General Letters in Mathematics

The enumeration of the construction due to "Audu and Aminu"(AUNU) Permutation patterns, of a [ 7 4 2 ]- linear code which is an extended code of the [ 6 4 1 ] code and is in one-one correspondence with the known [ 7 4 3 ] - Hamming code has been reported by the Authors. The [ 7 4 2 ] linear code, so constructed was combined with the known Hamming [ 7 4 3 ] code using the ( u|u+v)-construction method to obtain a new hybrid and more practical single [14 8 3 ] error- correcting code. In this paper, we provide an improvement by obtaining a much more practical and applicable double error correcting code whose extended version is a triple error correcting code, by combining the same codes as in [1]. Our goal is achieved through using the product code construction approach with the aid of some proven theorems.

The linear regression model is often used by researchers and data analysts for predictive, descriptive, and inferential purposes. When working with empirical data, this model is based on a set of assumptions that are not always satisfied. In this situation, using more complicated regression algorithms that do not strictly rely on the same assumptions might be one answer. Nevertheless, transformations provide a simpler technique for improving the validity of model assumptions and allow the user to continue using the well-known model of linear regression. The main objective of this project is to provide a transformation for the linear model’s response and predictor variables, as well as parameter estimation methods before the transformation and after the transformation. The bootstrap approach has been effectively used for many statistical estimates and inference issues, according to the paper.

Covid-19 epidemic continues to escalate globally posing life threats to humans. Time series modeling plays a key role for the prediction of data-driven scenarios. A case for Covid-19 pandemic future numbers occurrence is one of the open forecasting scenario for application of the time series modeling. We applied the Autoregressive Integrated Moving Average (ARIMA) model to forecast the possible numbers of Covid-19 deaths in the Republic of South Africa using the previously reported data for a period of 17 months (May 2020 to September 2021). We adapted the Box-Jenkins’ methodology to step-by-step achieve the entire forecasting process. We identified the MA(1) (ARIMA(0,0,1)) as the best model based on the Akaike Information Criterion and the Bayesian Information Criterion. The forecasting done at 95% confidence interval for a period of 7 months (October 1, 2021 to April 31, 2022) indicated that the Covid-19 associated deaths in South Africa would slightly increase during the month of October 2021 but remain constant throughout the entire prediction period.

In this work , we investigate the Aboodh transformation method to solve first order constant coefficients complex equations. This method provides an effective and efficient way of solving a wide range of linear operator equations.

In this paper, A new accurate solutions are obtained for classes of singular two-point boundary value problems (BVPs) using a new solution procedure based on the construction of the auxiliary functions of the standard optimal homotopy asymptotic method (OHAM). This procedure give us accurate approximate solutions using only one order of approximation compared with the solutions obtained previously by the standard OHAM approximation of three order. The obtained numerical results which are displayed in tables and plotted graphically in figures leads to concluded that this procedure is efficient and of third order reliable for finding the solutions of singular two BVPs.

In this paper, we used a hybrid method based on wavelet transforms and ARIMA models and applied on the time series annual data of rain precipitation in the Province of Erbil-Iraq in millimeters. A sample size has been taken during the period 1970 - 2014.We intended to obtain the ability to explain how the hybrid method can be useful when making a forecast of time series and how the quality of forecasting can be enhanced through applying it on actual data and comparing the classical ARIMA method and our suggested method depending on some statistical criteria. Results of the study proved an advantage of the statistical hybrid method and showed that the forecast error could be reduced when applying Wavelet-ARIMA technique and this helps to give the enhancement of forecasting of the classical model. In addition, it was found that out of wavelet families, Daubechies wavelet of order two using fixed form thresholding with soft function is very suitable when de-noising the data and performed better than the others. The annual rainfall in Erbil in the coming years will be close to 370 millimeters

This paper aimed at modeling and forecasting wholesale prices of maize in Tanzania using Autoregressive Integrated Moving average model for data from February 2004 to August 2017 obtained from the Bank of Tanzania. Maize crop growers lack fundamental knowledge on which periods do prices of their harvests rise up. The empirical study found 𝐀𝐑𝐈𝐌𝐀 (𝟑,𝟏,𝟏) as the best model for maize wholesale price based on minimum Akaike`s Information Criterion (AIC) and the fitted model was found to be adequate using Ljung-Box test. The forecasted prices show an increase from September 2017 to January 2018 and then to June 2018 with the maximum price in June 2018 for the forecasted horizon. The forecasted prices decrease up to January 2019 and increase thereafter.

In this paper, we present a spectral method for solving the heat equation in cylindrical coordinates in a case where the data are axisymmetric and independent of the z-coordinate at the same time. The spectral method considered is of GalerkintypewithaGauss-Radaunumericalquadratureformula, itisbasedonaweightedweakvariationalformulationofthe continuous problem. The method considered is discret only in r-variable, the time variable remains continuous. Consequently, the discret problem leads to a system of ordinary differential equations, we solve the system and estimate the error, we also give some numerical examples.

In this paper, a new 7th order continuous finite difference methods is proposed. These methods are derived using the Chebyshev polynomials as basis functions. The collocation approach is employed to obtain the main methods and additional methods used for solving general nonlinear fourth order two and four-points boundary value problems. Several numerical examples are shown to illustrate the strength of the method. To show the robustness of this method for high accuracy, we applied the method of line to discretize PDEs into system of fourth order ODEs and thus use the derived method to obtain approximate solution for the PDEs. The approximate solution obtained using the proposed methods is compared to the exact solutions of the problem, and other methods from existing literature. The Convergence of these methods is also guaranteed.

In this paper, we study the relation between subspace-hypercyclicity and the direct sum of two operators. In particular, we show that if the direct sum of two operators is subspace-hypercyclic, then both operators are subspace-hypercyclic; however, the converse is true for a stronger property than subspace-hypercyclicity. Moreover, we prove that if an operator T satisfies subspace-hypercyclic criterion, then T ⊕T is subspace-hypercyclic. However, we show that the converse is true under certain conditions.©2019 All rights reserved.

bstract In this paper, Modified Variational Iteration Method (MVIM) and Homotopy Analysis Method (HAM) are used to find approximate solutions for the Variable-Coefficient Variant Boussinesq System the (VCVB) system is able to describe the nonlinear and dispersive long gravity waves in shallow water traveling in two horizontal directions with varying depth, as an example we took the Boussinesq-Burgers (B-B) system, (B-B) system arise in the study of fluid flow and describing the long-wave propagation of shallow water waves. The solutions of these equations helpful for the coastal and civil engineering’s

In this paper, Modified Variational Iteration Method (MVIM) and Homotopy Analysis Method (HAM) are used to find approximate solutions for the Variable-Coefficient Variant Boussinesq System the (VCVB) system is able to describe the nonlinear and dispersive long gravity waves in shallow water traveling in two horizontal directions with varying depth, as an example we took the Boussinesq-Burgers (B-B) system, (B-B) system arise in the study of fluid flow and describing the long-wave propagation of shallow water waves. The solutions of these equations helpful for the coastal and civil engineering’s

المستخلص: يمعب النقل البحري دو ا رً هاماً وبار ا زً في الحياة الاقتصادية ويعتبر نشاطاً مهم اً من خلال مساهمته بتقديم خدمات النقل بالنسبة لاستي ا رد وتصدير مختمف أنواع السمع المتجانسة وغير المتجانسة باستخدام وسائل نقل بحرية متنوعة, حيث تم بناء أنموذج رياضي خاص بمشكمة النقل البحري ثلاثي الابعاد متعدد الاهداف المعدل والذي اخذ بالاعتبار بعض المؤش ا رت والمتغي ا رت الخاصة بالنقل البحري لنقل السمع غير المتجانسة وحمه بالط ا رئق الاستدلالية والكلاسيكية المعدلة, ولتحقيق هدف البحث تم تقسيمه الى خمسة فصول, تضمن الفصل الأول المقدمة وأهم الد ا رسات السابقة التي تناولت الموضوع, والفصل الثاني لاستع ا رض بعض الأساسيات الخاصة بنماذج النقل وأسموب البرمجة الخطية, أما الفصل الثالث فتضمن أنموذج النقل البحري ثلاثي الأبعاد متعدد الأهداف المعدل, حيث تم تقديم ثلاث ط ا رئق استدلالية لحل الأنموذج مع خوارزمياتها المقترحة وهي )طريقة المدى (RM) , طريقة الوسط الحسابي (AM) , طريقة ميل الكمف (CSM) ( ومقارنة نتائجها مع الط ا رئق الكلاسيكية المعدلة, وخصص الفصل ال ا ربع للإطار العممي بجانبيه التجريبي لمتحقق من الط ا رئق المقترحة من خلال استخدام برنامج (Matlab) لتوليد البيانات بأسموب المحاكاة ولأحجام العينات)الصغيرة, المتوسطة, الكبيرة(, اولجانب العممي طبق عمى بيانات الشركة العامة لتجارة المواد الغذائية, أما الفصل الخامس فتضمن أهم النتائج والتوصيات التي تم التوصل اليها, ويتضح من خلال الد ا رسات السابقة أن النماذج الثلاثية لمنقل البحري تم استع ا رضها نظرياً فقط من قبل الباحثين ولم تطبق عممياً عمى أرض الواقع, أضافة الى عدم تضمينها أهداف متعددة ومؤش ا رت ومتغي ا رت جديدة, ومن هذا المنطمق فأن ما يميز بحثنا هذا هو بناء أنموذج نقل بحري ثلاثي الأبعاد متعدد الأهداف, يكون الهدف الأول منه تقميل تكاليف النقل الاجمالية, أما الهدف الثاني تقميل الوقت الاجمالي لمنقل, كما وتضمن الأنموذج متغي ا رت ومؤش ا رت جديدة لنقل السمع غير المتجانسة من مصادرها المختمفة الى الوجهات الطالبة لها, اوستخدام معايير خاصة بالأوقات الاجمالية لعممية النقل النشطة لمسمع المختمفة, اوستخدم البحث الخوارزميات الكلاسيكية المعدلة والخوارزميات الاستدلالية )الاستكشافية( المقترحة التي اعتمدت عمى بعض المقاييس الاحصائية والمتمثمة ب )مقاييس النزعة المركزية ومقاييس التشتت(, وركز البحث عمى اختبار امثمية الط ا رئق الاستدلالية المقترحة فيما إذا كانت تعطي نتائج مثمى مقارنة مع الط ا رئق الكلاسيكية المعدلة المستخدمة في حل أنموذج النقل البحري ثلاثي الأبعاد المعدل من ناحية تخفيض التكاليف والأوقات الاجمالية لنقل السمع غير المتجانسة, ومن خلال الب رنامج المعد لحل الانموذج, تم الت وصل الى نتائج الط ا رئق الكلاسيكية المعدلة والط ا رئق الاستدلالية وخوارزمياتها المقترحة المستخدمة في أنموذج النقل البحري, وتم استخدام طريقة التوزيع المعدل والانح ا رفات المئوية كطرق لأمثمية الحل, وعميه تبين إن طريقة المدى (RM) الاستدلالية أعطت أفضل نتائج مثمى من ناحية تقميمها لمتكاليف والأوقات الاجمالية معاً, مقارنةً بنتائج جميع الط ا رئق المستخدمة, وحقق أنموذج النقل البحري انخفاضاً ممحوظاً في التكاليف والأوقات الإجمالية لنقل السمع السكر وزيت الطعام بواسطة وسيمة النقل السفينة مقارنة بالتكاليف والأوقات - - الإجمالية الخاصة بالآلية المعتمدة من قبل الشركة العامة لتجارة المواد الغذائية الع ا رقية )اب ا رم العقود(, فقد شهد انخفاضاً في تكاليف النقل الإجمالية بمقدار ($451,587,378)], $124,236,863( ( , 843,133,282( ($ [($364,711,052), لسنوات الد ا رسة عمى التوالي, أما بالنسبة لأوقات النقل الإجمالية فقد شهدت انخفاض اً بمقدار [(986h),(110h),(926h),(529h)] ساعة ذلك عند سرعة السفينة 61 عقدة, اما بالنسبة لسرعة السفينة ذات ال 02 عقدة فقد شهدت أوقات النقل الإجمالية انخفاضاً بمقدار [(2163h),(1229h),(1912h),(1794h)] ساعة لسنوات الد ا رسة عمى التوالي, وبناءً عمى ما جاء من نتائج البحث يوصى باستخدام واعتماد انموذج النقل البحري ثلاثي الابعاد المعدل واستخدام الخوارزميات الاستدلالية المقترحة لنقل السمع غير المتجانسة من مصادرها الى الوجهات الطالبة لها وباستخدام البرنامج الذي اعد لذلك الغرض في حالة قيام الشركات التجارية باستي ا رد كميات كبيرة من السمع المختمفة.

The objective of this research paper is to follow up on the work already started in order to install a new mathematical analysis, the one we called Cartesian analysis see our previous works[1],[2]. During these last two papers, we started with the definition of cartesian geometry and we defined and introduced to a new Cartesian topology which gave birth to new spaces called Saidou spaces. Thus, and to follow up on this way, we propose to studie the analytical and functional part of this analysis. We will define the notion of a Cartesian function and then its epigraph before to characterize the analytical properties of these functions, for example the continuity and the differentiablity. In an other hand, we will see the relationship between cartesian functions and the convex functions. According to the latest papers and this work we do the asset of the first foundations of the cartesian analysis.

In this work, we propose to define a new space that will be called locally Cartesian space (Saidou’Spaces). It is a space defined by a new topology whose fundamental system of neighborhood are compact cartesian subsets, theses subsets were already defined during our previous work, “Geometrical introduction to Cartesian geometry in complex shapes see [15]. It will have the same properties of a Banach space. Then, we will give the steps of a cartesianization method of complex shapes or region in this space. The objective sought by this technique is to find a cartesian form (denoted Car(A)), that approximates any form A, see Figure1 below. It should be noted that cartesianization will be a generalization of the polygonization whish remains the object of research for several researchers in the spaces R2 Ref [12] [13] [6].

Using a variant fountain theorem, we prove the existence of infinitely many homoclinic solutions of a class of fourth-order differential equations u ⁽ 4 ⁾ (x)+ωu ⁰⁰ (x)+a(x)u(x) = f(x,u(x)), ∀x ∈ R, where a ∈C(R,R) may be negative on a bounded interval and F(x,u) = R0u f(x,t)dt is superquadratic at infinity in the second variable but does not need to satisfy the known Ambrosetti-Rabinowitz superquadratic growth condition.

In this paper, we obtain all the symmetric semi-classical linear functionals of class four taking into account the irreducible expression of the corresponding Pearson equation. We focus our attention on their integral representations. Thus, some linear functionals very well known in the literature, associated with perturbations of semi-classical linear functionals of class two at most, appear as well as new linear functionals which have not been studied.

Recently, new types of (open) sets have been studied by some topologists. This note shows that these sets are identical to some other sets already exist in the literature.

T.K. Kwak and Y. Lee called a ring R satisfy the commutativity of nilpotent elements at zero[1] if ab = 0 for a, b ∈ N(R) implies ba = 0. For simplicity, a ring R is called CNZ if it satisfies the commutativity of nilpotent elements at zero. In this paper we study an extension of a CNZ ring with its endomorphism. An endomorphism α of a ring R is called strong right ( resp., left) CNZ if whenever aα(b) = 0(resp., α(a)b = 0 ) for a, b ∈ N(R) ba = 0. A ring R is called strong right (resp., left) α-CNZ if there exists a strong right (resp., left) CNZ endomorphism α of R, and the ring R is called strong α- CNZ if R is both strong left and right α- CNZ. Characterization of strong α- CNZ rings and their related properties including extensions are investigated . In particular, it’s shown that a ring R is reduced if and only if U2(R) is a CNZ ring. Furthermore extensions of strong α- CNZ rings are studied.

In this article, we defined a new coefficient formula of the conjugate gradient method for solving non linear unconstrained optimization problems. The new formula β new k is type of line search and the idea of our work is to focus on modification the Perry’s suggestion. We further show that global convergence result of new formula is recognized under Wolf-Powell line search. It is shown that the new CG coefficient satisfied sufficient descent conditions. In the end, numerical experiments with the collection of test functions show that the new β new k is more effective compared to some other standard formulas such as β H−S k , β Perry k and β D−Y k .

In this work, we examine the impact of magnetic fields on the moving particle trajectories by variational approach to the magnetic flow associated with the Killing magnetic field on 2−dimensional lightlike cone Q2 ⊂ E3 1. We give some characterizations for x−magnetic curve and x−magnetic surface of rotation using the Killing magnetic field of this curve in Q2 and we give the different types of axes of rotation, then creates three different types of magnetic surfaces of rotation in 2−dimensional lightlike cone Q2 ⊂ E3 1.

In this paper, we define a new concept in theory of graph energy called coneighbor energy of a graph G, denoted by CE(G), as the sum of the absolute value of eigenvalues of its coneighbor matrix. We are going to derive some results about the coneighbor energy of graphs and coneighboracation graph that possess some coneighbor vertices.