Finite-difference solutions of tenth-order boundary-value problems

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.In this thesis finite difference methods are used to obtain numerical solutions for a class of high-order ordinary differential equations with applications to eigenvalue problems. Two families of numerical methods are developed for tenth-order boundary-value problems and global extrapolations on two and three grids are considered for the special problem. Special nonlinear tenth-order boundary-value problems are solved using a family of direct finite difference methods which are adapted to solve a general linear and nonlinear boundary-value problem. These methods convert the ordinary differential equation into a set of algebraic equations. If the original ordinary differential equations are linear, the finite difference equations will give linear algebraic equations. If the ordinary differential equation are nonlinear, the resulting finite difference equations will be nonlinear algebraic equations. These nonlinear equations are first linearized by Newton's method. The methods developed are of orders two, four, six, eight, ten and twelve. The error analyses are discussed. A generalized form is given to solve a class of high-order boundary-value problems by converting the differential equation to a system of first-order equations. The method based on using a Pade rational approximant to the exponential function for general boundary-value problems is applied to a tenth-order eigenvalue problem associated with instability in a Benard layer and numerical results are compared with asymtotic estimates appearing in the literature. This method may be implernented on a parallel computer. The method is extended to a twelfth-order eigenvalue problern in an appendix. The algorithms developed are tested on a variety of problems from the literature. The REDUCE package is used to obtain the parameters in the numerical methods and all computations are carried out on a Sun Workstation at Brunel University using Fortran 77 with double precision arithmetic.This study is funded by the Ministry of Education of Pakistan, Islamabad

1-7-Sep-2014, A Dooms Day for Apple Farming in Kashmir

Apple industry is main source of income in Kashmir, especially the people living in rural areas. Apple farming, strengthened the economics states of Kashmir from last two decades and is now economic hub of Kashmir. Directly as well as indirectly about 70% of rural population in Kashmir earn their living through apple farming. On the basis of these beneficiaries, farmers have now changed their mood of production. They (farmers) are now transforming Agricultural land into the Apple farming because Apple farming has comparatively more advantages than other agricultural production. The area under apple production is now increasing rapidly day by day while as area under agriculture is shrinking day by day.Apple industry was functioning with speed and rhythm, but 2014 floods have paralysed it. These floods have destroyed this industry at a large magnitude. Floods have created the problems like soil erosion, siltation, falling of leaves, loss of blossoms, cankers, root rots and complete damage of some areas due to the accumulation of water in orchards for a long time. Damages to fruit production have been reported to the extent of 52.9% , an area  127232 ha have been effected with production loss of  1119738 MTs  resulting in to the economic loss of 1565.00 Crore approx. The farmers have taken KCC and CCF loans on behalf of orchard lands to meet the cost of capital used in the production of apple crop. Farmers have to refund these loans to respective banks with interest of 7% and 12% respectively. But unfortunately floods have left farmers paralysed and income less, as their main source of income has damaged. So refunding such loans is big challenge to farmers.  The top most demand of flood effected farmers to government is to remit their KCC and CCF loans which they had taken for the production of apple. This could lead to problem of unemployment and restlessness among people if not taken into the consideration.  The government should immediately come forward to save this industry and should cooperate with the farmers to resolve their problems. Keywords: Apple farming, Rural life, Luxury goods, Transforming land, 2014 floods, Soil erosion, root rots, cankers, production loss, KCC and CCF loans

Two new species of Pseudolasius (Hymenoptera: Formicidae) from India

Descriptions of two new species of Pseudolasius based on worker caste and sexuals are provided from India. With addition of these two species collected in lower Shivalik range of Northwest Himalaya, four species signify the genus Pseudolasius from India. An identification key to the workers of Indian Pseudolasius species is provided

Catalytic Activity of Tungstate & Molybdate Ions In the Epoxidation of Maleic Acid

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Assessment of seed quality parameters and effect of physical and chemical treatments on seed germination of Myriophyllum Spicatum L.

The present study was undertaken to understand the fruit and seed morphology, seed viability and effect of various physical and chemical factors on seed germination allowing us to explore the spread potential and/or seedling recruitment mechanism in Myriophyllum spicatum L.. The fruit of the species is a schizocarp, while as seed is a nutlet. The seed set was recorded to be ranging from 70.98-77.91% across the standing water populations, whereas no seed set was observed in running water populations due to the lack of an effective pollination system. The seed viability ranged from 85-90%. For in-vitro seed germination studies, the seeds were subjected to different physical and chemical treatments under alternate light and dark as well as continuous dark conditions. The seeds in control and those treated with different concentrations of GA3 and IAA and those whose epicarp and mesocarp were removed did not show any signs of germination. However, it was observed that surgical exposure of the embryo (cutting of hard endocarp of seed) has a promoter effect on germination and maximum percentage germination (76.66 ± 5.77) was recorded due to surgical exposure of embryo plus different concentrations of GA3. Moreover, a good germination percentage was recorded in seeds subjected to chilling treatment. Further, it was observed that seed germination of one-year-old seeds was less if compared to the current year seeds and overall percentage germination was higher in alternate light and dark if compared to continuous dark conditions in all the treatments.Thus, we conclude that the dormancy of the seeds is due to the hard endocarp and that the light has a promoting effect on germination. With the increase in the age of the seeds, there is decrease in their viability and hence germination. The chilling winter temperature of the Kashmir is responsible for breaking the hard endocarp of the seeds leading to their germination and hence spread of the populations.The present study was undertaken to understand the fruit and seed morphology, seed viability andeffect of various physical and chemical factors on seed germination allowing us to explore thespread potential and/or seedling recruitment mechanism in Myriophyllum spicatum L.. The fruit ofthe species is a schizocarp, while as seed is a nutlet. The seed set was recorded to be ranging from70.98-77.91% across the standing water populations, whereas no seed set was observed in runningwater populations due to the lack of an effective pollination system. The seed viability ranged from85-90%. For in-vitro seed germination studies, the seeds were subjected to different physical andchemical treatments under alternate light and dark as well as continuous dark conditions. Theseeds in control and those treated with different concentrations of GA3 and IAA and those whoseepicarp and mesocarp were removed did not show any signs of germination. However, it wasobserved that surgical exposure of the embryo (cutting of hard endocarp of seed) has a promotereffect on germination and maximum percentage germination (76.66 ± 5.77) was recorded due tosurgical exposure of embryo plus different concentrations of GA3. Moreover, a good germinationpercentage was recorded in seeds subjected to chilling treatment. Further, it was observed thatseed germination of one-year-old seeds was less if compared to the current year seeds and overallpercentage germination was higher in alternate light and dark if compared to continuous darkconditions in all the treatments.Thus, we conclude that the dormancy of the seeds is due to thehard endocarp and that the light has a promoting effect on germination. With the increase in theage of the seeds, there is decrease in their viability and hence germination. The chilling wintertemperature of the Kashmir is responsible for breaking the hard endocarp of the seeds leading totheir germination and hence spread of the populations.Avaliação de parâmetros de qualidade de sementes e efeito de tratamentos físicose químicos na germinação de sementes de Myriophyllum spicatum L.ResumoO presente estudo foi realizado para compreender a morfologia do fruto e da semente, a viabilidadeda semente e o efeito de vários fatores físicos e químicos na germinação de sementes, permitindo-nosexplorar o potencial de disseminação e/ou mecanismo de mudas de recrutamento em Myriophyllumspicatum L. O fruto da espécie é um chisocarpo, enquanto a semente é uma noz. A produção desementes variou de 70,98 a 77,91% entre as populações de água paradas, enquanto que nenhumconjunto de sementes foi observado em populações de água corrente, devido à falta de um sistemaeficaz de polinização. A viabilidade das sementes variou de 85-90%. Para estudos in vitro de germinaçãodas sementes, as sementes foram submetidas a diferentes tratamentos físicos e químicos sob luz eescuridão alternadas, bem como contínuo escuro. As sementes de controle e aquelas tratados comdiferentes concentrações de GA3 e IAA e aquelas cujo epicarpo e mesocarpo foram removidosnão mostraram quaisquer sinais de germinação. No entanto, observou-se que a exposição cirúrgicado embrião (corte do endocarpo rígido de semente) tem um efeito sobre a germinação e efeitopromotor sobre a germinação e um percentual máximo (76,66 ± 5,77) foi registada por exposiçãocirúrgica do embrião a diferentes concentrações de GA3. Além disso, a percentagem de germinaçãofoi observada em sementes submetidas ao tratamento de resfriamento. Ademais, observou-se quea germinação de sementes de um ano de idade foi menor em comparação com as sementes doano corrente e a percentagem de germinação em geral foi maior quando houve luz e escuridãoalternadasse comparadas com as em condições de escuridão em todos os tratamentos. Assim, podeseconcluir que a dormência das sementes é atribuída à rigidez de endocarpo e que a luz tem um efeitopromotor sobre a germinação. Com o aumento da idade das sementes, há redução na viabilidade e,portanto, na germinação destas. A temperatura do inverno frio da Caxemira é responsável por quebraro endocarpo duro das sementes, o que leva à sua germinação e, consequentemente, à disseminaçãodas populações.

Symmetry solutions of some nonlinear PDE's

To my beloved parents. iii ACKNOWLEDGEMENTS All praise and glory to Almighty Allah who gave me the courage and patience to carry out this work. Peace and Blessings of Allah be upon His last prophet Muhammad (Sallallah-Alaihe-Wasallam), who guided us to the right path. First and the foremost acknowledgement is due to the Department of Mathemat-ical Sciences at King Fahd University of Petroleum & Minerals, which provided a genial research environment and and a wonderful working place. I am also indebted to KFUPM for supporting my research work. My deep appreciation and heartfelt gratitude goes to my thesis advisor Dr. A. H. Bokhari for his constant endeavor, guidance and the encouragement throughout the course of this research work. His valuable suggestions made this work interesting and knowledgeable for me. Working with him in a friendly and motivating environment was really a joyful and learning experience—not easy to forget. I extend my deepest gratitude to my thesis co-advisor Dr. F. D. Zaman, thesi

Party Politics in West Bengal: Historical and Contemporary Dynamics

Party politics in West Bengal is a complex and ever-evolving phenomenon deeply rooted in the state\u27s socio-cultural history. This overview explores the dynamic landscape of party politics in West Bengal, tracing its historical evolution and examining the key players, ideological underpinnings, electoral strategies, and socio-economic factors that have influenced voter preferences over the years. From the pre-independence era\u27s freedom struggle to the contemporary political dynamics dominated by the All-India Trinamool Congress (AITC) and Bharatiya Janata Party (BJP), West Bengal\u27s political journey reflects its vibrant cultural mosaic and socio-political complexities. This paper also discusses the current scenario in West Bengal, highlighting the role of various political parties in recent local and assembly elections. The methodology involves a comprehensive review of academic papers and journals on various aspects of West Bengal\u27s politics, governance, and societal dynamics. While existing literature touches on governance-related aspects like healthcare policies, decentralisation, and power sector reforms, there is a research gap in integrating these elements to provide a holistic assessment of West Bengal\u27s governance model. The paper identifies this research gap and calls for a more comprehensive study that explores the interplay of political decisions, decentralisation efforts, and policy reforms in shaping the state\u27s development and governance outcomes