Sumit Banerjee

Method of substitution (()) () () f g x g x dx f u du ′ = ∫ ∫ Integration by parts () () () () () () f x g x dx f x g x g x f x dx ′ ′ = − ∫ ∫ Integrals of Rational and Irrational Functions 1 1 n n x x dx C n + = + + ∫ 1 ln dx x C x = + ∫ c dx cx C = + ∫ 2 2 x xdx C = +

Artist's idea of a black hole, with gas and dust swirling rapidly around it before being pulled in by its powerful gravitational field. You can't really see the black hole itself. Black holes are not really holes at all. They are the opposite of empty! Black holes have the most matter stuffed into the least space of any objects in the universe. Because they are so compact, they have very strong gravity. Here on Earth, gravity is what makes things fall down, rather than just float away, when you let go of them. Gravity is what you are measuring when you step on a scale to weigh yourself. Your weight is the amount of force that Earth's gravity exerts on you. The more matter your body contains, the more you weigh. Likewise, the more matter an object has, the stronger its gravity. The gravity of a black hole is so strong that not even light can escape. Even if a bright star is shining right next to a black hole, you cannot see the black hole. Instead of reflecting the light as other objects do, the black hole just swallows the starlight forever. Any matter that gets too close to a black hole gets swallowed up as well. There are at least two kinds of black holes One kind is called a stellar-mass black hole. You can think of it as a "one-big-star" black hole. This type of black hole forms when a big star burns up all its fuel and explodes (called a supernova). Then what's left collapses into a super-compact object—a black hole. Stars must contain quite a bit more matter than our Sun for this to happen. So our Sun, and most stars, will never become black holes. Stellar-mass black holes are only a few tens of kilometers across—maybe about 40 miles. Just imagine. Our Sun is so huge that about one million Earths would fit inside it. A star with enough matter to become a black hole contains maybe 10 times as much matter as the Sun. Now imagine a star with that much matter, shrinking into a space no farther across than the distance you can drive a car in less than one hour! A black hole with all the mass of Earth would be about the size of a fingernail!

Now that we've taken notice of many of the difficulties that can be caused by sloppy use of ordinary language in argumentation, we're ready to begin the more precise study of deductive reasoning. Here we'll achieve the greater precision by eliminating ambiguous words and phrases from ordinary language and carefully defining those that remain. The basic strategy is to create a narrowly restricted formal system—an artificial, rigidly structured logical language within which the validity of deductive arguments can be discerned with ease. Only after we've become familiar with this limited range of cases will we consider to what extent our ordinary-language argumentation can be made to conform to its structure. Our initial effort to pursue this strategy is the ancient but worthy method of categorical logic. This approach was originally developed by Aristotle, codified in greater detail by medieval logicians, and then interpreted mathematically by George Boole and John Venn in the nineteenth century. Respected by many generations of philosophers as the the chief embodiment of deductive reasoning, this logical system continues to be useful in a broad range of ordinary circumstances.

I Adhar Babu lives upon the interest of the capital left him by his father. Only the brokers, negotiating loans, come to his drawing room and smoke the silver-chased hookah, and the clerks from the attorney's office discuss the terms of some mortgage or the amount of the stamp fees. He is so careful with his money that even the most dogged efforts of the boys from the local football club fail to make any impression on his pocket. At the time this story opens a new guest came into his household. After a long period of despair, his wife, Nanibala, bore him a son. The child resembled his mother,—large eyes, well-formed nose, and fair complexion. Ratikanta, Adharlal's protégé, gave verdict,—"He is worthy of this noble house." They named him Venugopal. Never before had Adharlal's wife expressed any opinion differing from her husband's on household expenses. There had been a hot discussion now and then about the propriety of some necessary item and up to this time she had merely acknowledged defeat with silent contempt. But now Adharlal could no longer maintain his supremacy. He had to give way little by little when things for his son were in question. II As Venugopal grew up, his father gradually became accustomed to spending money on him. He obtained an old teacher, who had a considerable repute for his learning and also for his success in dragging impassable boys through their examinations. But such a training does not lead to the cultivation of amiability. This man tried his best to win the boy's heart, but the little that was left in him of the natural milk of human kindness had turned sour, and the child repulsed his advances from the very beginning. The mother, in consequence, objected to him strongly, and complained that the very sight of him made her boy ill. So the teacher left. Just then, Haralal made his appearance with a dirty dress and a torn pair of old canvas shoes. Haralal's mother, who was a widow, had kept him with great difficulty at a District school out of the scanty earnings which she made by cooking in strange houses and husking rice. He managed to pass the Matriculation and determined to go to College. As a result of his half-starved condition, his pinched face tapered to a point in an unnatural manner,—like Cape Comorin in the map of India; and the only broad portion of it was his forehead, which resembled the ranges of the Himalayas. The servant asked Haralal what he wanted, and he answered timidly that he wished to see the master. The servant answered sharply: "You can't see him." Haralal was hesitating, at a loss what to do next, when Venugopal, who had finished his game in the garden, suddenly came to the door. The servant shouted at Haralal: "Get away." Quite unaccountably Venugopal grew excited and cried: "No, he shan't get away." And he dragged the stranger to his father. Adharlal had just risen from his midday sleep and was sitting quietly on the upper verandah in his cane chair, rocking his legs. Ratikanta was enjoying his hookah, seated in a chair next to him. He asked Haralal how far he had got in his reading. The young man bent his head and answered that he had passed the Matriculation. Ratikanta looked stern and expressed surprise

ABSTRACT The paper presents an algorithm for reconfiguration of radial distribution networks based on fuzzy multiobjective approach by considering different types of loads. Multiple objectives are considered to minimize the real power loss, deviation of nodes voltage and improvement of voltage stability of the network while subject to a radial network structure, in which all loads must be energized. These objectives are modelled with fuzzy sets to evaluate their imprecise nature and one can provide his or her anticipated value of each objective. These multiple objectives are integrated into an objective function through appropriate weighting factors which is maximized for each tie switch operation. Heuristic rules are also incorporated in the algorithm for minimizing the number of tie switch operations. The effectiveness of the proposed method is demonstrated through one example.

Management of spina bifida is a complex issue with various systems of the body involved either directly or indirectly. Deformities of the bone and joints (especially spine and lower limbs) play a significant role in causation of deficits in the child. Management of these deficits require a focused, specialised and multidisciplinary approach with orthopaedician, physiotherapist, intensivist and psychologist apart from neurosurgeon playing an important part. To manage these deformities, one needs to understand the pathophysiology of causation of these defects. The corrective surgical intervention ranges from a simple release of contracture to highly complex spinal instrumentations. We reviewed the literature and have shared our experience on this aspect of spina bifida.

ABSTRACT The paper presents voltage stability analysis of radial distribution networks. A new voltage stability index is proposed for identifying the node, which is most sensitive to voltage collapse. It is shown that the node, at which the value of voltage stability index is minimum, is more sensitive to voltage collapse. For the purpose of voltage stability analysis, constant power, constant current, constant impedance and composite load modelling are considered. It is seen that with the insertion of shunt capacitor, load capability limit of the feeder has increased for all types of loads. By using this voltage stability index, one can measure the level of voltage stability of radial distribution networks and thereby appropriate action may be taken if the index indicates a poor level of stability. The proposed method is compared with the other two existing methods. The effectiveness of the proposed method is demonstrated through two examples.

The discovery of M41S materials by the supramolecular templating mechanism ushered in a new era in synthesis chemistry. 1 These mesoporous materials exhibit high surface area, narrow pore size distribution, large pore volume, and high thermal and hydrothermal stability. ...

ABSTRACT The paper presents voltage stability analysis of radial distribution networks under critical loading conditions. A new voltage stability index is proposed for identifying the node, which is most sensitive to voltage collapse. For the purpose of voltage stability analysis, constant power, constant current, constant impedance and composite load modeling are considered. The effectiveness of the proposed method is demonstrated through an 12.66 kV radial distribution networks consisting of 33 nodes.

ABSTRACT This paper presents status of all branches of radial distribution networks in chronological order using distributed generation at optimal position by considering the concept of reactive loading index technique. Although under different situations for all the branches the identified weakest branch remains same up to some specified conditions but the corresponding loading at different branches in chronological order has been categorically identified. The effectiveness of the proposed idea has been successfully tested on 12.66 kV radial distribution systems consisting of 33 nodes and the results are found to be in very good agreement.

ABSTRACT The paper presents voltage stability analysis of radial distribution networks under critical loading conditions without and with distributed generator (DG). A new voltage stability index is proposed for identifying the node, which is most sensitive to voltage collapse. The effectiveness of the proposed method without and with considering DG has been successfully tested on a 12.66 kV radial distribution network consisting of 33 nodes and the results are found to be in very good agreement.

Abstract— In recent years many authors largely given attention to the effect of active loading index for low voltage distribution system. But this paper presents a novel approach for determining the reactive loading index of a low voltage distribution system at the proximity of voltage ...

Intramedullary spinal cord tumors (IMSCT) are rare neoplasms of central nervous system but require proper evaluation and management to ensure a good outcome. This study was carried out to evaluate the functional outcome of IMSCT following surgery and to decipher the factors affecting optimal outcome of these cases. A prospective clinical study was carried out at a tertiary care center from 2003 to 2012. Forty three patients with intramedullary tumors diagnosed on magnetic resonance imaging were included. Their clinical details, neurological findings and demographic data were recorded. The patients were then subjected to surgery and adjuvant radiotherapy. The patients were followedup clinically and radiologically, and all parameters examined and recorded. Sensory and motor impairment was present preoperatively in majority of patients (n = 39 and n = 38, 90.7% and 88.4%, respectively). Gross total excision was performed in 30 cases (69.76%). The most common histological diagnosis was ...

ABSTRACT The paper presents voltage stability margin (VSM) of radial distribution network by considering a unique reactive loading index for composite loads. It is shown that the branch, at which the value of reactive loading index is minimum, is considered to be the weakest branch of the system. Then, the voltage stability margin (VSM) of the feeder is selected heuristically. It is the product of reactive loading indices of all branches of the feeder. The VSM of all feeders can be evaluated. The feeder which has the smallest value of VSM can be considered as the weakest feeder of the system and is at the proximity of voltage collapse. So, for multiple feeders, the voltage stability margin of a system may be considered as the VSM of the feeder which has the smallest value. The effectiveness of the proposed VSM has been successfully tested on a 12.66 kV radial distribution network consisting of 33 nodes and the results are found to be in very good agreement.

ABSTRACT The economic load dispatch (ELD) plays an important role in power system operation and control. Different techniques have been used to solve these problems. Recently, the soft computing techniques have widely used in practical applications. This paper shows successful implementation of four evolutionary algorithms, namely particle swarm optimization (PSO), particle swarm optimization with constriction factor approach (PSOCFA), particle swarm optimization with inertia weight factor approach (PSOIWA) and particle swarm optimization with constriction factor and inertia weight factor approach (PSOCFIWA) algorithms to economic load dispatch problem. Power output of each generating unit and optimum fuel cost obtained using all four algorithms have been compared.

ABSTRACT The economic load dispatch (ELD) plays an important role in power system operation and control. Different techniques have been used to solve these problems. Recently, the soft computing techniques have widely used in practical applications. This paper shows successful implementation of four evolutionary algorithms, namely particle swarm optimization (PSO), particle swarm optimization with constriction factor approach (PSOCFA), particle swarm optimization with inertia weight factor approach (PSOIWA) and particle swarm optimization with constriction factor and inertia weight factor approach (PSOCFIWA) algorithms are used to economic load dispatch problem. Here prohibited zone and ramp-rate limit constraints are considered to solve this problem. Power output of each generating unit and optimum fuel cost obtained using all four algorithms have been compared.

Monteggia fractures are uncommon and frequently missed injuries in children. This article aims to study, in a systematic manner, the surgical management and complications of treatment of chronic radial head dislocations. After screening of relevant abstracts, a total of 28 studies were included in the systematic review. A narrative synthesis of various treatment modalities has been discussed. This article concludes that open reduction should be attempted unless dysmorphism of the radial head restricts it. Open reduction with ulnar osteotomy with or without annular ligament reconstruction is the most commonly performed procedure and is expected to result in reduced pain and elbow deformity.

The purpose of this study was to review the principles involved in the management of proximal femoral fractures as reported in the literature. A medical literature search in the MEDLINE (PubMed) and Cochrane database was undertaken to review strategies and principles in proximal femoral fracture treatment. Randomized control trials and meta analysis were given preference while case reports/small series were rejected. Early anatomical reduction and surgical fixation remains the best option to reduce the risk of complications like non-union and avascular necrosis in treating fracture neck femurs. Cancellous screws continue to be the preferred treatment for fixation of neck femur fractures in younger population until the benefit of using sliding hip screws is validated by large multicentric studies. In the geriatric age group, early prosthetic replacement brings down the mortality and morbidity associated with neck femur fractures. Sliding hip screw (DHS) is the best available option for stable inter trochanteric fractures. The use of intramedullary nails e.g. PFN is beneficial in treating inter trochanteric fractures with comminution and loss of lateral buttress. Intramedullary implants have been proven to have increased success rates in subtrochanteric fractures and should be preferred over extramedullary plate fixation systems.

This paper presents Loading Status for all Branches in chronological order at different Conditions in Radial Distribution Systems using Reactive Loading Index. Although under different loading conditions for all the branches the identified weakest branch remains same but the corresponding loading at different branches in chronological order has been categorically identified for different values other than the lowest. The effectiveness

ABSTRACT This paper presents a novel teaching learning based optimization (TLBO) technique to solve economic load dispatch (ELD) of the thermal unit without considering transmission losses. The proposed methodology can take care of ELD considering nonlinearity such as valve point loading. The objective of economic load dispatch is to determine the optimal power generation of the units to meet the load demand, such that the overall cost of generation is minimized, while satisfying different operational constraints. TLBO is a recently developed evolutionary algorithm based on two basic concepts of education namely teaching phase and learning phase. At first, learners improve their knowledge through the teaching methodology of teacher and finally learners increase their knowledge by interactions among themselves. The effectiveness of the proposed algorithm has been verified on three different test systems with equality and inequality constraints. Compared with the other existing techniques demonstrates the superiority of the proposed algorithm.

The paper presents a simple approach on voltage stability analysis of radial distribution systems for different types of loads. A new voltage stability index is proposed for identifying the node, which is most sensitive to voltage collapse. It is shown that the node, at which the value of voltage stability index is maximum, is more sensitive to voltage collapse. For the purpose of voltage stability analysis, constant power, constant current, constant impedance and composite load modeling are considered. It is seen that with the insertion of shunt capacitor, load capability limit of the feeder has increased for all types of loads. By using this voltage stability index, one can measure the level of voltage stability of radial distribution systems and thereby appropriate action may be taken if the index indicates a poor level of stability. The effectiveness of the proposed method is demonstrated through two examples.

The discovery of M41S materials by the supramolecular templating mechanism ushered in a new era in synthesis chemistry. 1 These mesoporous materials exhibit high surface area, narrow pore size distribution, large pore volume, and high thermal and hydrothermal stability. ...

Hydro–wind–thermal scheduling is one of the most important optimization problems in power system.An aim of the short term hydro-thermal scheduling of power systems is to determine the optimal hydro,wind and thermal generations in order to meet the load demands over a scheduled horizon of time while satisfying the various constraints on the hydraulic, wind and thermal power system network. In this paper we present optimal hourly schedule of power generation in a hydro–wind–thermal power system applying PSO technique. The simulation results inform that the proposed PSO approach appears to be the powerful to minimize fuel cost and it has better solution quality and good convergence characteristics than other techniques.