Convex function and optimization techniques

Optimization is the process of maximizing or minimizing a desired objective function while satisfying the prevailing constraints. The optimization problems have two major divisions. One is linear programming problem and other is non-linear programming problem. But the modern game theory, dynamic programming problem, integer programming problem also part of the Optimization theory having wide range of application in modern science, economics and management. In the present work I tried to compare the solution of Mathematical programming problem by Graphical solution method and others as well as its theoretic descriptions. As we know that not like linear programming problem where multidimensional problems have a great deal of applications, non-linear programming problem mostly considered only in two variables. Therefore for nonlinear programming problems we have an opportunity to plot the graph in two dimensions and get a concrete graph of the solution space which will be a step ahead in its solutions. Nonlinear programming deals with the problem of optimizing an objective function in the presence of equality and inequality constraints. The development of highly efficient and robust algorithms and software for linear programming, the advent of high speed computers, and the education of managers and practitioners in regard to the advantages and profitability of mathematical modeling and analysis, have made linear programming an important tool for solving problems in diverse fields. However, many realistic problems cannot be adequately represented or approximated as a linear program owing to the nature of the nonlinearity of the objective function or the nonlinearity of any of the constraints

Design, comparative study and analysis of CDMA for different modulation techniques

AbstractIn this work, we have design a MIMO–CDMA using 4∗8 antennas with the combination of MMSE (Minimum Mean square Error Equalizer) for BPSK (Binary Phase shift Keying), QPSK (Quadrature Phase Shift Keying), 16-QAM, 64-QAM and 256-QAM (Quadrature Amplitude Modulation) modulation schemes. The analysis is built on the basis of transmit–received signal, constellation and MMSE plot simulated on a MatLab/Simulink. On the basis of BER (Bit-Error-Rate), it is also concluded that this work is mostly suitable for high order modulation schemes as the BER of 16-qam, 64-QAM and 256-QAM is zero. The proposed study has increased the quality of the wireless link and Inter-Symbol-Interference (ISI) is likewise cut by applying a combination of MMSE and MIMO (Multiple In and Multiple Out) with OSTBC (Orthogonal space Time Block Code) encoder and combiner

Preparation and mechanical properties of Nanoclay-MWCNT/Epoxy hybrid nanocomposites

[EN] Among the various kinds of reinforcing element, Multi Wall Carbon Nano-tubes (MWCNT) and Nanoclay have found much more attention as a filler element to upgrade the mechanical properties of polymer composite material. In this paper, production of hybrid nanocomposites and the effect of MWCNT and nanoclay on mechanical properties of hybrid nanocomposites have been evaluated. In hybrid nanocomposites, MWCNT and nanoclay are embedded in epoxy resin. The processing of hybrid nanocomposite is always been a difficult task for researcher to prepare defects free samples. Here, the processing of Epoxy/Nanoclay-MWCNT hybrid composites has been done by using homogenizer and ultrasonic techniques for complete dispersion of nanoparticles into epoxy resin. The MWCNT and nanoclay were embedded into epoxy resin in different weight fractions and mixtures were used for tensile test and hardness specimen production. The tensile modulus and tensile strength values have been calculated via tensile tests. The test result shows that tensile modulus of samples increases as the filler content increase up to certain extent but then start decreasing. Also the elongation reduces as the filler content rises in the epoxy which shows the brittleness present in the samples. Rockwell hardness on B-scale was conducted on Nanocomposite samples and found that increasing the filler content excessively does not improve hardness as much.Kumar, S.; Gupta, A. (2021). Preparation and mechanical properties of Nanoclay-MWCNT/Epoxy hybrid nanocomposites. Journal of Applied Research in Technology & Engineering. 2(1):17-21. https://doi.org/10.4995/jarte.2021.14239OJS172121Alsafee, A.B., Al-ajaj, I.A., Khalili, A.S. (2014). Concentration effect of multi walled carbon nanotube on mechanical properties of epoxies composites. International Journal of Application or Innovation in Engineering & Management, 3(2), 334-343.Ayatollahi, M.R., Shadlou, S., Shokrieh, M.M. (2011a). Mixed mode brittle fracture in epoxy/multi-walled carbon nanotube nanocomposites. Engineering Fracture Mechanics, 78, 2620-2632. https://doi.org/10.1016/j.engfracmech.2011.06.021Ayatollahi, M.R., Shokrein, M., Shadlou, S., Kefayati, A.R. (2011b). Mechanical and electrical properties of epoxy/multiwalled carbon nanotube/Nanoclay nanocomposites. Iranian Polymer Journal, 20(10), 835-843.Bhuvaneshwaran Mylsamy, Sathish Kumar Palaniappan, Sampath Pavayee Subramani, Samir Kumar Pal., Karthik Arucham. (2019). Impact of nanoclay on mechanical and structural properties of treated Coccinia indica fibre reinforced epoxy composites. Journal of Material research and Technology, 8(6), 6021-6028. https://doi.org/10.1016/j.jmrt.2019.09.076Gojny, F.H., Wichmann, M.H.G., Fiedler, B., Karl, S. (2005). Influence of different carbon nanotubes on the mechanical properties of epoxy matrix composites - a comparative study, Composites Science and Technology, 65, 2300-2313. https://doi.org/10.1016/j.compscitech.2005.04.021Ho, M.W., Lam, C.K., Lau, K.T., Ng, D.H.L., Hui, D. (2006). Mechanical properties of epoxy-based composites using Nano clays. Composite Structures 75, 415-421. https://doi.org/10.1016/j.compstruct.2006.04.051Karatas, S., Apohan, N.K., Demirer, H., Gungor, A. (2007). Polyimide-silica hybrid coatings: morphological, mechanical, and thermal investigations. Polymers for Advanced Technologies, 18(6), 490-496. https://doi.org/10.1002/pat.909Kim, M.T., Rhee, K.Y., Lee, J.H., Hui, D., Lau, A. K.T. (2011). Property enhancement of a carbon fiber/epoxy composite by using carbon nanotubes". Composites Part B: Engineering, 42(5), 1257-1261. https://doi.org/10.1016/j.compositesb.2011.02.005Lakshmi, M.S., Narmadha, B., Reddy, B.S.R. (2008). Enhanced thermal stability and structural characteristics of different MMT-clay/epoxy-nanocomposite materials. Polymer Degradation and Stability, 93(1), 201-213. https://doi.org/10.1016/j.polymdegradstab.2007.10.005Lee, D., Song, S.H., Hwang, J., Jin, S.H., Park, K.H., Kim, B.H., Hong, S.H., Jeon, S. (2013). Enhanced mechanical properties of epoxy nanocomposites by mixing noncovalently functionalized boron nitride nanoflakes. Small, 9(15), 2602-2610. https://doi.org/10.1002/smll.201203214Liu, W.D., Zhu, B.K., Zhang, J., Xu, Y.Y. (2007). Preparation and dielectric properties of polyimide/silica nanocomposite films prepared from sol-gel and blending process. Polymers for Advanced Technologies, 18(7), 522-528. https://doi.org/10.1002/pat.910Mat Yazik, M.H., Sultan, M.T.H., Norkhairunnisa Mazlan, Abu Talib, A.R., Naveen, J., Shah, A.U.M., Safri, S.N.A. (2020). Effect of hybrid multi-walled carbon nanotube and montmorillonite nanoclay content on mechanical properties of shape memory epoxy nanocomposite, Journal of Material research and Technology, 9(3), 6085-6100. https://doi.org/10.1016/j.jmrt.2020.04.012Mahesh, Hosur, Tanjheel, H. Mahdi, Mohammad E. Islam, Jeelani, S. (2017). Mechanical and viscoelastic properties of epoxy nanocomposites reinforced with carbon nanotubes, nanoclay, and binary nanoparticles, Journal of Reinforced Plastics and Composites, 36(9), 667-684. https://doi.org/10.1177/0731684417691365Mahesh, Hosur, Tanjheel, Mahdi, Jeelani, S. (2018). Studies on the performance of multi-phased carbon/epoxy composites with nanoclay and multi-walled carbon nanotubes. Multiscale and Multidiscip. Model. Exp. and Des., 1, 255-268. https://doi.org/10.1007/s41939-018-0017-9Rozenberg, B.A., Tenne, R. (2008). Polymer-assisted fabrication of nanoparticles and nanocomposites. Progress in Polymer Science, 33(1), 40-112. https://doi.org/10.1016/j.progpolymsci.2007.07.004Sun, D., Chu, C.C., Sue, H.J. (2010). Simple approach for preparation of epoxy hybrid nanocomposites based on carbon nanotubes and a model clay. Chemistry of Materials, 22(12), 3773-3778. https://doi.org/10.1021/cm1009306Zhou Y. X., Wu P. X., Cheng Z-Y., Ingram J., Jeelani S. (2011). Improvement in electrical, thermal and mechanical properties of epoxy by filling carbon nanotube. Express Polymer Letters, 2(1), 40-48. https://doi.org/10.3144/expresspolymlett.2008.

(SI10-057) Effect of Time-delay on an SIR Type Model For Infectious Diseases with Saturated Treatment

This study presents the complex dynamics of an SIR epidemic model incorporating a constant time-delay in incidence rate with saturated type of treatment rate. The system is studied to observe the effect of time lag in the asymptotic stability of endemic equilibrium states. We also establish global asymptotic stability of both disease-free and endemic equilibrium states by Lyapunov direct method with the help of suitable Lyapunov functionals. The existences of periodic solutions are ensured for the suitable choice of delay parameter. Finally, we perform numerical simulations supporting the analytical findings as well as to observe the effect of time-delay. The theoretical and numerical results together show delay can have both stabilizing and destabilizing effects on the system. Moreover, we observe that infection may die out from the population when the corresponding system without delay has two endemic equilibrium for appropriate choice of time-delay

Preliminary Investigation of Antimicrobial Property of Acacia leucophloea Leaves Extract

Leaves of indigenous plant Acacia leucophloea have been successively extracted using different solvents like hexane, methanol and water. Extract was evaluated for its antibacterial activity using two assay method Kirby bauer disc diffusion and tube dilution assay. Results of the given study revealed that the methanolic extract is potential antibacterial agent specifically for E coli & & S aureus

MANAGEMENT OF QUADRIPLEGIA INDUCED BY SPINAL CORD INJURY WITH PANCHAKARMA - A CASE STUDY

A 30 year old male patient with quadriplegia induced by spinal cord injury was treated with ayurvedic medicine and Panchkarma therapies. Patient presented with quadriplegia and inability to sit/stand even with support and having no bladder/bowel control. Spinal Cord Independence Measure (SCIM) was 16 showing high dependence and also muscle wasting was present. Patient had history of swimming pool accident causing fracture C4-C5 spine and fixation through surgery in 2011. Ayurveda explains this disease as Vatavyadhi. Snehana and Svedana formed the first line of treatment to pacify the vitiated Vata while Shalishashtikapindasveda and Matravasti worked as Balya for Mansa and Asthi dhatu and also Anulomana. Snehadhara improves motor and sensory system resulting in improved function of all limbs. Management was done with repeated admissions for Panchakarma therapy during which overall strength and reflexes improved with Spinal Cord Independence Measure (SCIM) score reaching 47 from original 16 indicating improvement in independence of patient from complete dependence to partial independence in six months time

Skellam Type Processes of Order K and Beyond

In this article, we introduce Skellam process of order k and its running average. We also discuss the time-changed Skellam process of order k. In particular we discuss space-fractional Skellam process and tempered space-fractional Skellam process via time changes in Poisson process by independent stable subordinator and tempered stable subordinator, respectively. We derive the marginal probabilities, Levy measures, governing difference-differential equations of the introduced processes. Our results generalize Skellam process and running average of Poisson process in several directions.Comment: 22 pages, 1 figur