The accelerated homotopy perturbation Elzaki transform method (AHPETM), which is based on the homotopy perturbation method (HPM), is used in this article to solve the Burgers equation and system of Burgers equations. AHPETM ...
In modern liquid–liquid contact components, there is an increasing use of droplet population balance models. These components include differential and completely mixed contractors. These models aim to explain the complex ...
The non-linear collision-induced breakage equation has significant applications in particulate processes. Two semi-analytical techniques, namely homotopy analysis method (HAM) and accelerated homotopy perturbation method ...
This article aims to establish a semi-analytical approach based on the homotopy perturbation method (HPM) to find the closed form or approximated solutions for the population balance equations such as Smoluchowski's ...
This work presents a unique semi-analytical approach based on the homotopy analysis method (HAM), called accelerated HAM, recently proposed in (Hussain et al., “Semi-analytical methods for solving non-linear differential ...
This work reviews the semi-analytical technique (SAT) and proposes a unique SAT based on the homotopy analysis method (HAM), called accelerated HAM (AHAM) (recently proposed in Hussain et al. (Hussain S, Arora G, Kumar R. ...
The phenomenon of coagulation and breakage of particles plays a pivotal role in diverse fields. It aids in tracking the development of aerosols and granules in the pharmaceutical sector, coagulation or breakage of droplets ...
The Redner–Ben-Avraham–Kahng (RBK) coagulation model, initially proposed as a discrete framework for investigating cluster growth kinetics, has recently been reformulated to encompass a continuous representation. While the ...
This article introduces a novel semi-analytical solution for the aggregation equation utilizing the Temimi–Ansari Method in conjunction with Pade approximants. The methodology is further adapted to address coupled ...
Let 𝓗0 be the set of rings R such that Nil(R) = Z(R) is a divided prime ideal of R. The concept of maximal non φ-chained subrings is a generalization of maximal non valuation subrings from domains to rings in 𝓗0. This ...
Let R be a commutative ring with identity. The ring R×R can be viewed as an extension of R via the diagonal map Δ:R↪R×R, given by Δ(r)=(r,r) for all r∈R. It is shown that, for any a,b∈R, the extension Δ(R)[(a,b)]⊂R×R is a ...
Let ℋ0 denote the set of all rings R such that Nil(R) is a divided prime ideal with Nil(R)=Z(R). We study the concept of maximal non-λ-rings in class ℋ0 and generalize the results of maximal non-λ-domains.
Let H be the set of all commutative rings R such that Nil(R) is a divided prime ideal
of R and let φ : T (R) → RNil(R) be a ring homomorphism defined as φ(x) = x for
all x ∈ T (R). An overring Ro of an integral domain R ...
Let R be a commutative ring with unity. The notion of almost 𝜙-integrally closed ring is introduced which generalizes the concept of almost integrally closed domain. Let ℋ be the set of all rings such that Nil(𝑅) is a ...
Let H be the set of all commutative rings with unity whose nilradical is a divided prime ideal. The concept of maximal non-nonnil-PIR is introduced to generalize the concept of maximal non-PID. A ring extension R⊂T in H ...
The notion of maximal non-pseudovaluation subring of an integral domain is introduced and studied. Let R ⊂ S be an extension of domains. Then R is called a maximal non-pseudovaluation subring of S if R is not a pseudovaluation ...
Euler's classical identity states that the number of partitions of an integer into odd parts and distinct parts are equinumerous. Franklin gave a generalization by considering partitions with exactly j different multiples ...
In 1984, Bressoud and Subbarao obtained an interesting weighted
partition identity for a generalized divisor function, by means of combinatorial
arguments. Recently, the last three named authors found an
analytic proof ...
In this article, we refine a result of Andrews and Newman, that is, the sum of minimal
excludants over all the partitions of a number n equals the number of partitions of n
into distinct parts with two colors. As a ...
The minimal excludant of an integer partition, first studied prominently by Andrews and Newman from a combinatorial viewpoint, is the smallest positive integer missing from a partition. Several generalizations of this ...