Introducing serendipity in a social network model of knowledge diffusion

In this paper, we study serendipity as a possible strategy to control the behavior of an agent-based network model of knowledge diffusion. The idea of considering serendipity in a strategic way has been first explored in Network Learning and Information Seeking studies. After presenting the major contributions of serendipity studies to digital environments, we discuss the extension to our model: Agents are enriched with random topics for establishing new communication according to different strategies. The results show how important network properties could be influenced, like reducing the prevalence of hubs in the network’s core and increasing local communication in the periphery, similar to the effects of more traditional self-organization methods. Therefore, from this initial study, when serendipity is opportunistically directed, it appears to behave as an effective and applicable approach to social network control.     

Moser’s Quadratic,Symplectic Map

In 1994, Jürgen Moser generalized Hénon’s area-preserving quadratic map to obtain a normal form for the family of four-dimensional, quadratic, symplectic maps. This map has at most four isolated fixed points. We show that the bounded dynamics of Moser’s six parameter family is organized by a codimension-three bifurcation, which we call a quadfurcation, that can create all four fixed points from none.The bounded dynamics is typically associated with Cantor families of invariant tori around fixed points that are doubly elliptic. For Moser’s map there can be two such fixed points: this structure is not what one would expect from dynamics near the cross product of a pair of uncoupled Hénon maps, where there is at most one doubly elliptic point. We visualize the dynamics by escape time plots on 2d planes through the phase space and by 3d slices through the tori.     

Nodal Bases for the Serendipity Family of Finite Elements

Using the notion of multivariate lower set interpolation, we construct nodal basis functions for the serendipity family of finite elements, of any order and any dimension. For the purpose of computation, we also show how to express these functions as linear combinations of tensor-product polynomials.     

A Note on Donaldson＇s ＂Tamed to Compatible＂, Question

Recently, Tedi Draghici and Weiyi Zhang studied Donaldson＇s ＂tamed to compatible＂ question （Draghici T, Zhang W. A note on exact forms on almost complex manifolds, arXiv： 1111. 7287vl [math. SC]. Submitted on 30 Nov. 2011）. That is, for a compact almost complex 4-manifold whose almost complex structure is tamed by a symplectic form, is there a symplectic form compatible with this almost complex structure？ They got several equivalent forms of this problem by studying the space of exact forms on such a manifold. With these equivalent forms, they proved a result which can be thought as a further partial answer to Donaldson＇s question in dimension 4. In this note, we give another simpler proof of their result.     

Optimal budget for system design series network DEA model

Wei and Chang (2011a) developed optimal system design (OSD) data envelopment analysis (DEA) models to design a decision-making unit (DMU)’s optimal system, in which the DMU could encounter the well-known economic phenomenon of budget congestion. To show how to verify the optimal budget and budget congestion, they develop a solution method. In this paper, we note that their method is incorrect for the OSD network DEA model in general. A new approach is developed to derive the DMU’s corresponding optimal budgets and to check for the existence of budget congestion not only for the OSD DEA models but also for the OSD network DEA models. In addition, the proposed approach is computationally economical. Finally, two numerical examples are used to illustrate the proposed approach.     

Dynamics of symplectic fluids and point vortices

We present the Hamiltonian formalism for the Euler equation of symplectic fluids, introduce symplectic vorticity, and study related invariants. In particular, this allows one to extend Ebin’s long-time existence result for geodesics on the symplectomorphism group to metrics not necessarily compatible with the symplectic structure. We also study the dynamics of symplectic point vortices, describe their symmetry groups and integrability.     

Moduli of rank 4 symplectic vector bundles over a curve of genus 2

Let X be a complex projective curve which is smooth and irreducibleof genus 2. The moduli space ₂ of semistable symplectic vectorbundles of rank 4 over X is a variety of dimension 10. Afterassembling some results on vector bundles of rank 2 and odddegree over X, we construct a generically finite cover of ₂by a family of 5-dimensional projective spaces, and outlinesome applications.     

Derivative superconvergent points in finite element solutions of Poisson's equation for the serendipity and intermediate families - a theoretical justification

Finite element derivative superconvergent points for the Poisson equation under local rectangular mesh (in the two dimensional case) and local brick mesh (in the three dimensional situation) are investigated. All superconvergent points for the finite element space of any order that is contained in the tensor-product space and contains the intermediate family can be predicted. In case of the serendipity family, the results are given for finite element spaces of order below 7. Any finite element space that contains the complete polynomial space will have at least all superconvergent points of the related serendipity family.

     

Donaldson’s <Emphasis Type="Italic">Q</Emphasis>-operators for symplectic manifolds

We prove an estimate for Donaldson’s Q-operator on a prequantized compact symplectic manifold. This estimate is an ingredient in the recent result of Keller and Lejmi (2017) about a symplectic generalization of Donaldson’s lower bound for the L ²-norm of the Hermitian scalar curvature.     

Simplectic spreads and finite semifields

It is well known that associated with a translation plane π there is a family of equivalent spreads. In this paper, we prove that if one of these spreads is symplectic and π is finite, then all the associated spreads are symplectic. Also, using the geometric intepretation of the Knuth’s cubical array, we prove that a symplectic semifield spread of dimension n over its left nucleus is associated via a Knuth operation to a commutative semifield of dimension n over its middle nucleus.      

Partitions of the set of natural numbers and symplectic homology

We illustrate a somewhat unexpected relation between symplectic geometry and combinatorial number theory by proving Tamura’s theorem on partitions of the set of positive integers (a generalization of the more famous Rayleigh–Beatty theorem) using the positive \({\mathbb{S}^1}\)-equivariant symplectic homology.     

Fourteen-Node Mixed Stiffness Element and Its Computational Comparisons with Twenty-Node Isoparametric Element

In this paper, a family of 3-dimensional elements different from isoparametric serendipity is developed according to the variational principle and the convergence criteria of the mixed stiffness finite element method. For the new family, which is named mixed stiffness elements, the number of nodes on the quadratic element is not 20 but 14. Theoretical analysis and various computational comparisons have found the mixed stiffness element superior over the isoparametric serendipity element, especially a substantial improvement in computational efficiency can be achieved by replacing the 20 node-isoparametric element with the 14-node mixed stiffness element.     

Applications of the odd symplectic group in Hamiltonian systems

In this paper we give two applications of the odd symplectic group to the study of the linear Poincaré maps of a periodic orbits of a Hamiltonian vector field, which cannot be obtained using the standard symplectic theory. First we look at the geodesic flow. We show that the period of the geodesic is a noneigenvalue modulus of the conjugacy class in the odd symplectic group of the linear Poincaré map. Second, we study an example of a family of periodic orbits, which forms a folded Robinson cylinder. The stability of this family uses the fact that the unipotent odd symplectic Poincaré map at the fold has a noneigenvalue modulus.     

Spherical Lagrangians via ball packings and symplectic cutting

In this paper, we prove the connectedness of symplectic ball packings in the complement of a spherical Lagrangian, $S^{2}$ or $\mathbb{RP }^{2}$ , in symplectic manifolds that are rational or ruled. Via a symplectic cutting construction, this is a natural extension of McDuff’s connectedness of ball packings in other settings and this result has applications to several different questions: smooth knotting and unknottedness results for spherical Lagrangians, the transitivity of the action of the symplectic Torelli group, classifying Lagrangian isotopy classes in the presence of knotting, and detecting Floer-theoretically essential Lagrangian tori in the del Pezzo surfaces.     

学英语（英文）

<正>In this essay we’re going to get introduced to the Pythagorean theorem,which is fun on its own.Named after the Greek philosopher who lived nearly2600years ago,the Pythagorean theorem is as good as math theorems.It’s simple.It’s beautiful.It’s powerful.In this topic,we’ll figure out what is the Pythagorean theorem and how to use it.     

Relative symplectic caps, 4-genus and fibered knots

We prove relative versions of the symplectic capping theorem and sufficiency of Giroux’s criterion for Stein fillability and use these to study the 4-genus of knots. More precisely, suppose we have a symplectic 4-manifold X with convex boundary and a symplectic surface Σ in X such that ?Σ is a transverse knot in ?X. In this paper, we prove that there is a closed symplectic 4-manifold Y with a closed symplectic surface S such that (X,Σ) embeds into (Y,S) symplectically. As a consequence we obtain a relative version of the symplectic Thom conjecture. We also prove a relative version of the sufficiency part of Giroux’s criterion for Stein fillability, namely, we show that a fibered knot whose mondoromy is a product of positive Dehn twists bounds a symplectic surface in a Stein filling. We use this to study 4-genus of fibered knots in \(\mathbb {S}^{3} \). Further, we give a criterion for quasipositive fibered knots to be strongly quasipositive.     

Symplectic structures¶on Heisenberg-type nilmanifolds

We use cohomological methods to study the existence of symplectic structures on nilmanifolds associated to two-step nilpotent Lie groups. We construct a new family of symplectic nilmanifolds with building blocks the quaternionic analogue of the Heisenberg group, determining the dimension of the space of all left invariant symplectic structures. Such structures can not be K?hlerian. Also, we prove that the nilmanifolds associated to H type groups are not symplectic unless they correspond to the classical Heisenberg groups. Received: 26 May 1999 / Revised version: 10 April 2000     

When is a symplectic quotient an orbifold?

Let K be a compact Lie group of positive dimension. We show that for most unitary K-modules the corresponding symplectic quotient is not regularly symplectomorphic to a linear symplectic orbifold (the quotient of a unitary module of a finite group). When K is connected, we show that even a symplectomorphism to a linear symplectic orbifold does not exist. Our results yield conditions that preclude the symplectic quotient of a Hamiltonian K  -manifold from being locally isomorphic to an orbifold. As an application, we determine which unitary _SU2${\mathrm{SU}}_2$-modules yield symplectic quotients that are Z⁺${\mathbb{Z}}^{+}$-graded regularly symplectomorphic to a linear symplectic orbifold. We similarly determine which unitary circle representations yield symplectic quotients that admit a regular diffeomorphism to a linear symplectic orbifold.     

吸湿老化影响下天然纤维增强复合圆柱壳屈曲分析的辛方法

针对一类天然纤维增强复合(natural fiber reinforced composite, NFRC)圆柱壳的屈曲问题展开研究,基于Reissner壳体理论和辛方法,建立了轴压NFRC圆柱壳在Hamilton体系下的屈曲控制方程。将原问题归结为辛空间下的辛本征问题,通过求解辛本征值和本征解可以直接获得高精度的临界载荷和解析的屈曲模态。数值算例分析了NFRC材料的吸湿老化过程对辛本征解表达式的影响,并详细讨论了老化时间、纤维含量和几何参数对NFRC圆柱壳屈曲行为的影响。