On the p-Ranks and Characteristic Polynomials of Cyclic Difference Sets

In this paper, the p-ranks and characteristic polynomials of cyclic difference sets are derived by expanding the trace expressions of their characteristic sequences. Using this method, it is shown that the 3-ranks and characteristic polynomials of the Helleseth–Kumar–Martinsen (HKM) difference set and the Lin difference set can be easily obtained. Also, the p-rank of a Singer difference set is reviewed and the characteristic polynomial is calculated using our approach.     

Spectrofluorometric Determination of Hydrogen Peroxide

A Spectrofluorometric method for microdetermination of H₂O₂ has been developed. The method is based on the oxidation of hydrogen peroxide with ceric ion in acid solution and measurement of the fluorescence during titration of the Ce(III) ions produced. The fluorescent species have excitation and emission maxima at 260 and 360 nm, respectively. The detection limit of measurement by this method was 0.1 ppm hydrogen peroxide.     

A class of permutation quadrinomials

In this paper, we investigate the permutation behavior of a class of quadrinomials. Each term of these quadrinomials has a Niho-type exponent, and two sets of coefficient triples making the quadrinomials to be permutations are obtained. We use a substitution to transform the permutation problem into the root distribution problem in the unit circle of certain quadratic and cubic equations.     

An Infinite Family of 3-Designs from Preparata Codes overZ4

We show that the support of minimum Lee weight codewords having Hamming weight 5 in the Preparata code over Z₄ form a 3-(2^m,5,10) design for any odd integer m 3.     

Single-ion activities and Mn(Hg)/Mn(II) reactions in aqueous solutions of alkaline-earth chlorides

Combined thermodynamic and kinetic studies have yielded convenient single-ion activity coefficients for manganese(II), alkaline-earth, and chloride ions and standard exchange currents for the two steps of the Mn(Hg)/Mn(II) electrode in 0.005 M MnCl₂+0.495 M MeCl₂ (for Me=Mg, Ca, Sr, Ba, and Mn) at 25°C. The results indicate that the fall in mean ionic activity coefficient for the alkaline-earth chlorides along the sequence from magnesium to barium is carried to a larger extent by the cation than by the anion, that also the activity coefficient for the minority cation Mn(II) falls along this sequence, and that other than activity-coefficient effects on the Mn(Hg)/Mn(II) reactions appear only with barium ions, which retard the reactions additionally. The results are discussed with emphasis on ionic interactions and double-layer effects.     

Fully symmetric integration rules for the 4-cube

In this paper we discuss fully symmetric integration rules of degree 7 and 9 for the 4-cube. In particular we are interested in good rules. (i.e. rules with all the evaluation points inside the cube and all the weights positive).This work was supported by the Norwegian Research Council for Sciences and Humanities.     

A semilinear equation with generalized Wentzell boundary condition

In this paper we consider a semilinear equation with a generalized Wentzell boundary condition. We prove the local well-posedness of the problem and derive the conditions of the global existence of the solution and the conditions for finite time blow-up. We also derive an estimate for the blow-up time.