Demand vs Supply Essay Example for Free

Demand vs Supply Essay The two main driving forces of the economy are supply and demand. Understanding the basic concepts of supply and demand can help an organization focus on the bottom line. According to Gretzen (2007), demand is the relationship between price and quantity. Supply refers to the amount of a good or service available at any particular price. The principle of supply and demand describes a balance that develops between the supply of an item or service and the demand for it (Kleinman, 2009). Economics plays a major role in the health care industry. As a resource, the health care workforce is a determinant of the balance between supply and demand. The health care workforce consists of nurses, physicians, and other ancillary health care workers such as certified nurses’ aides (CNA’s) and patient care associates (PCA’s). The supply of health care workers directly impacts the demand of quality care rendered to patients. SERVICE OR PRODUCT Health care organizations have specific stated missions and visions to map out their fundamental way of operation. In health care, the workforce is instrumental in assisting with the organizational delivery of services to consumers (patients). The primary issue for all health care workforce personnel is that of inadequate staffing. This paper focuses on the staffing effectiveness of supplemental staffing of health care personnel within the inpatient setting. IMPACT Nursing managers formulate staffing patterns on a daily basis. The staffing of inpatient units requires a knowledge of unit census (total bed capacity),  consideration of patient acuity (level of care required for the patient), and skill mix (nursing hours per patient per day and nurse patient ratio) (U. S. Department of Health and Human Services, 2002). Often times, inadequate staffing is due to a high rate of call outs of sickness or other emergencies. Inadequate staffing directly impacts patient safety and quality of care. All health care titles render supplemental staffing coverage in one of two ways, overtime and through per-diem agencies. Overtime employment provides regular full time employees with monies set at a rate of time and half for any extra work completed over the prescribed 40 hours a week. Per-diem agencies are outside contractors capable of providing their own qualified titled personnel to fill vacancies with monies defined at a set rate. Patients are admitted to inpatient setting with varied co-morbidities may or may not indirectly increase the necessity of staff. Patients are often admitted for diagnoses of altered mental status, agitation / combativeness, risk for falls, suicidal ideation, and alcohol or drug intoxication. Many patients require a higher level of skilled care, such as turning and repositioning, and assistance with activities of daily living such as toileting and eating. It requires a higher staff to patient ratio to provide safe, effective quality care. PERSPECTIVE AND RATIONALE According to published reports there are key factors affecting the adequacy of the health care workforce. Some key factors include an aging workforce of where 40 percent of practicing physicians are older than 55, and one-third of the nursing workforce is over 50 with a majority of both professionals seeking to retire within the next 10 years (Alliance for Health Reform, 2011). The largest groups of health professionals in the United States are composed of Registered Nurses. Statistically, there is a huge decline in the numbers of nurses within all regions of the U.S. An estimated 118,000 FTE RNs will exit the workforce within the next five years (Staiger, Auerbac, Buerhaus, 2012). This potentially leaves a major void in terms of numbers of bodies needed to fill vacated positions. Low staffing levels are associated with higher rates of adverse outcomes that are directly sensitive to nursing attention, such as urinary tract infections, pneumonia, pressure ulcers, and falls (American Federation of Teachers, 2012). Unintended additional costs  associated with the development of complications in patients are greater than labor savings when units are understaffed. Acquiring pressure ulcers are estimated to cost the health care industry $8.5 billion per year (Kleinman, 2009) Overtime costs and per-diem agency costs can’t stand alone to solve the issues of staffing shortage. Their combined usage enables institutions to deliver optimal health care services to consumers/ patients. The supply of overtime and per-diem staff meets the increased demands of patients. It also assists in the delivery of quality care through services rendered. In terms of patient safety, the potentiality of the risk of injury to patients via falls, medication errors, and or sentinel events decreases. CONCLUSION The United States is a great consumer demand for health care services. The supply of such services is affected by varied factors. These factors directly influence the financial stability of health care organizations. Recessional times cause delays in career and retirement plans for health care professionals. In recessional times, there are noted changes in the supply and demand of the health care workforce. The shortage of registered nurses and providers in the workforce may inadvertently lead to a reduction in health care access for consumers. Inadequate staffing levels place heavy burdens on the nursing staff. Adverse events such as falls, hospital acquired infections and medication errors are potentially painful and life threatening events. Adverse events can result in considerable costs to be paid by the understaffed institution. For this reason alone, supplemental staffing via agency and overtime personnel provides a measure of increased patient safety. The future is trending towards the assistance in the recovery of the health care workforce shortage. It will rely heavily on the provisions made by the Affordable Care Act of 2010 (Alliance for health reform, 2011). Recruitment and reinvestment in health care professions especially nurses and physicians will assure sufficient supply of workforce personnel to meet the increased demands of health care economy and its’ consumers( Kaiser Foundation (2012). The Joint Commission bolsters workforce infrastructure through in-service and continuing education, supporting nursing education, and the adoption of set staffing levels based on  competency and skill mix relative to patient mix and acuity (Stanton, 2012). It also supports the establishment of financial incentives for health care organizations investing in nursing and workforce services. REFERENCES Alliance for Health Reform. (April, 2011). Health care workforce: Future Supply vs. Demand. Retrieved from http://www.allhealth.org/publications/medicare / health_care_workforce. American Federation of Teachers. (2012). Issues: Healthcare Staffing. Retrieved from http://www.aft.org/issues/healthcare/staffing/index.cfm Changes in Health Care Financing Organization. (August, 2009). Issue brief: Impact of the economy on health care. Retrieved from http://www.academyhealth.org /files/hvfo/findings0809.pdf Getzen, T.E. (2007). Health economics and financing. (3rd ed.). John Wiley and Sons, Inc., Hoboken, NJ. Kleinman, C. (2009). Health care supply demand. Retrieved from http://www.community.advanceweb.com Staiger, D. O., Auerbach, D. I., Buerhaus, P. I. (2012, April). Registered nurse labor supply and the recession- Are we in a bubble? New England Journal of Medicine, (366), 1463-1465. Stanton, M. (2012). Hospital nurse staffing and quality of care. Retrieved from http://www.ahrq.gov/research/nursestaffing/nursestaff.htm U.S. Department of Health and Human Services. (July, 2002). Projected supply, demand, and shortages of registered nurses: 2000- 2020. Retrieved from http://hrsa.gov. The Kaiser Foundation. (2012). Nursing workforce: Background brief. Retrieved from http://www.kaiseredu.org/Issues-Modules

Fractal Geometry :: Mathematics Math Geometric Essays

Fractal Geometry In the past, mathematics has been concerned largely with sets and functions to which the methods of classical calculus could be applied. Sets or functions that are not sufficiently smooth or regular have tended to be named as " pathological" and not worthy of study. They were regarded as individual curiosities and only rarely were thought of as a class to which a general theory might be applicable. However, in recent years this attitude has changed. Irregular sets provide a much better representation of many natural phenomena than do the figures of classical geometry. Fractal geometry provides a general framework for the study of such irregular sets. (Falconer) The word ‘fractal’ was coined in 1975 by mathematician Benoit B. Mandelbrot to describe an intricate-looking set of curves, many of which were not yet seen before the creation of the computer. Fractals often exhibit self-similarity, which means that various copies of an object can be found in the original object a t smaller size scales. This continues for many magnifications – like an endless nesting of Russian dolls within dolls. (Pickover) Fractals appear everywhere in nature, in galaxies and landscapes, in earthquakes and geological cracks, in aggregates and colloids, and even in the human body. Fractal geometry is an important tool in the analysis of phenomena, ranging from rhythms in music melodies to the human heartbeat and DNA sequences. Many professions including, mathematics, astronomy, physics, chemistry, engineering, and biology use fractal geometry. (Bunde) Waclaw Sierpinski was born on March 14, 1882, in Warsaw, Poland. Sierpinski attended the University of Warsaw in 1899, when all classes were taught in Russian. He graduated in 1904 and went on to teach mathematics and physics at a girl's school in Warsaw. He left teaching in 1905 to get his doctorate at the Jagiellonian University in Cracow. After receiving his doctorate in 1908, Sierpinski went on to teach at the University of Lvov. During his years at Lvov, he wrote three books and many research papers. These books were The Theory of Irrational numbers (1910), Outline of Set Theory (1912), and The Theory of Numbers (1912). In 1919, Sierpinski accepted a job as a professor at the University of Warsaw, and this is where Waclaw Sierpinski (The Mactutor) he would spend the rest of his life. Throughout his career, Sierpinski wrote 724 papers and an amazing 50 books. Sierpinski studied many areas of mathematics, including, irrational numbers, set theory, fractal geometry, and theory of numbers.

The Da Vinci Code Chapter 10-12

CHAPTER 10 Silas sat behind the wheel of the black Audi the Teacher had arranged for him and gazed out at the great Church of Saint-Sulpice. Lit from beneath by banks of floodlights, the church's two bell towers rose like stalwart sentinels above the building's long body. On either flank, a shadowy row of sleek buttresses jutted out like the ribs of a beautiful beast. The heathens used a house of God to conceal their keystone.Again the brotherhood had confirmed their legendary reputation for illusion and deceit. Silas was looking forward to finding the keystone and giving it to the Teacher so they could recover what the brotherhood had long ago stolen from the faithful. How powerful that will make Opus Dei. Parking the Audi on the deserted Place Saint-Sulpice, Silas exhaled, telling himself to clear his mind for the task at hand. His broad back still ached from the corporal mortification he had endured earlier today, and yet the pain was inconsequential compared with the anguish of his life before Opus Dei had saved him. Still, the memories haunted his soul. Release your hatred, Silas commanded himself. Forgive those who trespassed against you. Looking up at the stone towers of Saint-Sulpice, Silas fought that familiar undertow†¦ that force that often dragged his mind back in time, locking him once again in the prison that had been his world as a young man. The memories of purgatory came as they always did, like a tempest to his senses†¦ the reek of rotting cabbage, the stench of death, human urine and feces. The cries of hopelessness against the howling wind of the Pyrenees and the soft sobs of forgotten men. Andorra, he thought, feeling his muscles tighten. Incredibly, it was in that barren and forsaken suzerain between Spain and France, shivering in his stone cell, wanting only to die, that Silas had been saved. He had not realized it at the time. The light came long after the thunder. His name was not Silas then, although he didn't recall the name his parents had given him. He had left home when he was seven. His drunken father, a burly dockworker, enraged by the arrival of an albino son, beat his mother regularly, blaming her for the boy's embarrassing condition. When the boy tried to defend her, he too was badly beaten. One night, there was a horrific fight, and his mother never got up. The boy stood over his lifeless mother and felt an unbearable up-welling of guilt for permitting it to happen. This is my fault! As if some kind of demon were controlling his body, the boy walked to the kitchen and grasped a butcher knife. Hypnotically, he moved to the bedroom where his father lay on the bed in a drunken stupor. Without a word, the boy stabbed him in the back. His father cried out in pain and tried to roll over, but his son stabbed him again, over and over until the apartment fell quiet. The boy fled home but found the streets of Marseilles equally unfriendly. His strange appearance made him an outcast among the other young runaways, and he was forced to live alone in the basement of a dilapidated factory, eating stolen fruit and raw fish from the dock. His only companions were tattered magazines he found in the trash, and he taught himself to read them. Over time, he grew strong. When he was twelve, another drifter – a girl twice his age – mocked him on the streets and attempted to steal his food. The girl found herself pummeled to within inches of her life. When the authorities pulled the boy off her, they gave him an ultimatum – leave Marseilles or go to juvenile prison. The boy moved down the coast to Toulon. Over time, the looks of pity on the streets turned to looks of fear. The boy had grown to a powerful young man. When people passed by, he could hear them whispering to one another. A ghost, they would say, their eyes wide with fright as they stared at his white skin. A ghost with the eyes of a devil! And he felt like a ghost†¦ transparent†¦ floating from seaport to seaport. People seemed to look right through him. At eighteen, in a port town, while attempting to steal a case of cured ham from a cargo ship, he was caught by a pair of crewmen. The two sailors who began to beat him smelled of beer, just as his father had. The memories of fear and hatred surfaced like a monster from the deep. The young man broke the first sailor's neck with his bare hands, and only the arrival of the police saved the second sailor from a similar fate. Two months later, in shackles, he arrived at a prison in Andorra. You are as white as a ghost, the inmates ridiculed as the guards marched him in, naked and cold. Mira el espectro! Perhaps the ghost will pass right through these walls! Over the course of twelve years, his flesh and soul withered until he knew he had become transparent. I am a ghost. I am weightless. Yo soy un espectro†¦palido coma una fantasma†¦caminando este mundo a solas. One night the ghost awoke to the screams of other inmates. He didn't know what invisible force was shaking the floor on which he slept, nor what mighty hand was trembling the mortar of his stone cell, but as he jumped to his feet, a large boulder toppled onto the very spot where he had been sleeping. Looking up to see where the stone had come from, he saw a hole in the trembling wall, and beyond it, a vision he had not seen in over ten years. The moon. Even while the earth still shook, the ghost found himself scrambling through a narrow tunnel, staggering out into an expansive vista, and tumbling down a barren mountainside into the woods. He ran all night, always downward, delirious with hunger and exhaustion. Skirting the edges of consciousness, he found himself at dawn in a clearing where train tracks cut a swath across the forest. Following the rails, he moved on as if dreaming. Seeing an empty freight car, he crawled in for shelter and rest. When he awoke the train was moving. How long? How far?A pain was growing in his gut. Am I dying? He slept again. This time he awoke to someone yelling, beating him, throwing him out of the freight car. Bloody, he wandered the outskirts of a small village looking in vain for food. Finally, his body too weak to take another step, he lay down by the side of the road and slipped into unconsciousness. The light came slowly, and the ghost wondered how long he had been dead. A day? Three days? It didn't matter. His bed was soft like a cloud, and the air around him smelled sweet with candles. Jesus was there, staring down at him. I am here, Jesus said. The stone has been rolled aside, and you are born again. He slept and awoke. Fog shrouded his thoughts. He had never believed in heaven, and yet Jesus was watching over him. Food appeared beside his bed, and the ghost ate it, almost able to feel the flesh materializing on his bones. He slept again. When he awoke, Jesus was still smiling down, speaking. You are saved, my son.Blessed are those who follow my path. Again, he slept. It was a scream of anguish that startled the ghost from his slumber. His body leapt out of bed, staggered down a hallway toward the sounds of shouting. He entered into a kitchen and saw a large man beating a smaller man. Without knowing why, the ghost grabbed the large man and hurled him backward against a wall. The man fled, leaving the ghost standing over the body of a young man in priest's robes. The priest had a badly shattered nose. Lifting the bloody priest, the ghost carried him to a couch. â€Å"Thank you, my friend,† the priest said in awkward French. â€Å"The offertory money is tempting for thieves. You speak French in your sleep. Do you also speak Spanish?† The ghost shook his head. â€Å"What is your name?† he continued in broken French. The ghost could not remember the name his parents had given him. All he heard were the taunting gibes of the prison guards. The priest smiled. â€Å"No hay problema.My name is Manuel Aringarosa. I am a missionary from Madrid. I was sent here to build a church for the Obra de Dios.† â€Å"Where am I?† His voice sounded hollow.† Oviedo. In the north of Spain.† â€Å"How did I get here?† â€Å"Someone left you on my doorstep. You were ill. I fed you. You've been here many days.† The ghost studied his young caretaker. Years had passed since anyone had shown any kindness. â€Å"Thank you, Father.† The priest touched his bloody lip. â€Å"It is I who am thankful, my friend.† When the ghost awoke in the morning, his world felt clearer. He gazed up at the crucifix on the wall above his bed. Although it no longer spoke to him, he felt a comforting aura in its presence. Sitting up, he was surprised to find a newspaper clipping on his bedside table. The article was in French, a week old. When he read the story, he filled with fear. It told of an earthquake in the mountains that had destroyed a prison and freed many dangerous criminals. His heart began pounding. The priest knows who I am! The emotion he felt was one he had not felt for some time. Shame. Guilt. It was accompanied by the fear of being caught. He jumped from his bed. Where do I run? â€Å"The Book of Acts,† a voice said from the door. The ghost turned, frightened. The young priest was smiling as he entered. His nose was awkwardly bandaged, and he was holding out an old Bible. â€Å"I found one in French for you. The chapter is marked.† Uncertain, the ghost took the Bible and looked at the chapter the priest had marked. Acts 16. The verses told of a prisoner named Silas who lay naked and beaten in his cell, singing hymns to God. When the ghost reached Verse 26, he gasped in shock. â€Å"†¦ And suddenly, there was a great earthquake, so that the foundations of the prison were shaken, and all the doors fell open.† His eyes shot up at the priest. The priest smiled warmly. â€Å"From now on, my friend, if you have no other name, I shall call you Silas.† The ghost nodded blankly. Silas.He had been given flesh. My name is Silas. â€Å"It's time for breakfast,† the priest said. â€Å"You will need your strength if you are to help me build this church.† Twenty thousand feet above the Mediterranean, Alitalia flight 1618 bounced in turbulence, causing passengers to shift nervously. Bishop Aringarosa barely noticed. His thoughts were with the future of Opus Dei. Eager to know how plans in Paris were progressing, he wished he could phone Silas. But he could not. The Teacher had seen to that. â€Å"It is for your own safety,† the Teacher had explained, speaking in English with a French accent. â€Å"I am familiar enough with electronic communications to know they can be intercepted. The results could be disastrous for you.† Aringarosa knew he was right. The Teacher seemed an exceptionally careful man. He had not revealed his own identity to Aringarosa, and yet he had proven himself a man well worth obeying. After all, he had somehow obtained very secret information. The names of the brotherhood's fourtop members! This had been one of the coups that convinced the bishop the Teacher was truly capable of delivering the astonishing prize he claimed he could unearth. â€Å"Bishop,† the Teacher had told him,† I have made all the arrangements. For my plan to succeed, you must allow Silas to answer only to me for several days. The two of you will not speak. I will communicate with him through secure channels.† â€Å"You will treat him with respect?† â€Å"A man of faith deserves the highest.† â€Å"Excellent. Then I understand. Silas and I shall not speak until this is over.† â€Å"I do this to protect your identity, Silas's identity, and my investment.† â€Å"Your investment?† â€Å"Bishop, if your own eagerness to keep abreast of progress puts you in jail, then you will be unable to pay me my fee.† The bishop smiled. â€Å"A fine point. Our desires are in accord. Godspeed.† Twenty million euro,the bishop thought, now gazing out the plane's window. The sum was approximately the same number of U. S. dollars. A pittance for something so powerful. He felt a renewed confidence that the Teacher and Silas would not fail. Money and faith were powerful motivators. CHAPTER 11 â€Å"Une plaisanterie numerique?† Bezu Fache was livid, glaring at Sophie Neveu in disbelief. A numeric joke?† Your professional assessment of Sauniere's code is that it is some kind of mathematical prank?† Fache was in utter incomprehension of this woman's gall. Not only had she just barged in on Fache without permission, but she was now trying to convince him that Sauniere, in his final moments of life, had been inspired to leave a mathematical gag? â€Å"This code,† Sophie explained in rapid French,† is simplistic to the point of absurdity. Jacques Sauniere must have known we would see through it immediately.† She pulled a scrap of paper from her sweater pocket and handed it to Fache. â€Å"Here is the decryption.† Fache looked at the card. 1-1-2-3-5-8-13-21 â€Å"This is it?† he snapped. â€Å"All you did was put the numbers in increasing order!† Sophie actually had the nerve to give a satisfied smile. â€Å"Exactly.† Fache's tone lowered to a guttural rumble. â€Å"Agent Neveu, I have no idea where the hell you're going with this, but I suggest you get there fast.† He shot an anxious glance at Langdon, who stood nearby with the phone pressed to his ear, apparently still listening to his phone message from the U.S. Embassy. From Langdon's ashen expression, Fache sensed the news was bad. â€Å"Captain,† Sophie said, her tone dangerously defiant,† the sequence of numbers you have in your hand happens to be one of the most famous mathematical progressions in history.† Fache was not aware there even existed a mathematical progression that qualified as famous, and he certainly didn't appreciate Sophie's off-handed tone. â€Å"This is the Fibonacci sequence,† she declared, nodding toward the piece of paper in Fache's hand.† A progression in which each term is equal to the sum of the two preceding terms.† Fache studied the numbers. Each term was indeed the sum of the two previous, and yet Fache could not imagine what the relevance of all this was to Sauniere's death. â€Å"Mathematician Leonardo Fibonacci created this succession of numbers in the thirteenth-century. Obviously there can be no coincidence that all of the numbers Sauniere wrote on the floor belong to Fibonacci's famous sequence.† Fache stared at the young woman for several moments. â€Å"Fine, if there is no coincidence, would you tell me why Jacques Sauniere chose to do this. What is he saying? What does this mean?† She shrugged. â€Å"Absolutely nothing. That's the point. It's a simplistic cryptographic joke. Like taking the words of a famous poem and shuffling them at random to see if anyone recognizes what all the words have in common.† Fache took a menacing step forward, placing his face only inches from Sophie's. â€Å"I certainly hope you have a much more satisfying explanation than that.† Sophie's soft features grew surprisingly stern as she leaned in. â€Å"Captain, considering what you have at stake here tonight, I thought you might appreciate knowing that Jacques Sauniere might be playing games with you. Apparently not. I'll inform the director of Cryptography you no longer need our services.† With that, she turned on her heel, and marched off the way she had come. Stunned, Fache watched her disappear into the darkness. Is she out of her mind? Sophie Neveu had just redefined le suicide professionnel. Fache turned to Langdon, who was still on the phone, looking more concerned than before, listening intently to his phone message. The U. S.Embassy.Bezu Fache despised many things†¦ but few drew more wrath than the U. S. Embassy. Fache and the ambassador locked horns regularly over shared affairs of state – their most common battleground being law enforcement for visiting Americans. Almost daily, DCPJ arrested American exchange students in possession of drugs, U. S. businessmen for soliciting underage Prostitutes, American tourists for shoplifting or destruction of property. Legally, the U. S. Embassy could intervene and extradite guilty citizens back to the United States, where they received nothing more than a slap on the wrist. And the embassy invariably did just that. L'emasculation de la Police Judiciaire, Fache called it. Paris Match had run a cartoon recently depicting Fache as a police dog, trying to bite an American criminal, but unable to reach because it was chained to the U. S. Embassy. Not tonight, Fache told himself. There is far too much at stake. By the time Robert Langdon hung up the phone, he looked ill. â€Å"Is everything all right?† Fache asked. Weakly, Langdon shook his head. Bad news from home, Fache sensed, noticing Langdon was sweating slightly as Fache took back his cell phone. â€Å"An accident,† Langdon stammered, looking at Fache with a strange expression. â€Å"A friend†¦Ã¢â‚¬  He hesitated. â€Å"I'll need to fly home first thing in the morning.† Fache had no doubt the shock on Langdon's face was genuine, and yet he sensed another emotion there too, as if a distant fear were suddenly simmering in the American's eyes. â€Å"I'm sorry to hear that,† Fache said, watching Langdon closely. â€Å"Would you like to sit down?† He motioned toward one of the viewing benches in the gallery. Langdon nodded absently and took a few steps toward the bench. He paused, looking more confused with every moment. â€Å"Actually, I think I'd like to use the rest room.† Fache frowned inwardly at the delay. â€Å"The rest room. Of course. Let's take a break for a few minutes.† He motioned back down the long hallway in the direction they had come from. â€Å"The rest rooms are back toward the curator's office.† Langdon hesitated, pointing in the other direction toward the far end of the Grand Gallery corridor.† I believe there's a much closer rest room at the end.† Fache realized Langdon was right. They were two thirds of the way down, and the Grand Gallery dead-ended at a pair of rest rooms. â€Å"Shall I accompany you?† Langdon shook his head, already moving deeper into the gallery. â€Å"Not necessary. I think I'd like a few minutes alone.† Fache was not wild about the idea of Langdon wandering alone down the remaining length of corridor, but he took comfort in knowing the Grand Gallery was a dead end whose only exit was at the other end – the gate under which they had entered. Although French fire regulations required several emergency stairwells for a space this large, those stairwells had been sealed automatically when Sauniere tripped the security system. Granted, that system had now been reset, unlocking the stairwells, but it didn't matter – the external doors, if opened, would set off fire alarms and were guarded outside by DCPJ agents. Langdon could not possibly leave without Fache knowing about it. â€Å"I need to return to Mr. Sauniere's office for a moment,† Fache said. â€Å"Please come find me directly, Mr. Langdon. There is more we need to discuss.† Langdon gave a quiet wave as he disappeared into the darkness. Turning, Fache marched angrily in the opposite direction. Arriving at the gate, he slid under, exited the Grand Gallery, marched down the hall, and stormed into the command center at Sauniere's office. â€Å"Who gave the approval to let Sophie Neveu into this building!† Fache bellowed. Collet was the first to answer. â€Å"She told the guards outside she'd broken the code.† Fache looked around. â€Å"Is she gone?† â€Å"She's not with you?† â€Å"She left.† Fache glanced out at the darkened hallway. Apparently Sophie had been in no mood to stop by and chat with the other officers on her way out. For a moment, Fache considered radioing the guards in the entresol and telling them to stop Sophie and drag her back up here before she could leave the premises. He thought better of it. That was only his pride talking†¦ wanting the last word. He'd had enough distractions tonight. Deal with Agent Neveu later, he told himself, already looking forward to firing her. Pushing Sophie from his mind, Fache stared for a moment at the miniature knight standing on Sauniere's desk. Then he turned back to Collet. â€Å"Do you have him?† Collet gave a curt nod and spun the laptop toward Fache. The red dot was clearly visible on the floor plan overlay, blinking methodically in a room marked TOILETTES PUBLIQUES. â€Å"Good,† Fache said, lighting a cigarette and stalking into the hall. I've got a phone call to make. Be damned sure the rest room is the only place Langdon goes.† CHAPTER 12 Robert Langdon felt light-headed as he trudged toward the end of the Grand Gallery. Sophie's phone message played over and over in his mind. At the end of the corridor, illuminated signs bearing the international stick-figure symbols for rest rooms guided him through a maze-like series of dividers displaying Italian drawings and hiding the rest rooms from sight. Finding the men's room door, Langdon entered and turned on the lights. The room was empty. Walking to the sink, he splashed cold water on his face and tried to wake up. Harsh fluorescent lights glared off the stark tile, and the room smelled of ammonia. As he toweled off, the rest room's door creaked open behind him. He spun. Sophie Neveu entered, her green eyes flashing fear. â€Å"Thank God you came. We don't have much time.† Langdon stood beside the sinks, staring in bewilderment at DCPJ cryptographer Sophie Neveu. Only minutes ago, Langdon had listened to her phone message, thinking the newly arrived cryptographer must be insane. And yet, the more he listened, the more he sensed Sophie Neveu was speaking in earnest. Do not react to this message.Just listen calmly.You are in danger rightnow.Follow my directions very closely.Filled with uncertainty, Langdon had decided to do exactly as Sophie advised. He told Fache that the phone message was regarding an injured friend back home. Then he had asked to use the rest room at the end of the Grand Gallery. Sophie stood before him now, still catching her breath after doubling back to the rest room. In the fluorescent lights, Langdon was surprised to see that her strong air actually radiated from unexpectedly soft features. Only her gaze was sharp, and the juxtaposition conjured images of a multilayered Renoir portrait†¦ veiled but distinct, with a boldness that somehow retained its shroud of mystery. â€Å"I wanted to warn you, Mr. Langdon†¦Ã¢â‚¬  Sophie began, still catching her breath,† that you are sous surveillance cachee.Under a guarded observation.† As she spoke, her accented English resonated off the tile walls, giving her voice a hollow quality. â€Å"But†¦ why?† Langdon demanded. Sophie had already given him an explanation on the phone, but he wanted to hear it from her lips. â€Å"Because,† she said, stepping toward him,† Fache's primary suspect in this murder is you.† Langdon was braced for the words, and yet they still sounded utterly ridiculous. According to Sophie, Langdon had been called to the Louvre tonight not as a symbologist but rather as a suspect and was currently the unwitting target of one of DCPJ's favorite interrogation methods – surveillance cachee – a deft deception in which the police calmly invited a suspect to a crime scene and interviewed him in hopes he would get nervous and mistakenly incriminate himself. â€Å"Look in your jacket's left pocket,† Sophie said. â€Å"You'll find proof they are watching you.† Langdon felt his apprehension rising. Look in my pocket? It sounded like some kind of cheap magic trick. â€Å"Just look.† Bewildered, Langdon reached his hand into his tweed jacket's left pocket – one he never used. Feeling around inside, he found nothing. What the devil did you expect? He began wondering if Sophie might just be insane after all. Then his fingers brushed something unexpected. Small and hard. Pinching the tiny object between his fingers, Langdon pulled it out and stared in astonishment. It was a metallic, button-shaped disk, about the size of a watch battery. He had never seen it before. â€Å"What the†¦ ?† â€Å"GPS tracking dot,† Sophie said. â€Å"Continuously transmits its location to a Global Positioning System satellite that DCPJ can monitor. We use them to monitor people's locations. It's accurate within two feet anywhere on the globe. They have you on an electronic leash. The agent who picked you up at the hotel slipped it inside your pocket before you left your room.† Langdon flashed back to the hotel room†¦ his quick shower, getting dressed, the DCPJ agent politely holding out Langdon's tweed coat as they left the room. It's cool outside, Mr.Langdon, the agent had said. Spring in Paris is not all your song boasts.Langdon had thanked him and donned the jacket. Sophie's olive gaze was keen. â€Å"I didn't tell you about the tracking dot earlier because I didn't want you checking your pocket in front of Fache. He can't know you've found it.† Langdon had no idea how to respond. â€Å"They tagged you with GPS because they thought you might run.† She paused. â€Å"In fact, they hopedyou would run; it would make their case stronger.† â€Å"Why would I run!† Langdon demanded. â€Å"I'm innocent!† â€Å"Fache feels otherwise.† Angrily, Langdon stalked toward the trash receptacle to dispose of the tracking dot. â€Å"No!† Sophie grabbed his arm and stopped him. â€Å"Leave it in your pocket. If you throw it out, the signal will stop moving, and they'll know you found the dot. The only reason Fache left you alone is because he can monitor where you are. If he thinks you've discovered what he's doing†¦Ã¢â‚¬  Sophie did not finish the thought. Instead, she pried the metallic disk from Langdon's hand and slid it back into the pocket of his tweed coat. â€Å"The dot stays with you. At least for the moment.† Langdon felt lost. â€Å"How the hell could Fache actually believe I killed Jacques Sauniere!† â€Å"He has some fairly persuasive reasons to suspect you.† Sophie's expression was grim. â€Å"There is a piece of evidence here that you have not yet seen. Fache has kept it carefully hidden from you.† Langdon could only stare. â€Å"Do you recall the three lines of text that Sauniere wrote on the floor?† Langdon nodded. The numbers and words were imprinted on Langdon's mind. Sophie's voice dropped to a whisper now. â€Å"Unfortunately, what you saw was not the entire message. There was a fourth line that Fache photographed and then wiped clean before you arrived.† Although Langdon knew the soluble ink of a watermark stylus could easily be wiped away, he could not imagine why Fache would erase evidence. â€Å"The last line of the message,† Sophie said,† was something Fache did not want you to know about.† She paused. â€Å"At least not until he was done with you.† Sophie produced a computer printout of a photo from her sweater pocket and began unfolding it. â€Å"Fache uploaded images of the crime scene to the Cryptology Department earlier tonight in hopes we could figure out what Sauniere's message was trying to say. This is a photo of the complete message.† She handed the page to Langdon. Bewildered, Langdon looked at the image. The close-up photo revealed the glowing message on the parquet floor. The final line hit Langdon like a kick in the gut. 13-3-2-21-1-1-8-5 O, Draconian devil! Oh, lame saint! P. S.Find Robert Langdon

Market Structure of Petrol Companies - 952 Words

Petrol companies have the market structure of an oligopoly. An oligopoly is a market structure where there are a few dominant firms whose behavior is interdependent. There are a few dominant firms relative to market size, and they each command a large proportion of the market share, thus having strong monopoly power. Examples of petrol companies include Shell, Caltex and Exxon Mobil. Their demand curve is downward sloping, meaning that they are price setters. Petrol is a homogeneous product, hence the oligopoly is known to be pure or perfect. Theoretically only one firm can prevail, but since the firm’s demand is not perfectly elastic, the firm has price control over its pricing policy. There is a great fear of rivals’ reactions to each†¦show more content†¦Due to the high barriers to entry, an oligopolistic firm is able to retain its supernormal profits in the long run. In an oligopoly, there is imperfect knowledge. Sellers and buyers have incomplete information regarding production methods and prices. As in the case of a monopoly, the imperfect knowledge serves as a barrier to entry of potential new firms and may at the same time; increase the price-setting ability of the oligopolistic firms. Due to the small number of competitors in the market, every action taken by any petrol company will affect all the other firms in the market significantly. Rivals’ actions cannot be ignored, as they are likely to result in adverse effects. Thus, there is a large degree of mutual interdependence. Each firm will have to assess or predict rivals’ actions to its pricing strategies. If a petrol company decides to raise its price above equilibrium price, it assesses that rivals are unlikely to follow. As a result, the quantity demanded for its petrol will fall by more than proportionate. Hence, above the equilibrium price, the demand is price elastic. On the other hand, if they were to reduce its price below equilibrium price, it predicts that rivals will match its price reduction, and quantity demanded for its petrol rises by only less than proportionate. With the price-inelastic demand, the total revenue for the firm will again fall. Hence, demand curve below the equilibrium priceShow MoreRelatedThe Indian Lubricant Market: Survival of the Slickest1452 Words   |  6 PagesLubricant Market: Survival of the Slickest Introduction The Indian automotive lubricant market is the sixth largest market in the world with revenues of approximately $1.30 billion in 2002. It is also one of the fastest growing retail markets in India. Until 1993, it was a highly regulated market with a clear dominance of the public sector. 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