Journal Vol – 17 No -9, September 2022

Abstract:

Basically, time scale calculus is the theory of unification of traditional calculus with that calculus of difference i.e. discrete calculus. Time Scale Calculus is a field of discussion in the area of traditional analysis of mathematics. It focuses on the dynamic system which has a lot of applications in various fields of life. Calculus of time scales is a valuable field due to numerous applications in covid-19 disease cases. Notably, Time scale calculus has a long relation with mathematical inequalities that can be discussed with fractional calculus. The Anderson Integral Inequality, which provides a lower constraint for the integration of convex mapping in the form of the averages of each constituent, is described in this research paper on ∇- time-scale calculus. On ∇-time scale we formulated Anderson’s integral inequality as given below: if φ_j (j=1,….,α) accomplish some appropriate cases.

Keywords:

Time scales,Anderson’s inequality,∇ - differentiable,

Refference:

I. A.M. Fink Anderson’s inequality, Math. Inequal. Appl. 6 (2003) 241-245.

II. B. Aulbach. S. Hilger, Linear dynamic processes with inhomogeneous time scales, in: Nonlinear Dynamics and Quantum Dynamical systems, Akademie Verlag, Berlin, 1990.

III. B. Kaymakcalan, V. Lakshmikantham, S. Sivasundaram, Dynamic Systems on Measure Chains, Kluwer academic Publishers, Dordrecht, 1996.
IV. B.Z. Anderson, An inequality for convex functions, Nordisk Mat. Tidsk 6
(1958) 25-26.
V. D.S. Mitrinovic, J.E. Pecaric, A.M. Fink, Classical and New inequalities in Analysis, Kluwer Academic Publisher, Dordrecht, Boston, London, 199.
VI. M Bohner, A. Peterson, Dynamic Equations on Time Scales, Birkhauser,
Boston, Basel, Berlin, 2001.
VII. S. Hilger, Analysis on measure chains –A unified approach to continuous and discrete calculus, Res Math. 18 (1990) 28-56.

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Abstract:

A comparative analysis of different linearization Techniques for sensor signals is presented. Several solutions in the analog, and digital domains are considered. The analysis will help designers to choose the linearization technique best suited for a given application

Keywords:

Sensors,Transducers,linearization,Analog Sensors,Digital Sensors,Sensor Linearization,

Refference:

I. “Analysis of Temperature Dependent Effects on I-V Characteristics of Heterostructure Tunnel Field Effect 9. Transistors” by Jie Min, IEEE Student Member, Lingquan (Dennis) Wang, Jianzhi Wu, IEEE Student 10 Member, and Peter M. Asbeck, IEEE Fellow, IEEE Journal of the Electron Devices Society · October 2016 11.
II. “A mixed signal sensor interface micro instrument” by Keith El Kraver et al. Published in Elsevier journal of Sensors and Actuator. A 91 (2001) 266-277.
III. “A stable solution-processed polymer semiconductor with record high-mobility for printed transistors”By Jun Li1*, Yan Zhao2*, Huei Shuan Tan1, Yunlong Guo2, Chong-An Di2, Gui Yu2, Yunqi Liu2, Ming Lin1, Suo Hon Lim1, Yuhua Zhou4, Haibin Su4 & Beng S. Ong1,3,5 in Scientific Reports · October 2012
IV. Callendar-Van Dusen Equation and RTD Temperature Sensors,1-800-459-9459 U.S. and Canada www.ilxlightwave.com.
V. “Digital Linearization & Display of Non-linear Analog (Sensor) Signals” by M. P. Kraska.
VI. “Dynamic system identification and sensor linearization using neural network techniques”. Doctoral Thesis by Prateek Mishra.
VII. “Introduction and Classification of Sensors by Prof. G. R Sinha of International Institute of Information Technology Bangalore”. Article presented in Research Gate at: https://www.researchgate.net/publication/321625555: introduction and Classification of Sensors.
VIII. “Linearized Thermistor Multivibrator Bridges for Temperature Measurement”, by Dragan k. Stankov16 in IEEE Transactions on Instrumentation and Measurement, June 1974.
IX. “Lookup Table Optimization for Sensor Linearization in Small Embedded Systems” by Lars E. Bengtsson, Journal of Sensor Technology, 2012, 2, 177-184.
X. “Linearization of Thermocouple Voltages” by Gerald Conrad, Review of Scientific Instruments 39, 1682 (1968); doi: 10.1063/1.1683201published by Published by the AIP Publishing.
XI. “Multi-Channel Sensor Linearization in Field Programmable Gate Array for Real Time Application,” by Durlav Sonowal, Manabendra Bhuyan, Journal of Sensors & Transducers, Vol. 191, Issue 8, August 2015, pp. 135-151.
XII. “Optimized Sensor Linearization for Thermocouple”. A White paper published by Texas Instruments in TIDUA11A–June 2015–Revised September 2015
XIII. Revised Thermocouple Reference Tables, Type K. Data Table by Omega Technologies, 2012.
XIV. RTD Temperature vs. resistance Table: Published by the Omega technologies in 2012
XV. “Signal Conditioning and Linearization of RTD Sensors”, by Collin Wells of Texas Instruments. HPA Precision Linear Applications 9/24/11
XVI. “Some Investigations on Measurement Techniques for Process Instrumentation” – An Article published by 6. Saibal Pradhan, Jadavpur University.
XVII. “Signal Conditioning and Linearization of RTD 7. Sensors” by Collin Wells of Texas Instruments. HPA Precision Linear Applications 9/24/11

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Abstract:

In this paper, we have analyzed the basic properties and related theorems of Jordan's right derivations on semiprime -rings with their mathematical simulation. We mainly focused on the characterizations of  and -torsion-free semiprime -ring by using Jordan Right Derivations. Important lemmas and theorems related to Jordan derivation on semiprime -ring have been derived here with sufficient calculations. Our main objective is to prove that if  is a -torsion free semiprime -ring and ,  be the Jordan right derivations on  provided that  then . In this paper, we have analyzed the basic properties and related theorems of Jordan's right derivations on semiprime -rings with their mathematical simulation. We mainly focused on the characterizations of  and -torsion-free semiprime -ring by using Jordan Right Derivations. Important lemmas and theorems related to Jordan derivation on semiprime -ring have been derived here with sufficient calculations. Our main objective is to prove that if  is a -torsion free semiprime -ring and ,  be the Jordan right derivations on  provided that  then .

Keywords:

Γ-Ring,Semiprime Γ-Ring,Derivation,Jordan Right Derivation,

Refference:

I. A.C. Paul and Md. Mizanor Rahman, Jordan left derivations on semiprime gamma rings, Int. J. Pure Appl. Sci. Technol., 6(2) (2011), 131-135.
II. A. K. Halder, A. C. Paul, Jordan Left Derivations on Lie Ideals of Prime Γ-rings, Punjab University Journal of Mathematics, Vol. 44(2012) pp.23-29.
III. A. K. Halder and A. C. Paul, Semiprime Γ-Rings with Jordan Derivations, Journal of Physical Sciences, Vol.17,2013,111-115.
IV. M.F. Hoque and A. C. Paul, Centralizers on Prime and Semiprime Gamma Rings, arXiv: Rings and Algebras (2015).
V. M. M. Rahman and A. C. Paul, DERIVATIONS ON LIE IDEALS OF COM- PLETELY SEMIPRIME Γ-RINGS, Bangladesh J. SCI. Res. 27(1):51-61, 2014 (June).
VI. Mustafa Asci and Sahin Ceran, The commutativity in prime gamma rings with left derivation, International Mathematical Forum, 2(3) (2007), 103-108.
VII. N. Nobusawa, On the generalization of the ring theory, Osaka J. Math., 1(1964), 81-89.
VIII. Omar Faruk, Md Mizanor Rahman, Lie Ideals on Prime Γ-Rings with Jordan Right Derivations, Annals of Pure and Applied Mathematics, Vol.19, No.2, 2019, 183-192.
IX. Omar Faruk, Md Mizanor Rahman, Generalized Jordan Right Derivations on Prime and Semiprime Γ-Rings, Journal of Mechanics of Continua and Mathematical Sci- ences, Vol.14, No.4, July-August (2019) pp 268-280.
X. S. Soyturk, The commutativity of prime gamma rings with derivation, Turk. J. Math. 18 (1999), 149-155.
XI. S. Sapanci and A. Nakajima, Jordan derivations on completely prime gamma rings, Math. Japonica, 46(1) (1997), 47-51.
XII. Y. Ceven, Jordan left derivations on completely prime Γ-ring, C.U. Fen-Edebiyat Fakultesi Fen Bilimlere Dergisi, 23(2), 2002, 39-43.
XIII. W.E. Barnes, On the Γ-rings of Nobusawa, Pacific J. Math. 18(1966), 411-422.

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Abstract:

This paper deals with the design and prototype development of an inverter to feed AC power to an induction motor coupled with a submersible pump. In this type of load, input power is proportional to the cube of the speed. The inverter is fed from a 48 V rechargeable battery, which is charged through the solar panel. Four numbers of the solar panel each of 165 W, 12 V rated are used for charging the battery. The basic intention of this research work is to start an induction motor with lower voltage and lower frequency, keeping v/f constant, such that the starting current is low. This concept can be utilized to run a submersible pump in a remote area where there is no electric power supply or where there is a problem in the distribution system. Submersible pumps are normally operated for a small interval (60 to 180 min). This energy can be supplied by a 48 V, 75 Amp-Hour Lead Acid type rechargeable battery. The experiment has been conducted with a Lead acid battery but the Lithium Ion battery gives better performance. The solar panel (cell) is used to charge the battery for around 8 hours from morning and with the fully charged battery, the pump is run through an inverter for a time of around 150 min. An inverter has been designed to run a 1 hp induction motor coupled with a submersible pump. The motor is started with low voltage with v/f control. Gradually the full voltage is applied and the motor runs at the rated speed. After an operation of a preset time, the motor is stopped. With VVVF drive the battery life has increased compared to a Direct online starter.

Keywords:

Lead acid battery,Li-Ion battery,V/f control of IM,Starting torque,Energy stored in battery,

Refference:

I. TabishNazir Mir and Abdul Hamid Bhat, “Comparative Analysis of Pulse Width Modulated Voltage Source Inverter Fed Induction Motor Drive and Matrix Converter Fed Induction Motor Drive” 1st IEEE international conference on Power Electronics, Intelligent control and energy systems, ICPEICES-2016
II. Abdul Shavan and R N Sharma, “Water Consumption Patterns in Domestic Households in Major cities”, Economic and Political weekly, June 9, 2007.
III. Asoke Kumar Paul, I Banerjee, B K Santra and N Neogi, “Adjustable speed drives for rolling mill applications”, Steel India, March 2008, Vol. 30, No. 2, pp 46-50, Published by Steel Authority of India Limited.
IV. Joon Sung Park etal, “Implementation of VVVF drive for three phase induction machine” Published in 2016 International Symposium on Power Electronics, Electrical Drives, Automation and Motion (SPEEDAM).
V. M Ramana Rao, P Vinnarasi Ponnury, V Parvathy and S Magesh, VVVF drive features, commissioning procedure and challenges”, International journal of electrical and electronics engineering and telecommunications, Special Issue, Vol. 1, No. 1, March 2015.

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