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  • Java: minimum number of operations for conjunctive inequalities?

    - by HH
    I try to simplify conditionals in for (int t=0,size=fo.getPrintViewsPerFile().size();t<size&&t<countPerFile;t++){, more precisely: t<s&&t<c You need to compare two times, then calc the boolean value from them. Is there any simpler way to do it? If no, how can you prove it? I can simplify it to some extent, proof tree.

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  • What Precalculus knowledge is required before learning Discrete Math Computer Science topics?

    - by Ein Doofus
    Below I've listed the chapters from a Precalculus book as well as the author recommended Computer Science chapters from a Discrete Mathematics book. Although these chapters are from two specific books on these subjects I believe the topics are generally the same between any Precalc or Discrete Math book. What Precalculus topics should one know before starting these Discrete Math Computer Science topics?: Discrete Mathematics CS Chapters 1.1 Propositional Logic 1.2 Propositional Equivalences 1.3 Predicates and Quantifiers 1.4 Nested Quantifiers 1.5 Rules of Inference 1.6 Introduction to Proofs 1.7 Proof Methods and Strategy 2.1 Sets 2.2 Set Operations 2.3 Functions 2.4 Sequences and Summations 3.1 Algorithms 3.2 The Growths of Functions 3.3 Complexity of Algorithms 3.4 The Integers and Division 3.5 Primes and Greatest Common Divisors 3.6 Integers and Algorithms 3.8 Matrices 4.1 Mathematical Induction 4.2 Strong Induction and Well-Ordering 4.3 Recursive Definitions and Structural Induction 4.4 Recursive Algorithms 4.5 Program Correctness 5.1 The Basics of Counting 5.2 The Pigeonhole Principle 5.3 Permutations and Combinations 5.6 Generating Permutations and Combinations 6.1 An Introduction to Discrete Probability 6.4 Expected Value and Variance 7.1 Recurrence Relations 7.3 Divide-and-Conquer Algorithms and Recurrence Relations 7.5 Inclusion-Exclusion 8.1 Relations and Their Properties 8.2 n-ary Relations and Their Applications 8.3 Representing Relations 8.5 Equivalence Relations 9.1 Graphs and Graph Models 9.2 Graph Terminology and Special Types of Graphs 9.3 Representing Graphs and Graph Isomorphism 9.4 Connectivity 9.5 Euler and Hamilton Ptahs 10.1 Introduction to Trees 10.2 Application of Trees 10.3 Tree Traversal 11.1 Boolean Functions 11.2 Representing Boolean Functions 11.3 Logic Gates 11.4 Minimization of Circuits 12.1 Language and Grammars 12.2 Finite-State Machines with Output 12.3 Finite-State Machines with No Output 12.4 Language Recognition 12.5 Turing Machines Precalculus Chapters R.1 The Real-Number System R.2 Integer Exponents, Scientific Notation, and Order of Operations R.3 Addition, Subtraction, and Multiplication of Polynomials R.4 Factoring R.5 Rational Expressions R.6 Radical Notation and Rational Exponents R.7 The Basics of Equation Solving 1.1 Functions, Graphs, Graphers 1.2 Linear Functions, Slope, and Applications 1.3 Modeling: Data Analysis, Curve Fitting, and Linear Regression 1.4 More on Functions 1.5 Symmetry and Transformations 1.6 Variation and Applications 1.7 Distance, Midpoints, and Circles 2.1 Zeros of Linear Functions and Models 2.2 The Complex Numbers 2.3 Zeros of Quadratic Functions and Models 2.4 Analyzing Graphs of Quadratic Functions 2.5 Modeling: Data Analysis, Curve Fitting, and Quadratic Regression 2.6 Zeros and More Equation Solving 2.7 Solving Inequalities 3.1 Polynomial Functions and Modeling 3.2 Polynomial Division; The Remainder and Factor Theorems 3.3 Theorems about Zeros of Polynomial Functions 3.4 Rational Functions 3.5 Polynomial and Rational Inequalities 4.1 Composite and Inverse Functions 4.2 Exponential Functions and Graphs 4.3 Logarithmic Functions and Graphs 4.4 Properties of Logarithmic Functions 4.5 Solving Exponential and Logarithmic Equations 4.6 Applications and Models: Growth and Decay 5.1 Systems of Equations in Two Variables 5.2 System of Equations in Three Variables 5.3 Matrices and Systems of Equations 5.4 Matrix Operations 5.5 Inverses of Matrices 5.6 System of Inequalities and Linear Programming 5.7 Partial Fractions 6.1 The Parabola 6.2 The Circle and Ellipse 6.3 The Hyperbola 6.4 Nonlinear Systems of Equations

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  • Which linear programming package should I use for high numbers of constraints and "warm starts"

    - by davidsd
    I have a "continuous" linear programming problem that involves maximizing a linear function over a curved convex space. In typical LP problems, the convex space is a polytope, but in this case the convex space is piecewise curved -- that is, it has faces, edges, and vertices, but the edges aren't straight and the faces aren't flat. Instead of being specified by a finite number of linear inequalities, I have a continuously infinite number. I'm currently dealing with this by approximating the surface by a polytope, which means discretizing the continuously infinite constraints into a very large finite number of constraints. I'm also in the situation where I'd like to know how the answer changes under small perturbations to the underlying problem. Thus, I'd like to be able to supply an initial condition to the solver based on a nearby solution. I believe this capability is called a "warm start." Can someone help me distinguish between the various LP packages out there? I'm not so concerned with user-friendliness as speed (for large numbers of constraints), high-precision arithmetic, and warm starts. Thanks!

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  • Multiple inequality conditions (range queries) in NoSQL

    - by pableu
    Hi, I have an application where I'd like to use a NoSQL database, but I still want to do range queries over two different properties, for example select all entries between times T1 and T2 where the noiselevel is smaller than X. On the other hand, I would like to use a NoSQL/Key-Value store because my data is very sparse and diverse, and I do not want to create new tables for every new datatype that I might come across. I know that you cannot use multiple inequality filters for the Google Datastore (source). I also know that this feature is coming (according to this). I know that this is also not possible in CouchDB (source). I think I also more or less understand why this is the case. Now, this makes me wonder.. Is that the case with all NoSQL databases? Can other NoSQL systems make range queries over two different properties? How about, for example, Mongo DB? I've looked in the Documentation, but the only thing I've found was the following snippet in their docu: Note that any of the operators on this page can be combined in the same query document. For example, to find all document where j is not equal to 3 and k is greater than 10, you'd query like so: db.things.find({j: {$ne: 3}, k: {$gt: 10} }); So they use greater-than and not-equal on two different properties. They don't say anything about two inequalities ;-) Any input and enlightenment is welcome :-)

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