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S. K. Sen,R. P. Agarwal,G. A. Shaykhian 장전수학회 2009 Advanced Studies in Contemporary Mathematics Vol.19 No.1
A k-digit rational approximation of an irrational number is defined as the rational number with k digits in the numerator. The actual best k digit rational approximation is unique and is the true/absolute one. The best k - digit rational approximation, when it exists, obtained from the convergents of the continued fraction representation of an irrational number is also unique and need not be the same as the absolute one. The best k digit decimal number for the irrational number is also unique but is not the true best k - digit rational approximation, in general. We discuss here the quality implying error, the cost implying computational/time complexity, and scope implying a possible usage/application of the concerned three computational algorithms.
Inheritance of Resistance to Nuclear Polyhedrosis Virus in Silkworm, Bombyx mori
Sen, Ratna,Ashwath, S.K.,Datta, R.K. Korean Society of Sericultural Science 2001 International Journal of Industrial Entomology Vol.3 No.2
Inheritance pattern of resistance to Bombyx mori nuclear polyhedrosis virus (BmNPV) was studied in an Indian silkworm stock TX by single back-cross test method. The resistant parent [TX], susceptible parent [HM], their Fl, F2, and Fl progeny back-crossed to TX [BC(R)] and HM [BC(S)] were inoculated per os with a fixed concentration of BmNPV($0.5{\times}10^{th} PIB/ml$) on the first day of second stadium. The cumulative mortality was recorded until day $10^{\times}$ post-inoculation. The results show that the resistance to BmNPV in TX fellow mono Mendelian inheritance pattern. The resistance dominated over the susceptibility at Fl. At F2, the resistant and susceptible offspring segregated in 3:1 ratio whereas at BC(S), the resistant and susceptible offspring segregated in 1:1 ratio. The response of BC(R) was more or less like the resistant parent TX which confirms the involvement of a major dominant gene conferring resistance to BmNPV in TX. The possible mechanism of inheritance of resistance in TX is discussed.
ILL-VERSUS WELL-POSED SINGULAR LINEAR SYSTEMS: SCOPE OF RANDOMIZED ALGORITHMS
Sen, S.K.,Agarwal, Ravi P.,Shaykhian, Gholam Ali The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.3
The linear system Ax = b will have (i) no solution, (ii) only one non-trivial (trivial) solution, or (iii) infinity of solutions. Our focus will be on cases (ii) and (iii). The mathematical models of many real-world problems give rise to (a) ill-conditioned linear systems, (b) singular linear systems (A is singular with all its linearly independent rows are sufficiently linearly independent), or (c) ill-conditioned singular linear systems (A is singular with some or all of its strictly linearly independent rows are near-linearly dependent). This article highlights the scope and need of a randomized algorithm for ill-conditioned/singular systems when a reasonably narrow domain of a solution vector is specified. Further, it stresses that with the increasing computing power, the importance of randomized algorithms is also increasing. It also points out that, for many optimization linear/nonlinear problems, randomized algorithms are increasingly dominating the deterministic approaches and, for some problems such as the traveling salesman problem, randomized algorithms are the only alternatives.
Sen, Sinol,Ingale, S.L.,Kim, J.S.,Kim, K.H.,Kim, Y.W.,Khong, Chou,Lohakare, J.D.,Kim, E.K.,Kim, H.S.,Kwon, I.K.,Chae, B.J. Asian Australasian Association of Animal Productio 2011 Animal Bioscience Vol.24 No.8
A feeding trial was conducted to investigate the effect of dietary supplementation of Bacillus subtilis LS 1-2 grown on citrus-juice waste and corn-soybean substrate on growth performance, nutrient retention, caecal microbial population and intestinal morphology in broilers. Three hundred twenty d-old Ross chicks were randomly allotted to 4 treatments on the basis of BW in a randomized complete block design. Each treatment had 4 replicates of 20 chicks in each. Experimental diets were fed in 2 phases, starter (d 0 to 21) and finisher (d 21 to 35). Dietary treatments were; negative control (NC: basal diet without any antimicrobial), positive control (PC: basal diet added with 20 mg/kg Avilamycin), basal diet added with 0.30% Bacillus subtilis LS 1-2 grown on corn-soybean substrate (P1), and basal diet added with 0.30% Bacillus subtilis LS 1-2 grown on citrus-juice waste substrate (P2). Overall BW gain, feed intake and FCR were better (p<0.05) in PC, P1 and P2 treatments as compared to NC. Moreover, overall BW gain and FCR in PC and P2 treatments were greater than P1. Retention of CP, GE (d 21, d 35) and DM (d 35) were increased (p<0.05) in treatments PC, P1 and P2 compared with NC. At d 35, caecal Clostridium and Coliform counts were lower (p<0.05) in treatments PC, P1 and P2 than NC. Moreover, Clostridium and Coliform counts in treatment PC was lower (p<0.05) than P1. Villus height and villus height to crypt depth ratio in both duodenum and ileum were increased (p<0.05) in treatments PC, P1, P2 as compared to NC. However, retention of nutrients, caecal microbial population and intestinal morphology remained comparable among treatments P1 and P2. It is concluded that Bacillus subtilis LS 1-2 inclusion at 0.30% level had beneficial effects on broilers' growth performance, nutrient retention, caecal microflora and intestinal morphology. Additionally, citrus-juice waste can be used as substrate for growth of probiotic Bacillus subtilis LS 1-2.
Ill- versus well-posed singular linear systems: scope of randomized algorithms
S.K. Sen,Ravi P. Agarwal,Gholam Ali Shaykhian 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.3
The linear system Ax = b will have (i) no solution, (ii) only one non-trivial (trivial) solution, or (iii) infinity of solutions. Our focus will be on cases (ii) and (iii). The mathematical models of many real- world problems give rise to (a) ill-conditioned linear systems, (b) singular linear systems (A is singular with all its linearly independent rows are suffi- ciently linearly independent), or (c) ill-conditioned singular linear systems (A is singular with some or all of its strictly linearly independent rows are near-linearly dependent). This article highlights the scope and need of a randomized algorithm for ill-conditioned/singular systems when a reason- ably narrow domain of a solution vector is specified. Further, it stresses that with the increasing computing power, the importance of randomized algorithms is also increasing. It also points out that, for many optimization linear/nonlinear problems, randomized algorithms are increasingly domi- nating the deterministic approaches and, for some problems such as the traveling salesman problem, randomized algorithms are the only alterna- tives. The linear system Ax = b will have (i) no solution, (ii) only one non-trivial (trivial) solution, or (iii) infinity of solutions. Our focus will be on cases (ii) and (iii). The mathematical models of many real- world problems give rise to (a) ill-conditioned linear systems, (b) singular linear systems (A is singular with all its linearly independent rows are suffi- ciently linearly independent), or (c) ill-conditioned singular linear systems (A is singular with some or all of its strictly linearly independent rows are near-linearly dependent). This article highlights the scope and need of a randomized algorithm for ill-conditioned/singular systems when a reason- ably narrow domain of a solution vector is specified. Further, it stresses that with the increasing computing power, the importance of randomized algorithms is also increasing. It also points out that, for many optimization linear/nonlinear problems, randomized algorithms are increasingly domi- nating the deterministic approaches and, for some problems such as the traveling salesman problem, randomized algorithms are the only alterna- tives.
M. K. Sen,S. K. Maity 한국수학교육학회 2006 純粹 및 應用數學 Vol.13 No.2
In [6], we have recently proved that an additive inverse semiring S is a Clifford semifield if and only if S is a subdirect product of a field and a distributive lattice. In this paper, we study the matrix semiring over a Clifford semifield.
Alaneme, K.K.,Hong, S.M.,Sen, I.,Fleury, E.,Ramamurty, U. Elsevier Sequoia 2010 Materials science & engineering. properties, micro Vol.527 No.18
Small additions of Cu to the SUS 304H, a high temperature austenitic stainless steel, enhance its high temperature strength and creep resistance. As Cu is known to cause embrittlement, the effect of Cu on room temperature mechanical properties that include fracture toughness and fatigue crack threshold of as-solutionized SUS 304H steel were investigated in this work. Experimental results show a linear reduction in yield and ultimate strengths with Cu addition of up to 5wt.% while ductility drops markedly for 5wt.% Cu alloy. However, the fracture toughness and the threshold stress intensity factor range for fatigue crack initiation were found to be nearly invariant with Cu addition. This is because the fracture in this alloy is controlled by the debonding from the matrix of chromium carbide precipitates, as evident from fractography. Cu, on the other hand, remains either in solution or as nano-precipitates and hence does not influence the fracture characteristics. It is concluded that small additions of Cu to 304H will not have adverse effects on its fracture and fatigue behavior.
Inheritance of Resistance to Nuclear Polyhedrosis Virus in Silkworm, Bombyx mori
( Ratna Sen ),( S. K. Ashwath ),( R. K. Datta ) 한국잠사학회 2001 International Journal of Industrial Entomology Vol.3 No.2
Inheritance pattern of resistance to Bombyx mori nuclear polyhedrosis virus (BmNPV) was studied in an Indian silkworm stock TX by single back-cross test method. The resistant parent [TX], susceptible parent [HM], their Fl, F2, and Fl progeny back-crossed to TX [BC(R)] and HM [BC(S)] were inoculated per os with a fixed concentration of BmNPV (0.5×10(7) PIB/ml) on the first day of second stadium. The cumulative mortality was recorded until day 10th post-inoculation. The results show that the resistance to BmNPV in TX fellow mono Mendelian inheritance pattern. The resistance dominated over the susceptibility at Fl. At F2, the resistant and susceptible offspring segregated in 3:1 ratio whereas at BC(S), the resistant and susceptible offspring segregated in 1:1 ratio. The response of BC(R) was more or less like the resistant parent TX which confirms the involvement of a major dominant gene conferring resistance to BmNPV in TX. The possible mechanism of inheritance of resistance in TX is discussed.