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In abstract algebra and formal logic, the **distributive property** of binary operations generalizes the **distributive law** from elementary algebra. In propositional logic, **distribution** refers to two valid rules of replacement. The rules allow one to reformulate conjunctions and disjunctions within logical proofs.

For example, in arithmetic:

In the left-hand side of the first equation, the 2 multiplies the sum of 1 and 3; on the right-hand side, it multiplies the 1 and the 3 individually, with the products added afterwards.
Because these give the same final answer (8), it is said that multiplication by 2 *distributes* over addition of 1 and 3.
Since one could have put any real numbers in place of 2, 1, and 3 above, and still have obtained a true equation, we say that multiplication of real numbers *distributes* over addition of real numbers.

Given a set *S* and two binary operators ∗ and + on *S*, we say that the operation:

∗ is *left-distributive* over + if, given any elements *x*, *y*, and *z* of *S*,

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In probability and statistics, a **probability distribution** assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference. Examples are found in experiments whose sample space is non-numerical, where the distribution would be a categorical distribution; experiments whose sample space is encoded by discrete random variables, where the distribution can be specified by a probability mass function; and experiments with sample spaces encoded by continuous random variables, where the distribution can be specified by a probability density function. More complex experiments, such as those involving stochastic processes defined in continuous time, may demand the use of more general probability measures.

In applied probability, a probability distribution can be specified in a number of different ways, often chosen for mathematical convenience:

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https://wn.com/Probability_distribution

In mathematics and computer science, a **history monoid** is a way of representing the histories of concurrently running computer processes as a collection of strings, each string representing the individual history of a process. The history monoid provides a set of synchronization primitives (such as locks, mutexes or thread joins) for providing rendezvous points between a set of independently executing processes or threads.

History monoids occur in the theory of concurrent computation, and provide a low-level mathematical foundation for process calculi, such as CSP the language of communicating sequential processes, or CCS, the calculus of communicating systems. History monoids were first presented by M.W. Shields.

History monoids are isomorphic to trace monoids (free partially commutative monoids) and to the monoid of dependency graphs. As such, they are free objects and are universal. The history monoid is a type of semi-abelian categorical product in the category of monoids.

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An **audio engineer** works on the recording, manipulation, mixing, reproduction, and reinforcement of sound. Audio engineers work on the "...technical aspect of recording—the placing of microphones, the turning of pre-amp knobs, the setting of levels. The physical recording of any project is done by an engineer ... the nuts and bolts." Many audio engineers creatively use technologies to produce sound for film, radio, television, music, electronic products and computer games. Audio engineers also set up and operate sound reinforcement systems for concert, corporate, theatre, sporting and other events.

Alternatively, the term audio engineer can refer to a scientist or professional engineer who holds a B.Sc. or M.Sc. who designs, develops and builds new audio technologies working within the field of acoustical engineering.

Audio engineering concerns the creative and practical aspects of sounds including speech and music, as well as the development of new audio technologies and advancing scientific understanding of audible sound.

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The **Cal Poly Pomona College of Engineering** is the engineering college at California State Polytechnic University, Pomona (Cal Poly Pomona) located in Pomona, California, United States. With over 5,600 undergraduate students (as of fall 2015), it is the largest engineering college in Southern California, the second largest college of engineering in the California State University system, and the seventeenth largest engineering college in the United States. In 2013 *U.S. News & World Report* ranks Cal Poly Pomona's undergraduate program 14th in the nation (for Master's-granting universities), and mentions that Cal Poly Pomona "has one of the top ranked engineering programs, and graduates roughly 1 of every 14 engineers in the state of California."

Because of the hands-on approach to academics and undergraduate focus, the college of engineering at Cal Poly Pomona is among the most selective engineering colleges in the nation and most of its departments are currently declared impacted (hold stringent standards for admissions). For fall 2015, the college admitted 45.3 percent of its total freshmen applicants who held an average unweighted GPA of 3.72 (out of 4.00) and SATs of 1178 (out of 1600), making the college admissions process statistically comparable to the University of California campuses at Davis, Irvine, and Santa Barbara.

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**Engineering** is a professional discipline.

**Engineering** may also refer to:

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In abstract algebra and formal logic, the **distributive property** of binary operations generalizes the **distributive law** from elementary algebra. In propositional logic, **distribution** refers to two valid rules of replacement. The rules allow one to reformulate conjunctions and disjunctions within logical proofs.

For example, in arithmetic:

In the left-hand side of the first equation, the 2 multiplies the sum of 1 and 3; on the right-hand side, it multiplies the 1 and the 3 individually, with the products added afterwards.
Because these give the same final answer (8), it is said that multiplication by 2 *distributes* over addition of 1 and 3.
Since one could have put any real numbers in place of 2, 1, and 3 above, and still have obtained a true equation, we say that multiplication of real numbers *distributes* over addition of real numbers.

Given a set *S* and two binary operators ∗ and + on *S*, we say that the operation:

∗ is *left-distributive* over + if, given any elements *x*, *y*, and *z* of *S*,

This page contains text from Wikipedia, the Free Encyclopedia -
https://wn.com/Distributive_property

Nebulas Partners with KingSoft Cloud (KSYUN) to Explore Blockchain Games. The Public Chain may Become the Main Battlefield of Blockchain Games ... Digital game **distribution** platform the Abyss, the game **engine** Cocos, the blockchain game Kexingqiu, and others, have successively joined the “Project-X” program ... However, public chains can realize the greater circulation of game virtual assets to the blockchain world ... Nebulas.io ... ... ....

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Decatur City Council President Paige Bibbee is proposing the city spend $50,000 on piloting the use of litter grates ... The interceptors are custom-built for each inlet. The installation of these devices in hot spots allows for a more **distributive** approach to floatable control … .”. Bibbee said City **Engineer** Carl Prewitt would pinpoint the big outlets for the best locations for the grates ... She opposes buying litter traps ... Subscribe ... ....

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The dispute reveals the complicated relationship between utility companies and new ways of generating power, said Juan Carlos Balda, the department head of electrical **engineering** at the University of Arkansas, Fayetteville. Net metering is a type of **distributed** generation, where power comes from multiple, smaller points instead of a big, central power plant....

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DeSousa previously worked as a project **engineer** ... Reilly joined in 1993 as an environmental **engineer** and held various management positions, most recently as division manager of environmental services ... Kortz joined as director of **engineering** and was named to the board of directors. Kortz has 20 years of experience in civil and environmental **engineering**, public works operations and administration and construction....

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CSPHCL Recruitment 2018 application process to fill 117 vacancies for the post of Assistant **Engineer**, Account Officers, ......

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manufactures, **distributes**, and installs Carbon Emission Reduction Technology for use with internal combustion **engines**. As part of the growing global hydrogen economy, our patent-pending technology creates hydrogen and oxygen on-demand through electrolysis and supplies these through the air intake to enhance combustion, resulting in lower ......

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By Alan Baldwin ... Ferrari announced on Saturday that 66-year-old Marchionne, who is seriously ill, had been replaced as chairman by John Elkann, a scion of Italy's Agnelli family ... "He´s a character and an important personality for Formula One ... They want to implement a cost cap, improve racing and have a fairer **distribution** of revenues so that all 10 teams can be competitive. They also want to keep **engines** hybrid and road relevant ... ....

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Polyvinyl chloride, better known as PVC, seems to be just about everywhere ... PVC also appears in life jackets ... Astral founder Philip Curry, Owen says, wanted to do something about the widespread use of PVC in the life jacket industry ... A verdant industry ... “We design, **engineer**, produce the tooling, manufacture our products and do all our marketing, sales and **distribution** out of this building,” he says about the firm’s Brevard facility ... ....

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�. BUFFALO COUNTY BOARD. OF COMMISSIONERS. INTERVIEW COMMITTEE. JULY 12 and JULY 13, 2018. �. The Buffalo County Board of. Commissioners Interview Commit-. tee met on Thursday, July 12, 2018. at 9.00 A.M. and Friday, July 13,. 2018 at 9.00 A.M. A copy of the ac-. knowledgment and receipt of no-. tice and agenda by the Board of. Commissioners is attached to. these minutes. Commissioners ... and ... $6,823.89 smcs; Eagle **Distributing** ... smcs; **Engineered** Controls....

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With a growing child population living in poverty, Awa Thiam is using her **engineering** background to connect West African food producers with school systems ... “I was working as a telecommunications **engineer** for 10 years, but I really cared about food **distribution** and children’s education,” Thiam said. “Then, I found 70 percent of the population are farmers and have a lot of **distribution** issues....

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A Facebook **engineering** manager described challenges in hardware and software scaling **distributed** systems at Web speed ... ....

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Advertisement ... **Distributed** by Gravity Industries, the suit features five miniature jet **engines** and runs on jet fuel or diesel .......

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This is in large part due to game **engines**, graphics and audio programs made readily available and affordable to the masses. Couple this with digital **distribution** and virtually anybody with even the smallest amount of drive can make a game and sell it to the public ... So, why am I yammering on about game **engines** and game jams? What does this all have to ......

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