• Kyungpook Mathematical Journal
• /
• v.55 no.3
• /
• pp.653-666
• /
• 2015

With the notion of weighted sharing of values we study the uniqueness of meromorphic functions when certain nonlinear differential polynomials share a nonzero polynomial. Our results improve some recent results including that of a present first author.

• The Pure and Applied Mathematics
• /
• v.29 no.1
• /
• pp.37-50
• /
• 2022

The purpose of the paper is to study the uniqueness problems of certain type of difference polynomials sharing a small function. With the concept of weakly weighted sharing and relaxed weighted sharing we obtain some results which extend and generalize some results due to P. Sahoo and G. Biswas [Tamkang Journal of Mathematics, 49(2)(2018), 85-97].

• The KIPS Transactions:PartA
• /
• v.10A no.3
• /
• pp.215-224
• /
• 2003

Since there are various networks and heterogeneity of nodes in Internet, the existing load-sharing algorithms are hardly adapted for use in Internet-based clustering systems. Therefore, in Internet-based clustering systems, a load-sharing algorithm must consider various conditions such as heterogeneity of nodes, characteristics of a network and imbalance of load, and so on. This paper has proposed an expanded-WF algorithm which is based on a WF (Weighted Factoring) algorithm for load-sharing in Internet-based clustering systems. The proposed algorithm uses an adaptive granularity strategy for load-sharing and duplicate execution of partial job for fault-tolerance. For the simulation, the to matrix multiplication using PVM is performed on the heterogeneous clustering environment which consists of two different networks. Compared to other algorithms such as Send, GSS and Weighted Factoring, the proposed algorithm results in an improvement of performance by 55%, 63% and 20%, respectively. Also, this paper shows that It can process the fault-tolerance.

• Journal of the Korean Mathematical Society
• /
• v.47 no.3
• /
• pp.467-482
• /
• 2010

We prove a uniqueness theorem for meromorphic functions sharing three weighted values which improves some existing results.

• Kyungpook Mathematical Journal
• /
• v.51 no.1
• /
• pp.43-58
• /
• 2011

Using the notion of weighted sharing of values we study the uniqueness of meromorphic functions when certain non-linear differential polynomials share the same 1-points. Though the main concern of the paper is to improve a result of Fang [5] but as a consequence of the main result we improve and supplement some former results of Lahiri-Sarkar [16], Fang-Fang[6] et. al.

• Communications of the Korean Mathematical Society
• /
• v.36 no.4
• /
• pp.729-741
• /
• 2021

We mainly study the value distributions of L-functions in the extended selberg class. Concerning weighted sharing, we prove an uniqueness theorem when certain differential monomial of a meromorphic function share a polynomial with certain differential monomial of an L-function which improve and generalize some recent results due to Liu, Li and Yi [11], Hao and Chen [3] and Mandal and Datta [12].

• Journal of Korea Multimedia Society
• /
• v.7 no.2
• /
• pp.264-271
• /
• 2004

A load-sharing algorithm must deal with load imbalance caused by characteristics of a network and heterogeneity of nodes in Internet-based clustering systems. This paper has proposed the Efficient Load-Sharing algorithm. Efficient-Load-Sharing algorithm creates a scheduler based on the WF(Weighted Factoring) algorithm and then allocates tasks by an adaptive granularity strategy and the refined fixed granularity algorithm for better performance. In this paper, adaptive granularity strategy is that master node allocates tasks of relatively slower node to faster node and refined fixed granularity algorithm is to overlap between the time spent by slave nodes on computation and the time spent for network communication. For the simulation, the matrix multiplication using PVM is performed on the heterogeneous clustering environment which consists of two different networks. Compared to other algorithms such as Send, GSS and Weighted Factoring, the proposed algorithm results in an improvement of performance by 75%, 79% and 17%, respectively.

• Communications of the Korean Mathematical Society
• /
• v.36 no.3
• /
• pp.515-526
• /
• 2021

The paper has been devoted to study the uniqueness problem of meromorphic function and its linear differential polynomial sharing two values. We have pointed out gaps in one of the theorem due to [1]. We have further extended the corrected form of Chen-Li-Li's result which in turn extend the an earlier result of [8] in a large extent. In fact, we have subtly use the notion of weighted sharing of values in this particular section of literature which was unexplored till now. A handful number of examples have been provided by us pertinent to different discussions. Specially we have given an example to show that one condition in a theorem can not be dropped.

• Kyungpook Mathematical Journal
• /
• v.49 no.1
• /
• pp.15-29
• /
• 2009

Dealing with a question of gross, we prove some uniqueness theorems concerning meromorphic functions with the notion of weighted sharing of sets. Our results will not only improve and supplement respectively two results of Lahiri-Banerjee [9] and Qiu and Fang [13] but also improve a very recent result of the present author [1].

• Kyungpook Mathematical Journal
• /
• v.51 no.2
• /
• pp.195-204
• /
• 2011

We prove a uniqueness theorem for meromorphic functions sharing three weighted values, which improves a result given by N. Terglane in 1989 and a result given by X. M. Li and H. X. Yi in 2003. Some examples are provided to show that the result of the paper is best possible.