Strong Normalizability of Typed Lambda-Calculi for Substructural Logics

The strong normalization theorem is uniformly proved for typed λ-calculi for a wide range of substructural logics with or without strong negation. We would like to thank the referees for their valuable comments and suggestions. This research was supported by the Alexander von Humboldt Foundation. The second author is grateful to the Foundation for providing excellent working conditions and generous support of this research. This work was also supported by the Japanese Ministry of Education, Culture, Sports, Science and Technology, Grant-in-Aid for Young Scientists (B) 20700015, 2008.     

The Poincaré series of divisorial valuations in the plane defines the topology of the set of divisors

With a plane curve singularity one associates a multi-index filtration on the ring of germs of functions of two variables defined by the orders of a function on irreducible components of the curve. The Poincaré series of this filtration turns out to coincide with the Alexander polynomial of the curve germ. For a finite set of divisorial valuations on the ring corresponding to some components of the exceptional divisor of a modification of the plane, in a previous paper there was obtained a formula for the Poincaré series of the corresponding multi-index filtration similar to the one associated with plane germs. Here we show that the Poincaré series of a set of divisorial valuations on the ring of germs of functions of two variables defines “the topology of the set of the divisors” in the sense that it defines the minimal resolution of this set up to combinatorial equivalence. For the plane curve singularity case, we also give a somewhat simpler proof of the statement by Yamamoto which shows that the Alexander polynomial is equivalent to the embedded topology.     

Uniform Convergence of Discrete Curvatures from Nets of Curvature Lines

We study discrete curvatures computed from nets of curvature lines on a given smooth surface and prove their uniform convergence to smooth principal curvatures. We provide explicit error bounds, with constants depending only on properties of the smooth limit surface and the shape regularity of the discrete net.     

Maximum Principle of Optimal Control of the Primitive Equations of the Ocean with Two Point Boundary State Constraint

We consider a class of stochastic impulse control problems of general stochastic processes i.e. not necessarily Markovian. Under fairly general conditions we establish existence of an optimal impulse control. We also prove existence of combined optimal stochastic and impulse control of a fairly general class of diffusions with random coefficients. Unlike, in the Markovian framework, we cannot apply quasi-variational inequalities techniques. We rather derive the main results using techniques involving reflected BSDEs and the Snell envelope.     

Lower Bounds for Dimensions of Sums of Sets

We study lower bounds for the Minkowski and Hausdorff dimensions of the algebraic sum E+K of two sets E,K⊂ℝ ^d .     

Local Geometry of Levi-Forms Associated with the Existence of Complex Submanifolds and the Minimality of Generic CR Manifolds

Let M be a generic CR manifold in \BbbC^m+d\Bbb{C}^{m+d} of codimension d, locally given as the common zero set of real-valued functions r ¹,…,r ^d . Given an integer δ=1,…,d, we find a necessary and sufficient condition for M to contain a real submanifold of codimension δ with the same CR structure. We also find a necessary and sufficient condition and several sufficient conditions for M to admit a complex submanifold of complex dimension n, for any n=1,…,m. We use the method of prolongation of an exterior differential system. The conditions are systems of partial differential equations on r ¹,…,r ^d of third order.     

Density of the polynomials in Hardy and Bergman spaces of slit domains

It is shown that for any t, 0<t<∞, there is a Jordan arc Γ with endpoints 0 and 1 such that G\{1} í \mathbbD:={z:|z| < 1}\Gamma\setminus\{1\}\subseteq\mathbb{D}:=\{z:|z|<1\} and with the property that the analytic polynomials are dense in the Bergman space \mathbbA^t(\mathbbD\G)\mathbb{A}^{t}(\mathbb{D}\setminus\Gamma) . It is also shown that one can go further in the Hardy space setting and find such a Γ that is in fact the graph of a continuous real-valued function on [0,1], where the polynomials are dense in H^t(\mathbbD\G)H^{t}(\mathbb{D}\setminus\Gamma) ; improving upon a result in an earlier paper.     

Non-Walker Self-Dual Neutral Einstein Four-Manifolds of Petrov Type III

The local structure of the manifolds named in the title is described. Although curvature homogeneous, they are not, in general, locally homogeneous. Not all of them are Ricci-flat, which answers an existence question about type III Jordan-Osserman metrics, raised by Díaz-Ramos, García-Río and Vázquez-Lorenzo (J. Geom. Anal. 16, 39–52, 2006). Work begun during the author’s visit to the University of Santiago de Compostela, supported by Grant MTM2006-01432 (Spain).     

Log-convexity properties of Schur functions and generalized hypergeometric functions of matrix argument

We establish a positivity property for the difference of products of certain Schur functions, s _λ (x), where λ varies over a fundamental Weyl chamber in ? ⁿ and x belongs to the positive orthant in ? ⁿ . Further, we generalize that result to the difference of certain products of arbitrary numbers of Schur functions. We also derive a log-convexity property of the generalized hypergeometric functions of two Hermitian matrix arguments, and we show how that result may be extended to derive higher-order log-convexity properties.     

The Intrinsic Diameter of the Surface of a Parallelepiped

In the paper we obtain an explicit formula for the intrinsic diameter of the surface of a rectangular parallelepiped in 3-dimensional Euclidean space. As a consequence, we prove that an parallelepiped with relation for its edge lengths has maximal surface area among all rectangular parallelepipeds with given intrinsic diameter.     

On the order of a non-abelian representation group of a slim dense near hexagon

In this paper we study the possible orders of a non-abelian representation group of a slim dense near hexagon. We prove that if the representation group R of a slim dense near hexagon S is non-abelian, then R is a 2-group of exponent 4 and |R|=2 ^β , 1+NPdim(S)≤β≤1+dimV(S), where NPdim(S) is the near polygon embedding dimension of S and dimV(S) is the dimension of the universal representation module V(S) of S. Further, if β=1+NPdim(S), then R is necessarily an extraspecial 2-group. In that case, we determine the type of the extraspecial 2-group in each case. We also deduce that the universal representation group of S is a central product of an extraspecial 2-group and an abelian 2-group of exponent at most 4. This work was partially done when B.K. Sahoo was a Research Fellow at the Indian Statistical Institute, Bangalore Center with NBHM fellowship, DAE Grant 39/3/2000-R&D-II, Govt. of India.     

Magnetically-Induced Buckling of a Whirling Conducting Rod with Applications to Electrodynamic Space Tethers

We study the effect of a magnetic field on the behaviour of a slender conducting elastic structure, motivated by stability problems of electrodynamic space tethers. Both static (buckling) and dynamic (whirling) instability are considered and we also compute post-buckling configurations. The equations used are the geometrically exact Kirchhoff equations. Magnetic buckling of a welded rod is found to be described by a surprisingly degenerate bifurcation, which is unfolded when both transverse anisotropy of the rod and angular velocity are considered. By solving the linearised equations about the (quasi-) stationary solutions, we find various secondary instabilities. Our results are relevant for current designs of electrodynamic space tethers and potentially for future applications in nano- and molecular wires.     

Arithmetic properties of partitions with odd parts distinct

In this work, we consider the function pod(n), the number of partitions of an integer n wherein the odd parts are distinct (and the even parts are unrestricted), a function which has arisen in recent work of Alladi. Our goal is to consider this function from an arithmetic point of view in the spirit of Ramanujan’s congruences for the unrestricted partition function p(n). We prove a number of results for pod(n) including the following infinite family of congruences: for all α≥0 and n≥0,

How to get the timing right. A computational model of the effects of the timing of contacts on team cohesion in demographically diverse teams

Lau and Murnighan’s faultline theory explains negative effects of demographic diversity on team performance as consequence of strong demographic faultlines. If demographic differences between group members are correlated across various dimensions, the team is likely to show a “subgroup split” that inhibits communication and effective collaboration between team members. Our paper proposes a rigorous formal and computational reconstruction of the theory. Our model integrates four elementary mechanisms of social interaction, homophily, heterophobia, social influence and rejection into a computational representation of the dynamics of both opinions and social relations in the team. Computational experiments demonstrate that the central claims of faultline theory are consistent with the model. We show furthermore that the model highlights a new structural condition that may give managers a handle to temper the negative effects of strong demographic faultlines. We call this condition the timing of contacts. Computational analyses reveal that negative effects of strong faultlines critically depend on who is when brought in contact with whom in the process of social interactions in the team. More specifically, we demonstrate that faultlines have hardly negative effects when teams are initially split into demographically homogeneous subteams that are merged only when a local consensus has developed.     

Regularity of the Laws of Shot Noise Series and of Related Processes

We investigate the regularity of shot noise series and of Poisson integrals. We give conditions for the absolute continuity of their law with respect to the Lebesgue measure and for their continuity in total-variation norm. In particular, the case of truncated series in addressed. Our method relies on a disintegration of the probability space based on a mere conditioning by the first jumps of the underlying Poisson process.     

Do we self-regulate actions or perceptions? A test of two computational models

Self-regulation theories in applied psychology disagree about whether action or perceptions are the focus of regulation. Computational models based on the two conceptualizations were constructed and simulated. In one scenario, they performed identically and in conjunction with participants in a study of the goal-level effect (Vancouver et al., Organ Res Methods 8:100–127, 2005). In another scenario they created differentiating predictions and only the computational model based on the self-regulation of perceptions matched the data of participants. Implications for research and practice are discussed.

The Method of Virtual Components in the Multivariate Setting

We describe the so-called method of virtual components for tight wavelet framelets to increase their approximation order and vanishing moments in the multivariate setting. Two examples of the virtual components for tight wavelet frames based on bivariate box splines on three or four direction mesh are given. As a byproduct, a new construction of tight wavelet frames based on box splines under the quincunx dilation matrix is presented.     

A Refinement of the Kolmogorov–Marcinkiewicz–Zygmund Strong Law of Large Numbers

Let {X _n ; n≥1} be a sequence of independent copies of a real-valued random variable X and set S _n =X ₁+???+X _n , n≥1. This paper is devoted to a refinement of the classical Kolmogorov–Marcinkiewicz–Zygmund strong law of large numbers. We show that for 0<p<2,

$\sum_{n=1}^{\infty}\frac{1}{n}\biggl(\frac{|S_{n}|}{n^{1/p}}\biggr)<\infty\quad \mbox{almost surely}$

if and only if

$\begin{cases}\mathbb{E}|X|^{p}<\infty &; \mbox{if }0 < p < 1,\\\mathbb{E}X=0,\ \sum_{n=1}^{\infty}\frac{|\mathbb{E}XI\{|X|\leq n\}|}{n}<\infty,\mbox{ and }\\\sum_{n=1}^{\infty}\frac{\int_{\min\{u_{n},n\}}^{n}\mathbb{P}(|X|>t)\,dt}{n}<\infty &; \mbox{if }p = 1,\\\mathbb{E}X=0\mbox{ and }\int_{0}^{\infty}\mathbb{P}^{1/p}(|X|>t)\,dt<\infty,&;\mbox{if }1 < p < 2,\end{cases}$

where \(u_{n}=\inf \{t:~\mathbb{P}(|X|>t)<\frac{1}{n}\}\), n≥1. Versions of the above result in a Banach space setting are also presented. To establish these results, we invoke the remarkable Hoffmann-Jørgensen (Stud. Math. 52:159–186, 1974) inequality to obtain some general results for sums of the form \(\sum_{n=1}^{\infty}a_{n}\|\sum_{i=1}^{n}V_{i}\|\) (where {V _n ; n≥1} is a sequence of independent Banach-space-valued random variables, and a _n ≥0, n≥1), which may be of independent interest, but which we apply to \(\sum_{n=1}^{\infty}\frac{1}{n}(\frac{|S_{n}|}{n^{1/p}})\).

     

Deformation of canonical morphisms and the moduli of surfaces of general type

In this article we study the deformation of finite maps and show how to use this deformation theory to construct varieties with given invariants in a projective space. Among other things, we prove a criterion that determines when a finite map can be deformed to a one-to-one map. We use this criterion to construct new surfaces of general type with birational canonical map, for different c₁²c_{1}^{2} and χ (the canonical map of the surfaces we construct is in fact a finite, birational morphism). Our general results enable us to describe some new components of the moduli of surfaces of general type. We also find infinitely many moduli spaces having one component whose general point corresponds to a canonically embedded surface and another component whose general point corresponds to a surface whose canonical map is a degree 2 morphism.     

Completely splittable representations of affine Hecke-Clifford algebras

We classify and construct irreducible completely splittable representations of affine and finite Hecke-Clifford algebras over an algebraically closed field of characteristic not equal to 2.