Let R be a commutative ring with identity 1 and M be a unitary left R-module. A submodule N of an R-module M is said to be approximately pure submodule of an R-module, if for each ideal I of R. The main purpose of this paper is to study the properties of the following concepts: approximately pure essentialsubmodules, approximately pure closedsubmodules and relative approximately pure complement submodules. We prove that: when an R-module M is an approximately purely extending modules and N be Ap-puresubmodulein M, if M has the Ap-pure intersection property then N is Ap purely extending.

Local food samples investigated for the presence of pathogenic bacteria. Hash meat sample was used to isolate Escherichia coli and chicken meat (poultry) was used to isolate Salmonella typhi. Biochemical tests and API20E system used in order to identify these isolates. Two natural vinegar samples (dates & apple cider) were used in order to study its antibacterial activity against the two tested bacteria. Disc diffusion method was used, the results showed that two vinegar samples have antibacterial activity against the two tested bacteria. Date vinegar showed inhibition zone 19mm against E. coli & 9mm against S. typhi, while Apple cider vinegar showed diameter of inhibi

A numerical study of the double-diffusive laminar natural convection in a right triangular solar collector has been investigated in present work. The base (absorber) and glass cover of the collector are isothermal and isoconcentration surfaces, while the vertical wall is considered adiabatic and impermeable. Both aiding and opposing buoyancy forces have been studied. Governing equations in vorticity-stream function form are discretized via finite-difference method and are solved numerically by iterative successive under relaxation (SUR) technique. Computer code for MATLAB software has been developed and written to solve mathematical model. Results in the form of streamlines, isotherms, isoconcentration, average Nusselt, and average Sherw

Two- dimensional numerical simulations are carried out to study the elements of observing a Dirac point source and a Dirac binary system. The essential features of this simulation are demonstrated in terms of the point spread function and the modulation transfer function. Two mathematical equations have been extracted to present, firstly the relationship between the radius of optical telescope and the distance between the central frequency and cut-off frequency of the optical telescope, secondly the relationship between the radius of the optical telescope and the average frequency components of the modulation transfer function.

    Soft clays are generally sediments deposited by rivers, seas, or lakes. These soils are fine-grained plastic soils with appreciable clay content and are characterized by high compressibility and low shear strength. To deal with soft soil problems there is more than one method that can be used such as soil replacement, preloading, stone column, sand drains, lime stabilization and Prefabricated Vertical Drains, PVDs. A numerical modeling of PVD with vacuum pressure was analyzed to investigate the effect of this technique on the consolidation behavior of fully and different depths of partially saturated soft soils.  Laboratory experiments were also conducted by using a specially-designed large consol

Image steganography is undoubtedly significant in the field of secure multimedia communication. The undetectability and high payload capacity are two of the important characteristics of any form of steganography. In this paper, the level of image security is improved by combining the steganography and cryptography techniques in order to produce the secured image. The proposed method depends on using LSBs as an indicator for hiding encrypted bits in dual tree complex wavelet coefficient DT-CWT. The cover image is divided into non overlapping blocks of size (3*3). After that, a Key is produced by extracting the center pixel (pc) from each block to encrypt each character in the secret text. The cover image is converted using DT-CWT, then the p

 In the present work a theoretical analysis depending on the new higher order . element in shear deformation theory for simply supported cross-ply laminated plate is developed. The new displacement field of the middle surface expanded as a combination of exponential and trigonometric function of thickness coordinate with the transverse displacement taken to be constant through the thickness. The governing equations are derived using Hamilton’s principle and solved using Navier solution method to obtain the deflection and stresses under uniform sinusoidal load. The effect of many design parameters such as number of laminates, aspect ratio and thickness ratio on static behavior of the laminated composite plate has been studied. The

The present work describes numerical and experimental investigation of the heat transfer characteristics in a plate-fin, having built-in piezoelectric actuator mounted on the base plate (substrate). The geometrical configuration considered in the present work is representative of a single element of the plate-fin and triple fins. Air is taken as the working fluid. A performance data for a single rectangular fin and triple fins are provided for different frequency levels (5, 30 and
50HZ) , different input power (5,10,20,30,40 and 50W) and different inlet velocity (0.5, 1, 2, 3, 4, 5 and 6m/s) for the single rectangular fin and triple fins with and without oscillation. The investigation was also performed with different geometrical fin