This paper derives a solution for the settling velocity of isolated coplanar aggregates of n identical spherical particles in creeping motion based on the Wall Shear-Pressure Gradient-Expansion model (WPE) previously derived by the author. The solution is reached by developing geometry-equilibrium mathematical constructs to decide on the dimensions of the free ambient expansions surrounding the aggregates to compute the entire velocity profile. A rational to decide on the orientation and stability of rotation is also proposed. The results compare well with the outcome of available theory and some relevant data sets.

Polishing is considered as the last and most important step in the manufacturing of optical components. Computer control polishing (CCP) methods are usually used to polish complex surfaces. In this method, material removal is controlled at each point, depending on error at that point. In contact polishing mechanism, tool feed rate is often controlled to eliminate local errors. It means that the higher the tool feed rate, the lower the material removal would be and vice versa. Tool influence function (TIF), which is defined as the instantaneous material removal under the polishing tool for a given tool motion, is the most important parameter in CCP and its predictability during the polishing process leads to reliable result. In this study, a new spherical tool which can polish complex surfaces by using a 3-axis CNC machine is presented. Because of spherical geometry of both tool and work piece, tool, material removal rate is variable because of changing the angle between tool axis and surface normal vector which leads to variation of relative speed. Tool influence function which depends on tool engagement’s angle was modeled based on Preston equation. Moreover, the simulation is modeled based on discretization of tool path. To evaluate the methodology, some polishing experimental tests were performed. The experimental results show that a 130 mm spherical convex lens with initial surface roughness of 1.114 micrometer for PV was decreased to 395 nm for PV using the CCP method developed in this study.

In this research article, new fuzzy K-algebras, namely, spherical fuzzy K-algebras and (∈ , ∈ ∨ q)-spherical fuzzy K-algebras are constructed. Certain properties of these spherical fuzzy K-structures are investigated. The behavior of spherical fuzzy K-algebras under homomorphism is characterized. The spherical fuzzy K-algebra with thresholds is also delineated.

Recycled concrete aggregates are one of the types of recycled aggregates that have the most abundance compared to other recycled aggregates. In this research, by using the replacement of recycled concrete aggregates instead of natural aggregates, the mechanical properties of this type of concrete have been investigated. The replacement of natural aggregates with recycled aggregates was done in four percentages of 0, 15, 30 and 45, and this replacement was done both independently (i.e. sand or gravel separately) and simultaneously (both sand and gravel together). According to the use of 50% sand and 50% sand in the reference mixing plan and by replacing the percentages with coarse and fine recycled concrete aggregates, 21 mixing plans were used. The ratio of water to cement was kept constant in all mixing plans and was considered equal to 0.42. To compensate for the decrease in strength due to the replacement of recycled aggregates, micro silica in different percentages of 7.5 and 15 and super plasticizers were used in the mixing designs. By performing various tests, the mechanical properties of concrete samples were investigated. The results showed that the best mixing design in terms of compressive strength is the design containing 7.5% micro silica and 15% recycled sand, in terms of tensile strength, the design containing 7.5% micro silica and 45% recycled sand, in terms of flexural strength, the design containing 7.5% micro silica and 30% recycled sand, the plan containing 15% micro silica and 15% recycled sand was determined. By examining the mechanical properties of concrete samples, it was determined that the recycled mixing plans contain 15%, 30% recycled gravel and 45% recycled sand with 7.5% microsilica, as well as the mixing plan of 15% recycled sand with 15% microsilica. , among the recycled mixing plans, they had the highest amount of overall utility.

Theory and experiment of a spherical probe-fed conformal antenna with a parasitic element mounted on a spherical multilayer structure are presented in this paper. Rigorous mathematical Method of Moments (MoMs) for analyzing various radiating spherical structures is presented in this paper by using Dyadic Green's Functions (DGFs) in conjunction with Mixed Potential Integral Equation (MPIE) formulation. Linear Rao-Wilton-Glisson (RWG) triangular basis functions are applied in MPIE formulation. Current distributions on coaxial probe and conformal radiating elements are computed by using spatial domain Dyadic Green's Function (DGF) and its asymptotic approximation. A prototype of such an antenna is fabricated and tested. The effect of the parasitic element on the input impedance and radiation patterns of the antenna is investigated. It is shown that the antenna characteristics are improved significantly with the presence of the conducting parasitic element. Good agreement is achieved between the results obtained from the proposed methods and the measurement results.

A spherical fuzzy set is an advanced extension of classical fuzzy set in which it has an added advantage to deal with a wider sense of applicability in uncertain situations. In this paper, regular spherical fuzzy graphs and totally regular spherical fuzzy graphs are introduced. A necessary and sufficient condition for regular spherical fuzzy graphs is given. Some properties of regular and totally regular spherical fuzzy graphs are studied.

The objective of this research is to investigate the influence of aggregate properties (material, shape, and surface texture) on the mechanical properties of concrete (compressive strength) and the interfaces between cement and aggregates. Different types of aggregates were used in concrete production, sourced from various geological regions within the province of Tehran. Selected samples include marl limestone, dolomite, tuff, and quartzite. The initial properties of the selected aggregates were studied, followed by crushing the rock specimens using the Los Angeles apparatus. The characteristics of aggregates, such as surface texture, shape, petrography, and particle size distribution, were determined. Concrete mixtures were prepared with a constant ratio of water to cement (0.55) for each type of angular and rounded aggregates to study the microscopic and compressive strength properties of concrete samples at ages of 28, 14, 7, and 90 days. Microscopic examinations revealed the presence of a transition zone in the matrix, demonstrating a uniform thickness in concrete samples with limestone aggregates compared to variable thickness in the case of tuff aggregates. The results also indicate that limestone aggregates, with suitable porosity and establishing a reaction with cement, create a stronger bond compared to other aggregates. The comparison of compressive strength results shows that concrete made with angular aggregates generally exhibits higher resistance compared to crushed aggregates of the same type. In general, aggregates suitable for use in concrete, including lightweight aggregates with low water absorption capabilities and angular shapes, tend to have higher short-term strength.