CONSTRUCTION OF SOME KIESSWETTER-LIKE FUNCTIONS-THE CONTINUOUS BUT NON-DIFFERENTIABLE FUNCTION DEFINED BY QUINARY DECIMAL

In this paper, we construct some continuous but non-differentiable functions defined by quinary decimal, that are Kiesswetter-like functions. We discuss their properties, then investigate the Hausdorff dimensions of graphs of these functions and give a detailed proof.     

A Multidimensional Branch-and-Prune Method for Interval Global Optimization

In this paper a new multidimensional extension of the recently developed one-dimensional enclosure method called kite is given for interval global optimization. A more sophisticated version of the pruning technique based on the kite method is introduced. By the new componentwise approach all the one-dimensional theoretical results and procedures can be used in the higher-dimensional case. The possibilities in the implementation of the new algorithm together with numerical results on 40 standard test problems are presented.     

Discrete mathematics in primary and secondary schools in the United States

This article provides a status report on discrete mathematics in America's schools, including an overview of publications and programs that have had major impact. It discusses why discrete mathematics should be introduced in the schools and the authors' efforts to advocate, facilitate, and support the adoption of discrete mathematics topics in the schools. Their perspective is that discrete mathematics should be viewed not only as a collection of new and interesting mathematical topics, but, more importantly, as a vehicle for providing teachers with a new way to think about traditional mathematical topics and new strategies for engaging their students in the study of mathematics.     

Self-consistent modelling of argon microwave discharge sustained by electromagnetic wave in dipole mode

Microwave discharges produced by travelling/standing electromagnetic waves have drawn considerable attention in recent years due to their wide application in microelectronic industry. Here are presented the axial distributions of the electrons and ions as well as those of excited atoms in an argon microwave discharge at a low gas pressure (400 mTorr) sustained by a 2.45 GHz travelling dipolar electromagnetic wave. The numerical calculations are based on a self-consistent kinetic-electrodynamic model and the results obtained are in a good agreement with the experimental data. The model yields also the magnitude of the wave power sustaining the discharge and the axial profiles of all electromagnetic-wave characteristics and the axial distribution of the neutral gas temperature.     

Divisible Effect Algebras

Divisible effect algebras and their relations to convex effect algebras and MV-algebras are studied. A categorical equivalence between divisible effect algebras and rational vector spaces is proved. Infinitesimal, sharp and extremal elements in divisible effect algebras are studied and their relations to properties of the state space are shown.     

Spectral enhancement of Polish vowels to improve their identification by hearing impaired listeners

Abnormalities in the cochlear function usually cause broadening of the auditory filters which reduces the speech intelligibility. An attempt to apply a spectral enhancement algorithm has been undertaken to improve the identification of Polish vowels by subjects with cochlear-based hearing-impairment. The identification scores of natural (unprocessed) vowels and spectrally enhanced (processed) vowels has been measured for hearing-impaired subjects. It has been found that spectral enhancement improves vowel scores by about 10% for those subjects, however, a wide variation in individual performance among subjects has been observed. The overall vowels identification scores obtained were 85% for natural vowels and 96% for spectrally enhanced vowels.     

A New Cohomology Theory of Orbifold

Based on the orbifold string theory model in physics, we construct a new cohomology ring for any almost complex orbifold. The key theorem is the associativity of this new ring. Some examples are computed.Both authors partially supported by the National Science Foundation     

Steady-state analytical solutions for the lattice boltzmann equation

A general class of analytical solutions of the lattice Boltzmann equation is derived for two-dimensional, steady-state unidirectional flows. A subset of the solutions that verifies the corresponding Navier-Stokes equations is given. It is pointed out that this class includes, e.g., the Couette and the Poiseuille flow but not, e.g., the basic Kolmogorov flow. For steady-state non-unidirectional flows, first and second order solutions of the lattice Boltzmann equation are derived. Practical consequences of the analysis are mentioned. Differences between the technique applied here and those used in some earlier works are emphasized.     

Groups in which every non-abelian subgroup is permutable

A subgroupH of a groupG is said to bepermutable ifHX=XH for every subgroupX ofG. In this paper the structure of groups in which every subgroup either is abelian or permutable is investigated. This work was done while the last author was visiting the University of Napoli Federico II. He thanks the “Dipartimento di Matematica e Applicazioni” for its financial support.     

The elastic theory of a single DNA molecule

We study the elastic responses of double-(ds) and single-stranded (ss) DNA at external force fields. A double-strand-polymer elastic model is constructed and solved by path integral methods and Monte Carlo simulations to understand the entropic elasticity, cooperative extensibility, and supercoiling property of dsDNA. The good agreement with experiments indicates that short-ranged base-pair stacking interaction is crucial for the stability and the high deformability of dsDNA. Hairpin-coil transition in ssDNA is studied with generating function method. A threshold force is needed to pull the ssDNA hairpin patterns, stabilized by base pairing and base-pair stacking, into random coils. This phase transition is predicted to be of first order for stacking potential higher than some critical level, in accordance with experimental observations.