In this paper, we first study $fs$-modules, i.e., modules with finitely many small submodules. We show that every $fs$-module with finite hollow dimension is Noetherian. Also, we prove that an $R$-module $M$ with finite Goldie dimension, is an $fs$-module if, and only if, $M = M_1 \oplus M_2$, where $M_1$ is semisimple and $M_2$ is an $fs$-module with $Soc(M_2) \ll M$. Then, we investigate multiplication $fs$-modules over commutative rings and we prove that the lattices of $R$-submodules of $M$ and $S$-submodules of $M$ are coincide, where $S=End_R(M)$. Consequently, $M_R$ and $_SM$ have the same Krull (Noetherian, Goldie and hollow) dimension. Further, we prove that for any self-generator multiplication module $M$, to be an $fs$-module as a right $R$-module and as a left $S$-module are equivalent.

The impact of persistent organic pollutant (POP) concentration in ambient air on vegetation and soil is investigated in the present study. Ambient air, vegetation, and soil samples were collected from the vicinity of an industrial complex. For each collected sample, the polychlorinated dibenzo-p-dioxins/dibenzofurans (PCDD/Fs), coplanar polychlorinated biphenyls (coplanar PCBs), brominated dibenzo-p-dioxins/dibenzofurans (PBDD/Fs), and polybrominated diphenyl ethers (PBDEs) concentrations were analyzed. Principal component analysis (PCA) was adopted to explore the relationships between the concentration of each POP type in ambient air with those in soil and vegetation. Results show that particle-phase PCDD/Fs, PBDD/Fs, and PBDEs, respectively, account for 60.6, 98.3, and 75.7% of the total concentration in the air, which are much higher than that of coplanar PCB (5.2%). Results obtained by PCA suggest that PCDD/Fs in vegetation are contributed by atmospheric gas-phase PCDD/Fs, whereas in soil they are contributed by particle-phase PCDD/Fs. Coplanar PCBs concentrations in both vegetation and soil are contributed by atmospheric gas-phase coplanar PCBs. PBDD/Fs concentrations are both contributed by particle phase. PBDEs in vegetation are contributed by both gas- and particle-phase PBDEs, while soil PBDEs are contributed mainly by the particle phase. In confirmation of these results, the researchers found that the above results are consistent with those obtained from theoretical calculations and previous studies. Therefore, it is concluded that the results obtained from the present study would provide useful information for assessing the fate of ambient air POP concentration.

n this work, 17-polychlorinated dibenzo-p-dioxin/furan (PCDD/Fs) isomers were measured in ambient air at four urban sites in Seoul, Korea (from February to June 2009). The concentrations of their summed values (åPCDD/Fs) across all four sites ranged from 1,947 (271 WHO05 TEQ) (Jong Ro) to 2,600 (349 WHO05 TEQ) fg/m3 (Yang Jae) with a mean of 2,125 (±317) fg/m3 (292 WHO05 TEQ fg/m3). The sum values for the two isomer groups of åPCDD and åPCDF were 527 (30 WHO05 TEQ) and 1,598 (263 WHO05 TEQ) fg/m3, respectively. The concentration profile of individual species was dominated by the 2, 3, 4, 7, 8-PeCDF isomer, which contributed approximately 36 % of the åPCDD/Fs value. The observed temporal trends in PCDD/F concentrations were characterized by relative enhancement in the winter and spring. The relative contribution of different sources, when assessed by principal component analysis, is explained by the dominance of vehicular emissions along with coal (or gas) burning as the key source of ambient PCDD/Fs in the residential areas studied.

An electrochemical sensor was developed by decorating a newly synthesized iron oxide magnetite nanoparticle capped silica dioxide (Fe3O4@SiO2 microspheres) on the surface of carbon paste electrode. The developed sensor was further used in the electrochemical determination of Rutin (Vitamin P). Cyclic and differential pulse voltammetric methods were carried out to study the kinetic parameters and the quantitative determination of Rutin respectively. Phosphate buffer solution (0. 1 M) with pH 7. 5 was used as supporting electrolyte in the present investigation. Various parameters like effect of pH, effect of concentration and effect of scan rate were studied in a systematic manner. A set of cyclic voltammogram redox peaks of Rutin was appeared at 397. 2 mV (Epa) and 367. 8 mV (Epc). The anodic peak currents were linearly increased with increase in the concentration of Rutin with a dynamic range of 1. 6×10− 6-1. 6×10− 5 M. The detection limit was calculated and found to be 1. 43×10− 6 M. Electrochemical parameters viz., number of electrons transferred (n), electrode reaction rate constant (ks), and the charge transfer coefficient (α ), were calculated and found to be 2. 0, 0. 00149 and 1. 09 respectively. Further the developed novel electrochemical sensor was successfully applied for the determination of real samples analysis. The results concluded that the Fe3O4@SiO2 modified carbon paste electrode (FS-MCPE) has showed the long lasting stability, high sensitivity and low detection limits, towards the determination of Rutin.

A square is a concatenation of two identical words, and a word $w$ is said to have a square $yy$ if $w$ can be written as $xyyz$ for some words $x$ and $z$. It is known that the ratio of the number of distinct squares in a word to its length is less than two, and any location of a word could begin with two distinct squares which are appearing in the word for the last time. A square whose first location starts with the last occurrence of two distinct squares is an FS-double square. We explore and identify the conditions under which a sequence of locations in a word starts with FS-double squares. We first find the structure of a word that begins with two consecutive FS-double squares and obtain its properties that enable us to extend the sequence of FS-double squares. It is proved that the length of the longest sequence of consecutive FS-double squares in a word of length $n$ is at most $\frac{n}{7}$. We show that the squares in the longest sequence of consecutive FS-double squares are conjugates.

Background: Febrile seizures (FS) are common in young children. Viral infections that result in high fever are frequent etiologic agents that lead to febrile seizures. Human Herpesvirus 6 (HHV6), Influenza virus, adenovirus, and enterovirus have been named as the most common viruses causing high fevers in young children. Although bacterial infections have rarely been found as causative agents, many children with febrile seizures are treated with empiric antibiotics. Objectives: To determine the epidemiology of the viral (HHV6, Adenovirus, HSV1, Enterovirus) and bacterial infection in children presenting with febrile seizures. Methods: In a descriptive study, data was collected from 93 children, 3 months to 5 years of age, hospitalized with febrile seizures between September 2016 and April 2017. Relevant information was documented on a previously designed questionnaire. Blood samples were collected for culture, Serum 16S rRNA for bacteria, and PCR assay for 4 viruses (HHV6, adenovirus, enterovirus and HSV), in addition to routine investigations. Results: Of the 93 patients, serum PCR results were negative for 73 patients (78. 49%) and 15 (16. 13%) were positive for viruses (11 for HHV6 and 4 for Adenovirus). Serum 16S rRNA for bacteria was detected in 5 cases and blood culture was positive in 4 cases. Conclusions: Findings of this study indicate a significant prevalence of viruses and a very low rate of bacterial infection in children with febrile seizures, thus, negating the use of empirical antibiotic therapy.