R. Vasuki [1] proved fixed point theorems for expansive mappings in Menger spaces. R. Gujetiya and et al [2] presented an extension of the main result of Vasuki, for four expansive mappings in Menger space. In this article, an important lemma is given to prove that the iteration sequence is Cauchy under suitable condition in Menger probabilistic G-metric space (shortly, MPGM-space). And then, used to obtain three common fixed point theorems for expansive type mappings.

Performance of gas-solid spouted bed benefit from solids uniformity structure (UI).Therefore, the focus of this work is to maximize UI across the bed based on process variables. Hence, UI is to be considered as the objective of the optimization process .Three selected process variables are affecting the objective function. These decision variables are: gas velocity, particle density and particle diameter. Steady-state solids concentration measurements were carried out in a narrow 3-inch cylindrical spouted bed made of Plexiglas that used 60° conical shape base. Radial concentration of particles (glass and steel beads) at various bed heights and different flow patterns were measured using sophisticated optical probes. Stochastic Genetic

      In this paper, we  introduce new concepts that relates to soft space based on   work that was previously presented by researchers in this regard. First we give  the definition of Soft Contraction Operator and some examples. After that we introduce the concepts of soft Picard iteration and soft Mann iteration processes. We also give  some examples to illustrate them.

    Many concepts in normed spaces have been generalized in soft normed spaces. One of the important concepts is the concept of stability of soft iteration in soft normed spaces. We discuss this concept by giving some lemmas that  are  used to prove some theorems about stability of soft i

Treatment of a high strength acidic industrial wastewater was attempted by activated carbon
adsorption to evaluate the feasibility of yielding effluents of reusable qualities. The experimental
methods which were employed in this investigation included batch and column studies. The
former was used to evaluate the rate and equilibrium of carbon adsorption, while the latter was
used to determine treatment efficiencies and performance characteristics. Fixed bed and expanded
bed adsorbers were constructed in the column studies. In this study, the adsorption behavior of acetic acid onto activated carbon was examined as a function of the concentration of the adsorbate, contact time and adsorbent dosage. The adsorption data was mo

In the present study the performance of drying process of dffirent solid materials by batch fluidized bed drying
under vacuum conditions was investigated. Three, different solid materials, namely; ion exchange resin-8528,
aspirin and paracetamol were used. The behavior of the drying curves as well as the rate of drying of these
materials had been studied. The experiments were caried out in a 0.0381 m column diameter fluidized by hot
air under yacuum conditions. Four variables affecting on the rate of drying were studied' these variables are
vacuum pressure (100 - 500 mm Hg), air temperature (303-323 K), particle size (0.3-0.8 mm) and initial
moisture content (0.35-0.55 g/g solid)-for resin and (0.1-0.2 g/g soltid) for a

A stochastic process {Xk, k = 1, 2, ...} is a doubly geometric stochastic process if there exists the ratio (a > 0) and the positive function (h(k) > 0), so that {α 1 h-k }; k ak X k = 1, 2, ... is a generalization of a geometric stochastic process. This process is stochastically monotone and can be used to model a point process with multiple trends. In this paper, we use nonparametric methods to investigate statistical inference for doubly geometric stochastic processes. A graphical technique for determining whether a process is in agreement with a doubly geometric stochastic process is proposed. Further, we can estimate the parameters a, b, μ and σ2 of the doubly geometric stochastic process by using the least squares estimate for Xk a

The  present study  deals  with successive  stages  of  productive

operations happened to produce a production within each stage befo re it  moves to the next one. ll cou ld  be deduced that this study is an extension  to what bas  been mentioned  in (1 ) .ln  (I),  the  optimum distribution of  di!Terent jobs of  workers and  machines  in  the productive operations has been st ud ied whi le the study  invol ves the optimum schedule for the succession of these operations presuming that thay have already been distributed on machines and workers (2).A mathematical form has been put for this study to define the "Object.ive Function "

Let Y be a"uniformly convex n-Banach space, M be a nonempty closed convex subset of Y, and S:M→M be adnonexpansive mapping. The purpose of this paper is to study some properties of uniform convex set that help us to develop iteration techniques for1approximationjof"fixed point of nonlinear mapping by using the Mann iteration processes in n-Banachlspace.