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  • Articles  (70,665)
  • Springer  (70,665)
  • American Physical Society
  • MDPI Publishing
  • 1975-1979  (42,892)
  • 1965-1969  (20,755)
  • 1950-1954  (3,545)
  • 1935-1939  (3,473)
  • Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics  (65,797)
  • Computer Science  (4,868)
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  • Articles  (70,665)
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  • 1
    Electronic Resource
    Electronic Resource
    Tenth International Symposium on Mathematical Programming (1979)
    Springer
    Mathematical programming 16 (1979), S. 261-261 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582113
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  • 2
    Electronic Resource
    Electronic Resource
    On a class of least-element complementarity problems (1979)
    Springer
    Mathematical programming 16 (1979), S. 111-126 
    Details
    ISSN: 1436-4646
    Keywords: Least Element ; Linear Complementarity ; Quadratic Programs ; Special Structure ; Applications ; Computational Experience
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The present paper studies the linear complementarity problem of finding vectorsx andy inR + n such thatc + Dx + y ≧ 0,b − x ≧ 0 andx T (c + Dx + y) = y T (b − x) = 0 whereD is aZ-matrix andb 〉 0. Complementarity problems of this nature arise, for example, from the minimization of certain quadratic functions subject to upper and lower bounds on the variables. Two least-element characterizations of solutions to the above linear complementarity problem are established first. Next, a new and direct method to solve this class of problems, which depends on the idea of “least-element solution” is presented. Finally, applications and computational experience with its implementation are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582097
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  • 3
    Electronic Resource
    Electronic Resource
    Editorial policy (1979)
    Springer
    Mathematical programming 16 (1979), S. 139-139 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582103
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  • 4
    Electronic Resource
    Electronic Resource
    An algorithm for a piecewise linear model of trade and production with negative prices and bankruptcy (1979)
    Springer
    Mathematical programming 16 (1979), S. 190-209 
    Details
    ISSN: 1436-4646
    Keywords: Algorithm ; Piecewise Linear ; Complementary Pivot ; Equilibrium Model ; Trade ; Production Prices ; Linear Programming ; Fixed Point Methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The general equilibrium model is approximated as a piecewise linear convex model and solved from the point of view of welfare economics using linear programming and fixed point methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582108
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  • 5
    Electronic Resource
    Electronic Resource
    Referees 1978 (1979)
    Springer
    Mathematical programming 16 (1979), S. 260-260 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582112
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  • 6
    Electronic Resource
    Electronic Resource
    The Mathematical Programming Society (1979)
    Springer
    Mathematical programming 16 (1979), S. 263-263 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582115
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  • 7
    Electronic Resource
    Electronic Resource
    On the solution of some (parametric) linear complementarity problems with applications to portfolio selection, structural engineering and actuarial graduation (1979)
    Springer
    Mathematical programming 16 (1979), S. 325-347 
    Details
    ISSN: 1436-4646
    Keywords: Complementarity Problem ; Computational Results ; Structural Engineering ; Applications ; Portfolio Selection ; Actuarial Graduation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we discuss three applications of a class of (parametric) linear complementarity problems arising independently from such diverse areas as portfolio selection, structural engineering and actuarial graduation. After explaining how the complementarity problems emerge in these applications, we perform some analytical comparisons (based on operation counts and storage requirements) of several existing algorithms for solving this class of complementarity problems. We shall also present computational results to support the analytical comparisons. Finally, we deduce some conclusions about the general performance of these algorithms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582119
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  • 8
    Electronic Resource
    Electronic Resource
    Call for papers: Conference on Combinatorial Optimization (1979)
    Springer
    Mathematical programming 16 (1979), S. 136-136 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582101
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  • 9
    Electronic Resource
    Electronic Resource
    A stable method for solving certain constrained least squares problems (1979)
    Springer
    Mathematical programming 16 (1979), S. 141-158 
    Details
    ISSN: 1436-4646
    Keywords: Constrained Least Squares Problems ; Positive Semidefinite Quadratic Programming ; Orthogonal Factorization ; Reorthogonalization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper presents a feasible descent algorithm for solving certain constrained least squares problems. These problems are specially structured quadratic programming problems with positive semidefinite Hessian matrices that are allowed to be singular. The algorithm generates a finite sequence of subproblems that are solved using the numerically stable technique of orthogonal factorization with reorthogonalization and Given's transformation updating.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582105
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  • 10
    Electronic Resource
    Electronic Resource
    The number of solutions of a class of linear complementarity problems (1979)
    Springer
    Mathematical programming 17 (1979), S. 104-105 
    Details
    ISSN: 1436-4646
    Keywords: Complementarity Problem ; Number of Solutions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588229
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  • 11
    Electronic Resource
    Electronic Resource
    Some remarks on condensation methods for geometric programs (1979)
    Springer
    Mathematical programming 17 (1979), S. 109-113 
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    ISSN: 1436-4646
    Keywords: Geometric Programs ; Kuhn—Tucker Conditions ; Condensation Methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The purpose of this paper is to present some points of clarification of a recently presented algorithm for geometric programs [7]. While presenting the clarification, we are able to identify the behavior of condensation type algorithms for generalized geometric programs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588231
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  • 12
    Electronic Resource
    Electronic Resource
    The Mathematical Programming Society (1979)
    Springer
    Mathematical programming 17 (1979), S. 121-121 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588236
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  • 13
    Electronic Resource
    Electronic Resource
    A multiplier method with automatic limitation of penalty growth (1979)
    Springer
    Mathematical programming 17 (1979), S. 140-155 
    Details
    ISSN: 1436-4646
    Keywords: Multiplier Methods ; Adaptive Penalization ; Nonlinear Programming ; Quadratic Convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper presents a multiplier method for solving optimization problems with equality and inequality constraints. The method realizes all the good features that were foreseen by R. Fletcher for this type of algorithm in the past, but which suffers from none of the drawbacks of the earlier attempts.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588240
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  • 14
    Electronic Resource
    Electronic Resource
    Editorial policy (1979)
    Springer
    Mathematical programming 17 (1979), S. 401-401 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588261
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  • 15
    Electronic Resource
    Electronic Resource
    Goal programming sensitivity analysis using interval penalty weights (1979)
    Springer
    Mathematical programming 17 (1979), S. 16-31 
    Details
    ISSN: 1436-4646
    Keywords: Goal Programming ; Sensitivity Analysis ; Vector-Maximum Algorithms ; Multiple Objective Linear Programming ; Multiple Criteria Decision Making
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper presents an application of the vector-maximum research [4–8] to the sensitivity analysis of goal programming problems as several of the criterion function penalty weights are simultaneously and independently varied. A generalized goal programming capability is presented and a six-stage analytic procedure is described. The problem is generalized in the sense that the regular goal programming penalty weights can be expanded to intervals if desired. The solution procedure is new in that it depends upon an algorithm for the vector-maximum problem, “criterion cone” contraction procedures, and “filtering” techniques. Together they are able to generate and process all extreme points on the portion of the surface of the goal programming “augmented” feasible region corresponding to the interval penalty weights specified. In effect, the procedure and adapted algorithm of this paper delivers to goal programming an operational power of sensitivity analysis not previously available to users. A numerical example is provided in order to illustrate the computerized application of the total goal programming procedure outlined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588223
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  • 16
    Electronic Resource
    Electronic Resource
    On the symmetric travelling salesman problem II: Lifting theorems and facets (1979)
    Springer
    Mathematical programming 16 (1979), S. 281-302 
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    ISSN: 1436-4646
    Keywords: Linear Inequalities ; Convex Polytopes ; Facets ; Lifting Theorems ; Travelling Salesman Problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Four lifting theorems are derived for the symmetric travelling salesman polytope. They provide constructions and state conditions under which a linear inequality which defines a facet of then-city travelling salesman polytope retains its facetial property for the (n + m)-city travelling salesman polytope, wherem ≥ 1 is an arbitrary integer. In particular, they permit a proof that all subtour-elimination as well as comb inequalities define facets of the convex hull of tours of then-city travelling salesman problem, wheren is an arbitrary integer.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582117
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  • 17
    Electronic Resource
    Electronic Resource
    The Mathematical Programming Society (1979)
    Springer
    Mathematical programming 16 (1979), S. 388-388 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582127
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  • 18
    Electronic Resource
    Electronic Resource
    A construction method in parametric programming (1979)
    Springer
    Mathematical programming 16 (1979), S. 21-36 
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    ISSN: 1436-4646
    Keywords: Parametric Linear Programming ; Construction Method ; Degeneracy ; Primal Lexicographic Method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We consider a linear programming problem, with two parameters in the objective function, and present an algorithm for finding the decomposition of the parameter space into maximal polyhedral areas in which particular basic solutions are optimal. Special attention is paid to fill up areas of degenerate solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582092
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  • 19
    Electronic Resource
    Electronic Resource
    A computational study of active set strategies in nonlinear programming with linear constraints (1979)
    Springer
    Mathematical programming 16 (1979), S. 81-97 
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    ISSN: 1436-4646
    Keywords: Nonlinear Programming ; Linear Constraints ; Computational Experience
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract An essential part of many iterative methods for linearly constrained nonlinear programming problems is a procedure for determining those inequality constraints which will be “active” (that is, satisfied as equalities) at each iteration. We discuss experiments in which we used several strategies for identifying active constraints in conjunction with two well-known algorithms for linearly constrained optimization. The results indicate that in most cases a strategy which keeps the number of constraints in the active set as small as possible is computationally most efficient.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582095
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  • 20
    Electronic Resource
    Electronic Resource
    A direct dual method for the mixed plant location problem with some side constraints (1979)
    Springer
    Mathematical programming 17 (1979), S. 198-228 
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    ISSN: 1436-4646
    Keywords: Plant Location ; Dual Method ; Orthogonality Conditions ; Enumeration ; Computational Results
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The mixed plant location problem (mixed in the sense of allowing capacitated as well as uncapacitated plants) is a difficult and important mixed integer problem. We give a direct dual method, consisting of several phases (each of which appears essential for some data), to resolve a strong relaxed form of the problem with additional constraints over the integer variables (user specified, or derived from the data themselves). When all features of the algorithm are employed, there appears to be no difficulty with problems of 100 plants, even in an inefficient computer implementation. The primal solutions which we derive from the orthogonality conditions and a simple greedy heuristic are almost always much better than those we obtain from a standard relaxed problem in the Lagrangean sense. With an enumeration code in an efficient implementation we would expect to be capable of resolving very large problems (of perhaps up to 500 or 1000 plants) to within practically well acceptable tolerances.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588244
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  • 21
    Electronic Resource
    Electronic Resource
    Mathematical programming study 10 (1979)
    Springer
    Mathematical programming 17 (1979), S. 115-118 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588233
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  • 22
    Electronic Resource
    Electronic Resource
    Optimization: Techniques and Applications (1979)
    Springer
    Mathematical programming 17 (1979), S. 122-122 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588237
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  • 23
    Electronic Resource
    Electronic Resource
    On perfect graphs and polyhedra with (0, 1)-valued extreme points (1979)
    Springer
    Mathematical programming 17 (1979), S. 239-242 
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    ISSN: 1436-4646
    Keywords: Anti-Blocking ; Perfect Graphs ; Polyhedra
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract LetC andA be (0, 1)-valued matrices with no zero columns. Fulkerson has shown that the extreme points of {x: Cx ≤ 1,x ≥ 0} are given by the rows ofA and their projections and the extreme points of {x: Ax ≤ 1,x ≥ 0} are given by the rows ofC and their projections if and only if the maximal rows ofC andA are the incidence vectors of maximal cliques and anticliques, respectively, of a perfect graph. This theorem is discussed and a new proof is given for the “only if” implication.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588246
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  • 24
    Electronic Resource
    Electronic Resource
    Exact penalty functions in nonlinear programming (1979)
    Springer
    Mathematical programming 17 (1979), S. 251-269 
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    ISSN: 1436-4646
    Keywords: Nonlinear Programming ; Penalty Functions ; Exact Penalty Functions ; Constraint Qualification ; Second Order Optimality Conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract It is shown that the existence of a strict local minimum satisfying the constraint qualification of [16] or McCormick's [12] second order sufficient optimality condition implies the existence of a class of exact local penalty functions (that is ones with a finite value of the penalty parameter) for a nonlinear programming problem. A lower bound to the penalty parameter is given by a norm of the optimal Lagrange multipliers which is dual to the norm used in the penalty function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588250
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  • 25
    Electronic Resource
    Electronic Resource
    Computational complexity of LCPs associated with positive definite symmetric matrices (1979)
    Springer
    Mathematical programming 17 (1979), S. 335-344 
    Details
    ISSN: 1436-4646
    Keywords: Linear Complementarity Problem ; Complementary Cones ; Complementary Pivot Methods ; Computational Complexity ; Exponential Growth
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Murty in a recent paper has shown that the computational effort required to solve a linear complementarity problem (LCP), by either of the two well known complementary pivot methods is not bounded above by a polynomial in the size of the problem. In that paper, by constructing a class of LCPs—one of ordern forn ≥ 2—he has shown that to solve the problem of ordern, either of the two methods goes through 2 n pivot steps before termination. However that paper leaves it as an open question to show whether or not the same property holds if the matrix,M, in the LCP is positive definite and symmetric. The class of LCPs in whichM is positive definite and symmetric is of particular interest because of the special structure of the problems, and also because they appear in many practical applications. In this paper, we study the computational growth of each of the two methods to solve the LCP, (q, M), whenM is positive definite and symmetric and obtain similar results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588254
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  • 26
    Electronic Resource
    Electronic Resource
    Call for papers: Second Symposium on Mathematical Programming with Data Perturbations (1979)
    Springer
    Mathematical programming 17 (1979), S. 398-399 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588258
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  • 27
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    Electronic Resource
    The Mathematical Programming Society (1979)
    Springer
    Mathematical programming 17 (1979), S. 402-402 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588262
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  • 28
    Electronic Resource
    Electronic Resource
    The computation of Lagrange-multiplier estimates for constrained minimization (1979)
    Springer
    Mathematical programming 17 (1979), S. 32-60 
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    ISSN: 1436-4646
    Keywords: Lagrange Multipliers ; Linearly-Constrained Optimization ; Augmented Lagrangian Functions ; Projected Lagrangian Methods ; Quadratic Sub Problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Almost all efficient algorithms for constrained optimization require the repeated computation of Lagrange-multiplier estimates. In this paper we consider the difficulties in providing accurate estimates and what tests can be made in order to check the validity of the estimates obtained. A variety of formulae for the estimation of Lagrange multipliers are derived and their respective merits discussed. Finally the role of Lagrange multipliers within optimization algorithms is discussed and in addition to other results, it is shown that some algorithms are particularly sensitive to errors in the estimates.
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    URL: http://dx.doi.org/10.1007/BF01588224
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  • 29
    Electronic Resource
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    Glass cutting in a small firm (1979)
    Springer
    Mathematical programming 17 (1979), S. 85-90 
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    ISSN: 1436-4646
    Keywords: Cutting Stock ; Glass Industry ; Approximate Solution ; Knapsack ; Small Firm ; Cutting Sequencing ; Small Order Size
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A description of some examples of the application of cutting stock problems is given. Focusing on a small firm and its special problems a case from the glass industry is presented. The case leads to a two-dimensional cutting stock problem where large rectangles have to be cut into smaller rectangles. At the same time a group of additional constraints have to be satisfied. The solution method is a near optimal method using knapsack functions. It is shown that the waste can be reduced by approximately 50% in comparison to the solution normally used by the company. Furthermore a sequencing procedure for the ordering of the glass sheets is suggested.
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    URL: http://dx.doi.org/10.1007/BF01588227
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  • 30
    Electronic Resource
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    Piecewise linear paths to minimize convex functions may not be monotonic (1979)
    Springer
    Mathematical programming 17 (1979), S. 106-108 
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    ISSN: 1436-4646
    Keywords: Fixed-point Algorithms ; Unconstrained Minimization ; Monotonic Paths
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The exact homotopy path when seeking the minimum of a convex function is monotonic in the homotopy parameter. This monotonicity is not inherited by the piecewise linear approximations to such paths produced by fixed-point algorithms.
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    URL: http://dx.doi.org/10.1007/BF01588230
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  • 31
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    Eleventh International Symposium for 1982 (1979)
    Springer
    Mathematical programming 17 (1979), S. 119-119 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    URL: http://dx.doi.org/10.1007/BF01588234
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  • 32
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    On conditions for optimality of the nonlinearl 1 problem (1979)
    Springer
    Mathematical programming 17 (1979), S. 123-135 
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    ISSN: 1436-4646
    Keywords: Nonlinearl 1 Problem ; Nondifferentiable Functions ; Optimality Conditions ; Nonlinear Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The purpose of this paper is to present necessary and sufficient conditions for optimality in the nonlinearl 1 problem. Furthermore, the relationship of thel 1 problem and the Pietrzykowski's approach to solve the nonlinear programming problem is discussed in detail.
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    URL: http://dx.doi.org/10.1007/BF01588238
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  • 33
    Electronic Resource
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    Penalty methods for computing points that satisfy second order necessary conditions (1979)
    Springer
    Mathematical programming 17 (1979), S. 229-238 
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    ISSN: 1436-4646
    Keywords: Constrained Optimization ; Penalty Methods ; Second Order Necessary Conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Penalty methods using second derivatives are presented for computing points that satisfy second order necessary conditions for the constrained case in nonlinear programming. Convergence to such points is proved.
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  • 34
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    The Mathematical Programming Society (1979)
    Springer
    Mathematical programming 17 (1979), S. 248-248 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    URL: http://dx.doi.org/10.1007/BF01588248
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  • 35
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    Acceleration of the leastpth algorithm for minimax optimization with engineering applications (1979)
    Springer
    Mathematical programming 17 (1979), S. 270-297 
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    ISSN: 1436-4646
    Keywords: Minimax Optimization ; Nondifferentiable Optimization ; Computer-Aided Circuit Design ; Leastpth Optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Over the past few years a number of researchers in mathematical programming and engineering became very interested in both the theoretical and practical applications of minimax optimization. The purpose of the present paper is to present a new method of solving the minimax optimization problem and at the same time to apply it to nonlinear programming and to three practical engineering problems. The original problem is defined as a modified leastpth objective function which under certain conditions has the same optimum as the original problem. The advantages of the present approach over the Bandler-Charalambous leastpth approach are similar to the advantages of the augmented Lagrangians approach for nonlinear programming over the standard penalty methods.
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    Updated triangular factors of the working basis in winkler's decomposition approach (1979)
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    Mathematical programming 17 (1979), S. 391-397 
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    ISSN: 1436-4646
    Keywords: Decomposition ; Forrest-Tomlin Update ; Large Scale LP ; Linear Programming ; Triangular Factors
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    The decomposition of nonlinear problems (1979)
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    Mathematical programming 17 (1979), S. 400-400 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    On the lower semicontinuity of optimal sets in convex parametric optimization (1979)
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    Mathematical programming 17 (1979), S. 400-400 
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    ISSN: 1436-4646
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    Topics: Computer Science , Mathematics
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    On the width—length inequality (1979)
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    Mathematical programming 17 (1979), S. 403-417 
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    ISSN: 1436-4646
    Keywords: Networks ; Graphs ; Resistor Networks ; Max-flow Min-Cut
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper was written at the Rensselaer Polytechnic Institute in 1963. A lecture based on it was given at the Rand Corporation in 1965 and this version is in the form in which Ray Fulkerson received it at Rand. The paper is the underpinning for results on resistor network inequalities (Reference [4]) which has not been published. A specific example, however, appears inProceedings of the IEEE 51 (1963) 1047–1048. There is also a parallel theory of the abstract assignment problem; every W—L matrix being an assignment matrix. More is known about minimal non-W—L matrices. U. Peled has found several additional classes of matrices which are also classically known in other contexts. A consequence of a recent matrix theorem is apparently that the degenerate projective planes are the only minimal matrices requiring unequal weights.
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    A unified derivation of quasi-Newton methods for solving non-sparse and sparse nonlinear equations (1979)
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    Computing 21 (1979), S. 113-125 
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    Source: Springer Online Journal Archives 1860-2000
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    Description / Table of Contents: Zusammenfassung Eine erweiterte Quasi-Newtonsche Gleichung wird gelöst unter Verwendung derW-V verallgemeinerten Inverse und ergibt eine einheitliche Ableitung der bekannten Quasi-Newtonschen Methode für die Lösung von nichtlinearen algebraischen Gleichungssystemen. Dieser Zugang ermöglicht es uns, neue Formeln für dünnbesetzte und nicht dünnbesetzte Systeme zu erhalten und auch zu bestimmen, welche Normen der Update-Matrizen bei verschiedenen brauchbaren Quasi-Newtonschen Update-Formeln minimisiert werden.
    Notes: Abstract An augmented quasi-Newton equation is solved by using theW-V generalized inverse to give a unified derivation of the known quasi-Newton methods for solving systems of nonlinear algebraic equations. This approach makes it possible to get new formulas for sparse and non-sparse systems, and also to determine what norms of the update matrices are minimized when several useful quasi-Newton update formulas are derived.
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    A quasi-Newton method for minimization under linear constraints without evaluating any derivatives (1979)
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    Computing 21 (1979), S. 127-141 
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    Source: Springer Online Journal Archives 1860-2000
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    Description / Table of Contents: Zusammenfassung Es wird ein Verfahren beschrieben, das nichtlineare Optimierungsprobleme mit linearen Nebenbedingungen löst, ohne daß Ableitungen der Zielfunktion berechnet werden müssen. Der Algorithmus verwendet das Konzept der aktiven Nebenbedingungen und vermeidet die Berechnung von Ableitungen, indem modifizierte Gradienten und Hessesche Matrizen mit Hilfe von Funktionswertdifferenzen approximiert werden. Diese Approximationen werden so berechnet, daß man dieselben Konvergenzergebnisse erhält wie für jede Quasi-Newton-Methode.
    Notes: Abstract In this paper a method is described for solving linearly constrained nonlinear programming problems without evaluating any derivatives of the objective function. The algorithm uses the concept of active constraints and avoids the calculation of derivatives by approximating modified gradients and Hessian matrices by the aid of differences of function values. These approximations are calculated in such a way that the same convergence results are obtained as for any Quasi-Newton method.
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    An algorithm for finding a minimal equivalent graph of a strongly connected digraph (1979)
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    Computing 21 (1979), S. 183-194 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird ein neuer Branch-and-Bound-Algorithmus vorgestellt, der aus einem stark zusammenhängenden Digraphen eine maximale Anzahl von Kanten entfernt, ohne die Zusammenhangsverhältnisse zu verändern. Eine FORTRAN IV Version des Algorithmus ist beigefügt. Das Verhalten des Algorithmus wird durch Abschätzung der Komplexität und durch Vergleich mit den Algorithmen von Moyles-Thompson und Hsu verdeutlicht.
    Notes: Abstract The paper presents a new branch and bound algorithm for removing the maximum number of edges from a strongly connected digraph without affecting its reachability properties. A FORTRAN IV implementation is given. The efficiency of the algorithm is analyzed through computational comparison with the methods of Moyles-Thompson and Hsu.
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    Square rooting is as difficult as multiplication (1979)
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    Computing 21 (1979), S. 221-232 
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    Source: Springer Online Journal Archives 1860-2000
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    Description / Table of Contents: Zusammenfassung Es wird gezeigt, daß Multiplikation von Zahlen und Bestimmen der Quadratwurzel von gleicher Komplexität sind, d. h. aus einem Programm zur Multiplikation kann man eines zum Wurzelziehen konstruieren, das größenordnungsmäßig die gleiche Zeitkomplexität hat (1 Schritt ≦ 1 Bit-Operation) und umgekehrt. Mit dem Schönhage-Strassen-Algorithmus erhält man so einen 0 (n logn log logn)-Algorithmus zum Berechnen der Quadratwurzel.
    Notes: Abstract It is shown that multiplication of numbers and square rooting have the same complexity, i. e. from a program for multiplication one can construct a program for square rooting with the same asymptotic time complexity (1 step≦1 bit-operation) and vice versa. It follows from the Schönhage-Strassen algorithm that square rooting can be performed in 0 (n logn log logn) bit-operations.
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    On the convergence of the discrete ART algorithm for the reconstruction of digital pictures from their projections (1979)
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    Computing 21 (1979), S. 105-111 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Für die bekannte Konvergenz des additiven und des linearen (unrestingierten) ART-Algorithmus werden neue Beweise gegeben. Die ART-Algorithmen gehören zu einer Klasse von Methoden für die Rekonstruktion von digitalen Bildern aus ihren Projektionen, Probleme, die z. B. in der Röntgentomographie auftreten. Unter Vermeidung des Umweges über die Lösung von Systemen von Ungleichungen wird hier ein sehr direkter und knapper simultaner Beweis für die Konvergenz des additiven und des linearen Algorithmus hergeleitet. Ein zweiter Beweis zeigt die geometrische Konvergenz des linearen Algorithmus, indem nur elementare Matrizenrechnung verwendet wird.
    Notes: Abstract New Proofs are given for the known convergence of the additive and linear (i.e. unconstrained) ART algorithms. These algorithms belong to a class of methods for the reconstruction of digitized pictures from one-dimensional views which are used e. g. in x-ray tomography. Avoiding the detour of solving systems of inequalities, the first proof gives, simultaneously and in a very direct way, the convergence of both the additive and the linear algorithms. A second proof shows the geometric convergence of the linear algorithm by using elementary matrix algebra only.
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    Superconvergence of collocation methods for Volterra integral equations of the first kind (1979)
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    Computing 21 (1979), S. 151-157 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wird eine Volterrasche Integralgleichung erster Art durch Kollokation im Raum der stückweisen Polynome vom Gradm≧0, welche Sprungstellen an den Knoten besitzen, gelöst, so ist die globale Konvergenzordnung der Näherungslösung durchp=m+1 gegeben. In dieser Arbeit wird gezeigt, daß eine spezielle Wahl der Kollokationspunkte (charakterisiert durch die Lobatto-Abszissen in (0, 1]) eine um Eins höhere Konvergenzordnung an den entsprechenden Legendre-Abszissen liefert.
    Notes: Abstract Collocation methods for solving first-kind Volterra equations in the space of piecewise polynomials possessing finite (jump) discontinuities at their knots and having degreem≧0 are known to have global order of convergencep=m+1. It is shown that a careful choice of the collocation points (characterized by the Lobatto points in (0, 1]) yields convergence of order (m+2) at the corresponding Legendre points.
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    Über eine Minimaleigenschaft der äquidistanten trigonometrischen Interpolation in 2n+1 Knoten (1979)
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    Computing 21 (1979), S. 177-182 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract We consider the problem posed by Erdös of minimizing the sum of the squares of the fundamental functions of the Lagrange interpolation by trigonometric polynomials at2n+1 points.
    Notes: Zusammenfassung Wir betrachten das von Erdös gestellte Problem, das Integral über die Summe der Quadrate der Grundfunktionen der Lagrange-Interpolation durch trigonometrische Polynome an2n+1 Knoten zu minimieren.
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    Height balanced 2–3 trees (1979)
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    Computing 21 (1979), S. 195-211 
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    Keywords: Balanced search trees ; height balanced trees ; 2–3 trees ; B-trees ; Balancierte Suchbäume ; höhenbalancierte Bäume ; 2–3 Bäume ; B-Bäume
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird die Klasse der höhenbalancierten 2–3 Bäume eingeführt. Diese Klasse umfaßt die Klasse der 2–3 Bäume echt. Einfüge- und Entferne-Algorithmen mit 0 (logn) Zeitkomplexität werden für diese Bäume angegeben. Mit dieser Arbeit wird gezeigt, daß das Konzept des Höhenbalancierens vorteilhaft auf Klassen von nichtbinären Bäumen angewandt werden kann. Dies stellt einen Beitrag zur Lösung eines Problems von Knuth dar.
    Notes: Abstract The class of height balanced 2–3 trees is defined. This class properly contains the class of 2–3 trees. Insertion and deletion algorithms for these trees having 0 (logn) performance are provided. This paper thus, effectively demonstrates that “height balancing” can be usefully applied to classes of trees other than binary trees, which is a contribution to the solution of one of Knuth's problems.
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    Applications of numerical double laplace transform algorithms to the solution of linear partial differential equations (1979)
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    Computing 21 (1979), S. 245-258 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Der Zweck dieser Arbeit ist eine Darstellung der Wirksamkeit der zweidimensionalen Laplace-Transformation als eine Methode für die Auflösung von zeitabhängigen, linearen, partiellen Differentialgleichungen mit verschiedenen zeitabhängigen Randbedingungen. Die Hauptergebnisse der zweidimensionalen Laplace-Transformationstheorie werden benutzt, zusammen mit einem wirksamen numerischen Umkehralgorithmus. Die Formulierung und numerische Resultate werden vorgestellt für eine Anzahl von Aufgaben, die auf halbunendlichen und endlichen räumlichen Gebieten bestimmt sind. Die modifizierte zweidimensionale Laplace-Transformation wird beschrieben für den Fall, wo die räumliche Variable auf ein endliches Intervall beschränkt ist.
    Notes: Abstract The purpose of this paper is to demonstrate the effectiveness of the double Laplace transform as a method for solving time-invariant linear partial differential equations with a variety of time-varying boundary conditions. The main results of double Laplace transform theory are utilized together with an efficient numerical inversion algorithm. The formulation and numerical solutions are presented for a number of problems defined on both a semi-infinite and a finite spatial domain. The modified double Laplace transform is developed with the spatial variable defined on a finite interval.
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    On the factorization of special symmetric periodic and non-periodic quindiagonal matrices (1979)
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    Computing 21 (1979), S. 259-266 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird eine Faktorisierungsmethode zur beschleunigten numerischen Lösung von konstanten quindiagonalen linearen Systemen beschrieben. Die Methode läßt sich u. a. anwenden auf die blockiterative Lösung der biharmonischen Gleichung unter einer Vielzahl von Randbedingungen.
    Notes: Abstract A factoring method is described for the fast numerical solution of constant five diagonal linear systems. Applications of the method include: block iterative solutions of the Biharmonic partial differential equation under a variety of boundary conditions.
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    Clique detection for nondirected graphs: Two new algorithms (1979)
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    Computing 21 (1979), S. 295-322 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die folgende Arbeit enthält zwei neue Algorithmen zur Bestimmung der Menge sämtlicher maximaler vollständiger Untergraphen (Cliquen) eines endlichen ungerichteten Graphen. Die Methoden verwenden spezielle Baumsuchalgorithmen. Die blockweise Erzeugung aller Cliquen führt zu charakteristischen Eigenschaften der Algorithmen, die eine effiziente Berechnung spezieller Untermengen von Cliquen, u.a. die Menge aller Cliquen von maximaler Länge, ermöglichen. Überdies erlaubt die Struktur beider Algorithmen die Berechnung der vollständigen Cliquenmenge auf parallel arbeitenden Rechnern. Die Algorithmen wurden an umfangreichen Serien charakteristischer Graphen getestet und mit dem wirksamsten der den Autoren bekannten Algorithmen, dem Algorithmus von Bron-Kerbosch (Algorithm 457 of CACM), verglichen.
    Notes: Abstract Making use of special tree search algorithms the present paper describes two new methods for determining all maximal complete subgraphs (cliques) of a finite nondirected graph. In both methods the blockwise generation of all cliques induces characteristic properties, which guarantee an efficient calculation of special clique subsets, especially the set of all cliques of maximal length. Moreover, by their structure both algorithms allow to calculate the complete clique set by parallel processing. The algorithms have been tested for many series of characteristic graphs and compared with the algorithm of Bron-Kerbosch (Algorithm 457 of CACM) the most efficient algorithm which is known to the authors.
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    Polymerization of propylene over titanium exchanged Y-zeolite (1979)
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    Polymer bulletin 1 (1979), S. 665-670 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary It was found that isotactic polymerization of propylene took place over titanium ion-exchanged Y-zeolite without organometallic compounds. The results obtained have led to the conclusions that Ti4+ species as well as Ti3+ species are active for the polymerization and that neither Ti-alkyl bonds nor Cl ligands are necessarily essential for polymerization of propylene.
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    Copolymers from 1-phenyl-2-(3-vinylphenylthio)-diazen and styrene and grafting with acrylonitrile (1979)
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    Polymer bulletin 1 (1979), S. 679-684 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary A new azo monomer (2) was synthesized and copolymerized with styrene. The resulting azo copolymer could be used as an initiator for the acrylonitrile polymerisation yielding grafted copolymers. Quantitative treatment of the grafting experiments leads to the conclusion that the intermediate thiyl radicals show less reactivity towards monomers than phenyl radicals.
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    Polymeric coordination complexes of some bipositive metal ions with 5,5′-(benzidinebisazo)-8-hydroxyquinoline (1979)
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    Polymer bulletin 1 (1979), S. 685-690 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Coordination chain polymers of Mn(II), Fe(II), Co(II), Ni(II), Cu(II), zn(II), and Cd(II) with 5,5-(benzidinebisazo)-8-hydroxyquinoline were synthesized by refluxing a mixture of metal acetate hydrates and ligand (1∶1) in DMSO. From analytical data an empirical formula of ML.2H2O is indicated. Ir spectra reveal coordination through O and N of oxine units, thus forming the polymeric chain; presence of coordinated water is also indicated. Magnetic moments and electronic spectra suggest octahedral geometry around the central metal ion. Besides the presence of 2H2O, TGA shows the order of thermal stability as : Cd∼Zn〉 Mn〉 Co∼Ni∼Cu〉Fe.
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    Poly(amidine)s and poly(guanidine)s — synthesis and some properties (1979)
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    Polymer bulletin 1 (1979), S. 715-722 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Synopsis Several poly(amidine) and poly(guanidine) copolymers and their hydrochloride salts were synthesized by introducing the functional groups into suitable polymers. The properties of the resulting copolymers were investigated by base and acid titration.
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    Load transfer through chain molecules after interpenetration at interfaces (1979)
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    Polymer bulletin 1 (1979), S. 697-707 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract A series of PMMA samples of different molecular weights and degrees of copolymerisation have been tested for their crack-healing behavior. Slightly above Tg, a diffusional interpenetration of chain segments takes place. The fracture toughness in the plane of the interpenetrated interface was measured in short- and longtime experiments. After very short penetration times of only 5 min, full material resistance was regained in short-time experiments, whereas the long-time properties were not restored. A qualitative explanation of these effects, based on structural parameters, is given.
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    Radiation grafting of acrylic acid onto polypropylene fibres (1979)
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    Polymer bulletin 1 (1979), S. 727-731 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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    Synthesis of some new divalent metal salts of mono(hydroxyethyl)phthalate (1979)
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    Polymer bulletin 1 (1979), S. 723-725 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Divalent metal salts of mono(hydroxyethyl)phthalate (HEP) were considered to be of interest as difunctional ionic monomers and are useful for the preparation of condensation polymers. Recently, Matsuda1 reported the preparation of Ca, Mg and Zn salts of mono-(hydroxyethyl)phthalate and their polymers2–7. He prepared these salts by the reaction of HEP with the respective divalent metal oxides. But so far there was no report on the preparation of Pb2+ and Mn2+ salts of HEP. Since metal dicarboxylates can be obtained by the reaction of organic dibasic acids and metal acetates8, Pb2+ and Mn2+ acetates can similarly react with HEP to give their respective salts at the optimum temperature. We report here the synthesis and characterisation of Pb2+ and Mn2+ salts of mono(hydroxyethyl)-phthalate (HEP).
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    Effect of cooling rate on the viscoelastic properties in the plastic zone of solid polymers (1979)
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    Polymer bulletin 1 (1979), S. 743-748 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract PMMA and PC samples were subjected to several cooling rates from the glass transition temperature. Stress-relaxation data, obtained with these samples under strains larger than the yield strain, were not influenced by the cooling rate previously experienced by the material. This shows that after yielding the effect of previous aging is quickly erased; similar indications, drawn from calorimetric measurements, were already available in (11–12).
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    The use of graft copolymers as enzyme supports (1979)
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    Polymer bulletin 1 (1979), S. 749-753 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary A new type of polymer support for immobilizing enzymes, a copolymer grafted onto nylon was investigated. Polyacrylamide was used and successfully coupled to β-galactosidase (from yeast and bacteria) using two different methods to give activities of the order of 5 units/g of polymer for the yeast enzyme, and 156 units/g for the E.coli enzyme. Lactose did not affect the yield. The azide method gave better results than the glutaraldehyde method. β-galactosidase coupled enzyme was fairly stable but not as good as the free enzyme. Papain was also coupled to the polyacrylamide grafted nylon using both methods; the glutaraldehyde gave better results with 1.5mg of enzyme being coupled for each gram of polymer.
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    Polymerization via zwitterion. 23. Terpolymerization among 2-phenyl-1,3,2-dioxaphospholane, methyl acrylate, and carbon disulfide (1979)
    Springer
    Polymer bulletin 1 (1979), S. 243-251 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The present paper describes the terpolymerization involving 2-phenyl-1,3,2-dioxaphospholane, methyl acrylate, and carbon disulfide, which took place without any added initiator in benzonitrile or dimethylformamide. The structure and composition of terpolymer were determined by NMR and IR spectra, as well as by elemental analysis. A reaction scheme proceeding via zwitterion was proposed (Eq. 2–5).
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    Preparation of poly(vinyl chloride-g-isobutylene) by BCl3 (1979)
    Springer
    Polymer bulletin 1 (1979), S. 253-258 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Poly(vinyl chloride-g-isobutylene) has been synthesized using mildly dehydrochlorinated (NaOH treated) PVC in conjunction with BCl3 coinitiator. Treatment of PVC with NaOH increases initial thermal dehydrochlorination rate and renders the polymer suitable for efficient grafting. Untreated PVC produces negligible grafting.
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    Theory of thermal decomposition and volatilization of normal alkanes and linear polyethylene (1979)
    Springer
    Polymer bulletin 1 (1979), S. 347-354 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The fragmentation of linear polyethylene of high molecular weight, of normal alkanes, and of other nonbranched poly- α- olefins in a pyrolyzer connected with a gas chromatograph was studied previously. From the evaluation of the fragments longer than C11 or than the respective pentamer random decomposition process was suggested for these polymers. This process was described with characteristic cleavage probabilities for the C-C-bonds in the backbone of the chain. It is not possible to apply this simple model to the decomposition of normal alkanes without consideration of the volatilization. An approach to this problem is presented in this paper.
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    Stress and recovery maxima in LDPE melt elongation (1979)
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    Polymer bulletin 1 (1979), S. 397-402 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary By means of a new tensile rheometer for polymer melts, stress-strain curves σ(ε) and the elastic recovery εR(ε) of a low density polyethylene melt were measured up to total strains ε=7, i.e. stretch λ=1097, at 150°C and two strain rates, ε=0.03 and 0.1 s−1. Tensile tests up to very high strains e give relevant results only if the test performance is characterized by quality parameters which are defined and given in this paper. The test results show a maximum in a as well as in εR at about ε=5.5. Hence, in the range of ε investigated, a rheologically steady-state of flow does not exist.
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    Cis-trans isomerization of aromatic azo compounds built in the polyester segment of poly(ester urethanes) (1979)
    Springer
    Polymer bulletin 1 (1979), S. 517-522 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The photochemical and thermal cis-trans isomerization of 4,4 -(diamido)azobenzene derivative built in the polyester segment of a segmented poly(ester urethane) has been investigated. The photoisomerization in bulk proceeds more slowly than in solution and lower fractions of cis-isomers are reached in the photostationary state. The thermal cis-trans isomerization follows first order kinetics in polymers with amorphous soft phase but can only be described by two simultaneous first order processes in annealed samples. This is attributed to restrictions in the chain segmental mobility; it is assumed that the isomerization behaviour reflects different molecular motions in the bulk polymer.
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    Correspondence between the theory of branching processes and the kinetic theory for random crosslinking in the post-gel stage (1979)
    Springer
    Polymer bulletin 1 (1979), S. 523-528 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The kinetic theory of crosslinking by step reactions (Kuchanov 1978) may be extended beyond the gel point, and the structure and amount of sol may be described. For random reactions, the kinetic theory yields results identical with the theory of branching processes based on cascade substitution (Gordon 1962, 1975, Dobson 1965). The extension of the kinetic theory may be employed in order to compare deviations between the two theories expected for the dependent reactivities of functional groups.
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    A new method for investigating the mechanism of initiation of radical polymerization (1979)
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    Polymer bulletin 1 (1979), S. 529-534 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The mechanism of initiation of polymerization of methyl acrylate by di-t-butyl peroxalate at 60°C, has been investigated using 2,2,6,6-tetramethylpiperidine-1-oxyl as a radical trapping agent and isolation of the resulting products. The following processes were identified: Tail addition of t-butoxy radicals to monomer, hydrogen abstraction from the methyl group of the monomer and fragmentation of the t-butoxy radicals to methyl radicals followed by tail addition of these to the methyl acrylate.
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    Effect of hindered piperidine derivatives on polypropylene photooxidation (1979)
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    Polymer bulletin 1 (1979), S. 647-652 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The photostabilizing effect of a hindered piperidine derivative was studied in the photooxidation of polypropylene films by following the formation of carbonyl and hydroperoxide groups, as well as the change of concentration of the stabilizer. This additive — the tetramethylpiperidine sebacate — proved to be more effective than hydroxybenzophenone, hydroxybenztriazole or a sulphur containing nickel complex, since no oxidation products were formed after irradiation with 20O Mlxh dose. Addition of the piperidine derivative together with hydroxybenztriazole or with the organic nickel complex was less effective than with hydroxybenzophenone. In latter case concentration of both stabilizers under irradiation decreased at a slower rate than in the case of separate application. The effect of Cyasorb UV 531 and Tinuvin 770 was additive and the spontaneous rupture of the samples took place only after a long period of irradiation (∼ 250 Mlxh).
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    Functionalization of soluble polymers (1979)
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    Polymer bulletin 1 (1979), S. 691-695 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary In a second example of the functionalization of soluble polymers the conversion of the hydroxyl groups of poly (oxyethylene) into carboxyl groups is reported. As protected carboxyl component, 4-toluenesulfonyl lactic acid ethyl ester was synthesized and was allowed to react with sodium salt of poly(oxyethylene). Polymer-analogous hydrolysis of the di(lactic acid ethyl ester) poly(oxyethylene) yielded the carboxyl derivative of poly (oxyethylene).
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    Aqueous polymerization of acrylamide initiated by Ce(IV)-thiomalic acid redox system (1979)
    Springer
    Polymer bulletin 1 (1979), S. 671-678 
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    ISSN: 1436-2449
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The use of a Ce (IV)-thiomalic acid (Ce4+-TMA) redox system as an initiator in the polymerization of acrylamide (M) in an aqueous medium has been investigated. The Ce4+ forms a 1∶1 complex with TMA, decomposing through free radical mechanism in an acid medium. From 5 to 15% conversion the rate equation is $$R_p = - \frac{{d[M]}}{{dt}} = k[M]^{3/2} [Ce^{4 + } ]^x [TMA]$$ where Rp is the rate of polymerization and x is 0.5 or 1.0 depending upon the concentration of monomer. The overall energy of activation has been calculated to be 9.12 k cal. deg−1 mol−1(38.12 kJ/mol) in the investigated range of temperature (25°–40°C) the degree of polymerization (P) of the polymer is directly proportional to [M]. The number of average molecular weight of the polymer remains unaffected at lower concentration of Ce4+ and is found to decrease at higher concentrations. In this investigation the kinetics and mechanism of the Ce(IV)-thiomalic acid (TMA) redox system to initiate the polymerization of acrylamide has been studied. Acrylamide (E. Merck) was purified by usual methods. Thiomalic acid and eerie ammonium sulfate were used without purification. All solutions were p repared in twice distilled water. The polymerization procedure adopted was similar to the one used by MISRA et al. [3, 4]. The polymerization was followed by quantitative estimation of the double bonds in acrylamide as described [8]. A small variable induction period was observed perhaps due tothe residual oxygen in the thiol solution. Curves were plotted after eliminating the induction period. The average molecular weights of the p olymers were determined by viscosity measurements at 30°C in an aqueous medium using the relationship of DAINTON et al. [2]. $$[\eta ] 30^\circ = 6.8 x 10^{ - 4} \bar Mn^{0.66} $$ Where [η]=intrinsic viscosity of the polymer solution and ¯Mn=molecular weight of the sample.
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    Ultrahigh-strength polyethylene filaments by solution spinning and hot drawing (1979)
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    Polymer bulletin 1 (1979), S. 733-736 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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    Environmental stress relaxation studies of polymers: effect of ketones on polyethylene and its temperature dependence (1979)
    Springer
    Polymer bulletin 1 (1979), S. 737-741 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The method of stress relaxation has been used to study the effect of ketones on polyethylene as it changes with temperature. From the observation of the stress relaxation in polyethylene under ketones and its temperature dependence, the activation energy of penetrant-enhanced relaxation of polyethylene caused by ketones were obtained and the effect of ketones on polyethylene were discussed.
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    The use of graft copolymers as enzyme supports (1979)
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    Polymer bulletin 1 (1979), S. 755-761 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary β-Galactosidase and glucose oxidase have been immobilized on cellulose-polyacrylamide (C-PAM) graft copolymers, using the azide method or through glutaraldehyde. The original (C-PAM) copolymers were prepared via radiation-induced grafting under controlled conditions by both post-irradiation and simultaneous procedures. The optimum conditions for coupling of the copolymers to the enzymes were established as were the levels of activity of the immobilized enzymes. Grafting by the simultaneous route was seen to be more efficient than postirradiation grafting. Indirect evidence of grafting was found from elemental and thermal analysis. Binding of β-galactoside was found to be more successful than that of glucose oxidase. A relationship between the level of immobilized enzyme activity and the extent of grafting in the copolymer was established for the β-galactosidase system.
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    Thermodynamic study on heat of mixing of polyisobutylene with ethylbenzene (1979)
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    Polymer bulletin 1 (1979), S. 763-770 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The heat of mixing of polyisobutylene with ethylbenzene was measured from 18.2 to 69.2° C with a Tian-Calvet twin micro-calorimeter, and the exchange enthalpy parameter X12 in Flory's theory was estimated. The X12 obtained was discussed also in comparison with the one based on Manzini model. Further combining with osmotic pressure data, temperature dependence of the entropy parameter Q12 was referred.
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    Effect of the chiral polymer chain in the anionic polymerization of styrene oxide (1979)
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    Polymer bulletin 1 (1979), S. 793-799 
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    Notes: Abstract Styrene oxide of different enantiomeric compositions was polymerized in bulk using a potassium alkoxide initiator. A preferential consumption of the enantiomer in excess was observed. The magnitude of this effect depends on the enantiomeric composition of the initial monomer: the more unbalanced is the latter, the stronger is the stereoelection observed. The stereoelective effect was almost completely suppressed by addition of complexing agents such as crown-ethers or cryptands. The observed phenomena are explained in terms of polymer-chain effects.
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    Kinetic study of the crystallization of stretched polyisobutylene using synchrotron radiation (1979)
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    Polymer bulletin 1 (1979), S. 709-714 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The change in the scattering pattern of polyisobutylene fibres following rapid stretching was measured using synchrotron radiation. The half-time for the crystallisation process is approximately 50 seconds. Upon release the crystalline portions disappear immediately.
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    Calculation of kinetic parameters of phase transitions in glassy polymers (1979)
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    Polymer bulletin 1 (1979), S. 845-848 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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    Polymerization of propylene with highly active MgCl2-supported TiCl3 catalyst (1979)
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    Polymer bulletin 1 (1979), S. 849-856 
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    Notes: Summary The MgCl2 supported TiCl3 catalyst was prepared by grinding the mixture of TiCl3·3Py and MgCl2 in a ball mill. The catalyst was treated either i.vac. at 50–200°C or with alkylaluminum halides to remove the residual pyridine, and propylene polymerization was conducted at 65°C using the resulting catalysts combined with triethylaluminum. The catalyst treated with diethylaluminum chloride showed an extremely high activity for the polymerization.
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    Two-component hydrogels (1979)
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    Polymer bulletin 1 (1979), S. 857-864 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The elastic equations of state for 2-component networks are derived from a joint Gaussian distribution function composed of Gaussians for each component. The free energy of elasticity is then applied to the case of uni-directional deformations for compatible systems. The stress-strain equations are shown to be equivalent to those for a single component network except in the case where the macroscopic strain is sufficient to cause the ratio of average chain lengths of the components to change with the strain. The stress-strain equations are developed for both dry and swollen networks.
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    On the concentration dependence of the elasticity modulus of soybean globulin gels (1979)
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    Polymer bulletin 1 (1979), S. 865-869 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The concentration dependence of the elasticity modulus (G) of gels produced by heating soybean globulins (SBG) has been investigated in the concentration range C=7.5–58.4%. The tests included constant rate loading and stress relaxation. The experimental results are presented in the form of a modulus reduction parameter b(C)=G(C) / G(C∘), where C∘=15% corresponds to the standard reference state. Whatever the testing conditions, the results are described by a single smooth curve similar, to a constant factor, to the concentration dependence of the equilibrium elasticity modulus of SBG gels. The experimental relationship b (C) agrees with the theoretical concentration dependence of the equilibrium polymer gel modulus according to Hermanns if it is assumed that the gel-point of SBG, Co=6.6 %. Within an order of magnitude this value of Co is consistent with the experimental data. We have to thank the European Branch Director of Central Soya Intern., Inc., Mr.J.F.Casey for kindly providing us defatted soya flour.
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    The fire-resistance properties of polycarbonates (1979)
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    Polymer bulletin 1 (1979), S. 897-907 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary This paper describes new fire-resistant bisphenol A and monoalkyl monoalkaline bis(hydroxy-4 phenyl) alkyl phosphonate copolycarbonates. We show that inclusion of minute quantities (in molar percentages of 0.5 to 1%) of monoalkaline potassium salts of bis(hydroxy-4 phenyl)-alkyl phosphonic acid considerably improves the fire-resistant of the bisphenol A polycarbonate. We obtain oxygen indices of 34 to 35.
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    Cyclopentadienylation of PVC (1979)
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    Polymer bulletin 1 (1979), S. 415-420 
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    Notes: Summary Cyclopentadienylation of PVC with alkaline (NaCPD, LiCPD) and acidic (Me2CPDAl) cyclopentadienylating agents has been investigated. In terms of product quality (absence of discoloration, gelation) Me2 CPDAl was found to be a superior cyclopentadienylating agent than NaCPD and LiCPD.
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    Functionalization of suluble polymers (1979)
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    Polymer bulletin 1 (1979), S. 427-431 
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    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary In a first example of the functionalization of soluble polymers the conversion of the hydroxyl groups of poly(oxyethylene) into primary amino groups has been studied. Starting from poly(oxyethylene), the preparation of the diphthalimido derivative via the disodium salt is described. Prom this regiospecific functionalized polymer the di(aminoethyl) poly(oxyethylene), which exhibits excellent solubility properties, can be obtained by polymeranalogous hydrazinolysis.
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    Determination of the monomer donor-acceptor complexes participation in the alternating propagating reaction based on the microtacticity of the alternating copolymers (1979)
    Springer
    Polymer bulletin 1 (1979), S. 441-444 
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    Notes: Summary It is shown that the probability for the formation of alternating macromolecules by monomer donor-acceptor complexes can be determined from the microtacticity of the copolymers. If the stereoregularity in the alternating copolymerization is described by the Bernoullian trial two other probabilities concerning the meso-diad formation can be determined by this method. If the stereoregularity is described by the first order Markov chain the transition probabilities can be calculated. Thus a more detailed analysis of the propagation mechanism in alternating copolymerization can be carried out.
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    Preliminary study of cationic copolymerization of α-methyl-styrene and isobutyl vinyl ether I (1979)
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    Polymer bulletin 1 (1979), S. 433-436 
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    Notes: Summary Cationic copolymerination of α-MS and IBVE was successfully carried out using “H2O”/EtAlCl2 initiator system and CH2Cl2 solvent at −50°C. The effect of monomer feed concentration on the copolymer yield and composition was studied. Small concentrations of IBVE had significant effect on the copolymer yield and composition, while that of α-MS had only marginal effect. Tg of the copolymers was linearly dependent on the α-MS content strongly indicating that the copolymerization was of random nature.
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    Evaporation of polymer-solvent mixtures (1979)
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    Polymer bulletin 1 (1979), S. 459-464 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The Stefan-Winkelmann diffusion technique has been used to determine vapor pressures of high boiling point compound-solvents mixtures. Data are reported at a temperature of 67°C for the mixtures polyphenyl ether (6 rings) — benzene and carbowax 1500 — benzene and at a temperature of 100°C for the mixtures polyphenyl ether (6 rings) — toluene and tricresylphosphate-toluene. The range of concentration is only limited by the appearance of a solid phase, and results are in good agreement with those determined by vapor pressure osmometry.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00255708
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  • 86
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    Dimerization of 1-isopropenyl anthracene by TiCl4 (1979)
    Springer
    Polymer bulletin 1 (1979), S. 469-473 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary 1-isopropenyl anthracene was dimerized by reaction with TiCl4 in CH2Cl2 and the structure of the dimer studied by 1H NMR spectroscopy. The spectrum was assigned and is in agreement with simulation. The structure results from the attack of carbocation on carbon 9.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00255710
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  • 87
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    Dimerization of 9-isopropenyl phenanthrene by TiCl4 (1979)
    Springer
    Polymer bulletin 1 (1979), S. 475-479 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary 9-isopropenyl phenanthrene was dimerized by reaction with TiCl4, in CH2Cl2 and the structure of the dimer studied by 1H NMR spectroscopy. The structure results from the attack of carbocation on carbon 9.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00255711
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  • 88
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    Solvent effect in radical copolymerisation of N-vinylcarbazole and methylmethacrylate (1979)
    Springer
    Polymer bulletin 1 (1979), S. 491-499 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Radical copolymerisation of MMA(r1) and NVC(r2) yields values of the apparent reactivity ratios r1 = 1.80, r2 = 0.06 (benzene) and r1 = 0.57, r2 = 0.75 (methanol) at 55°C. It is suggested that the apparent increase in reactivity of NVC in methanol arises from high local monomer concentrations due to formation of microphases containing the growing copolymer chains in which NVC is preferentially partitioned. Fluorescence emission and u.v. absorption spectra for copolymers prepared in both solvents are identical and consistent with the occurrence of only very short sequences of NVC units.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00255714
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  • 89
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    Ring-chain equilibrium in the anionic polymerization of δ-valerolactone (1979)
    Springer
    Polymer bulletin 1 (1979), S. 569-573 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The anionic polymerization of δ-valerolactone in tetrahydrofuran with lithium tert-butoxide was found to give a living ring-chain equilibrium system, in which the cyclic oligomers are produced by back-biting degradation from the initially formed linear polymers. The molar cyclization equilibrium constant for the trimer through hexamer decreased in proportion to −2.5 power of the ring size, in accord with the Jacobson-Stockmayer theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00254486
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  • 90
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    EPR study of enzymatic cleavage of side chains of water soluble polymers using spin-label as a leaving group (1979)
    Springer
    Polymer bulletin 1 (1979), S. 585-591 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Synopsis It was confirmed by EPR that 4-amino-2,2,6,6--tetramethylpiperidine-N-oxyl (TEMP-NH2) is cleaved by chymotrypsin from 4-(N-glycyl-L-phenylalanyl)amino −2,2,6,6-tetramethylpiperidine-N-oxyl attached as a substrate with paramagnetic leaving group to the end of side chains of water soluble hydroxypropyl methacrylamide (HPMA) compolymers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00254135
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  • 91
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    Synthesis and polymerization of γ-ethyl-L-glutamate derivatives of nucleic acid bases (1979)
    Springer
    Polymer bulletin 1 (1979), S. 599-602 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary γ-Ethyl-L-glutamate derivatives having pendant nucleic acid bases, that is, uracil, adenine and theophylline were synthesized. The γ-ethyl-L-glutamate having theophylline moiety was polymerized by using the N-carboxyamino acid anhydride (NCA) method.
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    URL: http://dx.doi.org/10.1007/BF00254137
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  • 92
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    Relationship between apparent and true molecular weight in GPC (1979)
    Springer
    Polymer bulletin 1 (1979), S. 619-623 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The analytical relationship between the molecular weight averages obtained from an experimental GPC elu tion curve and the true ones is calculated by use of one integration method in order to solve the convolution integral. The knowledge of these relationship signifies an useful tool to carry out critical considerations on the operation of different methods existing for the calculation of the spreading correction and for the elaboration of the calibration function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00254140
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  • 93
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    Synthesis and polymerization of 3-methylenecyclobutene-1-carbonitrile (1979)
    Springer
    Polymer bulletin 1 (1979), S. 625-629 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00254141
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  • 94
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    The solution polymerization of hexachlorocyclotriphosphazene (1979)
    Springer
    Polymer bulletin 1 (1979), S. 653-657 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The polymerization of hexachlorocyclotriphosphazene (trimer) is studied in different solvents. A soluble low molecular weight polymer is obtained when benzene is the solvent, a highly cross-linked polymer when cyclohexane is the solvent, and a mixture of soluble and insoluble polymers results when the solvent is chlorobenzene. The conversion-concentration curve for the trimer shows a dependence of the amount of soluble and insoluble polymer formed on the trimer concentration. No polymerization took place when the solvent was toluene, nitrobenzene or THF, but a reaction between solvent and trimer was detected.
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    URL: http://dx.doi.org/10.1007/BF00254146
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  • 95
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    The thermal effect in the photomechanical conversion of a photochromic polymer (1979)
    Springer
    Polymer bulletin 1 (1979), S. 659-664 
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    ISSN: 1436-2449
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The effect of radiation on the mechanical behaviour of the crosslinked copolymer of maleic anhydride and styrene containing photochromic azo groups was investigated. The analysis of results of the observed photomechanical conversion proved a considerable influence of the thermal effect in addition to the effect of photoisomerization of the photochrome. The interpretation of some photomechanical experiments described earlier may be obscured by a rise in temperature caused by the absorption of radiation.
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    URL: http://dx.doi.org/10.1007/BF00254147
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  • 96
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    Some examples of cycling in variable metric methods for constrained minimization (1979)
    Springer
    Mathematical programming 16 (1979), S. 378-383 
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    ISSN: 1436-4646
    Keywords: Constrained Minimization ; Variable Metric Methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Although variable metric methods for constrained minimization generally give good numerical results, many of their convergence properties are still open. In this note two examples are presented to show that variable metric methods may cycle between two points instead of converging to the required solution.
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    URL: http://dx.doi.org/10.1007/BF01582123
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  • 97
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    Minimum node covers and 2-bicritical graphs (1979)
    Springer
    Mathematical programming 17 (1979), S. 91-103 
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    ISSN: 1436-4646
    Keywords: Node Packing ; Node Covering ; Stable Set ; Bicritical Graphs ; 2-Bicritical Graphs ; Regularizable Graphs ; Matchings
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The problem of finding a minimum cardinality set of nodes in a graph which meet every edge is of considerable theoretical as well as practical interest. Because of the difficulty of this problem, a linear relaxation of an integer programming model is sometimes used as a heuristic. In fact Nemhauser and Trotter showed that any variables which receive integer values in an optimal solution to the relaxation can retain the same values in an optimal solution to the integer program. We define 2-bicritical graphs and give several characterizations of them. One characterization is that they are precisely the graphs for which an optimal solution to the linear relaxation will have no integer valued variables. Then we show that almost all graphs are 2-bicritical and hence the linear relaxation almost never helps for large random graphs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588228
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  • 98
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    Tenth International Symposium on Mathematical Programming (1979)
    Springer
    Mathematical programming 17 (1979), S. 114-114 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588232
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  • 99
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    Pivotal methods for computing equilibrium points: Unified approach and new restart algorithm (1979)
    Springer
    Mathematical programming 16 (1979), S. 210-227 
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    ISSN: 1436-4646
    Keywords: Pivotal Algorithms ; Equilibrium Point ; Primitive Sets ; Restart Method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract On the basis of a unified approach to pivotal algorithms and a generalization of the concept of primitive sets by Scarf we show that Scarf's algorithm for finding fixed points can be embedded into a class of more flexible and more efficient algorithms, allowing restarts. An example of this new restart method is described. Also the class of equilibrium problems solvable by this method is discussed.
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    URL: http://dx.doi.org/10.1007/BF01582109
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  • 100
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    Editorial policy (1979)
    Springer
    Mathematical programming 16 (1979), S. 262-262 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582114
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