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Pradip Narain,Andreas J. Stylianides 대한수학교육학회 2020 수학교육학연구 Vol.- No.특별호
The concept of proof is central to every undergraduate mathematics curriculum, but it is also a difficult concept for university students to understand and for university instructors to teach. Prior studies have contributed useful research knowledge about the nature and sources of undergraduate students’ difficulties with proof, but they have paid less attention to the development of effective instructional practices to enhance student learning of proof. As a step towards this direction, this paper makes a contribution to the limited body of case studies of promising or potentially effective teaching practices in undergraduate mathematics by reporting a case study of an instructor’s teaching, locally characterized as “effective,” in an undergraduate analysis course at a leading Indian university. The instructor did not deviate from the so called “Definition-Theorem-Proof” (DTP) format that is followed in most proof-oriented university mathematics courses, but her teaching presented a set of features that, collectively, form a rather innovative teaching practice at the undergraduate level. Specifically, our case study shows that, even in the context of a rather crowded university classroom, proof can be demystified for students through structured interaction between the instructor and the students, that is, an interactive, conversational style of proof instruction invoking the participation of students. This is based on a solid foundation in symbolic logic at the very outset and on a significant time investment in definitions being explained in depth using informal language, visual aids, and real-life analogies. In addition to contributing to existing images of potentially effective teaching practices in undergraduate mathematics, this paper draws attention to the Indian educational context that has had little representation in international forums of mathematics education research thus far.
태국과 한국을 중심으로 한 세계적 시각에서 불교의 배경
Kamakhiya Narain Tiwary 강원한국학연구원 2018 국제한국학저널 Vol.4 No.-
세계화 시대에 모든 나라가 서로 가까워지고 있다. 종교는 지정학적 협력의 여러 분야에서 상호 평등을 찾는 데 중요한 역할을 담당해 왔다. 이와 관련하여 불교는 가장 받아들여지는 종교 일뿐만 아니라 많은 아시아 국가에서 중요한 역할을 했다. 불교가 시작된 이래 인도의 많은 이웃 국가들은 불교문화에 더 많은 관심을 보였다. 이 논문은 세계적인 맥락에서 불교문화를 다룬다. 특히 태국과 한국 두 아시아 국가를 다루었다. 이 두 나라는 다양한 형태의 불교문화를 대표하지만, 대표적인 불교문화로 부상하고 있다. In this Era of globalization, all the countries are coming closer to each other. Religion has played an important role in finding mutual equality in different areas of geopolitical collaborations. In this regard, Buddhism is not only the most accepted religion, but also played an important role in many Asian countries. Since the inception of Buddhism, many neighboring countries of India showed deeper interest towards Buddhist culture. This paper deals with Buddhist culture in global context and particularly covers two Asian countries: Thailand and Korea. Although these two countries represent different forms of Buddhist culture, but they have been emerging as a representative Buddhist culture.
( Durgesh Narain Singh ),( Anil Kumar Tripathi ) 한국미생물 · 생명공학회 2011 Journal of microbiology and biotechnology Vol.21 No.11
The rise in global energy demand has prompted researches on developing strategies for transforming coal into a cleaner fuel. This requires isolation of microbes with the capability to degrade complex coal into simpler substrates to support methanogenesis in the coal beds. In this study, aerobic bacteria were isolated from an Indian coal bed that can solubilize and utilize coal as the sole source of carbon. The six bacterial isolates capable of growing on coal agar medium were identified on the basis of their 16S rRNA gene sequences, which clustered into two groups; Group I isolates belonged to the genus Rhizobium, whereas Group II isolates were identified as Chelatococcus species. Out of the 4 methods of whole genome fingerprinting (ERIC-PCR, REP-PCR, BOX-PCR, and RAPD), REPPCR showed maximum differentiation among strains within each group. Only Chelatococcus strains showed the ability to solubilize and utilize coal as the sole source of carbon. On the basis of 16S rRNA gene sequence and the ability to utilize different carbon sources, the Chelatococcus strains showed maximum similarity to C. daeguensis. This is the first report showing occurrence of Rhizobium and Chelatococcus strains in an Indian coal bed, and the ability of Chelatococcus isolates to solubilize and utilize coal as a sole source of carbon for their growth.
Beyond Prostate Specific Antigen: New Prostate Cancer Screening Options
Tushar Aditya Narain,Prasanna Sooriakumaran 대한남성과학회 2022 The World Journal of Men's Health Vol.40 No.1
Prostate specific antigen (PSA) is one of the best-known biomarkers for screening, diagnosis and follow-up of patients for prostate cancer. Owing to several inherent limitations with PSA, various newer blood and urinary based biomarkers have been evaluated in pursuit of better detection and risk stratification of prostate cancer cases. A combination of these different markers, in adjunct with clinical risk factors, and recent advances in imaging promises to offer better diagnostic performance with clearer risk stratification guiding therapeutics. We carried out an extensive literature search for the different biomarkers available for screening and diagnosis of prostate cancer, compared their performance with serum PSA to allow clinicians to draw meaningful conclusions to offer their patients a more personalized medical care.
EXISTENCE OF SOLUTIONS FOR BOUNDARY VALUE PROBLEMS VIA F-CONTRACTION MAPPINGS IN METRIC SPACES
Komi Afassinou,Ojen Kumar Narain 경남대학교 수학교육과 2020 Nonlinear Functional Analysis and Applications Vol.25 No.2
The purpose of this paper is to present some sufficient conditions for the existence and uniqueness of solutions of the nonlinear Hammerstein integral equations and thetwo-point boundary value problems for nonlinear second-ordinary differential equations. Toestablish this, we introduce the generalized Suzuki-(α, β)-F-contraction and the generalized(α, β)-F-contraction in the framework of a metric space and establish some fixed point results. The results obtained in this work provide extension as well as substantial generalizationand improvement of several well-known results on fixed point theory and its applications.
Constituents of Mallotus nepalensis Muell. Arg.: a Mild CNS Depressant
Subha Rastogi,Bishen Narain Mehrotra,Dinesh K. Kulshreshtha 한국생약학회 2004 Natural Product Sciences Vol.10 No.5
Mallotus nepalensis (Euphorbiaceae) is a small tree found in central and eastern Himalayas, Nepal,Wallich and Sikkim. The 90% ethanolic extract of Mallotus nepalensis exhibited mild CNS depressant activity. Four compounds, lupeol (1), β-sitosterol (2), ursolic acid (3) and β-sitosterol- β-D-glucoside (4) were isolated from the 90% ethanolic extract of this plant of which 1, 3 and 4 are being reported for the first time from this specie.
Szász-Kantorovich Type Operators Based on Charlier Polynomials
Kajla, Arun,Agrawal, Purshottam Narain Department of Mathematics 2016 Kyungpook mathematical journal Vol.56 No.3
In the present article, we study some approximation properties of the Kantorovich type generalization of $Sz{\acute{a}}sz$ type operators involving Charlier polynomials introduced by S. Varma and F. Taşdelen (Math. Comput. Modelling, 56 (5-6) (2012) 108-112). First, we establish approximation in a Lipschitz type space, weighted approximation theorems and A-statistical convergence properties for these operators. Then, we obtain the rate of approximation of functions having derivatives of bounded variation.
ON GENERALIZED (α,β)-NONEXPANSIVE MAPPINGS IN BANACH SPACES WITH APPLICATIONS
F. Akutsah,O.K. Narain 경남대학교 수학교육과 2021 Nonlinear Functional Analysis and Applications Vol.26 No.4
In this paper, we present some fixed point results for a general class of nonexpansive mappings in the framework of Banach space and also proposed\ a new iterative scheme for approximating the fixed point of this class of mappings in the frame work of uniformly convex Banach spaces. Furthermore, we establish some basic properties and convergence results for our new class of mappings in uniformly convex Banach spaces. Finally, we present an application to nonlinear integral equation and also, a numerical example to illustrate our main result and then display the efficiency of the proposed algorithm compared to different iterative algorithms in the literature with different choices of parameters and initial guesses. The results obtained in this paper improve, extend and unify some related results in the literature.
Komi Afassinou,Ojen Kumar Narain,Oluwaseun Elizabeth Otunuga 경남대학교 수학교육과 2020 Nonlinear Functional Analysis and Applications Vol.25 No.3
The goal of this paper is to introduce a modified Halpern iterative algorithm for approximating solutions of split monotone variational inclusion, variational inequality and fixed point problems of an infinite families of multi-valued type-one demicontractive mappings in the framework of real Hilbert spaces. Using our iterative algorithm, we state and prove a strong convergence result for approximating a common solution of split monotone variational inclusion, variational inequality problems and fixed point problem for countable family of multi-valued type-one demicontractive mappings. The iterative algorithm employed in this paper is designed in such a way that it does not require the knowledge of operator norm. Lastly, we give some consequences of our main result and give application of one of the consequences to split minimization problem. The result presented in this paper extends and generalizes some related results in literature.