Best k-digit Rational Approximations ― True Versus Convergent-, Decimal-based Ones: Quality, Cost, Scope

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.

ON SOME RECURSION RELATIONS FOR HORN'S HYPERGEOMETRIC FUNCTIONS OF THREE VARIABLES

P. Agarwal,A. SHEHATA,S. I. MOUSTAFA,K. CHAKRABORTY 장전수학회 2021 Proceedings of the Jangjeon mathematical society Vol.24 No.2

The principal aim of this paper to study the recursion formulas for the Horns hypergeometric functions of three variables. Earlier in [Shehata, A.; and Moustafa, S.I. Some new results for Horn's hypergeometric functions Γ1 and Γ2. Journal of Mathematics and Computer Science, (2021), 23 (1), 26{35.], and Pathan et al. [Pathan, M.A.; Shehata, A.; and Moustafa, S.I. Certain new formulas for the Horns hypergeometric functions. Acta Uni- versitatis Apulensis, (2020)] have studied the new results for Horns hypergeometric functions. Motivated by the above works here we will derive some contiguous relation for the families of Horn hypergeometric functions GA, GB, GC, GD and G C of three variables. After that we will establish the differential reclusion relations and differential operators for GA, GB, GC, GD and G* C of three variables, respectively.

Reduction of noxious Cr(VI) ion to Cr(III) ion in aqueous solutions using H2O2 and UV/H2O2 systems

M.H. Dehghani,B. Heibati,A. Asadi,I. Tyagi,S. Agarwal,V.K. Gupta 한국공업화학회 2016 Journal of Industrial and Engineering Chemistry Vol.33 No.-

Conversion of the toxic Cr(VI) to the less toxic Cr(III) in aqueous solutions by chemical andphotochemical reduction was carried out using H2O2 and UV radiation. The whole mechanism was wellelucidated and investigated using potassium dichromate (K2Cr2O7) as a standard model compound. Theeffects of potential factors affecting the reduction efficiency were well studied and optimized, theoptimized parameters such as concentration of H2O2 (from 0.5 to 1.5 M), pH (from 5 to 9), irradiationtime (0 to 140 min) and reaction time (0 to 120 min). Initial concentration of Cr(VI) in the solution wasvaried from 0.1 to 15 mg/L plays a significant role in the mechanism involves for the reduction of noxiousCr(VI) to less toxic Cr(III).

REAL COVERING OF THE GENERALIZED HANKEL-CLIFFORD TRANSFORM OF FOX KERNEL TYPE OF A CLASS OF BOEHMIANS

AGARWAL, PRAVEEN,AL-OMARI, S.K.Q.,CHOI, JUNESANG Korean Mathematical Society 2015 대한수학회보 Vol.52 No.5

We investigate some generalization of a class of Hankel-Clifford transformations having Fox H-function as part of its kernel on a class of Boehmians. The generalized transform is a one-to-one and onto mapping compatible with the classical transform. The inverse Hankel-Clifford transforms are also considered in the sense of Boehmians.

Development of a Triggering Arrangement For the KALI-30GW MARX Generator

S. Mitra,T. S. Kolge,Ritu Agarwal,P. C. Saroj,Ankur Patel,K. Senthil,Vishnu Sharma,S. V. Tewari,Archana Sharma,K. C. Mittal 한국물리학회 2015 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.66 No.4

This paper reports the design methodology and implementation experiments for a solid-statebasedtriggering arrangement for the MARX generator of the KALI-30GW (1 MV, 30 kA, 80 ns)pulsed power system. The 15-stage bipolar MARX generator of the KALI-30GW system is triggeredusing a trigatron-type spark gap. An insulated-gate bipolar-transistor (IGBT)-based trigger supplyis used to trigger the first spark gap, and the next two spark gaps are triggered by using internallygeneratedtrigger pulses. Optically-isolated arrangements are provided for a human interface. Theentire assembly was tested with a dummy copper sulphate load, and an excellent triggering rangeof 7 − 12 kV was achieved. The circuit diagram, analysis and experimental results of the triggeringarrangement are presented in the paper.

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.

VLS-like growth and characterizations of dense ZnO nanorods grown by e-beam process

Agarwal, D C,Chauhan, R S,Avasthi, D K,Sulania, I,Kabiraj, D,Thakur, P,Chae, K H,Chawla, Amit,Chandra, R,Ogale, S B,Pellegrini, G,Mazzoldi, P Institute of Physics [etc.] 2009 Journal of Physics. D, Applied Physics Vol.42 No.3

<P>We present a new approach to produce ZnO nanorods in a reproducible manner at a temperature lower than other physical vapour deposition techniques, such as the vapour–liquid–solid mechanism. Arrays of well-aligned ZnO nanorods of uniform diameter have been synthesized on the Si substrate precoated with Au, using a simple electron beam evaporation method without the flow of any carrier gas. Scanning electron microscopy and atomic force microscopy characterizations show that as-grown nanorods are well aligned and uniform in diameter. X-ray diffraction measurements and clear lattice fringes in high-resolution transmission electron microscopy image show the growth of good quality polycrystalline hexagonal ZnO nanorods and a ⟨0 0 2⟩ growth direction. The polarization-dependent studies of near edge x-ray absorption fine structure (NEXAFS) are performed to investigate the electronic structure of the zinc and oxygen ions. The analysis of NEXAFS spectra at different angles of incidence of photon flux indicates the formation of ZnO nanorods having anisotropic behaviour of O and Zn states. The photoluminescence spectrum exhibits strong ultraviolet emission at 385 nm and the UV–visible spectrum also shows a band-gap transition around 390 nm indicating the good quality of nanorods. The catalytic growth mechanism of the ZnO nanorods is discussed on the basis of experimental results in this work.</P>

Pathway fractional integral operator associated with struve function of first kind

K.S. NISAR,S.R. MONDAL,Praveen Agarwal 장전수학회 2016 Advanced Studies in Contemporary Mathematics Vol.26 No.1

The aim of this paper to study the pathway fractional integral operator as- sociated with the Struve function of rst kind which is expressed in terms of the general- izedWright hypergeometric function. Furthermore the special cases for the trigonometric functions are also consider.

Novel Time-Domain Parameters for Detection and Classification of Flaws Using Pulsed Eddy Current Technique

K. Sambasiva Rao,T. V. Beatriceveena,C. S. Angani,Lucky Agarwal 한국자기학회 2020 Journal of Magnetics Vol.25 No.3

Pulsed eddy current (PEC) testing is an electromagnetic nondestructive evaluation (NDE) technique which is used for detection and classification of flaws. This paper presents an approach for the extraction of novel timedomain flaw parameters viz. amplitude ratio (V1/V0) and time constant (τ) for detection and classification of different flaws. Experiments are carried out on stainless steel (SS-316) plate with artificial EDM notches whose width (1.0 mm & 3.0 mm) and depth (1.0 mm to 6.0 mm) varied. The proposed approach can classify both surface and sub-surface flaws in an 8.0 mm thick SS plate. The advantage of the proposed approach is that it doesn’t require a reference signal subtraction or signal processing methodologies for the detection and classification of flaws.

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.