Error control codes are widely used to increase the reliability of transmission of information over various forms of communications channels. The Hamming weight of a codeword is the number of nonzero entries in the word; the weights of the words in a linear code determine the error-correcting capacity of the code. The rth generalized Hamming weight for a linear code C, denoted by dr(C), is the ...

The relation $$xy-yx=h(y)$$ , where $$h$$ is a holomorphic function, occurs naturally in the definitions of some quantum groups. To attach rigorous meaning to right-hand side this equality, we assume that $$x$$ and $$y$$ are elements Banach algebra (or an Arens–Michael algebra). We prove universal generated by commutation kind can be represented explicitly as analytic Ore extension. An analysis...

Figure 1. Wavelength-dependent light intensity at different water depths (indicated by numbers assigned to contour lines). Light intensity is given in percent of surface light intensity, where 100% equals ~30,000 lux (~600 mmol quanta m22 s21), estimated to be 24 h average expected for light intensity on horizontal surface on clear summer day (Thimijan and Heins, 1983). Contour lines were deriv...

The Harary-Hill conjecture states that for every n > 0 the complete graph on n vertices Kn, the minimum number of crossings over all its possible drawings equals H(n) := 1 4 ⌊n 2 ⌋⌊n− 1 2 ⌋⌊n− 2 2 ⌋⌊n− 3 2 ⌋ . So far, the lower bound of the conjecture could only be verified for arbitrary drawings of Kn with n ≤ 12. In recent years, progress has been made in verifying the conjecture for certain ...

PURPOSE The purpose of this study was to evaluate the prevalence of and relationship between hypomineralized second primary molars (HSPM) and hypomineralized primary canines (HPC) with molar-incisor hypomineralization (MIH) in 1,963 schoolchildren. METHODS The European Academy of Paediatric Dentistry (EAPD) criterion was used for scoring HSPM/HPC and MIH. Only children with four permanent fir...