Divisible designs, Laguerre geometry, and beyond

In this paper, we bring together design theory and projective geometry over a ring. Both disciplines are well established, but the results on the interaction between them are rare and are scattered over the literature. Our main goal is to present the basics from either side, to develop, or at least sketch, the principal connections between them, and to make recommendations for further reading.     

On stability of three-dimensional periodic motions in hydrodynamics : PMM vol. 37, n6, 1973, pp. 1044–1048

We obtain exact conditions for the stability of periodic motions. We show that the conditions found in [1] are necessary and sufficient, but they are only applicable to motions not dependent on time. The conditions given in [2] are applicable in the general case but are only sufficient (necessary) conditions of instability (stability). We consider the dependence of stationary motions on parameters.     

Evolution equations,singular dispersion relations,and moving eigenvalues

A new approach for finding the class of integrable evolution equations associated with a given eigenvalue problem is developed. The key point to note is that the squares of the eigenfunctions form a natural basis in which to expand the solutions of the evolution equation. Once this step is taken, the class of integrable equations may usually be read off by inspection. Of particular interest are those equations for which the bound state eigenvalues are not invariant but move in a way prescribed by the coefficients of the evolution equation. The corresponding solitons have the property that they retain their identity on collision with other solution components, but this identity is no longer a constant one. The Hamiltonian structure and the causality properties of these systems are also explored.     

Particularism and individuation: Disappearing, not varying, features

Particularism denies that invariant valence is always possible and that it is needed in sound moral theorising. It relies on variabilism, namely the idea that the relevant features of a given situation can alter their moral valence even across seemingly similar cases. An alternative model is defended (the “disappearing model”), in which changes in the overall relevance of complex cases are explained by re-individuation of the constituent features: certain features do not alter their relevance in consequence of contextual changes, but rather they disappear, either because they are embedded within larger complexes or are substituted by different features. This view is shown to be compatible with the main premises of variabilism and explanatorily superior to it. Nevertheless, it does not involve particularism, but rather a peculiar form of generalism.     

Scarcity,competition, and value

We suggest a value for finite coalitional games with transferable utility that are enriched by non-negative weights for the players. In contrast to other weighted values, players stand for types of agents and weights are intended to represent the population sizes of these types. Therefore, weights do not only affect individual payoffs but also the joint payoff. Two principles guide the behavior of this value. Scarcity: the generation of worth is restricted by the scarcest type. Competition: only scarce types are rewarded. We find that the types’ payoffs for this value coincide with the payoffs assigned by the Mertens value to their type populations in an associated infinite game.     

Mirror symmetry,Langlands duality,and the Hitchin system

Among the major mathematical approaches to mirror symmetry are those of Batyrev-Borisov and Strominger-Yau-Zaslow (SYZ). The first is explicit and amenable to computation but is not clearly related to the physical motivation; the second is the opposite. Furthermore, it is far from obvious that mirror partners in one sense will also be mirror partners in the other. This paper concerns a class of examples that can be shown to satisfy the requirements of SYZ, but whose Hodge numbers are also equal. This provides significant evidence in support of SYZ. Moreover, the examples are of great interest in their own right: they are spaces of flat SL_r-connections on a smooth curve. The mirror is the corresponding space for the Langlands dual group PGL_r. These examples therefore throw a bridge from mirror symmetry to the duality theory of Lie groups and, more broadly, to the geometric Langlands program.     

形体老化与疾病的非线性主成分分析

本文把 5个形体老化指标及 13种慢性病指标分别做成两个综合指标 ,再去研究人体老化、疾病与性别及年龄的关系。文中使用非线性主成分法及指出一般线性主成分法的局限性     

Microbundles, manifolds and metrisability

The notion of a microbundle was introduced in the 1960s but the theory came to an abrupt halt when it was shown that for a metrisable manifold, microbundles are equivalent to fibre bundles. In this paper we consider microbundles over non-metrisable manifolds. In some cases microbundles are equivalent to fibre bundles but in others they are not. In particular, we show that a manifold is metrisable if and only if its tangent microbundle is equivalent to a fibre bundle. We also illustrate that for some non-metrisable manifolds every trivial microbundle contains a trivial fibre bundle whereas other manifolds may support a trivial microbundle not containing a trivial fibre bundle.

     

Alethic Functionalism,Manifestation, and the Nature of Truth

Michael Lynch has recently proposed an updated version of alethic functionalism according to which the relation between truth per se and lower-level truth properties is not the realization relation, as might be expected, and as Lynch himself formerly held, but the manifestation relation. I argue that the manifestation relation is merely a resemblance relation and is inadequate to properly relate truth per se to lower-level truth properties. I also argue that alethic functionalism does not justify the claim that truth per se exists, or that truth per se is a functional property. Finally, I suggest a replacement for the manifestation relation. I argue that the resulting theory is a strict improvement over alethic functionalism on two counts, but that the improved theory does not justify the claim that truth per se exists. Since no further improvements to the theory are apparent, the prospects for alethic functionalism are dim.     

Knowledge,Assertion, and Inference

This paper argues that three plausible principles are mutually inconsistent: (KA) One ought to assert only what one knows; (AP) If it is proper to assert some proposition q, then it is, barring special and not very common circumstances, proper to assert any proposition p from which q has been competently inferred; and (AKN) Some propositions are both properly assertible and known by competent inference from propositions which one does not know. Each pair of two principles constitutes an argument against the remaining principle, but which principle should one drop?     

On summation formulas due to Plana, Lindelöf and Abel, and related Gauss-christoffel rules, I

Three methods, old but not so well known, transform an infinite series into a complex integral over an infinite interval. Gauss quadrature rules are designed for each of them. Various questions concerning their construction and application are studied, theoretically or experimentally. They are so efficient that they should be considered for the development of software for special functions. Applications are made to slowly convergent alternating and positive series, to Fourier series, to the numerical analytic continuation of power series outside the circle of convergence, and to ill-conditioned power series.     

Clusters, outliers, and regression: fixed point clusters

Fixed point clustering is a new stochastic approach to cluster analysis. The definition of a single fixed point cluster (FPC) is based on a simple parametric model, but there is no parametric assumption for the whole dataset as opposed to mixture modeling and other approaches. An FPC is defined as a data subset that is exactly the set of non-outliers with respect to its own parameter estimators. This paper concentrates upon the theoretical foundation of FPC analysis as a method for clusterwise linear regression, i.e., the single clusters are modeled as linear regressions with normal errors. In this setup, fixed point clustering is based on an iteratively reweighted estimation with zero weight for all outliers. FPCs are non-hierarchical, but they may overlap and include each other. A specification of the number of clusters is not needed. Consistency results are given for certain mixture models of interest in cluster analysis. Convergence of a fixed point algorithm is shown. Application to a real dataset shows that fixed point clustering can highlight some other interesting features of datasets compared to maximum likelihood methods in the presence of deviations from the usual assumptions of model based cluster analysis.     

Supersymmetry, transfinite neural networks, hyperbolic manifolds, quantum gravity and the Higgs

Connections between the transfinite extension of neural networks and hyperbolic manifolds are pointed out. The found relations are subsequently used to elucidate a certain quantum gravity equation that is reinterpreted via Spinor varieties. Finally it is shown how a definite picture of ^(∞) spacetime may be obtained from a transfinite extension of a certain four dimensional hyperbolic manifold based on Coxeter 120-cell polytop and how this helps in understanding the need of postulating the existence of not only one but three Higgs particles.     

CME on March 16, 2001, electron pulsation event and solar-terrestrial phenomena related with CMEs

The electron pulsation event is defined in the paper. Firstly, a slow Halo CME on March 16, 2001 that led to low-energetic solar proton event, electron pulsation event and major geomagnetic storm was analyzed. And then, dozens of events are collected. The interrelations among the solar flare, CME, solar proton event, electron pulsation event and geomagnetic storm are studied. The results show that: (i) Solar proton events can be regarded as the indication that CMEs get to the earth and the electron pulsation events can be regarded as the indication of solar proton flux. (ii) Not only can fast CMEs strongly influence the earth, but also slow CMEs can influence the earth, and its influences are more frequent and cannot be neglected. (iii) Most of high-energetic solar proton events withE≥10 MeV can lead to geomagnetic storms, but most of the medium and weak geomagnetic storms result from low-energetic solar proton events that are caused by CMEs. (iv) Both the electron pulsation events and geomagnetic storms are the link effects of high- and low-energetic solar proton events, but the occurrence of electron pulsation event are generally prior to the geomagnetic storm. So in the circumstance where the near real-time observing data of the low-energetic solar proton event cannot be obtained, we can regard electron pulsation event as the indication of the low-energetic solar proton flux reaching the earth, which can be used as one of the important references of short-term prediction and alert of the geomagnetic storm.     

Multivariate Differences, Polynomials, and Splines

We generalize the univariate divided difference to a multivariate setting by considering linear combinations of point evaluations that annihilate the null space of certain differential operators. The relationship between such a linear functional and polynomial interpolation resembles that between the divided difference and Lagrange interpolation. Applying the functional to the shifted multivariate truncated power produces a compactly supported spline by which the functional can be represented as an integral. Examples include, but are not limited to, the tensor product B-spline and the box spline.     

Self‐organizing market structures,system dynamics,and urn theory

Using data from Fortune Magazine's 500 American largest corporations from 1955 to 2010, this article shows that firm sizes at national and industrial level are highly skew but not Zipf‐distributed. It also argues that, while self‐organizing industrial structures of this kind are due to increasing returns and hard to describe with conventional theories, system dynamics and urn theory are equipped with adequate tools to analyze them.     

CME on March 16, 2001, electron pulsation event and solar-terrestrial phenomena related with CMEs

The electron pulsation event is defined in the paper. Firstly, a slow Halo CME on March 16, 2001 that led to low-energetic solar proton event, electron pulsation event and major geomagnetic storm was analyzed. And then, dozens of events are collected. The interrelations among the solar flare, CME, solar proton event, electron pulsation event and geomagnetic storm are studied. The results show that: (ⅰ) Solar proton events can be regarded as the indication that CMEs get to the earth and the electron pulsation events can be regarded as the indication of solar proton flux. (ⅱ) Not only can fast CMEs strongly influence the earth, but also slow CMEs can influence the earth, and its influences are more frequent and cannot be neglected. (ⅲ) Most of high-energetic solar proton events with E≥10 MeV can lead to geomagnetic storms, but most of the medium and weak geomagnetic storms result from low-energetic solar proton events that are caused by CMEs. (ⅳ) Both the electron pulsation events and geomagnetic storms are the link effects of high- and low-energetic solar proton events, but the occurrence of electron pulsation event are generally prior to the geomagnetic storm. So in the circumstance where the near real-time observing data of the low-energetic solar proton event cannot be obtained, we can regard electron pulsation event as the indication of the low-energetic solar proton flux reaching the earth, which can be used as one of the important 参考文献 of short-term prediction and alert of the geomagnetic storm.     

On Spacetime, Points, and Bare Particulars

In his paper Bare Particulars, T. Sider claims that one of the most plausible candidates for bare particulars are spacetime points. The aim of this paper is to shed light on Sider’s reasoning and its consequences. There are three concepts of spacetime points that allow their identification with bare particulars. One of them, Moderate structural realism, is considered to be the most adequate due its appropriate approach to spacetime metric and moderate view of mereological simples. However, it pushes the Substratum theory to dismiss primitive thisness as the only identity condition for bare particulars, but the paper argues that such elimination is a legitimate step.     

Loop invariants,exploration of regularities,and mathematical games

Loop invariants are assertions of regularities that characterize the loop components of algorithms. They are fundamental components of computerprograms verification, but their relevance goes beyond verification—they can be significantly utilized for algorithm design and analysis. Unfortunately, they are only modestly introduced in the teaching of programming and algorithms. One reason for this is an unjustified notion that loop invariants are ‘tied to formality’, hard to illustrate, and difficult to comprehend. In this paper a novel approach is presented for illustrating on a rather intuitive level the significance of loop invariants. The illustration is based on mathematical games, which are attractive examples that require the exploration of regularities via problemsolving heuristics. Throughout the paper students' application of heuristics is described and emphasis is placed on the links between loop invariants, heuristic search activities, recognition of regularities and design and analysis of algorithms.     

Design,Concepts, and State of the Art of the swMATH Service

In this paper, the concepts and design for an efficient information service for mathematical software and further mathematical research data are presented. The publication-based approach and the web-based approach are the main building blocks of the service and will be discussed. Heuristic methods are used for identification, extraction, and ranking of information about software and other mathematical research data. The methods provide not only information about the research data but also link software and mathematical research data to the scientific context.