Number theorists believe that primes play a central role in Number theory and that solving problems related to primes could lead to the resolution of many other unsolved conjectures, including the prime k-tuples conjecture. This paper aims to demonstrate the existence of this conjecture for admissible k-tuples in a positive proportion. The authors achieved this by refining the methods of “Goldston, Pintz and Yildirim” and “James Maynard” for studying bounded gaps between primes and prime k-tuples. These refinements enabled to overcome the previous limitations and restrictions and to show that for a positive proportion of admissible k-tuples, there is the existence of the prime k-tuples conjecture holding for each “k”. The significance of this result is that it is unconditional which means it is proved without assuming any form of strong conjecture like the Elliott–Halberstam conjecture
The k-out-of-n:G (or k/n:G) system structure is a very popular of redundancy in
fault-tolerant systems, with wide applications in so many fields. This paper presents
two states of multi-state k/n:G systems. The first part, we present the definition that
introduced by Al-Neweihi et al [1], where the values are the same with respect
to all system states and we show that there exists an alternative equivalent definition
to Al-Neweihi's definition. In the second part of this paper we give more general
definition proposed by Huang et al [2], where it allows different values with
respect to different system states and we provide there exists an equivalent definition
to Huang's definition when the values are increasing.
We have studied some types of ideals in a KU-semigroup by using the concept of a bipolar fuzzy set. Bipolar fuzzy S-ideals and bipolar fuzzy k-ideals are introduced, and some properties are investigated. Also, some relations between a bipolar fuzzy k-ideal and k-ideal are discussed. Moreover, a bipolar fuzzy k-ideal under homomorphism and the product of two bipolar fuzzy k-ideals are studied.
Image compression plays an important role in reducing the size and storage of data while increasing the speed of its transmission through the Internet significantly. Image compression is an important research topic for several decades and recently, with the great successes achieved by deep learning in many areas of image processing, especially image compression, and its use is increasing Gradually in the field of image compression. The deep learning neural network has also achieved great success in the field of processing and compressing various images of different sizes. In this paper, we present a structure for image compression based on the use of a Convolutional AutoEncoder (CAE) for deep learning, inspired by the diversity of human eye
... Show MoreThe notion of interval value fuzzy k-ideal of KU-semigroup was studied as a generalization of afuzzy k-ideal of KU-semigroup. Some results of this idea under homomorphism are discussed. Also, we presented some properties about the image (pre-image) for interval~ valued fuzzy~k-ideals of a KU-semigroup. Finally, the~ product of~ interval valued fuzzyk-ideals is established.
This study has applied digital image processing on three-dimensional C.T. images to detect and diagnose kidney diseases. Medical images of different cases of kidney diseases were compared with those of healthy cases. Four different kidneys disorders, such as stones, tumors (cancer), cysts, and renal fibrosis were considered in additional to healthy tissues. This method helps in differentiating between the healthy and diseased kidney tissues. It can detect tumors in its very early stages, before they grow large enough to be seen by the human eye. The method used for segmentation and texture analysis was the k-means with co-occurrence matrix. The k-means separates the healthy classes and the tumor classes, and the affected
... Show MoreIn this paper, a design of the broadband thin metamaterial absorber (MMA) is presented. Compared with the previously reported metamaterial absorbers, the proposed structure provides a wide bandwidth with a compatible overall size. The designed absorber consists of a combination of octagon disk and split octagon resonator to provide a wide bandwidth over the Ku and K bands' frequency range. Cheap FR-4 material is chosen to be a substate of the proposed absorber with 1.6 thicknesses and 6.5×6.5 overall unit cell size. CST Studio Suite was used for the simulation of the proposed absorber. The proposed absorber provides a wide absorption bandwidth of 14.4 GHz over a frequency range of 12.8-27.5 GHz with more than %90 absorp
... Show MoreBackground: Calcaneus is a spongy cancellous bone with rich blood supply , its fracture heals more rapidly providing no occurrence of infection and soft tissue injury around ,no gross malposition of fragments. The associated pain leads to a major impairment in life quality. The aim of treatment for calcaneal fractures is the decrease of pain and rebuilding of walking ability for patients with normal foot shape and the ability to wear normal foot wear. To reduce complications, a minimally invasive technique for the treatment of displaced intra-articular fractures of the calcaneus was preferred to use.
The purpose of this study was to determine whether the closed reduction and percutaneous K. wire fixation of displ
... Show MoreThe purpose of this article is to partition PG(3,11) into orbits. These orbits are studied from the view of caps using the subgroups of PGL(4,11) which are determined by nontrivial positive divisors of the order of PG(3,11). The τ_i-distribution and c_i-distribution are also founded for each cap.
In this work, we construct and classify the projectively distinct (k,3)-arcs in PG(2,9), where k ≥ 5, and prove that the complete (k,3)-arcs do not exist, where 5 ≤ k ≤ 13. We found that the maximum complete (k,3)-arc in PG(2,q) is the (16,3)-arc and the minimum complete (k,3)-arc in PG(2,q) is the (14,3)-arc. Moreover, we found the complete (k,3)-arcs between them.