On unitary analogs of GCD reciprocal LCM matrices

A divisor d ∈ ?₊ of n ∈ ?₊ is said to be a unitary divisor of n if (d, n/d) = 1. In this article we examine the greatest common unitary divisor (GCUD) reciprocal least common unitary multiple (LCUM) matrices. At first we concentrate on the difficulty of the non-existence of the LCUM and we present three different ways to overcome this difficulty. After that we calculate the determinant of the three GCUD reciprocal LCUM matrices with respect to certain types of functions arising from the LCUM problematics. We also analyse these classes of functions, which may be referred to as unitary analogs of the class of semimultiplicative functions, and find their connections to rational arithmetical functions. Our study shows that it does make a difference how to extend the concept of LCUM.     

An analogue of Ramanujan’s sum with respect to regular integers (modr)

An integer a is said to be regular (modr) if there exists an integer x such that a ² x≡a (mod r). In this paper we introduce an analogue of Ramanujan’s sum with respect to regular integers (modr) and show that this analogue possesses properties similar to those of the usual Ramanujan’s sum.     

Ultrasonically aided mineral processing technique for remediation of soil contaminated by heavy metals

In this study, power ultrasound was used as aiding method for the mineral processing technique, which have recently been developed for the remediation of soil contaminated by heavy metal containing bullets, their broken parts and alteration products. Power ultrasound was used to disperse the soil to remove metals and metal compounds from soil particle surfaces instead of attrition conditioning. The soil diluted with water was treated using 22 kHz ultrasound power of 100 W up to 500 W. The effect of different ultrasonic treatment time and pulsation of ultrasound were studied on the purity of sink and float fractions in heavy medium separation process, screen fractions, and mineral concentrates and tailings from flotation process. Ultrasound enhanced the remediation of soil fractions in all the studied cases. Optimisation of the ultrasonic power will be done in the continuation study.     

Determination of Stoichiometric Dissociation Constants of Benzoic Acid in Aqueous Sodium or Potassium Chloride Solutions at 25°C

Equations were determined for the calculation of the stoichiometric (molality scale) dissociation constant K_m of benzoic acid in dilute aqueous NaCl and KCl solutions at 25°C from the thermodynamic dissociation constant K_a of this acid and from the ionic strength I_m of the solution. The salt alone determines mostly the ionic strength of the solutions considered in this study and the equations for K_m were based on the single-ion activity coefficient equations of the Hückel type. The existing literature data obtained by conductance measurements and by electromotive force (EMF) measurements on Harned cells were first used to revise the thermodynamic value of the dissociation constant of benzoic acid. A value of K_a = (6.326 ± 0.005) × 10^-5 was obtained from the most precise conductivity set [Brockman and Kilpatrick] and this value is supported within their precisions by the less precise conductivity set of Dippy and Williams and by the EMF data set measured by Jones and Parton with quinhydrone electrodes. The new data measured by potentiometric titrations in a glass electrode cell were then used for the estimation of the parameters of the Hückel equations of benzoate ions. The resulting parameters were also tested with the existing literature data measured by cells with and without a liquid junction. The Hückel parameters suggested here are close to those determined previously for anions resulting from aromatic and aliphatic carboxylic acids. By means of the calculation method based on the Hückel equations, K_m can be obtained almost within experimental error at least up to I_m of about 0.5 mol-kg_-1 for benzoic acid in NaCl and KCl solutions.     

The Quality of Statistical Reporting and Data Presentation in Predatory Dental Journals Was Lower Than in Non-Predatory Journals

Proper peer review and quality of published articles are often regarded as signs of reliable scientific journals. The aim of this study was to compare whether the quality of statistical reporting and data presentation differs among articles published in ‘predatory dental journals’ and in other dental journals. We evaluated 50 articles published in ‘predatory open access (OA) journals’ and 100 clinical trials published in legitimate dental journals between 2019 and 2020. The quality of statistical reporting and data presentation of each paper was assessed on a scale from 0 (poor) to 10 (high). The mean (SD) quality score of the statistical reporting and data presentation was 2.5 (1.4) for the predatory OA journals, 4.8 (1.8) for the legitimate OA journals, and 5.6 (1.8) for the more visible dental journals. The mean values differed significantly (p < 0.001). The quality of statistical reporting of clinical studies published in predatory journals was found to be lower than in open access and highly cited journals. This difference in quality is a wake-up call to consume study results critically. Poor statistical reporting indicates wider general lower quality in publications where the authors and journals are less likely to be critiqued by peer review.