Binary array PAIRs with optimal/ideal correlation values and their algebraic counterparts \DIFFERENCE SET PAIRs" (DSPs) in abelian groups are studied. In addition to generalizing known 1-dimensional (sequences) examples, we provide four new recursive constructions, unifying previously obtained ones. Any further advancements in the construction of binary sequences/arrays with opti-mal/ideal correlation values (equivalently cyclic/abelian DIFFERENCE SETs) would give rise to richer classes of DSPs (and hence binary perfect array PAIRs). Discrete signals arising from DSPs nd applications incryptography, CDMA systems, radar and wireless communications.

In this research, interaction and oblique coalescence of bubbles under buoyancy force was simulated, numerically. The governing equations are continuity and momentum equations which have been discretized using the finite volume method and the SIMPLE algorithm. For simulating the interface of two phases, the level SET method has been incorporated. Level SET method suffers from poor mass conservation of dispersed phase especially in the case of severe deformation of interface. In order to control of mass conservation of the level SET method, re-initialization equations and a geometric mass control loop are used which this loop is implemented in the level SET method for the first time in this research. Using proposed geometric mass control loop, mass dissipation drawback of the level SET method is handled in simulation of bubbles’ coalescence. The results outlined in the present study well agree with the existing experimental results. Also results of investigation of mass dissipation of the proposed scheme to simulation of oblique coalescence problem show that the maximum amount of this mass dissipation was less than 4%. Therefore, the level SET method with proposed geometric mass control loop could be used properly for simulation of oblique interactions and coalescence of bubbles in multiphase flows.

This paper is concerned with the best proximity PAIR problem in Hilbert spaces. Given two subSETs A and B of a Hilbert space H and the SET-valued maps F: A® 2B and G: A0®2A0, where A0= {xÎ A: ||x - y||=d (A, B) for some yÎ B}, best proximity PAIR theorems provide sufficient conditions that ensure the existence of anx0 2 A such thatd(G (x0), F (x0)) =d (A, B).

Background and Objective: The pressure on groundwater resources greatly increased with increase of human activities. Since the aquifers are majority drinking water supply, the correct evaluations of these resources are necessary. Due to the uncertainty of water quality standard ranges, a method that leads to reliable results can be valuable. So in this study, two approaches as EWOV and SPA was proposed in order to groundwater quality assessment using fuzzy concepts and entropy theory. Method: For qualitative evaluation of groundwater resources, two proposed approach are considered. In the EWOV method based on Euclidean distance between each parameter and their standard, the quality ratings of each sample is determined using certain quality ranges. In the SPA method, the samples are evaluated based on fuzzy interval of each parameter. To evaluate the effectiveness of the two approaches, the 21 samples of SARAYAN plain were used. Findings: With implementation of the proposed approachs and extract the results of quality rankings samples can be found that the 42 percentage of the samples in wet period were in the mid-range class using EWOV method. By applying the uncertainty in quality classes, these percentages of monitored samples have acceptable quality level. Samples quality rankings study due to its location in the plains shows the results of SPA are more coordination with natural conditions of the aquifer. The results of the SPA method imply that the parts of the northwest, north and mid-plains are good and have acceptable quality for drinking consumption. Also, 42 and 74 percent of samples are located in quality classification of acceptable and acceptable to moderate in the wet and dry seasons, respectively. Discussion and Conclusion: Comparison of two methods result are indicative the appropriate precision of quality ranking offered by the SPA method and being consistent with the hydrogeological characteristics of the aquifer (such as P11 and P15). So, SPA as a preferred method in quality assessment of groundwater is recommended.

In this article, we consider PAIR frames in Banach spaces and introduce Banach PAIR frames. Some various concepts in the frame theory such as frames, Schauder frames, Banach frames and atomic decompositions are considered as special kinds of (Banach) PAIR frames. Some frame-like inequalities for (Banach) PAIR frames are presented. The elements that participant in the construction of (Banach) PAIR frames are characterized. It is shown that a Banach space X has a Banach PAIR frame with respect to a Banach scalar sequence space `, when it is precisely isomorphic to a complemented subspace of `. It is shown that if we are allowed to choose the scalar sequence space, PAIR frames and Banach PAIR frames with respect to the chosen scalar sequence space denote the same concept.

In this paper we present some properties of SET-norm exhaustive SET multi functions and also of atoms and pseudo-atoms of SET multi functions taking values in the family of non-empty subSETs of a commutative semi group with unity.

In this paper, we consider some classes of DIFFERENCE equations and investigate the asymptotic behavior of solutions by using invariants.

In this paper, we introduce nilpotent and solvable PAIR of polygroups. By a PAIR of polygroups (P, N), we mean a polygroup P with a normal sub-polygroup N of P. In addition, we obtain a necessary and su cient condition between nilpotency (solvability) of PAIR of polygroups and PAIR of groups. In particular, we extend the theory of groups to a PAIR of polygroups. Finally, we study the relationship between nilpotent and solvable PAIR of poly-groups.

This study has considered the problem of finding best proximity PAIR in fuzzy metric spaces and uniformly convex fuzzy Banach spaces for fuzzy cyclic contraction map. We prove the uniqueness of this point in uniformly fuzzy Banach spaces. We also give an algorithm to find a best proximity point for the map S in SETting of a uniformly convex fuzzy Banach spaces.