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A PARTICULAR SOLUTION OF THE TWO AND THREE DIMENSIONAL TRANSIENT DIFFUSION EQUATIONS
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A particular solution of the two and three dimensional unsteady state thermal or mass diffusion equation is obtained by introducing a combination of variables of the form,
η = (x+y) / √ct , and η = (x+y+z) / √ct, for two and three dimensional equations
respectively. And the corresponding solutions are,
θ (t,x,y) = θ0 erfc (x+y)/√8ct and θ( t,x,y,z) =θ0 erfc (x+y+z/√12ct)

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Publication Date
Tue Aug 01 2017
Journal Name
International Journal Of Scientific & Engineering Research
Integrated System of Information hiding by Applying Three levels
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MB Mahmood, BN Dhannoon

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Publication Date
Wed Mar 13 2019
Journal Name
Al-khwarizmi Engineering Journal
Transient Behavior Analysis for Solar Energy Storage in PCM-CFM Material Using Equivalent Heat Capacity Method as Storage Model
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A paraffin wax and copper foam matrix were used as a thermal energy storage material in the double passes air solar chimney (SC) collector to get ventilation effect through daytime and after sunset. Air SC collector was installed in the south wall of an insulated test room and tested with different working angles (30o, 45o and 60o). Different SC types were used; single pass, double passes flat plate collector and double pass thermal energy storage box collector (TESB). A computational model based on the finite volume method for transient tw dimensional domains was carried out to describe the heat transfer and storage in the thermal energy storage material of collector. Also, equivalent specific heat metho

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Publication Date
Fri Jan 31 2020
Journal Name
Indian Journal Of Forensic Medicine & Toxicology
A comparative study to evaluate the effect of ultrasonic agitation on push-out bond strength of three root-end filling materials: An in vitro study
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Aim: To evaluate the effect of ultrasonic agitation for retrograde biodceramic root repair, MTA and biodentine filling materials on push-out bond strength to dentine walls. Materials and Methods: Ninety extracted human teeth with single straight roots were selected randomly. After disinfection and cleaning, the coronal portions were sectioned to standardize the root canal length at 15mm. following root canal shaping, obturation and apical roots resection, retrograde cavities were prepared. Teeth were categorized depending on the filling material used into three groups, 30 teeth each. Group A filled with bioceramic root repair material, B with MTA and C with Biodentine material. These groups were divided in to three subgroup (n= 10). Subgrou

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Publication Date
Sat Jul 01 2023
Journal Name
Heliyon
Effect of plasma surface treatment of three different CAD/CAM materials on the micro shear bond strength with resin cement (A comparative in vitro study)
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Objectives: This study aimed to evaluate and compare the effect of plasma treatment versus conventional treatment on the micro shear bond strength (μSBS), surface roughness, and wettability of three different CAD/CAM materials. Materials and methods: Sixty cylindrical specimens (5 mm diameter ×3 mm height) were prepared from three different CAD/CAM materials: Group A: Zirconia, Group B: Lithium disilicate, and Group C: Resin nano-ceramic. Each group was subdivided into two subgroups according to surface treatment used: Subgroup I: Conventional treatment, zirconia was sandblasted with Al2O3, while lithium disilicate and resin nano-ceramic were etched with hydrofluoric acid. Subgroup II: Plasma treatment, the surface of each material was tr

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Publication Date
Tue Sep 30 2014
Journal Name
Iosr Journal Of Mathematics
Modification Adomian Decomposition Method for solving Seventh OrderIntegro-Differential Equations
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In this paper, a method based on modified adomian decomposition method for solving Seventh order integro-differential equations (MADM). The distinctive feature of the method is that it can be used to find the analytic solution without transformation of boundary value problems. To test the efficiency of the method presented two examples are solved by proposed method.

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Publication Date
Mon Jan 01 2024
Journal Name
Aims Mathematics
Solving quaternion nonsymmetric algebraic Riccati equations through zeroing neural networks
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<abstract><p>Many variations of the algebraic Riccati equation (ARE) have been used to study nonlinear system stability in the control domain in great detail. Taking the quaternion nonsymmetric ARE (QNARE) as a generalized version of ARE, the time-varying QNARE (TQNARE) is introduced. This brings us to the main objective of this work: finding the TQNARE solution. The zeroing neural network (ZNN) technique, which has demonstrated a high degree of effectiveness in handling time-varying problems, is used to do this. Specifically, the TQNARE can be solved using the high order ZNN (HZNN) design, which is a member of the family of ZNN models that correlate to hyperpower iterative techniques. As a result, a novel

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Publication Date
Mon Mar 08 2021
Journal Name
Baghdad Science Journal
using collocation method for solving differential equations with time lag
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in this paper the collocation method will be solve ordinary differential equations of retarted arguments also some examples are presented in order to illustrate this approach

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Publication Date
Mon Mar 08 2021
Journal Name
Baghdad Science Journal
B-splines Algorithms for Solving Fredholm Linear Integro-Differential Equations
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Algorithms using the second order of B -splines [B (x)] and the third order of B -splines [B,3(x)] are derived to solve 1' , 2nd and 3rd linear Fredholm integro-differential equations (F1DEs). These new procedures have all the useful properties of B -spline function and can be used comparatively greater computational ease and efficiency.The results of these algorithms are compared with the cubic spline function.Two numerical examples are given for conciliated the results of this method.

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Publication Date
Sun Dec 01 2024
Journal Name
Baghdad Science Journal
Bernoulli Polynomials Method for Solving Integral Equations with Singular Kernel
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هناك دائما حاجة إلى طريقة فعالة لتوليد حل عددي أكثر دقة للمعادلات التكاملية ذات النواة المفردة أو المفردة الضعيفة لأن الطرق العددية لها محدودة. في هذه الدراسة ، تم حل المعادلات التكاملية ذات النواة المفردة أو المفردة الضعيفة باستخدام طريقة متعددة حدود برنولي. الهدف الرئيسي من هذه الدراسة هو ايجاد حل تقريبي لمثل هذه المشاكل في شكل متعددة الحدود في سلسلة من الخطوات المباشرة. أيضا ، تم افتراض أن مقام النواة

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Publication Date
Sat Jul 20 2024
Journal Name
Journal Of Interdisciplinary Mathematics
Elzaki transform decomposition approach to solve Riccati matrix differential equations
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Elzaki Transform Adomian decomposition technique (ETADM), which an elegant combine, has been employed in this work to solve non-linear Riccati matrix differential equations. Solutions are presented to demonstrate the relevance of the current approach. With the use of figures, the results of the proposed strategy are displayed and evaluated. It is demonstrated that the suggested approach is effective, dependable, and simple to apply to a range of related scientific and technical problems.

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