On codewords in the dual code of classical generalised quadrangles and classical polar spaces

In [J.L. Kim, K. Mellinger, L. Storme, Small weight codewords in LDPC codes defined by (dual) classical generalised quadrangles, Des. Codes Cryptogr. 42 (1) (2007) 73-92], the codewords of small weight in the dual code of the code of points and lines of Q(4,q) are characterised. Inspired by this result, using geometrical arguments, we characterise the codewords of small weight in the dual code of the code of points and generators of Q⁺(5,q) and H(5,q²), and we present lower bounds on the weight of the codewords in the dual of the code of points and k-spaces of the classical polar spaces. Furthermore, we investigate the codewords with the largest weights in these codes, where for q even and k sufficiently small, we determine the maximum weight and characterise the codewords of maximum weight. Moreover, we show that there exists an interval such that for every even number w in this interval, there is a codeword in the dual code of Q⁺(5,q), q even, with weight w and we show that there is an empty interval in the weight distribution of the dual of the code of Q(4,q), q even. To prove this, we show that a blocking set of Q(4,q), q even, of size q²+1+r, where 0<r<(q+4)/6, contains an ovoid of Q(4,q), improving on [J. Eisfeld, L. Storme, T. Sz?nyi, P. Sziklai, Covers and blocking sets of classical generalised quadrangles, Discrete Math. 238 (2001) 35-51, Theorem 9].     

A simple method for the study of salbutamol pharmacokinetics by ion chromatography with direct conductivity detection

A simple method for the study of the pharmacokinetics of salbutamol using ion chromatography with direct conductivity detection without chemical suppression is presented in this paper. Baseline separation of salbutamol from plasma components was achieved by using diluted HNO₃ (2 mmol l⁻¹) as mobile phase with acetonitrile (6%, v/v) as modifier. Atenolol was utilized as internal standard. Under the optimal conditions, the linear regression coefficients of the calibration curves are 0.996 within the concentration range of 1000-3 ng ml⁻¹ salbutamol. The detection limit (signal-to-noise ratio = 3) was 1 ng ml⁻¹ salbutamol. The noncompartmental pharmacokinetic parameters for salbutamol following administration of 8 mg salbutamol to 18 subjects were tested. The results coincided most satisfactorily with the results obtained by using reversed-phase high performance liquid chromatography (HPLC) with fluorescence detection.     

On the Structure of Solutions of the Moisil-Théodoresco System in Euclidean Space

Let be open, let be the Dirac operator in and let be the Clifford algebra constructed over the quadratic space . If for fixed, denotes the space of r-vectors in , then an -valued smooth function W = W ^r  + W ^r+2 in Ω is said to satisfy the Moisil-Théodoresco system if . In terms of differential forms, this means that the corresponding - valued smooth form w = w ^r  + w ^r+2 satisfies in Ω the system d ^* w ^r = 0, dw ^r  + d ^* w ^r+2 = 0; dw ^r+2 = 0. Based on techniques and results concerning conjugate harmonic functions in the framework of Clifford analysis, a structure theorem is proved for the solutions of the Moisil-Théodoresco system.      

The geometric field of linearity of linear sets

Designs, Codes and Cryptography - If an $${\mathbb {F}}_q$$ -linear set $$L_U$$ in a projective space is defined by a vector subspace U which is linear over a proper superfield of $${\mathbb...     

A generalised Christoffel-Darboux formula and reproducing kernels in spaces of polymonogenic and polyharmonic functions

Let ?_x be the Dirac operator in R^m+1, let t ∈ N and let K_t(x,y) be the Bergman kernel for the space L ₂M_t of square integrable polymonogenic functions of order t in the unit ball B(1) of R^m+1. Then expressions for K_t(x,y) are derived using a generalised Christoffel-Darboux formula related to the orthogonal basis of generalised Gegenbauer polynomials in the weighted L₂-space L₂(B(1);(1 + x²⁾α), α > ?1.     

Half Dirichlet Problems and Decompositions of Poisson Kernels

Following the previous study on the unit ball of Delanghe et al, half-Dirichlet problems for the upper-half space are presented and solved. The solutions further lead to decompositions of the Poisson kernels, and the fact that the classical Dirichlet problems may be solved merely by using Cauchy transformation in the respective two contexts. We show that the only domains for which the half-Dirichlet problems are solvable in the same pattern are balls and half-spaces. The work was supported by research grant of the University of Macau No. RG079/04- 05S/QT/FST.     

On-line microheterogeneity analysis and rapid phenotyping of haptoglobin by capillary electrophoresis using sodium dodecyl sulfate as additive

To improve the detection sensitivity and determine phenotypes of haptoglobin (Hp), a prefilling technique was developed and tested in capillary electrophoresis (CE) with UV–vis absorbance detection. Adding 0.01% sodium dodecyl sulfate (SDS) to the protein sample and 0.1% SDS to the prefilling buffer solution, on-line stacking and microheterogeneity separation of Hp were achieved. In addition, the influences of pH, buffer concentration, sample and prefilling buffer SDS concentration upon resolution were examined. Under optimized conditions, Hp-microheterogeneity was well resolved and two phenotypes of Hp (Hp 1-1 and Hp 2-2) were differentiated. This method was applied to the analysis of sera from normal individuals and β-Thalassemia patients. After the depletion of albumin (HSA) and immunoglobulin G (IgG), this method allowed to determine two phenotypes in different individuals and to detect the decrease of Hp in β-Thalassemia patients. Featuring high efficiency, speed and simplicity, the proposed method shows great potential for use in clinical diagnosis and proteome research.