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On Generalization of Inequalities for Monotone Functions

Thesis Info

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Author

Butt, Saad Ihsan

Supervisor

Josip Pecaric

Program

PhD

Institute

Government College University

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2012

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/2240/1/2480S.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726796236

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The thesis comprises of generalized inequalities for monotone functions from which we deduce important inequalities such as reversed Hardy type inequalities, general- ized Hermite-Hadamard’s inequalities etc by putting suitable functions. The present thesis is divided into three chapters. The first chapter includes generalized inequalities given for C-monotone functions and multidimensional monotone functions. As a result of these inequalities, we de- duce reversed Hardy inequalities for C-monotone functions and multidimensional re- versed Hardy type inequalities with the optimal constant. Furthermore, we construct functionals from the differences of above inequalities and gives their n-exponential convexity and exponential convexity. By using log-convexity of these functionals we give refinements of these inequalities. Also we give mean-value theorems for these functionals and deduce Cauchy means for them. The second chapter consists of inequalities valid for monotone functions of the form f /h and f /h. These are also very interesting as by putting suitable functions we get one side of Hermite-Hadamard’s inequality and generalized Hermite-Hadamard’s inequality. Similarly as in the first chapter, we make functionals of these inequalities and gives results regarding n-exponential convexity and exponential convexity. Also we give mean value theorems of Lagrange and Cauchy type as well as we obtain non- symmetric Stolarsky means with and without parameter. In the third and the last chapter we consider Petrovi ́ type functionals obtained from c Petrovi ́ type inequalities and investigate their properties like superadditivity, sub- c additivity, monotonicity and n-exponential convexity. Also at the end of each chapter we discuss examples in which we construct further exponential convex functions and their relative properties.
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مولوی مہیش پرشاد

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Molecular Investigation for the Role of Coat Protein in Transmission of Two Different Geminiviruses

The Chickpea chlorotic dwarf viruses (CpCDV) are members of the proposed genus Mastrevirus of the family Geminiviridae. They are single-stranded DNA viruses transmitted by the leafhopper Orosius albicinctus Distant. This virus is notorious to cause chickpea stunt disease in chickpea. Chickpea is the major developed host of CpCDV. It is a winter/spring season trim, though cotton is developed amid the mid-year months with little, assuming any, cover between the two. In the field, the infection has just been distinguished in chickpea, lentil, sugar and beans. Cotton leaf curl disease (CLCuD) is a serious disorder of several plant species that belong to the family Malvaceae, the most important of which is cotton. CLCuD is caused by infections caused by viruses belong to the genus Begomovirus (family Geminiviridae) exclusively transmitted by the whitefly Bemisia tabaci Gennadius. which is the absolute most critical biotic requirement to cotton creation crosswise over Pakistan and northwestern India. A distinctive strain of CpCDV recognized in cotton plants, co-infected with Cotton leaf curl Burewala virus (CLCuBuV). Co-infection is additionally an essential for recombination happening amongst infections, and the accessible confirmation proposes that the present ordered structure of the family Geminiviridae has come about because of intergeneric recombination. Geminiviruses are transmitted in a circulative persisted and non-propagative manner and do not replicate in their insect vector. The capsids of all the whitefly transmitted geminivirus have at least one antigenic epitopes in like manner, and it has been proposed that those might be determinants of vector specificity, which would demonstrate that the coat protein (CP) assumes a prime part in infection transmission. Very few experiments have been performed so far to study the co-infection of a begomovirus together with a dicot infecting mastrevirus (CpCDV), infecting the same host plants i.e., Xanthium strumarium L. (weed), cotton and squash (dicot plants). In the coinfection of mastrevirus with begomovirus, mastrevirus not only expanded its host range but also has amplified individually from host plant. However, at that time it was still unclear whether the leafhopper transmits the CpCDV to new host plant or the whitefly did this job due to transencapsidation. Hence to explore this aforementioned aspect this study was designed to replace CP gene of CpCDV (Genus: Mastrevirus, xv Family: Geminiviridae) with the CP gene of Cotton leaf curl Burewala virus (CLCuBuV; Genus: Begomovirus, Family: Geminiviridae). Polymerase chain reaction (PCR) amplification of whole genome of CpCDV (except CP region by using primers in opposite orientation) and CP gene of CLCuBuV was done. Ligate these two PCR amplified fragments in order to construct mastrebegomo chimeric virus. Infectivity assay was done by agroinfiltration of infectious clones of CpCDV, CLCuBuV+Cotton leaf curl Multan betasatellite (CLCuMβ) and mastrebegomo chimeric virus into tobacco (Nicotiana benthamiana Domin.) and tomato (Solanum lycopersicum L.). The entire infectious clones alone and in combination were successfully transmitted and replicated inside the host plants and produce characteristics symptoms in tobacco and tomato leaves. However the plants infected with combination of CpCDV and CLCuBuV+ CLCuMβ showed more severe symptoms than others. Virus acquisition and transmission experiments were done using screen cages in an insectary. For this purpose aviruliferous whiteflies were used which first acquired the viruses during 48-72 hours from the agroinfiltered plants and then liberated to healthy tobacco and tomato plants for transmission for the period of one month. It was evident from the results that the B. tabaci unable to acquire and transmit CpCDV and mastrebegomo chimeric virus and the plants showed no symptoms of infection. Although whitefly successfully acquired and transmitted the begomovirus whose presence later confirmed by DNA extraction from whiteflies and symptomatic plants followed by PCR amplification of CP gene and full length genome of viruses for authentication of results. So it has been confirmed that whiteflies are not responsible for transmission of CpCDV and mastrebegomo chimeric virus from diseased plants to healthy one. Full-length sequences of dicot infecting mastreviruses and monocot infecting mastreviruses were obtained from GenBank and their sequence names were cross verified according to the new International Committee on Taxonomy of Viruses (ICTV) Master Species List 2016v1.3. For phylogenetic investigation, groupings were first adjusted in MEGA6 programming utilizing MUSCLE. For deciding the percent nucleotide identity, viral sequences were adjusted by MUSCLE in the sequence demarcation tool (SDT) program. The Recombination detection program (RDP-4) was utilized to recognize likely parents and the degree of recombination in dicot and xvi monocot contaminating mastreviruses. The interaction of CP of mastrebegomo chimeric virus protein with whitefly inhabiting endosymbiotic GroEL protein was determined by using several proteomics tools. The three dimentional models of both proteins were designed by using Iterative Threading ASSEmbly Refinement (ITASSER) server and their stereochemical properties were determined by drawing ramachandaran plots. Physiochemical properties and hydropathy plot of mastrebegomo chimeric virus protein and GroEL protein was determined by using ProtScale while ProptParam tool was used to calculate the several chemical and physical parameters of the both proteins. Finally The Z-DOCK server was used which is well-known for protein-protein docking that runs top 10 predicates in the form of protein data bank (PDB) files. More or less it can be inferred that substitution of CP gene may expand our comprehension about the range and circulation of mastreviruses crosswise over world and will give the important data with respect to their control. Co-infection open ways to discover the potential variables, which made the mastreviruses to advance from monocotyledonous plants to dicotyledonous and their capacity to cause infection in non-host plants, along these lines extending its host run with the progression of time.