The goal of this research is to introduce the concepts of Large-coessential submodule and Large-coclosed submodule, for which some properties are also considered. Let M  be an R-module and K, N are submodules of M such that , then K is said to be Large-coessential submodule, if . A submodule N of M is called Large-coclosed submodule, if K is Large-coessential submodule of N in M, for some submodule K of N, implies that  .

The goal of this research is to introduce the concepts of Large-coessential submodule and Large-coclosed submodule, for which some properties are also considered. Let M  be an R-module and K, N are submodules of M such that , then K is said to be Large-coessential submodule, if . A submodule N of M is called Large-coclosed submodule, if K is Large-coessential submodule of N in M, for some submodule K of N, implies that  .

      In this paper, we introduce the concepts of Large-lifting and Large-supplemented modules as a generalization of lifting and supplemented modules.  We also give some results and properties of this new kind of modules.

      In this paper, we introduce the concepts of Large-lifting and Large-supplemented modules as a generalization of lifting and supplemented modules.  We also give some results and properties of this new kind of modules.

A coin has two sides. Steganography although conceals the existence of a message but is not completely secure. It is not meant to supersede cryptography but to supplement it. The main goal of this method is to minimize the number of LSBs that are changed when substituting them with the bits of characters in the secret message. This will lead to decrease the distortion (noise) that is occurred in the pixels of the stego-image and as a result increase the immunity of the stego-image against the visual attack. The experiment shows that the proposed method gives good enhancement to the steganoraphy technique and there is no difference between the cover-image and the stego-image that can be seen by the human vision system (HVS), so this method c

In thisipaper, we introduce the concepts of the modified tupledicoincidence points and the  mixed finiteimonotone property. Also the existenceiand uniquenessiof modified tupled coincidenceipoint is discusses without continuous condition for mappings having imixed finite monotoneiproperty in generalizedimetric spaces.

A procedure for the mutual derivatization and determination of thymol and Dapsone was developed and validated in this study. Dapsone was used as the derivatizing agent for the determination of thymol, and thymol was used as the derivatizing agent for the determination of Dapsone. An optimization study was performed for the derivatization reaction; i.e., the diazonium coupling reaction. Linear regression calibration plots for thymol and Dapsone in the direct reaction were constructed at 460 nm, within the concentration range of 0.3-7 μg ml-1 for thymol and 0.3-4 μg ml-1 for Dapsone, with limits of detection 0.086 and 0.053 μg ml-1, respectively. Corresponding plots for the cloud point extraction of thymol and Dapsone were constructed