Let f and g be a self – maps of a rational exterior space . A natural number m is called a minimal coincidence period of maps f and g if f^m and g^m have a coincidence point which is not coincidence by any earlier iterates. This paper presents a complete description of the set of algebraic coincidence periods for self - maps of a rational exterior space which has rank 2 .

The dynamic thermomechanical properties, sealing ability, and voids formation of an experimental obturation hydroxyapatite-reinforced polyethylene (HA/PE) composite/carrier system were investigated and compared with those of a commercial system [GuttaCore (GC)]. The HA/PE system was specifically designed using a melt-extrusion process. The viscoelastic properties of HA/PE were determined using a dynamic thermomechanical analyser. Human single-rooted teeth were endodontically instrumented and obturated using HA/PE or GC systems, and then sealing ability was assessed using a fluid filtration system. In addition, micro-computed tomography (μCT) was used to quantify apparent voids within the root-canal space. The data were statistically analys

Background: Using dual-energy X-ray absorptiometry, body fat mass has been determined. The assessment of body fat mass was conducted utilizing dual-energy X-ray absorptiometry analysis of the pelvis and vertebral column. While it is acknowledged that osteoporosis can impact both body fat mass and bone mineral density, the particulars of this relationship currently remain uncertain. Objective: The aim of the present investigation is to assess gender differences in the effects of osteoporosis on the body fat mass of the upper and lower extremities. Method: 170 individuals participated (85 males and 85 females) in this study. Patients who presented with bone discomfort consisted of 40 males and 40 females. In addition, 90 apparently he

In this research, the effect of adding two different types of reinforcing particles was investigated, which included: nano-zirconia (nano-ZrO₂) particles and micro-lignin particles that were added with different volume fractions of 0.5%, 1%, 1.5% and 2% on the mechanical properties of polymer composite materials. They were prepared in this research, as a complete prosthesis and partial denture base materials was prepared, by using cold cure poly methyl methacrylate (PMMA) resin matrix. The composite specimens in this research consist of two groups according to the types of reinforced particles, were prepared by using casting methods, type (Hand Lay-Up) method. The first group consists of PMMA resin reinforced by (nano-ZrO

Water covers more than 75% of the earth's surface in the form of the ocean. The ocean investigation is far-fetched because the underwater environment has distinct phenomenal activities. The expansion of human activities inside underwater environments includes environmental monitoring, offshore field exploration, tactical surveillance, scientific data collection, and port security. This led to increased demand for underwater application communication systems. Therefore, the researcher develops many methods for underwater VLC Visible Light Communications. The new technology of blue laser is a type of VLC that has benefits in the application of underwater communications. This research article investigated the benefits of underwater blu

The excellence and uniqueness is what makes the artwork creative or not, and the School of Op. Art in Iraq came to reveal new phenomena distinct style, unique in units built, although a few worked in this aspect of the art, but they left their mark distinct, in the research, construction and installation of what binds them in heritage and civilization, it is a new vision of linking the past with the present, they adopt and engineering units may be architectural sometimes in composition, concluded a researcher at the end of the research to the main findings and conclusions, which is that more business was a square-shaped or semi-square, which is commensurate painting with visual, which is a set of vocabulary or repeat units, we do not fin

In this work, a simple and new method is proposed to simultaneously improve the physical layer security and the transmission performance of the optical orthogonal frequency division multiplexing system, by combining orthogonal frequency division multiplexing technique with chaotic theory principles. In the system, a 2-D chaotic map is employed. The introduced system replaces complex operations such as matrix multiplication with simple operations such as multiplexing and inverting. The system performance in terms of bit error rate (BER) and peak to average ratio (PAPR) is enhanced. The system is simulated using Optisystem15 with a MATLAB2016 and for different constellations. The simulation results showed that the  BE

The convolutional neural networks (CNN) are among the most utilized neural networks in various applications, including deep learning. In recent years, the continuing extension of CNN into increasingly complicated domains has made its training process more difficult. Thus, researchers adopted optimized hybrid algorithms to address this problem. In this work, a novel chaotic black hole algorithm-based approach was created for the training of CNN to optimize its performance via avoidance of entrapment in the local minima. The logistic chaotic map was used to initialize the population instead of using the uniform distribution. The proposed training algorithm was developed based on a specific benchmark problem for optical character recog