• 대한수학회논문집
• /
• 제34권3호
• /
• pp.967-979
• /
• 2019

Chaotic dynamical systems, preferably on a Cantor-like space with some arithmetic operations are considered as good pseudo-random number generators. There are many definitions of chaos, of which Devaney-chaos and pos itive topological entropy seem to be the strongest. Let $A=\{0,1,{\dots},p-1\}$. We define a continuous map on $A^{\mathbb{Z}}$ using addition with a carry, in combination with the shift map. We show that this map gives rise to a dynamical system with positive entropy, which is also Devaney-chaotic: i.e., it is transitive, sensitive and has a dense set of periodic points.

• 대한수학회지
• /
• 제59권4호
• /
• pp.789-804
• /
• 2022

Striking result of Vybíral [51] says that Schur product of positive matrices is bounded below by the size of the matrix and the row sums of Schur product. Vybíral used this result to prove the Novak's conjecture. In this paper, we define Schur product of matrices over arbitrary C^*-algebras and derive the results of Schur and Vybíral. As an application, we state C^*-algebraic version of Novak's conjecture and solve it for commutative unital C^*-algebras. We formulate Pólya-Szegő-Rudin question for the C^*-algebraic Schur product of positive matrices.

• Journal of applied mathematics & informatics
• /
• 제41권4호
• /
• pp.765-780
• /
• 2023

In this paper, we explore the uniqueness property between the transcendental meromorphic functions and differential polynomial. With the notion of weighted sharing, we generalised the many previous results on uniqueness property. Here we discussed the uniqueness of [P(f)(αf^m + β)^s]^(k) - η(z) and [P(g)(αg^m + β)^s]^(k) - η(z). Meanwhile, we generalised the result of Harina P. waghamore and Rajeshwari S[1].

• 대한수학회논문집
• /
• 제38권3호
• /
• pp.787-805
• /
• 2023

Let (Ω, µ) be a measure space and {τ_α}_α∈Ω be a normalized continuous Bessel family for a finite dimensional Hilbert space 𝓗 of dimension d. If the diagonal ∆ := {(α, α) : α ∈ Ω} is measurable in the measure space Ω × Ω, then we show that $$\sup\limits_{{\alpha},{\beta}{\in}{\Omega},{\alpha}{\neq}{\beta}}\,{\mid}{\langle}{\tau}_{\alpha},\,{\tau}_{\beta}{\rangle}{\mid}^{2m}\,{\geq}\,{\frac{1}{({\mu}{\times}{\mu})(({\Omega}{\times}{\Omega}{\backslash}{\Delta})}\;\[\frac{{\mu}({\Omega})^2}{\({d+m-1 \atop m}\)}-({\mu}{\times}{\mu})({\Delta})\],\;{\forall}m{\in}{\mathbb{N}}.$$ This improves 48 years old celebrated result of Welch [41]. We introduce the notions of continuous cross correlation and frame potential of Bessel family and give applications of continuous Welch bounds to these concepts. We also introduce the notion of continuous Grassmannian frames.

• Asia pacific journal of information systems
• /
• 제31권3호
• /
• pp.433-447
• /
• 2021

The purpose of this paper is to shed light on the current status of Industry 4.0 policies in India and provide holistic policy recommendations in the transition towards Industry 4.0. The study was conducted based on the content-centric review of written policy documents like policy memoranda (memos), green papers and white papers, policy briefs, policy reports, opinion pieces, and newspaper and academic publications on Industry 4.0. India lacks infrastructure, regulatory framework, architectural reference model, incentives, skills, and standard roadmap towards Industry 4.0. The current policy status and policy recommendations presented in this study can serve as a great asset for academicians, policymakers, and practitioners to prepare a holistic roadmap for Industry 4.0 policy implementation. The study is first to assess India's current policy status and compare with Germany towards Industry 4.0. Besides, it is expected to assist government policymakers in formulating tangible policy outputs and strategic roadmaps.

• Asian Pacific Journal of Cancer Prevention
• /
• 제16권10호
• /
• pp.4193-4198
• /
• 2015

Background: Globally, retinoblastoma is the most common primary intraocular malignancy occurring in children. This paper documents the recent incidence rates of retinoblastoma by age and sex groups from the Population Based Cancer Registries (PBCRs) of Bangalore, Mumbai, Chennai, Delhi and Kolkata using the data from the National Cancer Registry Programme. Materials and Methods: Relative proportions, sex ratio, method of diagnosis, and incidence rates (crude and age standardized) for each PBCR and pooled rates of the five PBCRs were calculated for the years 2005/06 to 2009/10. Standard errors and 95% confidence limits of ASIRs by sex group in each PBCR were calculated using the Poisson distribution. Standardised rate ratios of ASIR by sex group and rate ratios at risk were also calculated. Results: The maximum retinoblastoma cases were in the 0-4 age group, accounting for 78% (females) and 81% (males) of pooled cases from five PBCRs. The pooled crude incidence rate in the 0-14 age group was 3.5 and the pooled ASIR was 4.4 per million. The pooled ASIR in the 0-4, 5-9 and 10-14 age group were 9.6, 2.0 and 0.1 respectively. The M/F ratio in Chennai (1.9) and Bangalore PBCRs (2.0) was much higher than the other PBCRs. Among the PBCRs, the highest incidence rate in 0-4 age group was found in males in Chennai (21.7 per million), and females in Kolkata (18.9 per million). There was a distinct variation in incidence rates in the PBCRs in different geographic regions of India.

• Biotechnology and Bioprocess Engineering:BBE
• /
• 제11권4호
• /
• pp.372-376
• /
• 2006

Ferulic acid is a phenolic compound that serves as a major biosynthetic precursor of vanillin in higher plants. We investigated the ability of the 3 commercial enzymes - Ultraflo L, Viscozyme L, and ${\alpha}-Amylase$ - to induce the release ferulic acid from the Ipomoea batatas L. (sweet potato) stem. The rate of release for ferulic acid was optimal when Ultraflo L (1.0%) was used compared with the other enzymes, whereas Viscozyme L was most effective for the release of vanillic acid and vanillin. Thus, these enzymes may be useful for the large-scale production of ferulic acid and other phenolic compounds from sweet potato stem.

• International Journal of Industrial Entomology and Biomaterials
• /
• 제8권2호
• /
• pp.129-133
• /
• 2004

The breeding work was initiated by utilizing two Japanese hybrids namely C135${\times}$N134 and N137${\times}$C146 along with two evolved Indian breeds, J14 and A24. The breed CSR16 which is characterized with marked larvae and white dumbbell cocoons was evolved from the Japanese hybrid C135${\times}$N134 by crossing with J14, while the breed CSR17 which is characterized with plain larvae and white oval cocoons was evolved from the Japanese hybrid N137${\times}$C146 by crossing with A24. The hybrid of these evolved breeds i.e., CSR16${\times}$CSR17 has shown superior over control hybrid $KA{\times}{NB_4}{D_2}$ and on par with the ruling hybrid of CSR2${\times}$CSR4. The hybrid CSR16${\times}$CSR17 was authorized during 1999 by Central Silk Board, Bangalore, Government of India for commercial exploitation during favourable months based on national level race authorization test.

• Journal of Plant Biotechnology
• /
• 제7권2호
• /
• pp.135-141
• /
• 2005

Protocols for in vitro conservation was developed for Coleus forskohlii. Plants maintained both in field served as explant source. Shoot tips and single node cuttings were used to optimize protocols for in vitro multiplication. MS basal medium supplemented with $0.54\;{\mu}M$ naphthalene acetic acid (NAA) and $8.87\;{\mu}M$ benzy-ladenine (BA) induced multiple shoots in shoot tips and nodes. Shoot multiplication was amplified with a gradual decrease of BA concentration, leading to its final omission after 4 months. Concomitant rooting on multiplication media enabled successful establishment extra vitrum. For in vitro conservation studies, experiments were carried out with 2-3 week maintained in vitro plants under standard and reduced culture conditions (SCC, RCC). In vitro plants could be successfully conserved in full strength MS medium (FMS) under SCC for 6 months without subculture with full potential to regenerate, producing viable shoots and nodes. The root production remained unaffected due to conservation, showing high rooting activity in mannitol and low temperature treatments. Preset low temperature (15 and $10^{\circ}C$) and reduction in media constituents does not appear to favour conservation, although the former accomplished conservation levels equal to (FMS) under SCC.

• 한국약용작물학회지
• /
• 제12권5호
• /
• pp.384-390
• /
• 2004

An in vtro nucellar polyembryo propagation method was established with mature seed of the Citrus junos Sieb. 7-8 nucellar polyembryos per seed were induced on MS basal medium without plant growth regulators. The polyembryos developed to complete plantlets on teatment with IBA. These shoots grew further in MS medium without plant growth regulators. Rooting of shoots occurred on MS medium supplemented with IBA. These plantlets were successfully transplanted to small plastic pot containing soil mixture. Somatic embryos were induced from nucellar polyembryo and maturation occurred spontaneously from proliferating cultures on MS medium without growth regulators. Random Amplified Polymorphic DNA (RAPD) marker analysis of in vitro and in vivo grown junos orange showed identical polymorphism indicative of their genetic stability. The RAPD polymorphism produced revealed same banding pattern in each regenerant. Hence, propagaton of junos orange by nucellalr polyembryos was efficient and produced in genetically stable plants under in vitro conditions.