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THE NUMBER OF UNARY CLONES CONTAINING THE
THE NUMBER OF UNARY CLONES CONTAINING THE

... lattice Cl(X). We wish to describe this lattice for infinite X, in which case |X| it has cardinality 22 . A clone is called unary iff it contains only essentially unary functions, i.e., functions which depend on only one variable. Unary clones correspond in an obvious way to submonoids of the full t ...
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... • Compiling miniTAJS takes 35 seconds – 4500 lines of code – 113 classes + 40 objects = 580 .class files ...
Standard to Vertex: Using algebraic methods to find exact answers
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... 3. Direct Instruction – Converting to vertex form from standard form. (20 minutes) Solve graphically (Each problem increases in difficulty because the landmarks are not shown in the last problem. 9  x2  4 x  8 ...
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... Sort by U1, U2 Sensitive to U1 Insensitive to U2 ...
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... In this grammar F represents a fraction of two polynomials, P are the polynomials and M are the monomials. One should think of P as a “list of monomials” (where + is the “cons” and the integers take the place of the “nil”) and of M as a “list of variables” (where · is the “cons” and again the intege ...
Locating and Computing Zeros of Airy Functions
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Exponential Functions

... calculator. Then multiply this answer by 4000. Round off only after you get the final answer. Continuous Compounding And “e” The more often money is compounded, the more money it makes. For example, in the previous example, if interest were compounded daily instead of quarterly, n would have equaled ...
Convergent Temporal-Difference Learning with Arbitrary Smooth
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...  You should see Screencasts. They illustrate “how to” for various web interface activities; more use cases continue to be added.  You should see Tutorials. The help learn specific principles; more tutorials are under development. ...
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... Formal languages (Java). Though combinatory parsers were introduced by Burge in 1975, it was Wadler (1985) who first popularized the use of combinatory parsers. Combinatory parsers are written and used within the same programming language as the rest of the program. There is no gap between the gramm ...
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... • How do we perform an action? • We need a function with type: –Io a -> a • If we have such a function then we break the abstraction which hides how Io is implemented. • In Haskell, the real IO can only be preformed at top level, when because the main function must have type IO() ...
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... Notice our functional decomposition generalizes in a straightforward way to binary (or in general, n-ary) operations: we can use pattern-matching over tuples to enumerate all the cases. Although nine cases might seem too many, that complexity is inherent to the problem. If many cases work the same w ...
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... unknown but last entry (special/sentinel value) is known  General form: ...
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... difference of the functions, even though we don't know any more about the functions themselves. This is what allows us to look at the graphs of two functions and give their sums, differences, etc. ...
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... 4. Integrating products of tangent and secants:  tan m x sec n xdx , m and n are positive integers. (a) If n is even: Split off a factor of sec 2 x . Apply the identity sec 2 x  tan 2 x  1 . Make the substitution u=tanx. (b) If m is odd: Split off a factor of secxtanx. Apply the identity tan 2 x ...
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... Hybrid systems are promising to model network traffic in the context of congestion control: • retain the low-dimensionality of continuous approximations to traffic flow • are sufficiently expressive to represent event-based control mechanisms Hybrid models are interesting even as a simulation tool f ...
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Corecursion

In computer science, corecursion is a type of operation that is dual to recursion. Whereas recursion works analytically, starting on data further from a base case and breaking it down into smaller data and repeating until one reaches a base case, corecursion works synthetically, starting from a base case and building it up, iteratively producing data further removed from a base case. Put simply, corecursive algorithms use the data that they themselves produce, bit by bit, as they become available, and needed, to produce further bits of data. A similar but distinct concept is generative recursion which may lack a definite ""direction"" inherent in corecursion and recursion. Where recursion allows programs to operate on arbitrarily complex data, so long as they can be reduced to simple data (base cases), corecursion allows programs to produce arbitrarily complex and potentially infinite data structures, such as streams, so long as it can be produced from simple data (base cases). Where recursion may not terminate, never reaching a base state, corecursion starts from a base state, and thus produces subsequent steps deterministically, though it may proceed indefinitely (and thus not terminate under strict evaluation), or it may consume more than it produces and thus become non-productive. Many functions that are traditionally analyzed as recursive can alternatively, and arguably more naturally, be interpreted as corecursive functions that are terminated at a given stage, for example recurrence relations such as the factorial.Corecursion can produce both finite and infinite data structures as result, and may employ self-referential data structures. Corecursion is often used in conjunction with lazy evaluation, to only produce a finite subset of a potentially infinite structure (rather than trying to produce an entire infinite structure at once). Corecursion is a particularly important concept in functional programming, where corecursion and codata allow total languages to work with infinite data structures.
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