Efficient computation of the exponential operator for large,sparse, symmetric matrices

In this paper we compare Krylov subspace methods with Chebyshev series expansion for approximating the matrix exponential operator on large, sparse, symmetric matrices. Experimental results upon negative‐definite matrices with very large size, arising from (2D and 3D) FE and FD spatial discretization of linear parabolic PDEs, demonstrate that the Chebyshev method can be an effective alternative to Krylov techniques, especially when memory bounds do not allow the storage of all Ritz vectors. We also discuss the sensitivity of Chebyshev convergence to extreme eigenvalue approximation, as well as the reliability of various a priori and a posteriori error estimates for both methods. Copyright © 2000 John Wiley & Sons, Ltd.     

New exact solutions of the massive Dirac equation with electric or scalar potential

A new class of exact solutions for the massive Dirac equation with electric or scalar potential depending on one independent variable is constructed. This construction is based on quaternionic reformulation of the Dirac equation. Copyright © 2000 John Wiley & Sons, Ltd.     

Drug Design: Where We Are and Future Prospects

Medicinal chemistry is facing new challenges in approaching precision medicine. Several powerful new tools or improvements of already used tools are now available to medicinal chemists to help in the process of drug discovery, from a hit molecule to a clinically used drug. Among the new tools, the possibility of considering folding intermediates or the catalytic process of a protein as a target for discovering new hits has emerged. In addition, machine learning is a new valuable approach helping medicinal chemists to discover new hits. Other abilities, ranging from the better understanding of the time evolution of biochemical processes to the comprehension of the biological meaning of the data originated from genetic analyses, are on their way to progress further in the drug discovery field toward improved patient care. In this sense, the new approaches to the delivery of drugs targeted to the central nervous system, together with the advancements in understanding the metabolic pathways for a growing number of drugs and relating them to the genetic characteristics of patients, constitute important progress in the field.     

On-line liquid chromatography/electrospray tandem mass spectrometry to investigate acrylamide adducts with cysteine residues: implications for polyacrylamide gel electrophoresis separations of proteins

Adduction between acrylamide and cysteine residues is a post-translational modification associated with proteins separated by gel electrophoresis. In the present article, three model peptides containing 2–4 cysteine residues were reduced with dithiothreitol, incubated with acrylamide monomers and examined by on-line liquid chromatography coupled to electrospray tandem mass spectrometry. Each of the solutions examined in this work revealed the presence of four distinct components: the free peptide, two different peptide–acrylamide 1:1 adducts involving two cysteine residues at different positions within the same sequence, and peptide–acrylamide 1:2 adducts. The use of liquid chromatography allowed the separation of components which differed only by the site of complexation of acrylamide, while the application of tandem mass spectrometry furnished reliable sequencing information permitting the identification of most cysteine residues involved in such complexation. © 1998 John Wiley & Sons, Ltd.     

A Chemically and Electrochemically Switchable [2]Catenane Incorporating a Tetrathiafulvalene Unit

A mechanical switch in a [2]catenane , made up of a cyclobis(paraquat-p-phenylene) tetracation interlocked with a macrocyclic polyether containing a redox-active tetrathiafulvalene (TTF) unit and a 1,5-dioxynaphthalene ring system, can be thrown either chemically or electrochemically. The neutral TTF unit resides “inside” the tetracationic cyclophane in the reduced state and “alongside” it in the oxidized species (TTF⁺/ TTF²⁺). Switching between the reduced (I⁴⁺) and oxidized state (I⁵⁺(I⁶⁺)) is accompanied by a dramatic color change.     

Recursive constructions for difference matrices and relative difference families

We present a new recursive construction for difference matrices whose application allows us to improve some results by D. Jungnickel. For instance, we prove that for any Abelian p-group G of type (n₁, n₂, …, n_t) there exists a (G, p^e, 1) difference matrix with e = Also, we prove that for any group G there exists a (G, p, 1) difference matrix where p is the smallest prime dividing |G|. Difference matrices are then used for constructing, recursively, relative difference families. We revisit some constructions by M. J. Colbourn, C. J. Colbourn, D. Jungnickel, K. T. Phelps, and R. M. Wilson. Combining them we get, in particular, the existence of a multiplier (G, k, λ)-DF for any Abelian group G of nonsquare-free order, whenever there exists a (p, k, λ)-DF for each prime p dividing |G|. Then we focus our attention on a recent construction by M. Jimbo. We improve this construction and prove, as a corollary, the existence of a (G, k, λ)-DF for any group G under the same conditions as above. © 1998 John Wiley & Sons, Inc. J Combin Designs 6: 165–182, 1998