Vapoluminescent Behavior and the Single-Crystal-to-Single-Crystal Transformations of Chloroform Solvates of [Au2(μ-1,2-bis(diphenylarsino)ethane)2](AsF6)2

The mono- and di-chloroform solvates of [Au₂(μ-1,2-bis(diphenylarsino)ethane)₂](AsF₆)₂ undergo single-crystal-to-single-crystal transformations that result in gain (over 12 hours) or slow loss (over five years) of only one chloroform molecule. The change in solvation results in changes in the structure and luminescence of the digold cation. The cation consists of a pair of slightly bent As-Au-As units that are connected through the two bridging dpae ligands and by aurophilic interactions with Au⋅⋅⋅Au contacts of 3.05152(15) Å in the disolvate or 2.9570(5) Å in the monosolvate.     

Some remarks on Nelson's stochastic field

An attempt to extend Nelson's stochastic quantization procedure to tensor fields indicates that the results of Guerra et al. on the connection between a euclidean Markov scalar field and a stochastic scalar field fails to hold for tensor fields.     

Features in Distribution of Wavefunctions of Few-Body Systems

The bbody, 4-body and 5-body quantum mechanical systems with pairwise interactions having repulsive core and attractive tail and with completely symmetric permutation symmetry in the spatial wavefunctions are studied. The spatial distribution of the wavefunctions of the low-lying O⁺ states is investigated in detail. The features of the geometric structures and of the internal motions of each of these states are revealed. Certain modes of the internal motions are discovered.     

A pair of orthogonal frames

We start with a characterization of a pair of frames to be orthogonal in a shift-invariant space and then give a simple construction of a pair of orthogonal shift-invariant frames. This is applied to obtain a construction of a pair of Gabor orthogonal frames as an example. This is also developed further to obtain constructions of a pair of orthogonal wavelet frames.     

Square classes of totally positive units

In this article, we investigate some conditions for a real cyclic extension K over Q to satisfy the property that every totally positive unit of K is a square. As an application, we give a partial answer to Taussky's conjecture. We then extend our result to real abelian extensions of certain type.     

A stochastic model for risk management in global supply chain networks

With the increasing emphasis on supply chain vulnerabilities, effective mathematical tools for analyzing and understanding appropriate supply chain risk management are now attracting much attention. This paper presents a stochastic model of the multi-stage global supply chain network problem, incorporating a set of related risks, namely, supply, demand, exchange, and disruption. We provide a new solution methodology using the Moreau–Yosida regularization, and design an algorithm for treating the multi-stage global supply chain network problem with profit maximization and risk minimization objectives.     

High-Temperature Phase Transition in N(CH3)4CdCl3 Studied Using Static NMR and MAS NMR

To clarify the nature of microscopic structural changes of N(CH₃)₄CdCl₃ at high temperatures, the nuclear magnetic resonance (NMR) spectra of the protons and carbons in N(CH₃)₄CdCl₃ were measured. NMR studies of the ¹H and ¹³C spin–lattice relaxation time, T _1ρ, in the rotating frame were also performed. No changes in the T _1ρ of ¹H and ¹³C associated with the N(CH₃)₄ groups were observed at the high-temperature transition from phase I to phase I′. However, the ¹⁴N NMR spectra reflected changes in the structural geometry during the transition to phase I′, indicating that this transition is driven by N(CH₃)₄.     

Laser writing techniques for photomask fabrication using a femtosecond laser

Photomasks are the backbone of microfabrication industries. Currently they are fabricated by a lithographic process, which is very expensive and time consuming since it is a multi-step process. These issues can be addressed by fabricating photomasks by direct femtosecond laser writing, which is a single-step process and comparatively cheaper and faster than lithography. In this paper we discuss our investigations on the effect of two types of laser writing techniques, namely front- and rear-side laser writing, with regard to the feature size and the edge quality of a feature. It is proved conclusively that for the patterning of masks, front-side laser writing is a better technique than rear-side laser writing with regard to smaller feature size and better edge quality. Moreover the energy required for front-side laser writing is considerably lower than that for rear-side laser writing. Received: 22 May 2001 / Accepted: 14 September 2001 / Published online: 17 October 2001     

Crossdocking—JIT scheduling with time windows

In this paper, we study a problem central to crossdocking that aims to eliminate or minimize storage and order picking activity using JIT scheduling. The problem is modelled naturally as a machine scheduling problem. As the problem is NP-hard, and for real-time applications, we designed and implemented two heuristics. The first uses Squeaky Wheel Optimization embedded in a Genetic Algorithm and the second uses Linear Programming within a Genetic Algorithm. Both heuristics offer good solutions in experiments where comparisons are made with the CPLEX solver.     

Linear spaces and preservers of symmetric matrices of bounded rank-two

Let 𝔽 be a field of characteristic two. Let S _n (𝔽) denote the vector space of all n?×?n symmetric matrices over 𝔽. We characterize i. subspaces of S _n (𝔽) all whose elements have rank at most two where n???3,

ii. linear maps from S _m (𝔽) to S _n (𝔽) that sends matrices of rank at most two into matrices of rank at most two where m, n???3 and |𝔽|?≠?2.