It was known that every left (?,?) -derivation is a Jordan left (?,?) – derivation on ?-prime rings but the converse need not be true. In this paper we give conditions to the converse to be true.

     In this paper, we study a new concept of fuzzy sub-module, called  fuzzy socle semi-prime sub-module that is a generalization the concept of semi-prime fuzzy sub-module and fuzzy of approximately semi-prime sub-module in the ordinary sense.  This leads us to introduce level property which studies the relation between the ordinary and fuzzy sense of approximately semi-prime sub-module. Also, some of its characteristics and notions such as the intersection, image and external direct sum of fuzzy socle semi-prime sub-modules are introduced. Furthermore, the relation between the fuzzy socle semi-prime sub-module and other types of fuzzy sub-module presented.

The biggest problem of structural materials for fusion reactor is the damage caused by the fusion product neutrons to the structural material. If this problem is overcomed, an important milestone will be left behind in fusion energy. One of the important problems of the structural material is that nuclei forming the structural material interacting with fusion neutrons are transmuted to stable or radioactive nuclei via (n, x) (x; alpha, proton, gamma etc.) reactions. In particular, the concentration of helium gas in the structural material increases through deuteron- tritium (D-T) and (n, α) reactions, and this increase significantly changes the microstructure and the properties of the structural materials. T

nouns , because deriving these names will lead to eternity which is impossible, and restrict the derivation only in agent nouns from their verbs, and the adjective names from their adjectives with the condition of truth in derivation.
The derivation of “Allah” names was denied due to a creed thoughts, because saying that “Allah” names is derived will not describe the eternal essence of “Allah”, and if it were derived this will make “Allah” is a Compound from his essence and Attributes.
The Al-Zaher people had recant the derivation of the agent nouns by preventing the derivation of “Allah” names because it will make “Allah” is a Compound from his essence and Attributes.
The Al-Zaher people had recant from

EDIRKTO, an Implicit Type Runge-Kutta  Method of Diagonally Embedded pairs, is a novel approach presented in the paper that may be used to solve 4th-order ordinary differential equations of the form . There are two pairs of EDIRKTO, with three stages each: EDIRKTO4(3) and EDIRKTO5(4). The derivation techniques of the method indicate that the higher-order pair is more accurate, while the lower-order pair provides superior error estimates. Next, using these pairs as a basis, we developed variable step codes and applied them to a series of -order ODE problems. The numerical outcomes demonstrated how much more effective their approach is in reducing the quantity of function evaluations needed to resolve fourth-order ODE issues.

In this paper we introduce G-Rad-lifting module as aproper generalization of lifting module, some properties of this type of modules are investigated. We prove that if M is G-Rad- lifting and
, then
, and
are G-Rad- lifting, hence we Conclude the direct summand of G-Rad- lifting is also G-Rad- lifting. Also we prove that if M is a duo module with
and
are G- Rad- lifting then M is G-Rad- lifting.

Let R be any ring with identity, and let M be a unitary left R-module. A submodule K of M is called generalized coessential submodule of N in M, if Rad( ). A module M is called generalized hollow-lifting module, if every submodule N of M with is a hollow module, has a generalized coessential submodule of N in M that is a direct summand of M. In this paper, we study some properties of this type of modules.

It is often needed to have circuits that can display the decimal representation of a binary number and specifically in this paper on a 7-segment display. In this paper a circuit that can display the decimal equivalent of an n-bit binary number is designed and it’s behavior is described using Verilog Hardware Descriptive Language (HDL). This HDL program is then used to configure an FPGA to implement the designed circuit.

Suppose R has been an identity-preserving commutative ring, and suppose V has been a legitimate submodule of R-module W. A submodule V has been J-Prime Occasionally as well as occasionally based on what’s needed, it has been acceptable: x ∈ V + J(W) according to some of that r ∈ R, x ∈ W and J(W) an interpretation of the Jacobson radical of W, which x ∈ V or r ∈ [V: W] = {s ∈ R; sW ⊆ V}. To that end, we investigate the notion of J-Prime submodules and characterize some of the attributes of has been classification of submodules.