In this paper, modified hat functions and improved hat functions are proposed to solve stochastic Ito ̂-Volterra integral equations with multi stochastic terms. A linear system of equations are achieved by replacing the vector and matrix coefficients and operational matrices in the equation which is easy to solve with mathematical softwares. Also, under some conditions the error of these methods are o(h^3) and o(h^4 ) . The accuracy and reliability of these two methods are studied by solving and comparing the answers with block pulse functions and hat functions.

In this article, two numerical approaches are presented to solve a system of three fractional differential equations that express the pollution of lakes.In our recent study, a new class of hat functions, called quasi-hat functions (QHFs), are constructed.The proposed approaches utilize modified hat functions (MHFs) and quasi-hat functions (QHFs).Fractional-order operational of MHFs and QHFs are used to build algorithms that transform the main problem into a system of six equations with six unknowns and three equations with three unknowns, respectively.Absolute errors of obtained approximate solutions and convergence analysis of the utilized approach will be studied.Finally, three examples are provided to illustrate the capabilities of these algorithms.The pollution monitoring results are reported in some tables and figures for different values of $\alpha$.

Automatic detection and tracking of small target in infrared images is the great importance in the modern world. Top-Hat transformation is the important class of nonlinear transformation morphology that has wide usages in the detection and tracking the target in infrared images. The most important problem in improving the efficiency of conversion of Top-Hat transformation, the use of structural elements according to the SNR of each image. Since the images have different clutter and targets, the use of structural elements with fixed shape and dimations for images with different SNR cannot lead to accurate detection. Therefore, to improve the detection, adaptive structural elements should be used. For this purpose, in this paper, we use continuous genetic algorithm to achieve Top-Hat transformation adaptive structural elements, in order to identify more precisely target point. Qualitative and quantitative evaluation results on real images show that the proposed method compared with other methods based on morphology with fixed structural element has a better performance in target detection in infrared image and produce fewer false alarms.

In this paper, using a new method based on the generalized hat functions, we solve a class of fractional delay differential equations in which the fractional derivative is considered in the sense of Caputo. First, we introduce the generalized hat functions and their corresponding operational matrices. Then, in order to solve the considered problem, the existing functions are approximated using the basis functions. By employing the properties of generalized hat functions, the Caputo fractional derivative and the Riemann-Liouville fractional integral, a system of algebraic equations is obtained which by solving it, the unknown coefficients are determined. By substituting the resulting values, an approximation of the solution of the problem is obtained. In addition, the computational complexity of the resulting system is investigated. In continue, an error analysis of the method is given. Finally, the accuracy and efficiency of the proposed method are shown by presenting two examples.

A numerical method to solve nonlinear quadratic integral equations (QIE) is presented in this work. The method is based upon modification of hat functions (MHFs) and their operational matrices. By using this approach and the collocation points, solving the nonlinear QIE reduces to solve a nonlinear system of algebraic equations. The proposed method does not need any integration for obtaining the constant coefficients. Hence, it can be applied in a simple and fast technique. Convergence analysis and associated theorems are considered. Some numerical examples illustrate the accuracy and computational efficiency of the proposed method.

Background & Aim: Phototherapy plays a significant role in the treatment and prevention of hyperbilirubinemia in neonates. However, this treatment modality may itself result in the development of some complications. A lesser-known complication of the phototherapy is hypocalcemia. Some studies reported hypocalcemia accompanied by a decrease in serum melatonin concentration, yet this effect can be prevented by shielding the occiput. The aim of the present study was determining the prevalence of phototherapy-induced hypocalcemia and comparing its incidence between groups of neonates whose heads were covered during phototherapy and a group of neonates who received phototherapy without hat.Patients and Method: In a randomized clinical trial, 120 icteric neonates were evaluated in two groups of 60. All of the subjects were full term and weighed more than 2500 grams. For group A routine phototherapy was done without shielding the head and the second group(B) used hats that covered occipital area. All neonates were completely normal on physical examination. Serum bilirubin and calcium was checked on arrival, 48 hours after starting phototherapy, and 24 hours after discontinuation of the treatment. Group A was considered as the control group. A comparative study was made between these groups to determine the efficacy of hat for prevention of hypocalcemia.Results: 18 neonates (15%) developed hypocalcemia after starting phototherapy. There was a statistically significant difference between the prevalence of hypocalcemia in group A (77.77%) and group B (22.22%)(p=0.000). None of the hypocalcemic neonates was clinically symptomatic. Serum level of calcium returned to normal 24 hours after discontinuation of phototherapy in almost all hypocalcemic neonates.Conclusion: The study showed that covering neonate's head and occipital area during phototherapy decreases phototherapy-induced hypocalcemia.

n this paper, ‎numerical solution of a system of fractional differential equations which is the model of an epidemic disease is considered‎. ‎To this aim‎, ‎first‎, ‎third degree hat functions and their properties are introduced‎. After that‎, ‎using the expansion of the existing functions in the system in terms of the basis functions‎, ‎the system under consideration is transformed to a system of algebraic equations that can be solved using iterative methods‎. Then‎, ‎by solving the problem with a given initial data and comparing the results with the reported real data‎, ‎efficiency of the method is shown‎.

Top-hat monopole antennas loaded with radially layered dielectric are analyzed using the finite-difference time-domain (FDTD) method. Unlike the mode-matching method (MMM) (which was previously used for analyzing these antennas) the FDTD method enables us to study such structures accurately and easily. Using this method, results can be obtained in a wide frequency band by performing only one time-domain simulation. For the FDTD modeling, the type of medium at each grid point is specified by a code. Also an efficient non-uniform meshing scheme and a novel perfectly matched layer (PML) are presented and used. The excitation signal can be chosen in the form of Gaussian pulse (GP) or sine carrier modulated by Gaussian pulse (SCMGP). These enable us to increase the accuracy of simulation and decrease the required memory and CPU time. Simulation results are presented in the form of graphical figures, which display the spatial variations in amplitude and phase of radiated field. Also, the FDTD computed input impedances of several top-hat monopole antennas are compared with those obtained by measurement. The agreement between computed and measured results is quite well.