford, Connecticut campus, on Pratt's company-owned former airfield of the same name. In 2015, the stadium was renamed to Pratt & Whitney Stadium at Rentschler Field in time for the 2015–2016 University of Connecticut football season. Pratt & Whitney is a business unit of industrial conglomerate United Technologies, making it a sister company to Collins Aerospace, Otis Elevator Company, UTC Fire & Security, UTC Power and refrigeration giant Carrier Corporation.
It is involved in two major joint ventures, the Engine Alliance with GE which manufactures engines for the Airbus A380, International Aero Engines company with Rolls-Royce, MTU Aero Engines, the Japanese Aero Engines Corporation which manufactures engines for the Airbus A320 and the McDonnell Douglas MD-90 aircraft. Pratt & Whitney's large commercial engines power more than 25 percent of the world’s passenger aircraft fleet and serve more than 800 customers in 160 countries. With more than 16,000 large commercial engines installed today, Pratt & Whitney provides power to hundreds of airlines and operators, from narrow-bodied airplanes to wide-bodied jumbo jetliners. In June 2007, Pratt & Whitney’