Hannu Nurmi (1982)
Stochastica
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This paper deals with two ways in which uncertainty notions enter social science models: 1) They can be used in an effort to make intelligible some phenomena that would otherwise be difficult to comprehend, or 2) They can be use to generalize or modify the domain of validity of some theoretical results.
J. Matkowski, M. Sablik (1986)
Stochastica
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Equation [1] f(x+y) + f (f(x)+f(y)) = f (f(x+f(y)) + f(f(x)+y)) has been proposed by C. Alsina in the class of continuous and decreasing involutions of (0,+∞). General solution of [1] is not known yet. Nevertheless we give solutions of the following equations which may be derived from [1]: [2] f(x+1) + f (f(x)+1) = 1, [3] f(2x) + f(2f(x)) = f(2f(x + f(x))). Equation [3] leads to a Cauchy functional equation: ...
Heinz J. Skala (1982)
Stochastica
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After a short discussion of the first application of measure theoretic tools to economics we show that it is consistent relative to the usual axioms of set theory that there exists no nonatomic probability space of power less than the continuum. This together with other results shows that Aumann's continuum-of-agents methodology provides a sound framework at least for the cooperative theory. There are, however, other problems in economics where, without further assumptions,...
Mirko Polonijo (1985)
Stochastica
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The notion of a TST-space is introduced and its connection with a parallelogram space is given. The existence of a TST-space is equivalent to the existence of a parallelogram space, which is a new characterization of a parallelogram space. The structure of a TST-space is described in terms of an abelian group.
Barbara Baccheli (1986)
Stochastica
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Strengthened forms of Ling's representation theorem concerning a class of continuous associative functions are given: Firstly the monotonicity condition is removed. Then the associativity condition is replaced by the power associativity.
Michael Katz (1982)
Stochastica
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We describe restricted and extended versions of the logic of approximation which is meant to handle formally the problems of measurement error and of deduction under conditions of uncertainty. We apply the logic to the foundations of social and behavioral inquiry, axiomatizing in it an inexact similarity predicate which behaves like a metric approximation to identity. In the restricted version of the logic we formulate conditions for the imbeddability of similarity models in the real...
Robert C. Harris, Travis Mackoy, Marcia O. Fenley (2013)
Molecular Based Mathematical Biology
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A stochastic generalized Born (GB) solver is presented which can give predictions of energies arbitrarily close to those that would be given by exact effective GB radii, and, unlike analytical GB solvers, these errors are Gaussian with estimates that can be easily obtained from the algorithm. This method was tested by computing the electrostatic solvation energies (ΔGsolv) and the electrostatic binding energies (ΔGbind) of a set of DNA-drug complexes, a set of protein-drug complexes,...
Tao Liao, Yongjie Zhang, Peter M. Kekenes-Huskey, Yuhui Cheng, Anushka Michailova, Andrew D. McCulloch, Michael Holst, J. Andrew McCammon (2013)
Molecular Based Mathematical Biology
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Multi-scale modeling plays an important role in understanding the structure and biological functionalities of large biomolecular complexes. In this paper, we present an efficient computational framework to construct multi-scale models from atomic resolution data in the Protein Data Bank (PDB), which is accelerated by multi-core CPU and programmable Graphics Processing Units (GPU). A multi-level summation of Gaussian kernel functions is employed to generate implicit models for biomolecules....
Isabelle Chalendar, Jonathan R. Partington (2013)
Concrete Operators
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This paper presents an account of some recent approaches to the Invariant Subspace Problem. It contains a brief historical account of the problem, and some more detailed discussions of specific topics, namely, universal operators, the Bishop operators, and Read’s Banach space counter-example involving a finitely strictly singular operator.