Agent-behaviour and network influence on energy innovation diffusion

An agent-based model is developed for investigating the role of individual behaviour and network influence on energy innovation diffusion. Behaviour is based on how agents value specific attributes of a technology, and network effects are disaggregated into indirect influence through exposure to a larger population, and direct influence through personal contacts. We find that network influence can have a positive effect on accelerating the diffusion of new energy innovations, but can be counteracted by risk adverse behaviour. Combined direct and indirect network effects can have as strong an influence on adoption behaviour as personal preferences. Interestingly, we find that indirect influence from the larger population can have a greater effect than direct personal contacts on an individual. This implies a feedback between population and sub-population level signals on adoption behaviour which warrants further exploration as a mechanism to induce individual level change.     

A time delay model for the diffusion of a new technology

In this paper, we propose a mathematical model with time delay to describe the process of diffusion of a new technology. This model is suitable for modeling diffusion processes of all those technologies that require great initial investments and public subsidies, such as technologies used for producing renewable energy. We consider external factors, such as the government policy and the production costs, that influence the decision of adoption of the new technology. We also consider the internal influence from adopters. The adoption process is described by a delay differential equation. The time delay represents the evaluation stage at which the potential consumers decide whether to adopt the new technology or not. A qualitative analysis is carried out in order to assess the stability of the equilibrium for certain parameters and to find the final level of adopters.     

新媒体环境中品牌粉丝效应形成机理研究

随着新媒体技术的不断发展以及消费模式的变迁,电子商务呈现出新型业态,对品牌新媒体营销提出了新的挑战。消费者的品牌消费已经从传统的功能性需求转移到更多的价值需求,营销领域的“粉丝效应”应运而生。本文即研究新媒体环境中粉丝效应的形成机理。结合新媒体环境,文中描述了粉丝效应的概念及内涵,探讨了新媒体环境中新型电商的业态及价值产出模式的变革,提出了粉丝效应的实现过程并实证分析了粉丝效应的形成机理。文中提出粉丝效应实现的三种影响因素,包括品牌体验、品牌认同、品牌形象。研究结果表明,品牌体验对品牌认同有正向影响;品牌认同分为个人品牌认同及社会品牌认同,个人品牌认同对社会品牌认同有正向影响;品牌认同对品牌形象有正向影响;品牌认同和品牌形象均对品牌粉丝效应有正向影响。     

Generalized Euler identity for subdifferentials of homogeneous functions and applications

In this paper, we mainly consider subdifferentials and basic subdifferentials of homogeneous functions defined on real Banach space and Asplund space respectively, and obtain the generalized Euler identity. As applications, we consider constrained optimization problems and several geometric properties of Banach space.     

A MacWilliams type identity for matroids

In this paper, we consider the coboundary polynomial for a matroid as a generalization of the weight enumerator of a linear code. By describing properties of this polynomial and of a more general polynomial, we investigate the matroid analogue of the MacWilliams identity. From coding-theoretical approaches, upper bounds are given on the size of circuits and cocircuits of a matroid, which generalizes bounds on minimum Hamming weights of linear codes due to I. Duursma.     

The Flagged Cauchy Determinant

We consider a flagged form of the Cauchy determinant, for which we provide a combinatorial interpretation in terms of nonintersecting lattice paths. In combination with the standard determinant for the enumeration of nonintersecting lattice paths, we are able to give a new proof of the Cauchy identity for Schur functions. Moreover, by choosing different starting and end points for the lattice paths, we are led to a lattice path proof of an identity of Gessel which expresses a Cauchy-like sum of Schur functions in terms of the complete symmetric functions.     

Detailed wordlength pattern of regular fractional factorial split-plot designs in terms of complementary sets

With reference to regular fractional factorial split-plot designs, we consider a detailed wordlength pattern taking due cognizance of the distinction between the whole-plot and sub-plot factors. A generalized version of the MacWilliams’ identity is employed to express the detailed wordlength pattern in terms of complementary sets. Several special features make this result intrinsically different from the corresponding one in classical fractional factorial designs where all factors have the same status. An application to robust parameter designs is indicated and examples given.     

两类Chebyshev级数在平面上的延拓

第一、二类Chebyshev级数在应用数学的各个领域有着广泛的应用，它们一直被分别地研究着，但当拓广到复平面考察它们时，发现之间存在着紧密地联系：准确地说，本文给出了联系两类级数部分和的一个恒等式，这样在平面上对第二类Chebyshev级数的研究就归结为“频谱分析”领域．     

Mathematics identity and achievement among Black students

Employing data from the National Center of Educational Statistics' High School Longitudinal Study and utilizing critical race theory and intersectionality as theoretical frameworks, this article interrogates the relationship between mathematics identity and math success for a nationwide sample of Black secondary school students. More specifically, hierarchical regression modeling is employed to examine the relative impact of math identity, demographic variables, and school/parent social capital variables on the math grade point averages of this sample. The article ends with a discussion of specific steps for teaching mathematics that put the identity of those from traditionally marginalized communities at the center of mathematics instruction. Thus making experiences, histories, culture, and abilities essential elements of students' learning, that are to be supported and built upon.     

关于有限形式的Hilbert不等式

利用一个积分恒等式部分地解决有限形式Hilbert不等式中常数C（p,q）的渐近性态问题.     

非参数混合效应模型中的删除诊断

本文考虑了非参数混合模型中的子集删除诊断．在非参数混合模型的框架下,得到了用两种方法所得非参数元素估计的系数矩阵相等,同时用两种方法得到的随机效应预测的系数矩阵也相同．在此等价性的基础上,我们将现有文献中对线性模型的11删除=替代”准则推广至非参数混合模型场合．不仅得到了固定效应的删除诊断公式,还得到了随机效应的删除诊断公式．此外,我们通过模拟数据分析和真实数据分析说明了我们方法的有效性．     

关于斐波那契数列倒数的无限和

In this paper,we consider infinite sums of the reciprocals of the Fibonacci numbers.Then applying the floor function to the reciprocals of this sums,we obtain a new identity involving the Fibonacci numbers.     

Semiprimality and Nilpotency of Nonassociative Rings Satisfying x(yz) = y(zx)

In this article we study nonassociative rings satisfying the polynomial identity x(yz) = y(zx), which we call “cyclic rings.” We prove that every semiprime cyclic ring is associative and commutative and that every cyclic right-nilring is solvable. Moreover, we find sufficient conditions for the nilpotency of cyclic right-nilrings and apply these results to obtain sufficient conditions for the nilpotency of cyclic right-nilalgebras.     

Minimal Characteristic Algebras for Some Properties of Identities

We consider algebras of a type , without nullary fundamental operation symbols. A structural property p of an identity of type is hereditary if for every set I of identities of type having the property p every consequence of I (derived identity) has the property p. An algebra of type we call characteristic for a hereditary property p if for every variety V of type we have: V if and only if every identity from Id(V) has the property p. In this paper we show minimal characteristic algebras for several hereditary properties, e.g., to be regular, to be normal, etc.1991 Mathematics Subject Classification 08B05     

Licensing radical product innovations to speed up the diffusion

We present a differential game to study how companies can simultaneously license their innovations to other firms when launching a new product. The licensee may cannibalize licensor’s sales, albeit this can be compensated by gains from royalties. Nonetheless, patent royalties are generally so low that licensing is not an attractive strategy. In this paper we consider the role of licensing to speed up the product diffusion. Word of mouth by licensee’s customers and licensee’s advertising indirectly push forward sales of the licensing company, accelerating new product diffusion. We find evidence that licensing can be a potentially profitable strategy. However, we also find that a weak Intellectual Property Right (IPR) protection can easily diminish the financial attractiveness of licensing.     

Combinatorial proofs of the Newton–Girard and Chapman–Costas-Santos identities

In this paper we give combinatorial proofs of some well known identities and obtain some generalizations. We give a visual proof of a result of Chapman and Costas-Santos regarding the determinant of sum of matrices. Also we find a new identity expressing the permanent of sum of matrices. Besides, we give a graph theoretic proof of the Newton–Girard identity in a generalized form.     

Sturm–Picone comparison theorem of a kind of conformable fractional differential equations on time scales

In this paper, we consider the Sturm–Picone comparison theorem of conformable fractional differential equations on arbitrary time scales. Since the Picone identity plays an important role in discussing the Sturm comparison theorem. Firstly, we establish the Picone identity of conformable fractional differential equations on arbitrary time scales. By using this identity, we obtain our main result—the Sturm–Picone comparison theorem of conformable fractional differential equations on time scales. This result not only extends and improves the corresponding continuous and discrete time statement, but also contains the usual time scale case when the order of differentiation is one.     

Option Valuation with a Discrete-Time Double Markovian Regime-Switching Model

Abstract

This article develops an option valuation model in the context of a discrete-time double Markovian regime-switching (DMRS) model with innovations having a generic distribution. The DMRS model is more flexible than the traditional Markovian regime-switching model in the sense that the drift and the volatility of the price dynamics of the underlying risky asset are modulated by two observable, discrete-time and finite-state Markov chains, so that they are not perfectly correlated. The states of each of the chains represent states of proxies of (macro)economic factors. Here we consider the situation that one (macro)economic factor is caused by the other (macro)economic factor. The market model is incomplete, and so there is more than one equivalent martingale measure. We employ a discrete-time version of the regime-switching Esscher transform to determine an equivalent martingale measure for valuation. Different parametric distributions for the innovations of the price dynamics of the underlying risky asset are considered. Simulation experiments are conducted to illustrate the implementation of the model and to document the impacts of the macroeconomic factors described by the chains on the option prices under various different parametric models for the innovations.     

Banach空间中的一类非光滑齐次优化问题

本文主要研究了一类非光滑齐次优化问题(HOP).通过运用Clarke次微分的广义欧拉恒等式获得了使得(HOP)问题的最优解成为KKT点的充分条件并给出了(HOP)问题与(HOP)问题的KKT点及最优解之间的等价刻画.本文的结果是文[1]中已有结果的推广.文中还举例说明了结果的正确性.     

Subdifferential representation of homogeneous functions and extension of smoothness in Banach spaces

In this paper, we mainly consider proximal subdifferentials of lower semicontinuous functions defined on real Hilbert space and Clarke＇s subdifferentials of locally Lipschitzian functions defined on Banach space respectively, and obtain the generalized Euler identity of homogenous functions. Then, by introducing a multifunction F, we extend the smoothness of sphere and differentiability of norm function in Banach space.