Leibnizian,Robinsonian, and Boolean valued monads

This is an overview of the present-day versions of monadology with some applications to vector lattices and linear inequalities. Two approaches to combining nonstandard set-theoretic models are sketched and illustrated by order convergence, principal projection, and polyhedrality.     

Essence,Application, and Explanation

It is often thought that a notion of general term rigidity could help explain the particular behavior of natural kind terms in modal contexts. An influential strategy for developing a non-trivial account of general term rigidity appeals to essential properties of the things to which such terms apply. I show that essentialism cannot underpin a notion of rigidity that can play the expected explanatory roles. Essentialists are committed to presuppositions that themselves play those roles without implying essentialism.     

Cosmological constant,scalar field,and the coincidence problem

Theoretical and Mathematical Physics - We study a phenomenological model in which dark matter in the cosmological constant form is identified with the mean energy–momentum tensor of a...     

Non-Singular,Vacuum, Stationary Space-Times with a Negative Cosmological Constant

We construct infinite dimensional families of non-singular stationary space times, solutions of the vacuum Einstein equations with a negative cosmological constant. Submitted: December 12, 2005. Accepted: May 22, 2006.     

Cosmological quantum tunneling and the holographic principle

The probable trajectory of the ground-state wave function of the universe arises through quantum tunneling by gravitational instantons. We calculate the quantum tunneling rate for an (n>2)-dimensional closed Friedmann-Robertson-Walker universe with a positive cosmological constant. In four dimensions, we use the holographic principle to relate the tunneling rate to the maximal entropy of the early universe after quantum tunneling.     

Cosmological models with homogeneous and isotropic spatial sections

The assumption that the universe is homogeneous and isotropic is the basis for the majority of modern cosmological models. We give an example of a metric all of whose spatial sections are spaces of constant curvature but the space–time is nevertheless not homogeneous and isotropic as a whole. We give an equivalent definition of a homogeneous and isotropic universe in terms of embedded manifolds.     

The Darboux Transformation and Exactly Solvable Cosmological Models

We present a simple and effective method for constructing exactly solvable cosmological models containing inflation with exit. This method does not involve any parameter fitting. We discuss the problems arising with solutions that violate the weak energy condition.     

Cosmological simulations of structure formation and the Vlasov equation

In cosmology numerical simulations of structure formation are now of central importance, as they are the sole instrument for providing detailed predictions of current cosmological models for a whole class of important constraining observations. These simulations are essentially molecular dynamics simulations of N (≫1, now up to of order several billion) particles interacting through their self-gravity. While their aim is to produce the Vlasov limit, which describes the underlying (“cold dark matter”) models, the degree to which they actually do produce this limit is currently understood, at best, only very qualitatively, and there is an acknowledged need for “a theory of discreteness errors”. In this talk I will describe, for non-cosmologists, both the simulations and the underlying theoretical models, and will then focus on the issue of discreteness, describing some recent progress in addressing this question quantitatively.     

Cosmological natural selection and the purpose of the universe

The cosmological natural selection (CNS) hypothesis holds that the fundamental constants of nature have been fine‐tuned by an evolutionary process in which universes produce daughter universes via the formation of black holes. Here, we formulate the CNS hypothesis using standard mathematical tools of evolutionary biology. Specifically, we capture the dynamics of CNS using Price's equation, and we capture the adaptive purpose of the universe using an optimization program. We establish mathematical correspondences between the dynamics and optimization formalisms, confirming that CNS acts according to a formal design objective, with successive generations of universes appearing designed to produce black holes. © 2013 Wiley Periodicals, Inc. Complexity 18: 48–56, 2013     

Program Explanation and Higher-Order Properties

Our aim in this paper is to evaluate Frank Jackson and Philip Pettit’s ‘program explanation’ framework as an account of the autonomy of the special sciences. We argue that this framework can only explain the autonomy of a limited range of special science explanations. The reason for this limitation is that the framework overlooks a distinction between two kinds of properties, which we refer to as ‘higher-level’ and ‘higher-order’ properties. The program explanation framework can account for the autonomy of special science explanations that appeal to higher-level properties but it does not account for the autonomy of most of those explanations that appeal to higher-order properties.     

Dynamics of Extended Objects and a Stationary Axially Symmetric Cosmological Model

We find a new solution describing a homogeneous stationary axially symmetric model, which, in contrast to the Gödel model, does not contain closed timelike lines. We find exact solutions corresponding to the motion of a null string in the rotating Universe and show that these solutions crucially depend on the initial data. To obtain more detailed information on the cosmic string dynamics, we performed numerical simulations indicating essential differences in the behavior of strings and null strings in the presence of global rotation of the Universe. These numerical solutions show that the string manifests involved oscillations, varies its shape with the appearance of loops and cusps, and twists into a spiral.     

Arguments for the compactness and multiple connectivity of our cosmic spacetime

Some global topological as well as quantative arguments are given, indicating that our universe is most probably compact, multiply connected and without boundaries. The analysis leading to this tentative conclusion is based on a combination of Nash Euclidean embedding theorems, the local isomorphism theorem, cosmic crystallography and the theory of fractal-Cantorian spacetime. It is shown that the correct topological dimension D = 4 of space is derived from the Euclidean embedding of spacetime quanta when the corresponding manifold is assumed to be compact. This and other conclusions regarding multi-connectivity seems to reinforce the findings of relatively recent research results on topological cosmology by Luminet et al. (see Nature 425;9 Oct. 2003:593–95).     

具连续变量和最大值项的二阶差分方程的振动性

研究了一类具有最大值项和连续变量的非线性二阶中立型时滞差分方程的振动性,利用Banach空间的不动点原理和一些不等式技巧,得到了这类方程存在最终正解的充分条件,并得到了该方程振动的一些判别准则.     

The Klein Group,Squares of Opposition and the Explanation of Fallacies in Reasoning

During the last decades, the psychology of reasoning has identified experimentally many fallacies committed by spontaneous reasoners. Given these experimental results, some theories have been developed about this phenomenon, mainly algorithmic theories. This paper develops instead a computational modelling of these current fallacies which appear as simplifications in the treatment of information that do not respect the formal rules of classical propositional logic. These fallacies are explained as crushes in the Klein group structure and so, in squares of opposition. These crushes are an effect of not to take into account the dual of the binary operator at work in the major premise of the inference. This analysis allows predictions on fallacies not identified before, which are fallacies produced when reasoning with incompatibilities. The paper concludes with consequences of the analysis on pedagogical strategies for the teaching of logic.