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In this work, an optimization model (MILP) for the energetic refurbishment planning of buildings is developed. It provides decision support for owner-occupiers and/or landlords. The approach considers simultaneously the selection of refurbishment measures, the operation of energy supply technologies (incl. CHP/PV), and the financing structure from an economic point of view. The evaluation scheme is based on a visualization of financial implications and factors public funds into the analysis.

Wohngebäude --- Techno-ökonomische Planung --- Energetische Modernisierung --- Residential buildings --- Vollständige Finanzplanung --- Gemischt-ganzzahlige lineare OptimierungEnergetic refurbishment --- Visualization of Financial Implications --- Mixed-integer linear programming --- Techno-economic planning

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Linear and integer programming are fundamental toolkits for data and information science and technology, particularly in the context of today’s megatrends toward statistical optimization, machine learning, and big data analytics. Drawn from over 30 years of classroom teaching and applied research experience, this textbook provides a crisp and practical introduction to the basics of linear and integer programming. The authors’ approach is accessible to students from all fields of engineering, including operations research, statistics, machine learning, control system design, scheduling, formal verification, and computer vision. Readers will learn to cast hard combinatorial problems as mathematical programming optimizations, understand how to achieve formulations where the objective and constraints are linear, choose appropriate solution methods, and interpret results appropriately. •Provides a concise introduction to linear and integer programming, appropriate for undergraduates, graduates, a short course or boot camp, or self-learning; •Targets not only computer scientists and engineers, but those in management science and operations research as well; •Emphasizes basics and intuitive concepts, and gives corresponding numerical examples; •Includes exercises to test and reinforce the concepts introduced, along with a website containing additional material matched to the book’s contents.

Engineering. --- Computer science --- Applied mathematics. --- Engineering mathematics. --- Electronic circuits. --- Circuits and Systems. --- Math Applications in Computer Science. --- Appl.Mathematics/Computational Methods of Engineering. --- Applications of Mathematics. --- Mathematics. --- Electron-tube circuits --- Engineering --- Engineering analysis --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Construction --- Mathematics --- Systems engineering. --- Computer science. --- Mathematical and Computational Engineering. --- Computer science—Mathematics. --- Mathematical analysis --- Electric circuits --- Electron tubes --- Electronics --- Linear programming. --- Integer porgramming.

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We use addition on a daily basis-yet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity? Summing It Up uses addition as a springboard to present a fascinating and accessible look at numbers and number theory, and how we apply beautiful numerical properties to answer math problems. Mathematicians Avner Ash and Robert Gross explore addition's most basic characteristics as well as the addition of squares and other powers before moving onward to infinite series, modular forms, and issues at the forefront of current mathematical research.Ash and Gross tailor their succinct and engaging investigations for math enthusiasts of all backgrounds. Employing college algebra, the first part of the book examines such questions as, can all positive numbers be written as a sum of four perfect squares? The second section of the book incorporates calculus and examines infinite series-long sums that can only be defined by the concept of limit, as in the example of 1+1/2+1/4+. . .=? With the help of some group theory and geometry, the third section ties together the first two parts of the book through a discussion of modular forms-the analytic functions on the upper half-plane of the complex numbers that have growth and transformation properties. Ash and Gross show how modular forms are indispensable in modern number theory, for example in the proof of Fermat's Last Theorem.Appropriate for numbers novices as well as college math majors, Summing It Up delves into mathematics that will enlighten anyone fascinated by numbers.

Number theory. --- Mathematics --- Number study --- Numbers, Theory of --- Algebra --- Absolute value. --- Addition. --- Analytic continuation. --- Analytic function. --- Automorphic form. --- Axiom. --- Bernoulli number. --- Big O notation. --- Binomial coefficient. --- Binomial theorem. --- Book. --- Calculation. --- Chain rule. --- Coefficient. --- Complex analysis. --- Complex number. --- Complex plane. --- Computation. --- Congruence subgroup. --- Conjecture. --- Constant function. --- Constant term. --- Convergent series. --- Coprime integers. --- Counting. --- Cusp form. --- Determinant. --- Diagram (category theory). --- Dirichlet series. --- Division by zero. --- Divisor. --- Elementary proof. --- Elliptic curve. --- Equation. --- Euclidean geometry. --- Existential quantification. --- Exponential function. --- Factorization. --- Fourier series. --- Function composition. --- Fundamental domain. --- Gaussian integer. --- Generating function. --- Geometric series. --- Geometry. --- Group theory. --- Hecke operator. --- Hexagonal number. --- Hyperbolic geometry. --- Integer factorization. --- Integer. --- Line segment. --- Linear combination. --- Logarithm. --- Mathematical induction. --- Mathematician. --- Mathematics. --- Matrix group. --- Modular form. --- Modular group. --- Natural number. --- Non-Euclidean geometry. --- Parity (mathematics). --- Pentagonal number. --- Periodic function. --- Polynomial. --- Power series. --- Prime factor. --- Prime number theorem. --- Prime number. --- Pythagorean theorem. --- Quadratic residue. --- Quantity. --- Radius of convergence. --- Rational number. --- Real number. --- Remainder. --- Riemann surface. --- Root of unity. --- Scientific notation. --- Semicircle. --- Series (mathematics). --- Sign (mathematics). --- Square number. --- Square root. --- Subgroup. --- Subset. --- Sum of squares. --- Summation. --- Taylor series. --- Theorem. --- Theory. --- Transfinite number. --- Triangular number. --- Two-dimensional space. --- Unique factorization domain. --- Upper half-plane. --- Variable (mathematics). --- Vector space.

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There is a sympathy of ideas among the fields of knot theory, infinite discrete group theory, and the topology of 3-manifolds. This book contains fifteen papers in which new results are proved in all three of these fields. These papers are dedicated to the memory of Ralph H. Fox, one of the world's leading topologists, by colleagues, former students, and friends.In knot theory, papers have been contributed by Goldsmith, Levine, Lomonaco, Perko, Trotter, and Whitten. Of these several are devoted to the study of branched covering spaces over knots and links, while others utilize the braid groups of Artin.Cossey and Smythe, Stallings, and Strasser address themselves to group theory. In his contribution Stallings describes the calculation of the groups In/In+1 where I is the augmentation ideal in a group ring RG. As a consequence, one has for each k an example of a k-generator l-relator group with no free homomorphs. In the third part, papers by Birman, Cappell, Milnor, Montesinos, Papakyriakopoulos, and Shalen comprise the treatment of 3-manifolds. Milnor gives, besides important new results, an exposition of certain aspects of our current knowledge regarding the 3- dimensional Brieskorn manifolds.

Knot theory. --- Group theory. --- Three-manifolds (Topology) --- 3-manifold. --- 3-sphere. --- Additive group. --- Alexander duality. --- Algebraic equation. --- Algebraic surface. --- Algebraic variety. --- Automorphic form. --- Automorphism. --- Big O notation. --- Bilinear form. --- Borromean rings. --- Boundary (topology). --- Braid group. --- Cartesian product. --- Central series. --- Chain rule. --- Characteristic polynomial. --- Coefficient. --- Cohomological dimension. --- Commutative ring. --- Commutator subgroup. --- Complex Lie group. --- Complex coordinate space. --- Complex manifold. --- Complex number. --- Conjugacy class. --- Connected sum. --- Coprime integers. --- Coset. --- Counterexample. --- Cyclic group. --- Dedekind domain. --- Diagram (category theory). --- Diffeomorphism. --- Disjoint union. --- Divisibility rule. --- Double coset. --- Equation. --- Equivalence class. --- Euler characteristic. --- Fiber bundle. --- Finite group. --- Fundamental group. --- Generating set of a group. --- Graded ring. --- Graph product. --- Group ring. --- Groupoid. --- Heegaard splitting. --- Holomorphic function. --- Homeomorphism. --- Homological algebra. --- Homology (mathematics). --- Homology sphere. --- Homomorphism. --- Homotopy group. --- Homotopy sphere. --- Homotopy. --- Hurewicz theorem. --- Infimum and supremum. --- Integer matrix. --- Integer. --- Intersection number (graph theory). --- Intersection theory. --- Knot group. --- Knot polynomial. --- Loop space. --- Main diagonal. --- Manifold. --- Mapping cylinder. --- Mathematical induction. --- Meromorphic function. --- Monodromy. --- Monomorphism. --- Multiplicative group. --- Permutation. --- Poincaré conjecture. --- Principal ideal domain. --- Proportionality (mathematics). --- Quotient space (topology). --- Riemann sphere. --- Riemann surface. --- Seifert fiber space. --- Simplicial category. --- Special case. --- Spectral sequence. --- Subgroup. --- Submanifold. --- Surjective function. --- Symmetric group. --- Symplectic matrix. --- Theorem. --- Three-dimensional space (mathematics). --- Topology. --- Torus knot. --- Triangle group. --- Variable (mathematics). --- Weak equivalence (homotopy theory).

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Written and revised by D. B. A. Epstein.

Category theory. Homological algebra --- 515.14 --- Algebraic topology --- Homology theory. --- 515.14 Algebraic topology --- Cohomology theory --- Contrahomology theory --- Algebra homomorphism. --- Algebra over a field. --- Algebraic structure. --- Approximation. --- Axiom. --- Basis (linear algebra). --- CW complex. --- Cartesian product. --- Classical group. --- Coefficient. --- Cohomology operation. --- Cohomology ring. --- Cohomology. --- Commutative property. --- Complex number. --- Computation. --- Continuous function. --- Cup product. --- Cyclic group. --- Diagram (category theory). --- Dimension. --- Direct limit. --- Embedding. --- Existence theorem. --- Fibration. --- Homomorphism. --- Hopf algebra. --- Hopf invariant. --- Ideal (ring theory). --- Integer. --- Inverse limit. --- Manifold. --- Mathematics. --- Monomial. --- N-skeleton. --- Natural transformation. --- Permutation. --- Quaternion. --- Ring (mathematics). --- Scalar (physics). --- Special unitary group. --- Steenrod algebra. --- Stiefel manifold. --- Subgroup. --- Subset. --- Summation. --- Symmetric group. --- Symplectic group. --- Theorem. --- Uniqueness theorem. --- Upper and lower bounds. --- Vector field. --- Vector space. --- W0.