Diffeological Clifford algebras and pseudo-bundles of Clifford modules

Abstract

We consider the diffeological version of the Clifford algebra of a diffeological finite dimensional vector space; we start by commenting on the notion of a diffeological algebra (which is the expected analogue of the usual one) and that of a diffeological module (also an expected counterpart of the usual notion). After considering the natural diffeology of the Clifford algebra, and considering which of its standard properties re-appear in the diffeological context (most of them), we turn to our main interest, which is constructing the pseudo-bundles of Clifford algebras associated to a given (finite dimensional) diffeological vector pseudo-bundle, and those of the usual Clifford modules (the exterior algebras). The substantial difference that emerges with respect to the standard context, and paves the way to various questions that do not have standard analogues, stems from the fact that the notion of a diffeological pseudo-bundle is very different from the usual bundle, and this under two main respects: it may have fibres of different dimensions, and even if it does not, its total and base spaces frequently are not smooth, or even topological, manifolds.     

On the global convergence of Chebyshev's iterative method

In [A. Melman, Geometry and convergence of Euler's and Halley's methods, SIAM Rev. 39(4) (1997) 728–735] the geometry and global convergence of Euler's and Halley's methods was studied. Now we complete Melman's paper by considering other classical third-order method: Chebyshev's method. By using the geometric interpretation of this method a global convergence theorem is performed. A comparison of the different hypothesis of convergence is also presented.     

双层分形油藏的压力动态分析

本文研究了双层分形油藏不定常径向渗流,给出了广义对流扩散方程组在拉氏空间中的通解,得到了考虑和不考虑井筒存储和表皮效应时的不同内边界条件下的解,讨论了在不考虑井储和表皮效应时的解的特征.     

Progressive and merging-proof taxation

We investigate the implications and logical relations between progressivity (a principle of distributive justice) and merging-proofness (a strategic principle) in taxation. By means of two characterization results, we show that these two principles are intimately related, despite their different nature. In particular, we show that, in the presence of continuity and consistency (a widely accepted framework for taxation) progressivity implies merging-proofness and that the converse implication holds if we add an additional strategic principle extending the scope of merging-proofness to a multilateral setting. By considering operators on the space of taxation rules, we also show that progressivity is slightly more robust than merging-proofness.     

A general limit lifting theorem for 2-dimensional monad theory

We give a definition of weak morphism of T-algebras, for a 2-monad T, with respect to an arbitrary family Ω of 2-cells of the base 2-category. By considering particular choices of Ω, we recover the concepts of lax, pseudo and strict morphisms of T-algebras. We give a general notion of weak limit, and define what it means for such a limit to be compatible with another family of 2-cells. These concepts allow us to prove a limit lifting theorem which unifies and generalizes three different previously known results of 2-dimensional monad theory. Explicitly, by considering the three choices of Ω above our theorem has as corollaries the lifting of oplax (resp. σ, which generalizes lax and pseudo, resp. strict) limits to the 2-categories of lax (resp. pseudo, resp. strict) morphisms of T-algebras.     

The precore: converse consistent enlargements and alternative axiomatic results

Since the precore violates (weak) converse consistency, two converse consistent enlargements are proposed. These two converse consistent enlargements are the smallest (weak) converse consistent solutions that contain the precore. On the other hand, we turn to a different notion of the reduction by considering the players and the activity levels simultaneously. Based on such revised reductions, we offer several axiomatizations of the precore.     

A bi-objective generalized data envelopment analysis model and point-to-set mapping projection

This work introduces a bi-objective generalized data envelopment analysis (Bi-GDEA) model and defines its efficiency. We show the equivalence between the Bi-GDEA efficiency and the non-dominated solutions of the multi-objective programming problem defined on the production possibility set (PPS) and discuss the returns to scale under the Bi-GDEA model. The most essential contribution is that we further define a point-to-set mapping and the mapping projection of a decision making unit (DMU) on the frontier of the PPS under the Bi-GDEA model. We give an effective approach for the construction of the point-to-set-mapping projection which distinguishes our model from other non-radial models for simultaneously considering input and output. The Bi-GDEA model represents decision makers’ specific preference on input and output and the point-to-set mapping projection provides decision makers with more possibility to determine different input and output alternatives when considering efficiency improvement. Numerical examples are employed for the illustration of the procedure of point-to-set mapping.     

Pricing permanent convertible bonds in EVG model

By considering the failure of normal distribution and continuous assumption in financial modeling, this paper attempts to apply the Exponential Variance Gamma (EVG) model into the pricing framework of permanent convertible bonds with call clause. Following framework of Gapeev & Kühn(2005), we obtain an explicit solution to the bond price and optimal stopping strategies, which shows that the new pricing framework is quite different from the continuous model and even the Jump Diffusion model. Compared with the numerical calculation, the closed form results price convertible bonds quickly and accurately.     

Recognizing graphs without asteroidal triples

We consider the problem of recognizing AT-free graphs. Although there is a simple O(n³) algorithm, no faster method for solving this problem had been known. Here we give three different algorithms which have a better time complexity for graphs which are sparse or have a sparse complement; in particular we give algorithms which recognize AT-free graphs in , , and O(n^2.82+nm). In addition we give a new characterization of graphs with bounded asteroidal number by the help of the knotting graph, a combinatorial structure which was introduced by Gallai for considering comparability graphs.     

Virtual Teams: What are their Characteristics, and Impact on Team Performance?

To date, efforts to understand virtual teaming have been largely anecdotal and atheoretical. Therefore, drawing from the extant research in the groups domain, we attempt to ground the definition of a virtual team in well-established group-level constructs, and design a simulation study to investigate the impact of different virtual team characteristics on team performance. Essentially, we argue that the virtual team is defined by three key characteristics—the virtual team context, the virtual team composition, and the virtual team structure. Using the VDT computational discrete event simulation model as our experimental platform, we simulated different virtual team models, and examined their impact on various team performance dimensions. We found that virtual team characteristics have different effects on different aspects of team performance. The virtual context team had a lower rework volume but higher coordination volume and longer project duration than the virtual composition team. Interestingly, we also found that the virtual structure team performed better than the software development team baseline model in all aspects of team performance. Based on these results, we proposed strategies to improve performance in different types of virtual team. Specifically, we propose (1) increasing the ease of communication and availability of routines in the virtual context team; (2) clarifying role expectations and fostering a team culture in the virtual composition team; and (3) implementing a lateral structure in the virtual team. Our results also suggest that firms should consider situational demands, specifically tolerance for errors and coordination volume, when considering the design of virtual teams.     

Strategic behavior in queues with the effect of the number of customers behind

In this paper, we investigate the strategic behavior in queues by considering the effect of the number of customers behind. The equilibrium joining strategy of customers is obtained and its implications for the service system are examined. We find that the complete queue transparency (i.e., disclosing the real-time system information) can have positive effect on customers, which might encourage more customers to join. Further, the follow-the-crowd (FTC) behavior can be observed, which results in multiple equilibria. By comparing the customer welfare under two different information levels, we demonstrate that, somewhat surprisingly, the queue transparency does not necessarily hurt the customer welfare, and a higher customer welfare can be obtained in the transparent case than that in opaque case when the demand volume is large.     

Mature or emerging markets: Competitive duopoly investment decisions

We develop a competitive investment model wherein two competing firms consider investing into two projects targeting, separately, a mature and an emerging market. The returns firms obtain from investments into these markets are assumed to follow an S-shaped curve and depend on both firms’ actions. Considering symmetric environments (in terms of investment opportunities), we find that different forms of interactions may arise (e.g., Prisoner’s Dilemma and Game of Chicken) and outline corresponding strategies that offer higher returns by exploiting first-mover advantages, cooperation opportunities and aggressive choices. We also discuss the market conditions that can lead to these outcomes. Finally, considering non-symmetric environments, we show that a firm may be better off when its competitor’s budget increases.     

Entire solutions of reaction-advection-diffusion equations with bistable nonlinearity in cylinders

This paper deals with entire solutions and the interaction of traveling wave fronts of bistable reaction-advection-diffusion equation with infinite cylinders. Assume that the equation admits three equilibria: two stable equilibria 0 and 1, and an unstable equilibrium θ. It is well known that there are different wave fronts connecting any two of those three equilibria. By considering a combination of any two of those different traveling wave fronts and constructing appropriate subsolutions and supersolutions, we establish three different types of entire solutions. Finally, we analyze a model for shear flows in cylinders to illustrate our main results.     

Composite Likelihood Inference in a Discrete Latent Variable Model for Two-Way “Clustering-by-Segmentation” Problems

We consider a discrete latent variable model for two-way data arrays, which allows one to simultaneously produce clusters along one of the data dimensions (e.g., exchangeable observational units or features) and contiguous groups, or segments, along the other (e.g., consecutively ordered times or locations). The model relies on a hidden Markov structure but, given its complexity, cannot be estimated by full maximum likelihood. Therefore, we introduce a composite likelihood methodology based on considering different subsets of the data. The proposed approach is illustrated by simulation, and with an application to genomic data.     

Cooperative advertising models in supply chain management: A review

This paper reviews articles on cooperative advertising, a topic which has gained substantial interest in the recent years. Thereby, we first briefly distinguish five different definitions of cooperative advertising which can be found in operations research literature. After that, we concentrate on vertical cooperative advertising, which is the most common object of investigation and is understood as a financial agreement where a manufacturer offers to pay a certain share of his retailer’s advertising expenditures. In total, we identified 58 scientific papers considering mathematical modeling of vertical cooperative advertising. These articles are then analyzed with regard to their general model setting (e.g., the underlying supply chain structure and design of the cooperative advertising program). After that, we explain the different demand and cost functions that are employed, whereupon we distinguish between static and dynamic models. The last dimension of our review is dedicated to the game-theoretic concepts which are mostly used to reflect different forms of distribution of power within the channel.     

Essentiality and injectivity relative to sequential purity of acts

For a class ℳ of monomorphisms of a category, mathematicians consider different types of essentiality, depending on ℳ. In this paper, considering the category of acts over a semigroup, we first briefly study the class ℳ _p of a certain kind of pure monomorphisms, in a manner borrowed from V. Gould, to be called sequentially pure. Then, we study in detail three kinds of essentiality with respect to this class, and give some useful criteria to get (internal) characterizations (in terms of elements) for essentialities. Finally, the relations between injectivity, essentiality, retractness, and injective hulls, all with respect to the class of sequentially pure monomorphisms, are investigated. The second author is thankful to Iran National Science Foundation (INSF) for their financial support.     

Convergence en moyenne quadratique de l'estimateur de la régression par splines hybrides

In this work, we consider the estimation of a smooth regression function, belonging to C^m [0, 1], by hybrid splines. We give the asymptotic behavior of the integrated mean square error by considering two different assumptions on the noise.     

Markov Chain Analysis for One-Dimensional Asynchronous Cellular Automata

We consider the finite homogeneous Markov chain induced by a class of one-dimensional asynchronous cellular automata—automata that are allowed to change only one cell per iteration. Furthermore, we confine to totalistic automata, where transitions depend only on the number of 1s in the neighborhood of the current cell. We consider three different cases: (i) size of neighborhood equals length of the automaton; (ii) size of neighborhood two, length of automaton arbitrary; and (iii) size of neighborhood three, length of automaton arbitrary. For each case, the associated Markov chain proves to be ergodic. We derive simple-form stationary distributions, in case (i) by lumping states with respect to the number of 1s in the automaton, and in cases (ii) and (iii) by considering the number of 0–1 borders within the automaton configuration. For the three-neighborhood automaton, we analyze also the Markov chain at the boundary of the parameter domain, and the symmetry of the entropy. Finally, we show that if the local transition rule is exponential, the stationary probability is the Boltzmann distribution of the Ising model.     

The partition function p(n) in terms of the classical Möbius function

The Ramanujan Journal - In this paper, we investigate decompositions of the partition function p(n) from the additive theory of partitions considering the famous Möbius function $$\mu (n)$$...     

Genetic learning of accurate and compact fuzzy rule based systems based on the 2-tuples linguistic representation

One of the problems that focus the research in the linguistic fuzzy modeling area is the trade-off between interpretability and accuracy. To deal with this problem, different approaches can be found in the literature. Recently, a new linguistic rule representation model was presented to perform a genetic lateral tuning of membership functions. It is based on the linguistic 2-tuples representation that allows the lateral displacement of a label considering an unique parameter. This way to work involves a reduction of the search space that eases the derivation of optimal models and therefore, improves the mentioned trade-off.Based on the 2-tuples rule representation, this work proposes a new method to obtain linguistic fuzzy systems by means of an evolutionary learning of the data base a priori (number of labels and lateral displacements) and a simple rule generation method to quickly learn the associated rule base. Since this rule generation method is run from each data base definition generated by the evolutionary algorithm, its selection is an important aspect. In this work, we also propose two new ad hoc data-driven rule generation methods, analyzing the influence of them and other rule generation methods in the proposed learning approach. The developed algorithms will be tested considering two different real-world problems.