An (a; b) elementary trapping set (ETS), where a and b denote the size and the number of unsatis ed check nodes in the ETS, in uences the performance of low-density parity-check (LDPC) codes. The smallest size of an ETS in LDPC codes with column weight 3 and girth 6 is 4. In this paper, we concentrate on a well-known algebraic-based construction of girth-6 QC-LDPC codes based on powers of a primitive element in a  nite  eld Fq. For this structure, we provide the su cient conditions to obtain 3 n submatrices of an exponent matrix in constructing girth-6 QC-LDPC codes whose ETSs have the size of at least 5. For structures on  nite  eld Fq, where q is a power of 2, all non-isomorphic 3  n submatrices of the exponent matrix which yield QC-LDPC codes free of small ETSs are presented.

This research analyzes and examines the use of plasmonic tweezers in the field of biotechnology, focusing on an inclined twine-core plasmonic optical fiber tweezer. This tweezer was designed and modeled using COMSOL software and through numerical simulations, it exhibits its capacity to trap polystyrene particles on a nano-scale. The results obtained from the research show that changes in different parameters such as the wavelength used, the radius of the trapped particle, and the refractive index of the medium used, lead to changes in the trapping force. The increase in the refractive index of the environment and the dimensions of the particles causes a significant increase in the applied force, especially in short wavelengths, the problem is more visible. These findings show that the proposed plasmonic structure has a very high trapping force, and this has the ability to significantly improve compared to previous researches. These advances in the field of biotechnology not only allow for more accurate and effective manipulation of nanoscale particles, but also facilitate the creation of new technologies in the field of medicine and other biological sciences. These developments will directly and indirectly help to improve diagnostic and treatment systems.

Gene trapping technique is a powerful method for mutational engineering works on specific genes in cell, which is defined as a kind of in vitro site directed mutagenesisThis method is used for gene knock out or analysis of gene function. Interestingly this approach can be used as therapeutic device for correction of mutated genes. Gene trapping has been staged in three steps: gene cloning, the study of the pattern of gene expression and the analysis of respective mutated phenotype. This method is based on homologous recombination.For detection of homologous recombination, several approaches like RT-PCR; RACE-PCR would be useful. Thus, designing a set of specific primers pairs, for marker gene and insetred gene is essential for such PCR methods.

In this paper we present some properties of set-norm exhaustive set multi functions and also of atoms and pseudo-atoms of set multi functions taking values in the family of non-empty subsets of a commutative semi group with unity.

In this paper we define the Soft set Product as a product of many soft sets and afterwards we extend it to the HyperSoft set. Similarly, the IndetermSoft Product is extended to the IndetermHyperSoft set. We also present several applications of the Soft set Product to Fuzzy (and fuzzy-extensions)  Soft set Product and to IndetermSoft set and IndetermHyperSoft set.

This review paper will serve to explain how a particle is trapped on a porous media, and describe the mobility of those particles when passing through a media. It also presents the different parameters that play an important role on the trapping mechanism and the role of biofilm formation. The deposition and trapping mechanism of particles in porous media is governed by the action of different mechanisms such as interception, sieving, diffusion, gravitational and Van Der Waals forces, Brownian diffusion, and inertia. The particle retention through the porous media leads to the formation of a biofilm and the clogging of the media. The understanding of particle retention, clogging, and biofilm formation is interesting because it plays a major role in soil recovery process such as bioremediation, biosorption and filtration (on sand and activated carbon) used for degradation of particles (colloids and microorganisms) and harmful contaminants (heavy metals, drugs) by microorganisms.

Onchocerciasis, usually referred to as river blindness, a skin and eye parasitic infestation is caused by the filarial nematode Onchocerca volvulus. Current control and eradication efforts are being frustrated by the continued existence and thriving of blackflies which are the disease transmitting vectors that breed along the banks of fast flowing and highly oxygenated rivers and streams. This study aims at assessing the effect of using vector traps on the transmission and control of onchocerciasis. A host-vector deterministic model which incorporates vector trapping by use of a system of ordinary differential equations is developed. The model is analysed for steady states and the basic reproduction number is obtained using the next generation method. It is found that the disease free steady state is stable if the basic reproduction number R0 < 1. There exists a unique endemic equilibrium which is locally and globally asymptotically stable if R0 > 1. Numerical simulations show that trapping the blackfly vectors has an effect on the spread and control of the disease. However, it is discovered that using traps alone is not a sufficient strategy and needs to be combined with other methods if the disease is to be completely wiped out of the population.