On Gröbner bases under specialization

We extend a result of Gianni and Kalkbrener concerning the stability of the Gröbner basis property under specializations. In particular, we prove that the Gröbner basis property is preserved if one specializes variables from bottom up in a Gröbner basis of a zero-dimensional radical ideal w.r.t. a lexicographical term order. The proof makes use of a connection between Gröbner bases and D-Gröbner bases which is proved separately. Computational aspects of this connection are discussed briefly.     

Minimal Homogeneous Bases for Polynomial Ideals

The minimal homogeneous basis is defined. It is shown that every minimal homogeneous basis of an ideal has the same number of elements. An algorithm for finding a minimal homogeneous basis is developed. The main idea is to modify the classical Buchbergers algorithm for finding a Gröbner basis so that a minimal homogeneous basis can be obtained as a subset of a Gröbner basis.     

Gröbner bases of ideals defined by functionals with an application to ideals of projective points

In this paper we study 0-dimensional polynomial ideals defined by a dual basis, i.e. as the set of polynomials which are in the kernel of a set of linear morphisms from the polynomial ring to the base field. For such ideals, we give polynomial complexity algorithms to compute a Gröbner basis, generalizing the Buchberger-Möller algorithm for computing a basis of an ideal vanishing at a set of points and the FGLM basis conversion algorithm.As an application to Algebraic Geometry, we show how to compute in polynomial time a minimal basis of an ideal of projective points.Dedicated to our friend Mario Raimondo     

On the number of term orders

By an admissible order on a finite subsetQ of ⁿ we mean the restriction toQ of a linear order on ⁿ compatible with the group structure of ⁿ and such that ⁿ is contained in the positive cone of the order. We first derive upper and lower bounds on the number of admissible orders on a given setQ in terms of the dimensionn and the cardinality ofQ. Better estimates are possible if the setQ enjoys symmetry properties and in the case whereQ is a discrete hyperbox of the form In the latter case, we also give asymptotic results as d _k for fixedn. We finally present algorithms which compute the set of admissible orders that extend a given binary relation onQ and their number. The algorithms are useful in connection with the construction of universal Gröbner bases.AMS Classification: primary 06F20 secondary 06-04, 11N25     

On the parameterization of algebraic curves

In this paper, by using the concept of resolvents of a prime ideal introduced by Ritt, we give methods for constructing a hypersurface which is birational to a given irreducible variety and birational transformations between the hypersurface and the variety. In the case of algebraic curves, this implies that for an irreducible algebraic curveC, we can construct a plane curve which is birational toC. We also present a method to find rational parametric equations for a plane curve if it exists. Hence we have a complete method of parameterization for rational algebraic curves.The work reported here was supported in part by the NSF Grants CCR-8702108 and 9117870On leave from Institute of Systems Science, Academia Sinica, Beijing 100080, P.R. China     

How to compute the Chow form of an unmixed polynomial ideal in single exponential time

LetK be a field andF ₁,, F _m homogeneous polynomials in the indeterminatesX ₀ ,, X _n with coefficients inK. We describe anefficiently parallelizable single exponential time algorithm which computes the Chow form of the idealI:= (F ₁ ,, F _m ), provided that I is unmixed. This algorithm requires only linear algebra computations overK.     

Semi-Invariants,equivariants and algorithms

The results from Invariant Theory and the results for semi-invariants and equivariants are summarized in a suitable way for combining with Gröbner basis computation. An algorithm for the determination of fundamental equivariants using projections and a Poincaré series is described. Secondly, an algorithm is given for the representation of an equivariant in terms of the fundamental equivariants. Several ways for the exact determination of zeros of equivariant systems are discussed.     

Gröbner basis approach to list decoding of algebraic geometry codes

We show how our Gröbner basis algorithm, which was previously applied to list decoding of Reed Solomon codes, can be used in the hard and soft decision list decoding of Algebraic Geometry codes. In addition, we present a linear functional version of our Gröbner basis algorithm in order to facilitate comparisons with methods based on duality.     

A solution to Kronecker's problem

Consider [x ₁,...,x _n], the multivariate polynomial ring over integers involvingn variables. For a fixedn, we show that the ideal membership problem as well as the associated representation problem for [x ₁,...,x _n] are primitive recursive. The precise complexity bounds are easily expressible by functions in the Wainer hierarchy.Thus, we solve a fundamental algorithmic question in the theory of multivariate polynomials over the integers. As a direct consequence, we also obtain a solution to certain foundational problem intrinsic to Kronecker's programme for constructive mathematics and provide an effective version of Hilbert's basis theorem. Our original interest in this area was aroused by Edwards' historical account of theKronecker's problem in the context of Kronecker's version of constructive mathematics.Supported by an Italian grant Italian MURST 40% Calcolo Algebraico e Simbolico 1993 and an NSF grant: #CCR-9002819.     

Processing maps of Ti662 unreinforced and reinforced with TiC particles according to dynamic models

Ti–6Al–6V–2Sn produced by powder metallurgy by Dynamet unreinforced (CermeTi^®-C-662) and reinforced with 12 vol.% of TiC particles (CermeTi^®-C-12-662), and ingot Ti662 are deformed at high temperatures. The processing maps of these materials are derived using the dynamic material model (DMM) developed by Prasad et al., and the modified DMM developed by Murty and Rao. Although both models result in similar power dissipation values, the instability zones predicted by them are quite different. The processing maps predicted by the modified DMM can be correlated to the deformation behaviour of these materials, with respect to the shape of their flow curves and to their microstructure after deformation. The concentration of stresses produced during compression is released by cracking at the triple junction of grain boundaries in the CermeTi^®-C-662, whereas in the CermeTi^®-C-12-662 by fracture or debonding of the reinforcing particles.     

Experimental tests and FE simulations to compute the mechanical and fracture properties of the shot-earth 772

The present paper is dedicated to the mechanical and fracture characterization of a specific earthen material, that is, the shot-earth 772. Although such a material has been recently characterized from a microstructural, chemical and physical point of view, the knowledge of its mechanical and fracture properties (essential for extending its use in construction industry) is still lacking. Such characterizations are here performed both experimentally, through laboratory tests, and numerically, through a FE model. The experimental tests (i.e., flexural, compression, and fracture tests) are carried out on shot-earth specimens according to recommendations available for concrete and a method proposed by the present authors, named Modified Two-Parameter Model. The numerical analyses are performed by employing a micromechanical model (implemented in a nonlinear 2D FE homemade code), which allows to simulate both flexural and fracture behavior of the shot-earth examined. Finally, the obtained numerical results are compared with the experimental ones.     

ESD Monitor circuit—a tool to investigate the susceptibility and failure mechanisms of the charged device model

ESD-monitor circuits are introduced and used to evaluate failure mechanisms and susceptibilities with respect to the charged device model. The performance of protection elements is studied by means of transmission line pulsing, electron beam probing and non-contact, non-socketed CDM tests. The capacitance connected to the source of the protection transistor and the resistance of this connection are critical. With respect to the circuitry and protection element, CDM-failure signatures of the monitor vary from an energy induced junction failure to a voltage induced gate oxide breakdown.     

Integrating TTF and UTAUT2 theories to investigate the adoption of augmented reality technology in education: Perspective from a developing country

Augmented reality (AR) has gained increased recognition in varying fields, in particular educational contexts. In the wake of the Covid-19 pandemic, home-based learning becomes a reality and is already in place across the globe, and learning via augmented reality technology will help learners comprehend learning content in a more creative frame of mind than ever before. Very little research has examined the adoption behavior of augmented reality in developing country perspectives. Therefore, there is a pressing necessity to understand the dynamics of augmented reality adoption for the benefit of motivating and inspiring students to adopt this highly innovative and impactful type of technology in the learning process. Against this background, the authors proposed and tested a model based on integrating Task-Technology Fit (TTF) and UTUAT2 theories. The results reveal the positive effect of task technology fit, performance expectancy, effort expectancy, social influence, facilitating condition, and hedonic motivation on behavioral intention (BI) in the adoption process of augmented reality in educational settings, where price value is found to exert little influence on behavioral intention. This model explains 49% of the variance in intentional behavior to adopt AR technology in the educational context. The conclusions of this study will add to the literature more informative knowledge leading to increased awareness of the dynamics and behaviors of AR adoption in a developing country perspective. We present and discuss the theoretical contributions and practical implications of our findings.     

Design of experiments to investigate main effects and all two-factor interactions when one of the factors has more than two levels—application to nuclear waste cementation

When both main effects and first-order interactions are looked for, experimental designs usually require a high number of experiments as soon as one of the investigated factors has more than two levels of variation. A new strategy, based on the use of a series of two-level saturated designs, allowed to reduce the number of trials without compromising the quality of the achieved results. This approach revealed very fruitful in a practical case aiming at selecting a proper binder for nuclear waste encapsulation, and at investigating factors which influence the stability of the resulting solidified waste forms.     

Pooling data from fatality analysis reporting system (FARS) and generalized estimates system (GES) to explore the continuum of injury severity spectrum

Fatality Analysis Reporting System (FARS) and Generalized Estimates System (GES) data are most commonly used datasets to examine motor vehicle occupant injury severity in the United States (US). The FARS dataset focuses exclusively on fatal crashes, but provides detailed information on the continuum of fatality (a spectrum ranging from a death occurring within thirty days of the crash up to instantaneous death). While such data is beneficial for understanding fatal crashes, it inherently excludes crashes without fatalities. Hence, the exogenous factors identified as critical in contributing (or reducing) to fatality in the FARS data might possibly offer different effects on non-fatal crash severity levels when a truly random sample of crashes is considered. The GES data fills this gap by compiling data on a sample of roadway crashes involving all possible severity consequences providing a more representative sample of traffic crashes in the US. FARS data provides a continuous timeline of the fatal occurrences from the time to crash – as opposed to considering all fatalities to be the same. This allows an analysis of the survival time of victims before their death. The GES, on the other hand, does not offer such detailed information except identifying who died in the crash. The challenge in obtaining representative estimates for the crash population is the lack of readily available “appropriate” data that contains information available in both GES and FARS datasets. One way to address this issue is to replace the fatal crashes in the GES data with fatal crashes from FARS data thus augmenting the GES data sample with a very refined categorization of fatal crashes. The sample thus formed, if statistically valid, will provide us with a reasonable representation of the crash population.This paper focuses on developing a framework for pooling of data from FARS and GES data. The validation of the pooled sample against the original GES sample (unpooled sample) is carried out through two methods: (1) univariate sample comparison and (2) econometric model parameter estimate comparison. The validation exercise indicates that parameter estimates obtained using the pooled data model closely resemble the parameter estimates obtained using the unpooled data. After we confirm that the differences in model estimates obtained using the pooled and unpooled data are within an acceptable margin, we also simultaneously examine the whole spectrum of injury severity on an eleven point ordinal severity scale – no injury, minor injury, severe injury, incapacitating injury, and 7 refined categories of fatalities ranging from fatality after 30 days to instant death – using a nationally representative pooled dataset. The model estimates are augmented by conducting elasticity analysis to illustrate the applicability of the proposed framework.     

测量系统存在幅值和相位误差时准确测量频率响应函数的方法

给出了一种在测量系统存在幅值和相位误差时准确测量频率响应函数的方法，导出了频率响应函数测量系统的系统函数一般表达式；确定了测量系统误差特征函数，并以此为基础消除了测量系统误差对测量结果的影响。实验结果表明，该方法行之有效，并具有一般性。     

制氧(全)系统停车的迅速恢复和预防

介绍了安阳钢铁公司制氧厂结合实际总结出的制氧 (全 )系统停车的迅速恢复的操作方案和预防停车的措施 ;分析了经济效益。现机组自启动到送氧只需 2 3个小时 ,比设计值减少约 2 5小时。     

Using minimal cuts to evaluate the system reliability of a stochastic-flow network with failures at nodes and arcs

This paper deals with a stochastic-flow network in which each node and arc has a designated capacity, which will have different lower levels due to various partial and complete failures. We try to evaluate the system reliability that the maximum flow of the network is not less than a demand (d+1). A simple algorithm in terms of minimal cuts is first proposed to generate all upper boundary points for d, and then the system reliability can be calculated in terms of such points. The upper boundary point for d is a maximal vector, which represents the capacity of each component (arc or node), such that the maximum flow of the network is d. A computer example is shown to illustrate the solution procedure.