Natural gas consumption fluctuates due to seasonal demand, extraction limitations, price changes, and political conflicts. These fluctuations necessitate the storage of natural gas. Among various storage methods, salt caverns have several advantages for storing hydrocarbons compared to other methods. These advantages include the low permeability of rock salt and the low cost of construction. However, salt caverns may be affected by Weak layers such as marl or mudstone within the formation’s layering sequence. This research aimed to numerically study the long-term behavior of a salt cavern excavated in interbedded salt rock with Weak interlayers. The effects of placement angle (0°, 30°, 45° and 60°), layer thickness (10, 15 and 20 meters), number of (1 or 2 or 3) and three different levels on operational time were analyzed. FLAC3D finite difference software was selected because of its Cpower creep behavior model. A total of twenty-two numerical models were executed. The results emphasize the importance of level, placement angle, thickness and interlayers numbers on displacement, stability and safety of a salt cavern over its operational time. The Ratigan dilatancy safety factor is not suitable for assessing the effects of geometric parameters of interlayers on salt cavern stability. Generally, constructing a cavern in salt layers containing Weak interlayers is not recommended.

In this paper, we study a generalization of z-ideals in the ring C (X) of continuous real valued functions on a completely regular Hausdorff space X. The notion of a Weak ideal and naturally a Weak z-ideal and a prime Weak ideal are introduced and it turns out that they behave such as z -ideals in C (X).

The first use of the largest class of hyper-structures, the Hv-structures, and their fundamental relations was to define the general hyper-field. Moreover, the enormous number Hv-structures defined on the same set, admits a partial order and has a lot of applications in pure mathematics and other sciences. We present ways to obtain appropriate Hv-fields from given well-known classical rings.

For a Banach algebra A, A00 is (􀀀 1)-Weakly amenable if A0 is a Banach A00-bimodule and H1(A00; A0) = f0g. In this paper we prove some important properties of this notion, for instance if A00 is (􀀀 1)-Weakly amenable then A is essential and there is no non-zero point derivation on A. We also give some examples, namely, the second dual of every C-algebras is (􀀀 1)-Weakly amenable. Finally, we study the relationships between the (􀀀 1)-Weakly amenability of A00 and the Weak amenability of A00 or A.

Let $R$ be an associative ring and let $n$ be a non-negative integer‎. ‎In this paper‎, ‎we consider $n$-super finitely presented‎, ‎Gorenstein $n$-Weak injective and Gorenstein $n$-Weak flat modules under change of rings‎. For‎ ‎an excellent extension‎ $S\geq R$, ‎w‎e show ‎that the Gorenstein $n$-super finitely presented dimensions (resp‎. ‎Weak Gorenstein $n$-super finitely presented dimensions) of rings $R$ and $S$ coincide‎.