In this paper, Interval Legendre wavelet method is investigated to approximated the solution of the Interval Volterra-Fredholm-Hammerstein integral equation. The shifted Interval Legendre polynomials are introduced and based on Interval Legendre wavelet method is de ned. The existence and uniqueness theorem for the Interval Volterra-Fredholm-Hammerstein integral equations is proved. Some examples show the e ectiveness and e ciency of the approach.

We consider Interval linear programming (ILP) problems in the current paper. Best-worst case (BWC) is one of the methods for solving ILP models. BWC determines the values of the target function, but some of the solutions obtained through BWC may result in an infeasible space. To guarantee that solution is completely feasible (i.e. avoid constraints violation), improved twostep method (ITSM) has been proposed. Many solutions are lost in this method. By using an algorithm, we introduce closed ball method (namely, CBM) as a new method for solving ILP models. In this method, feasibility test ensures that solution space is feasible. To demonstrate the effectiveness of the proposed approach, we solve two numeric examples and we compare the results obtained through BWC, ITSM, and CBM.

In this article, multi-objective linear programming problems with Interval coefficients in objective functions are investigated. By using the acceptance index, the concepts of different answers corresponding to such problems are presented. In order to achieve such answers, a new solution method is introduced. Characteristics of the answer/answersobtained from the new solution method are also expressed. For example, the unique optimal solution resulting from thenew solution method is a strict A-efficient solution of the multi-objective linear programming problem with Interval coefficients in the objective functions. In order to better understand the presented concepts and solution method, numerical examples are also examined.

This work studies Interval Initial Value Problems (IIVPs), where the derivative is given by the generalized Hukuhara derivative ($gH$-derivative) and the initial condition is given by an Interval. The focus of the paper is to provide the numerical approximations for the solutions associated with the $gH$-derivative of IIVPs. This article considers the Euler numerical method, where the classical arithmetic operation is adapted for Intervals. The arithmetic considered here is obtained using sup-$J$ extension principle, where $J$ is a particular family of joint possibility distributions. This family gives raise to different types of interactivity and this work shows what kind of interactivity is necessary in the numerical method, in order to approximate the solution via $gH$-derivative. To illustrate the results, the paper focuses in the decay Malthusian model.

Background: Cold crystalloid cardioplegic solution is used for cardiac arrest and myocardial protection during CABG intermittently. There is no defined safety Interval time for cardioplegia infusion. Measuremen of the metabolite release from myocardial cells in coronary sinus implicateis accurate protective effect and safety Interval of cardioplegia. There is no study that surveys the metabolites of coronary sinus during CABG.Materials and Methods: 13 patients that was scaduled for elective CABG cold crystalloid cardioplegia transfused via aortic root. Coronary sinus blood samples were taken in different times, before and after cross clamping of the aorta at the times of 7, 14 and 20 minutes. The samples were analyzed for pH and lactate immediately.Results: The pH and lactae concentration in coronary sinus at the time of 15 minute after transfusion of the first dose (pH=7.18±0.043 lactate=30±3.983 r=0.02) and 10 minute after the second dose of antegrade cold crystalloid cardioplegia (pH=7.19±0.045 lactate=28±3.438 r=0.03) were out of the range of acceptable level.Conclusion: This study indicates that safe Interval time between the first and second dose of cold crystalloid cardioplegia transfusion was 15 minute and the between second and third dose was 10 minutes.

This paper deals with linear programming problem with Interval numbers as coefficients to exhibit with uncertainty. Since, the set of common Intervals is not a field, we define generalized Interval numbers to produce an algebraic Interval field and on this field, we propose principle of uncertainty traverse instead of extension principle which permits to define operators on Intervals exactly similar to the same operators on real numbers. In addition, we apply a total order on this field to transform Interval linear programming into a traditional problem. The proposed order can be extended either pessimistically or optimistically. The numerical experiments are given to demonstrate the efficiency of the proposed scheme in comparison with the previous established works. The approach in this paper can be generalized to fuzzy linear programming problems taking the fuzzy cuts into account.

In this paper an coupled Burgers' equation is considered and then a method entitled Interval finite-difference method is introduced to find the approximate Interval solution of Interval model in level wise cases. Finally for more illustration, the convergence theorem is confirmed and a numerical example is solved.

Background: During CABG cardioplefic solution is used for cardiac arrest and myocardial protection but there is no defined safety Interval time for cardioplegia infusion. Measuremen of the metabolite release from myocardial cells in coronary sinus implicateis accurate protective effect and safety Interval of cardioplegia Materials and Methods: Thirteen patients that were scaduled for CABG cold blood cardioplegia transfused via aortic root. Coronary sinus blood samples were taken before and after cross clamping of the aorta at the times of 7, 14 and 20 minutes. The samples were analyzed for pH and lactate immediately.Results: The pH and lactate concentration in coronary at the time of 15 minute after the second dose of transfusion of blood cardioplegia were out of the range of acceptable level (pH=7.22±0.047 lactate=21±2.859mg/dl r=0.02).Conclusion: This study indicates that safe Interval time between the first and second dose of cardioplegia transfusion was 20 minute and the between second and third dose was 15 minutes.

In this paper, Bernoulli wavelets are presented for solving (approximately) fractional differential equations in a large Interval. Bernoulli wavelets operational matrix of fractional order integration is derived and utilized to reduce the fractional differential equations to system of algebraic equations. Numerical examples are carried out for various types of problems, including fractional Van der Pol and Bagley-Torvik equations for the application of the method. Illustrative examples are presented to demonstrate the efficiency and accuracy of the proposed method.