Krawtchouk polynomials (KPs) and their moments are promising techniques for applications of information theory, coding theory, and signal processing. This is due to the special capabilities of KPs in feature extraction and classification processes. The main challenge in existing KPs recurrence algorithms is that of numerical errors, which occur during the computation of the coefficients in large polynomial sizes, particularly when the KP parameter (p) values deviate away from 0.5 to 0 and 1. To this end, this paper proposes a new recurrence relation in order to compute the coefficients of KPs in high orders. In particular, this paper discusses the development of a new algorithm and presents a new mathematical model for computing the initial value of the KP parameter. In addition, a new diagonal recurrence relation is introduced and used in the proposed algorithm. The diagonal recurrence algorithm was derived from the existing n direction and x direction recurrence algorithms. The diagonal and existing recurrence algorithms were subsequently exploited to compute the KP coefficients. First, the KP coefficients were computed for one partition after dividing the KP plane into four. To compute the KP coefficients in the other partitions, the symmetry relations were exploited. The performance evaluation of the proposed recurrence algorithm was determined through different comparisons which were carried out in state-of-the-art works in terms of reconstruction error, polynomial size, and computation cost. The obtained results indicate that the proposed algorithm is reliable and computes lesser coefficients when compared to the existing algorithms across wide ranges of parameter values of p and polynomial sizes N. The results also show that the improvement ratio of the computed coefficients ranges from 18.64% to 81.55% in comparison to the existing algorithms. Besides this, the proposed algorithm can generate polynomials of an order ∼8.5 times larger than those generated using state-of-the-art algorithms.
In this article, the solvability of some proposal types of the multi-fractional integro-partial differential system has been discussed in details by using the concept of abstract Cauchy problem and certain semigroup operators and some necessary and sufficient conditions.
Background: Surface treatment of machined dental zirconia for enhancement of the adhesion to resin cement, using Er,Cr:YSGG Laser. Materials and Methods: Total number of 42 zirconia disc specimens (9 mm diameter, and 2 mm height) was sintered according to the manufacturer instruction. They are divided into six groups, each group of seven samples. Laser groups (Experiment parameters) were depend on laser total irradiation time, pulse duration, and power. Group (A): 20 sec., 60 µs pulse duration. Group (B): 30 sec., 60 µs pulse duration. Group (C): 40 sec., 60 µs pulse duration. Group (D): 20 sec., 700 µs pulse duration. Group (E): 30 sec., 700 µs pulse duration, with different powers used (1, 1
... Show MoreCopula modeling is widely used in modern statistics. The boundary bias problem is one of the problems faced when estimating by nonparametric methods, as kernel estimators are the most common in nonparametric estimation. In this paper, the copula density function was estimated using the probit transformation nonparametric method in order to get rid of the boundary bias problem that the kernel estimators suffer from. Using simulation for three nonparametric methods to estimate the copula density function and we proposed a new method that is better than the rest of the methods by five types of copulas with different sample sizes and different levels of correlation between the copula variables and the different parameters for the function. The
... Show MoreThe flow in a manifolds considered as an advanced problem in hydraulic engineering applications. The objectives of this study are to determine; the uniformity qn/q1 (ratio of the discharge at last outlet, qn to the discharge at first outlet, q1) and total head losses of the flow along straight and rectangular loop manifolds with different flow conditions. The straight pipes were with 18 m and 19 m long and with of 25.4 mm (1.0 in) in diameter each. While, the rectangular close loop configuration was with length of 19 m and with diameter of 25.4 mm (1.0 in) also. Constant head in the supply tank was used and the head is 2.10 m. It is found that outlets spacing and manifold configuration are the main factors aff
... Show MoreThe present study aims at assessing the status of heavy metals such as nickel, cadmium and lead to pollute some areas of Baghdad city. In this study the spectral absorption device and the program ArcGIS 10.2 will using. The soil samples were taken from five different locations in Baghdad, including Ameriya, Kadhimiya, Palestine Street, Jadiriyah and Taji for the 5cm depth layer on both sides of the road. This work on soil samples has been completed in two :phases 1 - Preparation of samples: For the purpose of converting solid material into a extract containing elements in the form of single ions can be estimated by the device 2-Determination of elements: Samples prepared to the device
Information systems and data exchange between government institutions are growing rapidly around the world, and with it, the threats to information within government departments are growing. In recent years, research into the development and construction of secure information systems in government institutions seems to be very effective. Based on information system principles, this study proposes a model for providing and evaluating security for all of the departments of government institutions. The requirements of any information system begin with the organization's surroundings and objectives. Most prior techniques did not take into account the organizational component on which the information system runs, despite the relevance of
... Show MoreLasers, with their unique characteristics in terms of excellent beam quality, especially directionality and coherency, make them the solution that is key for many processes that require high precision. Lasers have good susceptibility to integrate with automated systems, which provides high flexibility to reach difficult zones. In addition, as a processing tool, a laser can be considered as a contact-free tool of precise tip that became attractive for high precision machining at the micro and nanoscales for different materials. All of the above advantages may be not enough unless the laser technician/engineer has enough knowledge about the mechanism of interaction between the laser light with the processed material. Several sequential phenom
... Show MoreThe textbook is the primary means of creativity and thinking, which has a major role in the development of the readership and mental abilities of the student. It is the basic tool in education in Iraq for the teacher and the student, which cannot be dispensed in any educational program. The current study aimed at the book of the biology of the sixth grade of science in Iraq (comparative study). It was compared to the book of biology for the twelve grade in the Kingdom of Jordan to identify the ratio of similarity and differences between them, in addition, to identify the weaknesses in the Iraq curriculum and developing appropriate solutions and suggestions to address them. The sample was represented with books of biology (six-science cla
... Show MoreIn this study, chemical oxidation was employed for the synthesis of polypyrrole (PPy) nanofiber. Furthermore, PPy has been subjected to treatment using nanoparticles of neodymium oxide (Nd2O3), which were produced and added in a certain ratio. The inquiry centered on the structural characteristics of the blend of polypyrrole and neodymium oxide after their combination. The investigation utilises X-ray diffraction (XRD), FTIR, and Field Emission Scanning Electron Microscopy (FE-SEM) for PPy, 10%, 30%, and 50% by volume of Nd2O3. According to the electrochemical tests, it has been noted that the nanocomposites exhibit a substantial amount of pseudocapacitive activity.