• Kyungpook Mathematical Journal
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• 제59권2호
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• pp.293-299
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• 2019

A number of identities associated with the product of generalized hypergeometric series have been investigated. In this paper, we aim to establish an identity involving the product of the generalized hypergeometric series $_2F_2$. We do this using the generalized Kummer-type II transformation due to Rathie and Pogany and another identity due to Bailey. The result presented here, being general, can be reduced to a number of relatively simple identities involving the product of generalized hypergeometric series, some of which are observed to correspond to known ones.

• 대한수학회논문집
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• 제37권1호
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• pp.31-43
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• 2022

In his notebooks, Srinivasa Ramanujan recorded several modular equations that are useful in the computation of class invariants, continued fractions and the values of theta functions. In this paper, we prove some new modular equations of signature 2 by well-known and useful theta function identities of composite degrees. Further, as an application of this, we evaluate theta function identities.

• East Asian mathematical journal
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• 제25권4호
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• pp.481-486
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• 2009

The first object of this note is to show that a summation formula due to Padmanabham for three-variables hypergeometric function $X_8$ introduced by Exton can be proved in a different (from Padmanabham's and his observation) yet, in a sense, conventional method, which has been employed in obtaining a variety of identities associated with hypergeometric series. The second purpose is to point out that one of two seemingly new hypergeometric identities due to Exton was already recorded and the other one is easily derivable from the first one. A corrected and a little more compact form of a general transform involving hypergeometric functions due to Exton is also given.

• 한국과학교육학회지
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• 제32권3호
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• pp.532-540
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• 2012

This research investigated the motivation and interests of a sample of predominately-underrepresented populations to better understand whether informal STEM learning experiences offer support for developing STEM identities. A valid and reliable three-section self-reporting survey was administered to 169 secondary students as the primary data source. Identity was used as a theoretical lens along with descriptive statistics to reveal students' perceived benefits of the informal STEM learning experience, a Mathematics, Engineering, Science Achievement (MESA) program in the western U.S., for improving their understanding of science, mathematics, and engineering concepts, increasing their interest in science, mathematics, and engineering careers, and increasing their belief of the importance of these STEM disciplines. In summary, the findings emerging, considered alongside current identity research, suggest that informal STEM learning experiences offer students from underrepresented STEM populations the space needed for successful STEM identity bids, either for future career pursuits or participation in a STEM literate populace as a non-STEM professional societal member.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제13권12호
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• pp.6214-6242
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• 2019

Routing in mobile ad hoc networks is performed in a distributed fashion where each node acts as host and router, such that it forwards incoming packets for others without relying on a dedicated router. Nodes are mostly resource constraint and the users are usually inclined to conserve their resources and exhibit selfish behaviour by not contributing in the routing process. The trust and reputation models have been proposed to motivate selfish nodes for cooperation in the packet forwarding process. Nodes having bad trust or reputation are detected and secluded from the network, eventually. However, due to the lack of proper identity management and use of non-persistent identities in ad hoc networks, malicious nodes can pose various threats to these methods. For example, a malicious node can discard the bad reputed identity and enter into the system with another identity afresh, called whitewashing. Similarly, a malicious node may create more than one identity, called Sybil attack, for self-promotion, defame other nodes, and broadcast fake recommendations in the network. These identity-based attacks disrupt the overall detection of the reputation systems. In this paper, we propose a reputation-based scheme that detects selfish nodes and deters identity attacks. We address the issue in such a way that, for normal selfish nodes, it will become no longer advantageous to carry out a whitewash. Sybil attackers are also discouraged (i.e., on a single battery, they may create fewer identities). We design and analyse our rationale via game theory and evaluate our proposed reputation system using NS-2 simulator. The results obtained from the simulation demonstrate that our proposed technique considerably diminishes the throughput and utility of selfish nodes with a single identity and selfish nodes with multiple identities when compared to the benchmark scheme.

• Journal of Microbiology and Biotechnology
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• 제29권5호
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• pp.765-775
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• 2019

A new ${\alpha}$-amylase-encoding gene (amySL3) of glycoside hydrolase (GH) family 13 was identified in soda lake isolate Alkalibacterium sp. SL3. The deduced AmySL3 shares high identities (82-98%) with putative ${\alpha}$-amylases from the genus Alkalibacterium, but has low identities (<53%) with functionally characterized counterparts. amySL3 was successfully expressed in Escherichia coli, and the recombinant enzyme (rAmySL3) was purified to electrophoretic homogeneity. The optimal temperature and pH of the activity of the purified rAmySL3 were determined to be $45^{\circ}C$ and pH 7.5, respectively. rAmySL3 was found to be extremely halophilic, showing maximal enzyme activity at a nearly saturated concentration of NaCl. Its thermostability was greatly enhanced in the presence of 4 M NaCl, and it was highly stable in 5 M NaCl. Moreover, the enzyme did not require calcium ions for activity, and was strongly resistant to a range of surfactants and hydrophobic organic solvents. The major hydrolysis products of rAmySL3 from soluble starch were maltobiose and maltotriose. The high ratio of acidic amino acids and highly negative electrostatic potential surface might account for the halophilic nature of AmySL3. The extremely halophilic, calcium-independent, and surfactant-resistant properties make AmySL3 a promising candidate enzyme for both basic research and industrial applications.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제12권4호
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• pp.1674-1692
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• 2018

An RFID network is a network in which a reader inquire about the identities of tags and tags respond with their identities to a reader. The diversity of RFID networks has brought about many applications including an inexpensive system where a single reader supports a small number of tags. Such a system needs a tag cognizance scheme that is able to arbitrate among contending tags as well as is simple enough. In this paper, confining our attention to a clan of simple schemes, we propose a randomized scheme with aiming at enhancing the tag cognizance rate than a conventional scheme. Then, we derive an exact expression for the cognizance rate attained by the randomized scheme. Unfortunately, the exact expression is not so tractable as to optimize the randomized scheme. As an alternative way, we develop an upper bound on the tag cognizance rate. In a closed form, we then obtain a nearly optimal value for a key design parameter, which maximizes the upper bound. Numerical examples confirm that the randomized scheme is able to dominate the conventional scheme in cognizance rate by employing a nearly optimal value. Furthermore, they reveal that the randomized scheme is robust to the fallacy that the reader believes or guesses a wrong number of neighboring tags.

• 대한수학회보
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• 제55권3호
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• pp.937-956
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• 2018

This article gives the foundations of the colored Jones polynomial for singular knots. We extend Masbum and Vogel's algorithm [26] to compute the colored Jones polynomial for any singular knot. We also introduce the tail of the colored Jones polynomial of singular knots and use its stability properties to prove a false theta function identity that goes back to Ramanujan.

• 대한수학회보
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• 제45권4호
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• pp.621-629
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• 2008

Let R be a prime ring of characteristic different from 2, C the extended centroid of R, and $\delta$ a generalized derivations of R. If [[$\delta(x)$, x], $\delta(x)$] = 0 for all $x\;{\in}\;R$ then either R is commutative or $\delta(x)\;=\;ax$ for all $x\;{\in}\;R$ and some $a\;{\in}\;C$. We also obtain some related result in case R is a Banach algebra and $\delta$ is either continuous or spectrally bounded.

• 대한수학회논문집
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• 제38권4호
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• pp.1175-1189
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• 2023

The main purpose of this paper is to give some new identities and properties related to Bernoulli type numbers and polynomials associated with the Bessel function of the first kind. We give symmetric properties of the Bernoulli type numbers and polynomials. Moreover, using generating functions and the Faà di Bruno's formula, we derive some new formulas and relations related to not only these polynomials, but also the Bernoulli numbers and polynomials and the Euler numbers and polynomials.