Comparative study of Mixed product and quaternion product

Mixed number is the sum of a scalar and a vector. The quaternion can also be written as the sum of a scalar and a vector but the product of mixed numbers and the product of quaternions are different. Here we studied the Mixed product which is derived from the product of mixed numbers and the quaternion product which is derived from the product of quaternions. It was observed that Mixed product is more consistent with Physics than that of quaternion product.     

矩阵乘法的推广及运用

利用矩阵的Kronecker积定义了一种矩阵乘积"*积",并且对这种乘积的性质进行了研究,发现它对于任意两个矩阵都有意义而且具有通常矩阵乘积的所有性质,并且在一些特殊情况下它比通常的矩阵乘积更和谐对称,而且当在"合适维数"下它就是通常的矩阵乘积,所以可以把这种"*积"看作是对通常矩阵乘积的推广.     

Product numerical range in a space with tensor product structure

We study operators acting on a tensor product Hilbert space and investigate their product numerical range, product numerical radius and separable numerical range. Concrete bounds for the product numerical range for Hermitian operators are derived. Product numerical range of a non-Hermitian operator forms a subset of the standard numerical range containing the barycenter of the spectrum. While the latter set is convex, the product range needs not to be convex nor simply connected. The product numerical range of a tensor product is equal to the Minkowski product of numerical ranges of individual factors.     

Analytical and managerial implications of integrating product substitutability in the joint pricing and procurement problem

This paper studies the analytical and managerial implications of product substitutability on the joint pricing and procurement decisions. We consider a single-period model with two products: an existing product and an improved new product that can substitute the demand for the existing product in case of a shortage. Demand for each product follows a general distribution with an expected value that is a linear function of the price of the new product. While the price of the existing product is determined by the market, it is necessary to determine the new product’s price and the procurement quantities of both products so as to maximize the profits. We analytically show that the expected profit function is unimodal and in the existence of substitution: the expected total profit is higher; the optimal price and the safety stock of the new product are higher; and the optimal safety stock of the existing product is less. Using these properties an efficient algorithm is developed. We also provide a numerical analysis to demonstrate that considering substitution in advance could increase the profitability by 58% and the new product price by 5% while decreasing the total procurement quantity by 15%.     

基于时间序列的挖掘算法在流程工业产品质量控制模型中的应用

针对目前流程工业产品质量控制采用人工检查和统计质量控制方法,缺乏产品质量预先预报以及时时调整生产过程的工艺参数存在一定困难.利用生产过程采集到的实际数据,采用基于时间序列的动态数据挖掘技术和BP神经元网络,预测产品质量和分析产品生产过程的工艺,最大限度减少不合格产品的产出,提高生产效率.根据上述理论建立流程工业数据动态质量控制平台,以中厚钢板生产过程为例,应用表明了这种方法在实际应用中的正确性和有效性.     

The Cauchy–Schwarz inequality and the induced metrics on real vector spaces mainly on the real line

It is very well known that the Cauchy–Schwarz inequality is an important property shared by all inner product spaces and the inner product induces a norm on the space. A proof of the Cauchy–Schwarz inequality for real inner product spaces exists, which does not employ the homogeneous property of the inner product. However, it is shown that a real vector space with a product satisfying properties of an inner product except the homogeneous property induces a metric but not a norm. It is remarkable to see that the metric induced on the real line by such a product has highly contrasting properties relative to the absolute value metric. In particular, such a product on the real line is given so that the induced metric is not complete and the set of rational numbers is not dense in the real line.     

退货情形下基于替代率的两产品联合订货决策研究

研究了一类在产品订货模型中考虑客户退货和产品间替代的两产品联合最优订货决策问题.假定客户以一概率退回其所购产品,退货产品经修复后可重新在市场上进行销售,销售期末未售出的商品只能在二级市场上降价处理,且不同产品间存在替代关系,销售商以自身利润最大化为目标确定两产品的订货量,得到其最优订货量及一些性质.研究结果表明:在允许退货的背景下,替代策略的采用将会进一步提高销售商利润.     

Toric fiber products versus Segre products

The toric fiber product is an operation that combines two ideals that are homogeneous with respect to a grading by an affine monoid. The Segre product is a related construction that combines two multigraded rings. The quotient ring by a toric fiber product of two ideals is a subring of the Segre product, but in general this inclusion is strict. We contrast the two constructions and show that any Segre product can be presented as a toric fiber product without changing the involved quotient rings. This allows to apply previous results about toric fiber products to the study of Segre products. We give criteria for the Segre product of two affine toric varieties to be dense in their toric fiber product, and for the map from the Segre product to the toric fiber product to be finite. We give an example that shows that the quotient ring of a toric fiber product of normal ideals need not be normal. In rings with Veronese type gradings, we find examples of toric fiber products that are always Segre products, and we show that iterated toric fiber products of Veronese ideals over Veronese rings are normal.     

技术不确定环境下新产品策略的设计应用

技术的动态发展和企业间的竞争对企业新产品策略有很大影响,直接决定新产品的引进周期。本文在产业技术动态变化的随机环境下构建随机动态规划模型,关注产业技术进步、投资成本和产品市场竞争等影响因素,探讨企业进行新产品引进的周期选择,对新产品引进的周期和质量决策进行方法设计和应用举例。利用随机动态规划模型得出新产品引进的最优时间周期,用算例分析技术进步和产品研发成本对企业引进周期策略的影响,采取策略迭代的方法进行求解,发现技术进步较快时企业的新产品引进步伐也较快,研发成本的提高使企业的新产品引入步伐降低。     

基于产品平台的多目标供应商预选方法研究

由于供应商选择问题直接影响着企业的最终收益, 所以它对企业来说一直是一个重要的决策问题. 在以往的研究中, 供应商选择仅仅是从产品零部件的角度去考虑而没有从产品的整体出发. 此外, 传统的供应商选择都是发生在产品设计阶段之后的产品生产阶段. 然而, 在产品设计初期考虑供应商选择问题可以有效地避免合适供应商的短缺问题. 提出了一个基于产品平台的多目标供应商预选方法, 并在产品设计初期从产品整体角度建立了一个以最小化产品族外包成本、最小化产品族生产风险以及最小化供应商供应时间为多目标的优化模型, 从而有助于决策者在产品开发的早期对产品整体设计方案进行改善. 此外, 由于产品平台存在部件共享问题, 因此在优化模型中也考虑了部件共享对供应商预选结果的影响. 采用非支配排序遗传算法(NSGA-II)对优化模型进行求解, 并通过实际案例来说明提出的优化方法以及求解算法的合理性和有效性.     

Distance regularity in direct-product graphs

The direct product (also called Kronecker product, tensor product, and cardinal product) G × H of distance-regular graphs is investigated. It is demonstrated that the product is distance-regular only when G and H are very restricted distance-regular graphs.     

Self-dual Co des with Symplectic Inner Pro duct

In this paper, we discuss a kind of Hermitian inner product — symplectic inner product, which is different from the original inner product — Euclidean inner product. According to the definition of symplectic inner product, the codes under the symplectic inner product have better properties than those under the general Hermitian inner product. Here we present the necessary and sufficient condition for judging whether a linear code C over Fp with a generator matrix in the standard form is a symplectic self-dual code. In addition, we give a method for constructing a new symplectic self-dual codes over Fp, which is simpler than others.     

Function spaces and product topologies on powers of spaces

A study is made of two classes of product topologies on powers of spaces: the general box product topologies, and the general uniform product topologies. Some examples are given and some results are shown about the properties of these general product spaces. This is applied to show that certain spaces of continuous functions with the fine topology are homeomorphic to box product spaces, and certain spaces of continuous functions with the uniform topology are homeomorphic to uniform product spaces.     

Understanding the impacts of product knowledge and product type on the accuracy of intentions-based new product predictions

New product development involves several critical decisions. A key decision making area in new product development is the evaluation of the viability and the market potentials of a new product. In the absence of any relevant historical data, companies ask the potential buyers of their products about their intentions to buy those products when assessing their viability. Despite the popularity of the use of behavioral intentions in predicting the market acceptance of new product ideas, both survey and empirical studies suggest that the accuracy of such predictions is usually very low. Although earlier case-based studies suggest that a number of factors can affect the quality of new product decisions, it is still empirically unclear how product knowledge and the type of new products might impact the predictive accuracy of intentions-based new product forecasting. This study utilized a longitudinal research design and empirically tested the hypotheses across two new products. The study first collected purchase intentions data about the new products. Second, it collected subsequent actual purchase data about the new products. The results of series of hierarchical regression analyses comparing the initial purchase intentions and subsequent actual behaviors showed that while product knowledge is positively related to the predictive accuracy and consistency of intentions-based new product forecasting, product type is negatively related to them.     

Dynamic strategic interaction between an innovating and a non-innovating incumbent

This paper analyzes the effects of product innovation on the firms’ investment behavior in a dynamic duopoly framework. A differential game setting is considered where initially two firms are active on a homogeneous product market. One of the firms has an option to introduce a new product that is horizontally and vertically differentiated from the established product. The resulting differential game has three states corresponding to three capital stocks: one for each firm to produce the established product, and one for the innovating firm to produce the new product. We numerically derive Markov perfect equilibria. One of the most remarkable results is that in most cases the non-innovating firm benefits when the other firm carries out the innovation option. The intuition is that, to increase demand for the innovative product, the innovative firm reduces capacity on the established market, which increases the price of the established product and thus the payoff of the non-innovating firm.     

模糊数无穷乘积

在定义了区间无穷乘积、模糊数无穷乘积及其收敛的基础上 ,利用 [3]中得到的关于模糊级数收敛的某些结论 ,得出模糊数无穷乘积与实数无穷乘积理论类似的结果 ,从而说明本文定义的模糊数无穷乘积确为实数无穷乘积的推广。     

Certain free products of operator spaces

Certain free products are introduced for operator spaces and dual operator spaces. It is shown that the free product of operator spaces does not preserve the injectivity. The linking C*-algebra of the full free product of two ternary rings of operators (simply, TRO's) is *-isomorphic to the full free product of the linking C*-algebras of the two TRO's. The operator space-reduced free product of the preduals of von Neumann algebras agrees with the predual of the reduced free product of the von Neumann algebras. Each of two operator spaces can be embedded completely isometrically into the reduced free product of the operator spaces. Finally, an example is presented to show that the C*-algebra-reduced free product of two C*-algebras may be contractively isomorphic to a proper subspace of their reduced free product as operator spaces.     

A generalization of the vector product

The vector product, often called the cross‐product, is well known in classical mechanics; it is generally assumed to be characteristic of three‐dimensional space. In this paper a vector product is defined on spaces of arbitrary dimension (excluding one‐dimensional spaces) and the definition is shown to coincide with that of the well‐known cross‐product in the case of three‐dimensional spaces; the generalization throws additional light on some of the properties of the classical vector product.     

Product action

This paper studies the cycle indices of products of permutation groups. The main focus is on the product action of the direct product of permutation groups. The number of orbits of the product on n-tuples is trivial to compute from the numbers of orbits of the factors; on the other hand, computing the cycle index of the product is more intricate. Reconciling the two computations leads to some interesting questions about formal power series. We also discuss what happens for infinite (oligomorphic) groups and give detailed examples. Finally, we briefly turn our attention to generalised wreath products, which are a common generalisation of both the direct product with the product action and the wreath product with the imprimitive action.     

广告价格折扣与在线卖方产品质量的激励——中介型电子商务交易平台的视角

研究了信息不对称下电子商务交易平台对在线卖方提高产品质量的激励问题.在线卖方提高产品质量需要付出质量成本,电子商务交易平台监督卖方产品质量需要付出监督成本.当作为理性人的卖方和交易平台提供商考虑自身利益最大化时,导致电子商务中的产品质量不高.将在线卖方在交易平台处的广告费用与其提供的产品质量相联系,证明了通过建立广告费用价格折扣与产品合格率正向相关的契约可以激励在线卖方提高产品质量,并且证明了该契约对在线卖方和电子商务交易平台是双赢的.