Besicovitch and other generalizations of Bohr`s almost periodic
... theorem is a statement about L2 functions on a compact interval, and we are thus far dealing with uniformly continuous functions, so it appears we are not in the correct setting yet. Before moving on, we note that there is a third equivalent definition to the above two. Definition 1.9 (normality). A ...
... theorem is a statement about L2 functions on a compact interval, and we are thus far dealing with uniformly continuous functions, so it appears we are not in the correct setting yet. Before moving on, we note that there is a third equivalent definition to the above two. Definition 1.9 (normality). A ...
A Short Cut to Deforestation
... (Section 4). Standard compilation techniques for list comprehensions build an intermediate list in expressions such as [ f x | x <- map g xs, odd x ] ...
... (Section 4). Standard compilation techniques for list comprehensions build an intermediate list in expressions such as [ f x | x <- map g xs, odd x ] ...
LOGIC I 1. The Completeness Theorem 1.1. On consequences and
... verify a claim to be a proof is a non-negotiable requirement, we want a different approach. What we want is a sub-collection of the logical validities that we can actually describe, thus making it possible to check whether a statement in the proof belongs to this collection, but from which all other ...
... verify a claim to be a proof is a non-negotiable requirement, we want a different approach. What we want is a sub-collection of the logical validities that we can actually describe, thus making it possible to check whether a statement in the proof belongs to this collection, but from which all other ...
Examples - Department of Computer and Information Science
... Top-Down Programming, also called functional decomposition, uses functions to hide details of an algorithm inside the function. In the prior example, main called calculate_triangular_number without regards to how the function is implemented. You can write a call to calculate_triangular_number withou ...
... Top-Down Programming, also called functional decomposition, uses functions to hide details of an algorithm inside the function. In the prior example, main called calculate_triangular_number without regards to how the function is implemented. You can write a call to calculate_triangular_number withou ...
Solutions for the exercises - Delft Center for Systems and Control
... Figure 3: Feasible set and contour plot for Exercise 2.1 Solution: Figure 3 shows the contour plot and the feasible region of the optimization problem. The solution is in a vertex of the feasible set, which is obtained with the graphical method (we shift one of the contour lines in a parallel way in ...
... Figure 3: Feasible set and contour plot for Exercise 2.1 Solution: Figure 3 shows the contour plot and the feasible region of the optimization problem. The solution is in a vertex of the feasible set, which is obtained with the graphical method (we shift one of the contour lines in a parallel way in ...
Computability and Incompleteness
... and then, all of a sudden, they shot up like weeds. Turing provided a notion of mechanical computability, Gödel and Herbrand characterized computability in terms of the recursive functions, Church presented the notion of lambda computability, Post offered another notion of mechanical computability, ...
... and then, all of a sudden, they shot up like weeds. Turing provided a notion of mechanical computability, Gödel and Herbrand characterized computability in terms of the recursive functions, Church presented the notion of lambda computability, Post offered another notion of mechanical computability, ...
continuations
... • (throw) causes a return from the
nearest matching (catch ) found on stack
(defun foo-outer () (catch (foo-inner)))
(defun foo-inner () … (if x (throw t)) ...)
...
... • (throw
No Slide Title - University of Pennsylvania
... Stack inspection properties (security/access control) If setuuid bit is being set, root must be in call stack ...
... Stack inspection properties (security/access control) If setuuid bit is being set, root must be in call stack ...
Pattern matching in concatenative programming languages
... It is not immediately obvious how to do pattern matching in a concatenative programming language, when variables are not used. A fundamental rethink of pattern matching, as calculating the inverse of a function, leads to a clear solution to this problem. We have constructed an efficient pattern matc ...
... It is not immediately obvious how to do pattern matching in a concatenative programming language, when variables are not used. A fundamental rethink of pattern matching, as calculating the inverse of a function, leads to a clear solution to this problem. We have constructed an efficient pattern matc ...
Lecture Slides (PowerPoint)
... – Start with a 64-bit hash key initialized to 0 – Loop through current position, XOR’ing hash key with Zobrist value of each piece found (note: once a key has been found, use an incremental approach that XOR’s the “from” location and the “to” location to move a piece) ...
... – Start with a 64-bit hash key initialized to 0 – Loop through current position, XOR’ing hash key with Zobrist value of each piece found (note: once a key has been found, use an incremental approach that XOR’s the “from” location and the “to” location to move a piece) ...
Lecture Slides (PowerPoint)
... – Start with a 64-bit hash key initialized to 0 – Loop through current position, XOR’ing hash key with Zobrist value of each piece found (note: once a key has been found, use an incremental approach that XOR’s the “from” location and the “to” location to move a piece) ...
... – Start with a 64-bit hash key initialized to 0 – Loop through current position, XOR’ing hash key with Zobrist value of each piece found (note: once a key has been found, use an incremental approach that XOR’s the “from” location and the “to” location to move a piece) ...
SECTION 10.3 LECTURE NOTES
... Describe the xbase multiplier property as applied to the given function. 22 x x 3. 3.f (x) ...
... Describe the xbase multiplier property as applied to the given function. 22 x x 3. 3.f (x) ...
Advanced Logic —
... formed formulae. If we want to use induction, we may do this by doing the induction on the complexity of the formulae. R EMARK 22. The complexity amounts to much the same thing as the stage in the construction. It is conventional in proofs by induction on complexity not to explicitly mention the com ...
... formed formulae. If we want to use induction, we may do this by doing the induction on the complexity of the formulae. R EMARK 22. The complexity amounts to much the same thing as the stage in the construction. It is conventional in proofs by induction on complexity not to explicitly mention the com ...
Mathematical Social Sciences
... depends on other constraints (pi , i = 1, . . . , N, and S) in (1), see also Section 4. Observe further that the base + prop + floor and base + prop + cup functions are in a sense extremal allocation functions satisfying boundary conditions: A (p) = m and A (P ) = M, since it is clear that every suc ...
... depends on other constraints (pi , i = 1, . . . , N, and S) in (1), see also Section 4. Observe further that the base + prop + floor and base + prop + cup functions are in a sense extremal allocation functions satisfying boundary conditions: A (p) = m and A (P ) = M, since it is clear that every suc ...
Table of contents
... is known to have no side-effects, may be efficiently computed without multiple calls. A function in this sense has zero or more parameters and a single return value. The parameters—or arguments, as they are sometimes called—are the inputs to the function, and the return value is the function's outpu ...
... is known to have no side-effects, may be efficiently computed without multiple calls. A function in this sense has zero or more parameters and a single return value. The parameters—or arguments, as they are sometimes called—are the inputs to the function, and the return value is the function's outpu ...
Gödel`s correspondence on proof theory and constructive mathematics
... of interpreting the propositional connectives when applied to formulas containing quantifiers. Gödel’s remark in the paper on Russell is in the context of discussing a certain on again-off again constructivist thread in Principia Mathematica. But Russell’s interpretation is just an application of t ...
... of interpreting the propositional connectives when applied to formulas containing quantifiers. Gödel’s remark in the paper on Russell is in the context of discussing a certain on again-off again constructivist thread in Principia Mathematica. But Russell’s interpretation is just an application of t ...
Common Lisp - cse.sc.edu
... Cons and Implicit Typing • Lisp uses lists as its primary data structure. • Lists are constructed similarly to other functional languages, using cons, append, etc. • Data is implicitly typed in list and can therefore be mixed in a given list. • For example, (cons ‘a (2 3)) evaluates to (a 2 3). ...
... Cons and Implicit Typing • Lisp uses lists as its primary data structure. • Lists are constructed similarly to other functional languages, using cons, append, etc. • Data is implicitly typed in list and can therefore be mixed in a given list. • For example, (cons ‘a (2 3)) evaluates to (a 2 3). ...
Project Five
... Functional languages promote conciseness, abstractness and simplicity in the coding structure. Conversely, the structure of the simple procedural languages is pretty simple. A good example would be that of FORTRAN, which doesn’t allow new variables or space during run time. This feature is tantamoun ...
... Functional languages promote conciseness, abstractness and simplicity in the coding structure. Conversely, the structure of the simple procedural languages is pretty simple. A good example would be that of FORTRAN, which doesn’t allow new variables or space during run time. This feature is tantamoun ...
Intermediate Logic
... as members. You will remember the various sets of numbers: N is the set of natural numbers {0, 1, 2, 3, . . . }; Z the set of integers {. . . , −3, −2, −1, 0, 1, 2, 3, . . . }; Q the set of rationals (Q = {z/n : z ∈ Z, n ∈ N, n 6= 0}); and R the set of real numbers. These are all infinite sets, that ...
... as members. You will remember the various sets of numbers: N is the set of natural numbers {0, 1, 2, 3, . . . }; Z the set of integers {. . . , −3, −2, −1, 0, 1, 2, 3, . . . }; Q the set of rationals (Q = {z/n : z ∈ Z, n ∈ N, n 6= 0}); and R the set of real numbers. These are all infinite sets, that ...
Homework 4: Solutions
... this is equal to previous(y) next(y) x, which in turn is equal to next(y) since previous(y) = x so that previous(y) x = 0. To start the traversal, we must know the address of two nodes in direct succession of each other. Starting in the head, which still has the previous and next pointers, we ...
... this is equal to previous(y) next(y) x, which in turn is equal to next(y) since previous(y) = x so that previous(y) x = 0. To start the traversal, we must know the address of two nodes in direct succession of each other. Starting in the head, which still has the previous and next pointers, we ...
Transaction-oriented library for persistent objects with applications
... tail.next = node; // Crash in the middle of a transaction. if (node.num == 4) throw new Error(); tail = node; ...
... tail.next = node; // Crash in the middle of a transaction. if (node.num == 4) throw new Error(); tail = node; ...
Unconstrained Univariate Optimization
... A major drawback of Newton’s method is that it requires us to have analytically determined both the first and second derivatives of our objective function. Often this is considered onerous, particularly in the case of the second derivative. The large family of optimization algorithms that use finite ...
... A major drawback of Newton’s method is that it requires us to have analytically determined both the first and second derivatives of our objective function. Often this is considered onerous, particularly in the case of the second derivative. The large family of optimization algorithms that use finite ...
5.7.2 Operating on Functions Building
... As is true with linear and exponential functions, we can perform operations on quadratic functions. Such operations include addition, subtraction, multiplication, and division. This lesson will focus on adding, subtracting, multiplying, and dividing functions to create new functions. The lesson will ...
... As is true with linear and exponential functions, we can perform operations on quadratic functions. Such operations include addition, subtraction, multiplication, and division. This lesson will focus on adding, subtracting, multiplying, and dividing functions to create new functions. The lesson will ...
Recursion (computer science)
Recursion in computer science is a method where the solution to a problem depends on solutions to smaller instances of the same problem (as opposed to iteration). The approach can be applied to many types of problems, and recursion is one of the central ideas of computer science.""The power of recursion evidently lies in the possibility of defining an infinite set of objects by a finite statement. In the same manner, an infinite number of computations can be described by a finite recursive program, even if this program contains no explicit repetitions.""Most computer programming languages support recursion by allowing a function to call itself within the program text. Some functional programming languages do not define any looping constructs but rely solely on recursion to repeatedly call code. Computability theory proves that these recursive-only languages are Turing complete; they are as computationally powerful as Turing complete imperative languages, meaning they can solve the same kinds of problems as imperative languages even without iterative control structures such as “while” and “for”.