http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
오늘 본 자료
On the Tensor Product of m-Partition Algebras
Kennedy, A. Joseph,Jaish, P. Department of Mathematics 2021 Kyungpook mathematical journal Vol.61 No.4
We study the tensor product algebra P<sub>k</sub>(x<sub>1</sub>) ⊗ P<sub>k</sub>(x<sub>2</sub>) ⊗ ⋯ ⊗ P<sub>k</sub>(x<sub>m</sub>), where P<sub>k</sub>(x) is the partition algebra defined by Jones and Martin. We discuss the centralizer of this algebra and corresponding Schur-Weyl dualities and also index the inequivalent irreducible representations of the algebra P<sub>k</sub>(x<sub>1</sub>) ⊗ P<sub>k</sub>(x<sub>2</sub>) ⊗ ⋯ ⊗ P<sub>k</sub>(x<sub>m</sub>) and compute their dimensions in the semisimple case. In addition, we describe the Bratteli diagrams and branching rules. Along with that, we have also constructed the RS correspondence for the tensor product of m-partition algebras which gives the bijection between the set of tensor product of m-partition diagram of P<sub>k</sub>(n<sub>1</sub>) ⊗ P<sub>k</sub>(n<sub>2</sub>) ⊗ ⋯ ⊗ P<sub>k</sub>(n<sub>m</sub>) and the pairs of m-vacillating tableaux of shape [λ] ∈ Γ<sub>k</sub><sup>m</sup>, Γ<sub>k</sub><sup>m</sup> = {[λ] = (λ<sub>1</sub>, λ<sub>2</sub>, …, λ<sub>m</sub>)|λ<sub>i</sub> ∈ Γ<sub>k</sub>, i ∈ {1, 2, …, m}} where Γ<sub>k</sub> = {λ<sub>i</sub> ⊢ t|0 ≤ t ≤ k}. Also, we provide proof of the identity $(n_1n_2{\cdots}n_m)^k={\sum}_{[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}$ f<sup>[λ]</sup>m<sub>k</sub><sup>[λ]</sup> where m<sub>k</sub><sup>[λ]</sup> is the multiplicity of the irreducible representation of $S{_{n_1}}{\times}S{_{n_2}}{\times}....{\times}S{_{n_m}}$ module indexed by ${[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}$, where f<sup>[λ]</sup> is the degree of the corresponding representation indexed by ${[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}$ and ${[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}=\{[{\lambda}]=({\lambda}_1,{\lambda}_2,{\ldots},{\lambda}_m){\mid}{\lambda}_i{\in}{\Lambda}^k_{n_i},i{\in}\{1,2,{\ldots},m\}\}$ where ${\Lambda}^k_{n_i}=\{{\mu}=({\mu}_1,{\mu}_2,{\ldots},{\mu}_t){\vdash}n_i{\mid}n_i-{\mu}_1{\leq}k\}$.
Shuffling of Elliptic Curve Cryptography Key on Device Payment
Kennedy, Chinyere Grace,Cho, Dongsub Korea Multimedia Society 2019 멀티미디어학회논문지 Vol.22 No.4
The growth of mobile technology particularly smartphone applications such as ticketing, access control, and making payments are on the increase. Elliptic Curve Cryptography (ECC)-based systems have also become widely available in the market offering various convenient services by bringing smartphones in proximity to ECC-enabled objects. When a system user attempts to establish a connection, the AIK sends hashes to a server that then verifies the values. ECC can be used with various operating systems in conjunction with other technologies such as biometric verification systems, smart cards, anti-virus programs, and firewalls. The use of Elliptic-curve cryptography ensures efficient verification and signing of security status verification reports which allows the system to take advantage of Trusted Computing Technologies. This paper proposes a device payment method based on ECC and Shuffling based on distributed key exchange. Our study focuses on the secure and efficient implementation of ECC in payment device. This novel approach is well secure against intruders and will prevent the unauthorized extraction of information from communication. It converts plaintext into ASCII value that leads to the point of curve, then after, it performs shuffling to encrypt and decrypt the data to generate secret shared key used by both sender and receiver.
Note on Cellular Structure of Edge Colored Partition Algebras
Kennedy, A. Joseph,Muniasamy, G. Department of Mathematics 2016 Kyungpook mathematical journal Vol.56 No.3
In this paper, we study the cellular structure of the G-edge colored partition algebras, when G is a finite group. Further, we classified all the irreducible representations of these algebras using their cellular structure whenever G is a finite cyclic group. Also we prove that the ${\mathbb{Z}}/r{\mathbb{Z}}$-Edge colored partition algebras are quasi-hereditary over a field of characteristic zero which contains a primitive $r^{th}$ root of unity.
Kennedy Chinedu Okafor,Omowunmi Mary Longe 한국인터넷정보학회 2022 KSII Transactions on Internet and Information Syst Vol.16 No.7
Cyber-physical systems (CPS) have been growing exponentially due to improved cloud-datacenter infrastructure-as-a-service (CDIaaS). Incremental expandability (scalability), Quality of Service (QoS) performance, and reliability are currently the automation focus on healthy Tier 4 CDIaaS. However, stable QoS is yet to be fully addressed in Cyber-physical data centers (CP-DCS). Also, balanced agility and flexibility for the application workloads need urgent attention. There is a need for a resilient and fault-tolerance scheme in terms of CPS routing service including Pod cluster reliability analytics that meets QoS requirements. Motivated by these concerns, our contributions are fourfold. First, a Distributed Non-Recursive Cloud Model (DNRCM) is proposed to support cyber-physical workloads for remote lab activities. Second, an efficient QoS stability model with Routh-Hurwitz criteria is established. Third, an evaluation of the CDIaaS DCN topology is validated for handling large-scale, traffic workloads. Network Function Virtualization (NFV) with Floodlight SDN controllers was adopted for the implementation of DNRCM with embedded rule-base in Open vSwitch engines. Fourth, QoS evaluation is carried out experimentally. Considering the non-recursive queuing delays with SDN isolation (logical), a lower queuing delay (19.65%) is observed. Without logical isolation, the average queuing delay is 80.34%. Without logical resource isolation, the fault tolerance yields 33.55%, while with logical isolation, it yields 66.44%. In terms of throughput, DNRCM, recursive BCube, and DCell offered 38.30%, 36.37%, and 25.53% respectively. Similarly, the DNRCM had an improved incremental scalability profile of 40.00%, while BCube and Recursive DCell had 33.33%, and 26.67% respectively. In terms of service availability, the DNRCM offered 52.10% compared with recursive BCube and DCell which yielded 34.72% and 13.18% respectively. The average delays obtained for DNRCM, recursive BCube, and DCell are 32.81%, 33.44%, and 33.75% respectively. Finally, workload utilization for DNRCM, recursive BCube, and DCell yielded 50.28%, 27.93%, and 21.79% respectively.