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In this paper, we discussed a new subclass J Q ⅁ , A B (q) of bi-univalent functions in the unit disk U using q-generalized Janowski function and q-derivative. Additionally, certain properties were examined and effectively demonstrated, such as the second Hankel determinant, Fekete–Szegö estimates, and Coefficients Bounds. Each of these bounds were precise and were confirmed by finding the extremal function for the new class. Furthermore, there are in-depth conversations available regarding certain intriguing specific cases of the outcomes achieved. [ABSTRACT FROM AUTHOR]

In this research, we combine ideas from geometric function theory and fuzzy set theory. We define a new operator D τ − λ L α , ζ m : A → A of analytic functions in the open unit disc Δ with the help of the Riemann–Liouville fractional integral operator, the linear combination of the Noor integral operator, and the generalized Sălăgean differential operator. Further, we use this newly defined operator D τ − λ L α , ζ m together with a fuzzy set, and we next define a new class of analytic functions denoted by R ϝ ζ (m , α , δ). Several innovative results are found using the concept of fuzzy differential subordination for the functions belonging to this newly defined class, R ϝ ζ (m , α , δ). The study includes examples that demonstrate the application of the fundamental theorems and corollaries. [ABSTRACT FROM AUTHOR]

In this paper, we find values of depth, Stanley depth, and projective dimension of the quotient rings of the edge ideals associated with r-fold bristled graphs of ladder graphs, circular ladder graphs, some king's graphs, and circular king's graphs. [ABSTRACT FROM AUTHOR]

In this study, we investigate a possible relationship between fuzzy differential subordination and the theory of geometric functions. First, using the Al-Oboudi differential operator and the Babalola convolution operator, we establish the new operator BS α , λ m , t : A n → A n in the open unit disc U. The second step is to develop fuzzy differential subordination for the operator BS α , λ m , t . By considering linear transformations of the operator BS α , λ m , t , we define a new fuzzy class of analytic functions in U which we denote by T ϝ λ , t (m , α , δ) . Several innovative results are found using the concept of fuzzy differential subordination and the operator BS α , λ m , t for the function f in the class T ϝ λ , t (m , α , δ) . In addition, we explore a number of examples and corollaries to illustrate the implications of our key findings. Finally, we highlight several established results to demonstrate the connections between our work and existing studies. [ABSTRACT FROM AUTHOR]

In this paper, we apply the pseudospectral method based on the Chebyshev cardinal function to solve the parabolic partial integro-differential equations (PIDEs). Since these equations play a key role in mathematics, physics, and engineering, finding an appropriate solution is important. We use an efficient method to solve PIDEs, especially for the integral part. Unlike when using Chebyshev functions, when using Chebyshev cardinal functions it is no longer necessary to integrate to find expansion coefficients of a given function. This reduces the computation. The convergence analysis is investigated and some numerical examples guarantee our theoretical results. We compare the presented method with others. The results confirm the efficiency and accuracy of the method. [ABSTRACT FROM AUTHOR]