Extending a matroid by a cocircuit

Our main result describes how to extend a matroid so that its ground set is a modular hyperplane of the larger matroid. This result yields a new way to view Dowling lattices and new results about line-closed geometries. We complement these topics by showing that line-closure gives simple geometric proofs of the (mostly known) basic results about Dowling lattices. We pursue the topic of line-closure further by showing how to construct some line-closed geometries that are not supersolvable.     

Levenberg-Marquardt method with a general LM parameter and a nonmonotone trust region technique

We propose a new Levenberg-Marquardt (LM) method for solving the nonlinear equations. The new LM method takes a general LM parameter \lambda_k=\mu_k[(1-\theta)\|F_k\|^\delta+\theta\|J_k^TF_k\|^\delta] where \theta\in[0,1] and \delta\in(0,3) and adopts a nonmonotone trust region technique to ensure the global convergence. Under the local error bound condition, we prove that the new LM method has at least superlinear convergence rate with the order \min\{1+\delta,4-\delta,2\}. We also apply the new LM method to solve the nonlinear equations arising from the weighted linear complementarity problem. Numerical experiments indicate that the new LM method is efficient and promising.     

Experiments with a new selection criterion in a fast interval optimization algorithm

Usually, interval global optimization algorithms use local search methods to obtain a good upper (lower) bound of the solution. These local methods are based on point evaluations. This paper investigates a new local search method based on interval analysis information and on a new selection criterion to direct the search. When this new method is used alone, the guarantee to obtain a global solution is lost. To maintain this guarantee, the new local search method can be incorporated to a standard interval GO algorithm, not only to find a good upper bound of the solution, but also to simultaneously carry out part of the work of the interval B&B algorithm. Moreover, the new method permits improvement of the guaranteed upper bound of the solution with the memory requirements established by the user. Thus, the user can avoid the possible memory problems arising in interval GO algorithms, mainly when derivative information is not used. The chance of reaching the global solution with this algorithm may depend on the established memory limitations. The algorithm has been evaluated numerically using a wide set of test functions which includes easy and hard problems. The numerical results show that it is possible to obtain accurate solutions for all the easy functions and also for the investigated hard problems.     

Bounds from a card trick

We describe a new variation of a mathematical card trick, whose analysis leads to new lower bounds for data compression and estimating the entropy of a Markov source.     

Symplectic Householder transformations for a QR-like decomposition,a geometric and algebraic approaches

The aim of this paper is to show how geometric and algebraic approaches lead us to a new symplectic elementary transformations: the 2-D symplectic Householder transformations. Their features are studied in details. Their interesting properties allow us to construct a new algorithm for computing a SR factorization. This algorithm is based only on these 2-D symplectic Householder transformations. Its new features are highlighted. The study shows that, in the symplectic case, the new algorithm is the corresponding one to the classical QR factorization algorithm, via the Householder transformations. Some numerical experiments are given.     

Asymptotic approximations for a new eigenvalue in linear problems without a threshold

We study the criterion for a new eigenvalue to appear in the linear spectral problem associated with the intermediate long-wave equation. We compute the asymptotic value of the new eigenvalue in the limit of a small potential using a Fourier decomposition method. We compare the results with those for the Schrödinger operator with a radially symmetrical potential.     

复流形局部q-凸楔形上带权的同伦公式

本文得到复流形局部q-凸楔形上(r,s)型微分形式的带权的同伦公式和(r,s)型的方程的带权的连续解,并给出(r,s)型微分形式的不含边界积分的新的带权的同伦公式和(r,s)型的方程的新的带权的连续解.这些新的带权公式尤其适用于具有非光滑边界的局部q-凸楔形,这时不但可以避免边界积分的复杂估计,而且积分密度也不必在边界有定义,只要在区域上有定义就行.其次,引进权因子,带权的积分公式在应用上(比如在函数的插值方面)具有更大的灵活性.     

Measuring accuracy in a post-enumeration survey

"The U.S. Bureau of the Census will use a post-enumeration survey to measure the coverage of the 1990 Decennial Census. The Census Bureau has developed and tested new procedures aimed at increasing the accuracy of the survey. This paper describes the new methods. It discusses the categories of error that occur in a post-enumeration survey and means of evaluation to determine that the results are accurate. The new methods and the evaluation of the methods are discussed in the context of a recent test post-enumeration survey."     

Univariate Interpolation on a Regular Finite Grid by a Multiquadric Plus a Linear Polynomial

Univariate multiquadric interpolation to a twice continuouslydifferentiable function on a regular infinite grid enjoys secondorder convergence and some excellent localization properties,but numerical calculations suggest that, if the grid is finite,then usually the convergence rate deteriorates to first ordernear the grid boundaries, ibis conjecture is proved. It is alsoshown that one can recover superlinear convergence by addinga linear polynomial term to the multiquadric approximation.Making such additions is a standard technique, but we find thatthe usual way of choosing the polynomial fails to provide superlinearconvergence m general. Therefore some new procedures are giventhat pick a suitable polynomial automatically. Thus it is notunusual to reduce the maximum error of the interpolation bya factor of 10³. Further, it is straightforward to include oneof the new procedures in multiquadric interpolation to functionsof several variables when the data points are in general position.     

Locating a competitive facility in the plane with a robustness criterion

A new model for locating a competitive facility in the plane in a robust way is presented and embedded in the literature on robustness in facility location. Its mathematical properties are investigated and new sharp bounds for a deterministic method that guarantees the global optimum are derived and evaluated.     

On a casimir element of a finite group

In this note we use different representations of a Casimir element of a finite group to give simple proofs for some new and old facts about commutators and character degrees.     

Analysis of a quadratic functional with a partly degenerate legendre condition

The question of nonnegativity of a quadratic functional such that its matrix at the square of control is degenerate in part of controls is studied. After some transformation of the phase variables, the “degenerate” part of controls disappears, while its role passes to new phase variables. The obtained quadratic functional can have a non-degenerate matrix at the square of new control variables, allowing us to study its sign definiteness by standard methods.     

On a class of quasi variational inequalities

In this paper, we introduce and study a new class of quasi variational inequalities. Using essentially the projection technique and its variant forms, we establish the equivalence between generalized nonlinear quasi variational inequalities and the fixed point problems. This equivalence is then used to suggest and analyze a number of new iterative algorithms. These new results include the corresponding known results for generalized quasi variational inequalities as special cases.     

Optimising a general repair kit problem with a service constraint

Field services are a particular type of after-sales service performed at the customer’s location where technicians repair malfunctioning machines. The inventory decisions about which spare part types to take to the repair site and in what quantities is called the repair kit problem. This problem is characterized by an order-based performance measure since a customer is only satisfied when all required spare parts are available to fix the machine. As a result, the service level in the decision making process is defined as a job fill rate. In this paper we derive a closed-form expression for the expected service level and total costs for the repair kit problem in a general setting, where multiple units of each part type can be used in a multi-period problem. Such an all-or-nothing strategy is a new characteristic to investigate, but commonly used in practice. Namely, items are only taken from the inventory when all items to perform the repair are available in the right quantity. We develop a new algorithm to determine the contents of the repair kit both for a service and cost model while incorporating this new expression for the job fill rate. We show that the algorithm finds solutions which differ on average 0.2% from optimal costs. We perform a case study to test the performance of the algorithm in practice. Our approach results in service level improvements of more than 30% against similar holding costs.     

Price subsidies and guaranteed buys of a new technology

We consider a problem of a government that wishes to stimulate the adoption of a new technology in order to replace an older, environmentally less desirable, technology. The new technology is manufactured by a monopolist firm which has learning-by-doing in its production process. The firm sells the new product to both private households and government institutions and wishes to determine an optimal pricing policy. The government has at its disposal two instruments: subsidizing the consumer price and making purchases of the new technology from the firm. We assume profit maximization on the part of the firm. The government wishes to maximize the cumulative number of units of the new technology sold to private households by the terminal date of the government program. The problem is set up as a Stackelberg differential game in which we identify an open-loop equilibrium, supposing that the government can credibly precommit to its subsidy and buying program.     

Supply chain dynamic configuration as a result of new product development

This study considers supply chain network configuration in an innovative environment while the new product development (NPD) will affect the supply chain configuration (SCC). The time of new product introduction has a significant effect on the market performance while it has an effect on the supply chain configuration. Supplier integration into the new product introduction is the key parameter for successfully new product introduction, which may contribute to supply chain reconfiguration. Consequently By considering the new product development concept, we may face with dynamic supply chain configuration during a planning horizontal time. In this study, a new model is presented to consider the dynamic configuration of a supply chain by developing new products. In the proposed model, the dynamic configuration of a supply chain and the new product launching time is optimized simultaneously. The proposed model considers production, sales and transportation planning for the entire supply chain in order to achieve an integrative and efficient supply as well. Then some numerical analyses have been done to show the applicability of the proposed model. The results show that the new product development has a significant effect on the configuration of supply chain.     

On the relative profiles of a linear code and a subcode

Relative dimension/length profile (RDLP), inverse relative dimension/length profile (IRDLP) and relative length/dimension profile (RLDP) are equivalent sequences of a linear code and a subcode. The concepts were applied to protect messages from an adversary in the wiretap channel of type II with illegitimate parties. The equivocation to the adversary is described by IRDLP and upper-bounded by the generalized Singleton bound on IRDLP. Recently, RLDP was also extended in wiretap network II for secrecy control of network coding. In this paper, we introduce new relations and bounds about the sequences. They not only reveal new connections among known results but also find applications in trellis complexities of linear codes. The state complexity profile of a linear code and that of a subcode can be bounded from each other, which is particularly useful when a tradeoff among coding rate, error-correcting capability and decoding complexity is considered. Furthermore, a unified framework is proposed to derive bounds on RDLP and IRDLP from an upper bound on RLDP. We introduce three new upper bounds on RLDP and use some of them to tighten the generalized Singleton bounds by applying the framework. The approach is useful to improve equivocation estimation in the wiretap channel of type II with illegitimate parties.     

结合修正Curry-Altman步长搜索一个新的共轭梯度算法的收敛性

Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameter in the search directions. In this note, conditions are given on the parameter in the conjugate gradient directions to ensure the descent property of the search directions. Global convergence of such a class of methods is discussed. It is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continuously differentiable function with a modification of the Curry-Altman‘s step-size rule and a bounded level set. Combining PR method with our new method, PR method is modified to have global convergence property.Numerical experiments show that the new methods are efficient by comparing with FR conjugate gradient method.     

On the image of a constrained extremum problem and some applications to the existence of a minimum

A new approach to constrained optimization, which has appeared recently under various forms and in several contexts, is presented in a general and unifying setting. This approach is then employed to establish some new conditions for the existence of the minimum of a constrained minimum problem.