On the characterization of periodic generalized Horadam sequences

The Horadam sequence is a direct generalization of the Fibonacci numbers in the complex plane, which depends on a family of four complex parameters: two recurrence coefficients and two initial conditions. In this article a computational matrix-based method is developed to formulate necessary and sufficient conditions for the periodicity of generalized complex Horadam sequences, which are generated by higher order recurrences for arbitrary initial conditions. The asymptotic behaviour of generalized Horadam sequences generated by roots of unity is also examined, along with upper boundaries for the disc containing periodic orbits. Some applications are suggested, along with a number of future research directions.     

The rational development of molecularly imprinted polymer-based sensors for protein detection

The detection of specific proteins as biomarkers of disease, health status, environmental monitoring, food quality, control of fermenters and civil defence purposes means that biosensors for these targets will become increasingly more important. Among the technologies used for building specific recognition properties, molecularly imprinted polymers (MIPs) are attracting much attention. In this critical review we describe many methods used for imprinting recognition for protein targets in polymers and their incorporation with a number of transducer platforms with the aim of identifying the most promising approaches for the preparation of MIP-based protein sensors (277 references).     

New high-energy luminescence bands from Co2+ in ZnSe

Three sharp absorption features in the energy range 2.36–2.55 eV have been detected in the transmission spectrum of Co-diffused ZnSe, and a number of luminescence transitions originating from the lowest of these states at 2.361 eV have been observed. Photoluminescence excitation spectra prove that these are high energy excited states of the Co²⁺_Zn impurity, a conclusion confirmed by comparison of measured and predicted luminescence energies. This represents the first identification of luminescence branching from a higher excited state of a transition metal ion in any semiconductor. The sharp, weakly phonon-coupled transitions involve either intra-impurity excitation or transitions from the impurity to localised states split off from a minimum in the conduction band. The implications of these observations for the mechanism of host-impurity energy transfer and for the nature of the excited state wavefunctions are discussed.     

Z4-Kerdock Codes, Orthogonal Spreads, and Extremal Euclidean Line-Sets

When m is odd, spreads in an orthogonal vector space of type⁺(2m + 2,2) are related to binary Kerdock codes and extremalline-sets in 2^{m + 1} with prescribed angles. Spreads in a 2m-dimensionalbinary symplectic vector space are related to Kerdock codesover Z₄ and extremal line-sets in with prescribed angles. These connections involve binary, realand complex geometry associated with extraspecial 2-groups.A geometric map from symplectic to orthogonal spreads is shownto induce the Gray map from a corresponding Z₄-Kerdock codeto its binary image. These geometric considerations lead tothe construction, for any odd composite m, of large numbersof Z₄-Kerdock codes. They also produce new Z₄-linear Kerdockand Preparata codes. 1991 Mathematics Subject Classification:primary 94B60; secondary 51M15, 20C99.     

Application of Combinatorial Procedures in the Search for Serine-Protease-Like Activity with Focus on the Acyl Transfer Step

Recursive deconvolution of a 729-membered peptide library has identified three active sequences, in which both Ser and His are present in one of the two tripeptidic chains generated on a steroidal scaffold (see structural formula), for the cleavage of an activated p-nitrophenyl ester. This combinatorial approach aims at searching for serine-protease-like activity.     

Simultaneous attainment of high electron and ion temperatures in discharges with internal transport barriers in ASDEX upgrade

Internal transport barriers have been demonstrated to exist also under conditions with T(e) approximately T(i) approximately 10 keV and predominant electron heating of the tokamak core region. Central electron cyclotron heating was added to neutral beam injection-heated ASDEX Upgrade discharges with a preexisting internal transport barrier, established through programmed current ramping leading to shear reversal. Compared to a reference internal transport barrier discharge without electron cyclotron resonance heating, the electron heat conductivity in the barrier region was found not to increase, in spite of a fivefold increase in electron heat flux, and also angular momentum and ion energy transport did not deteriorate.