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In each of 23 through 28, compute the windowed Fourier transform of f for the given

Advanced Engineering Mathematics | 7th Edition | ISBN: 9781111427412 | Authors: Peter V. O'Neill ISBN: 9781111427412 173

Solution for problem 14.46 Chapter 14

Advanced Engineering Mathematics | 7th Edition

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Advanced Engineering Mathematics | 7th Edition | ISBN: 9781111427412 | Authors: Peter V. O'Neill

Advanced Engineering Mathematics | 7th Edition

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Problem 14.46

In each of 23 through 28, compute the windowed Fourier transform of f for the given window function w. Also compute the center and RMS bandwidth of the window function.f (t) = cos(at), w(t) = 1 for 4 t 4, 0 for |t| > 4.

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Bio Notes – Week 13 Chapter 44.1-44.5 44.1 Osmoregulation: the general term for the processes by which control solute concentrations and balance water gain and loss Excretion: the process that rids the body of nitrogenous metabolites and other metabolic waste products Osmolarlity: The number of moles of solute per liter of solution Isoosmotic: Two solutions with the same osmolarity; no net movement Hyperosmotic: The solution with the higher concentration of solutes Hypoosmotic: The more dilute solution Osmoconfomer: to be isoosmotic with its surroundings Osmoregulator: To control internal osmolarity independent of the external environment Stenohaline: Most animals that cannot tolerate substantial changes in external osmolarity Euryhaline: Animals that can survive large fluctuations in external osmolarity  Ex. Barnacles and Mussels, Stripped Bass and Salmon Desiccation: extreme dehydration Anhydrobiosis: An adaptation that occurs when animals enter a dormant state when their habitats dry up, and they survive Transport Epithelia: One or more layers of epithelial cells specialized for moving particular solutes in controlled amounts in specific directions  Typically arranged into complex tubular networks with extensive surface areas 44.2 Ammonia: very toxic because it’s ion ammonium (NH ) can4interfere with oxidative phosphorylation; need access to lots of water because this can be tolerated at very low concentrations; common in aquatic species Urea: the product of a metabolic cycle that combines ammonia with carbon dioxide in the liver; very low toxicity; animals expend energy to produce this; mammals, most amphibians, sharks, some bony fishes; excreted only in large volumes of very dilute solutions Uric Acid: Relatively non-toxic and does not readily dissolve in water – excreted as a semi-solid paste with very little water loss; more energetically expensive than urea; found in many reptiles (including birds) insects, and land snails 44.3 Excretory Processes 1. Filtration: the excretory tubule collects a filtrate from the blood. Water and solutes (salts, sugars, amino acids, and nitrogenous wastes) are forced by blood pressure across the selectively permeable membranes of a cluster of capillaries and into the excretory tubules 2. Reabsorption: The transport epithelium reclaims valuable substances from the filtrate and returns them to the body fluids through active transport 3. Secretion: Other substances such as toxins and excess ions, are extracted from body fluids and added to the contents of the excretory tubule; active transport 4. Excretion: The altered filtrate (urine) leaves the system and the body Protonephridia: form a network of dead-end tubules which are connected to external openings, branch throughout the flatworm body, which lacks a coelom (body cavity) 1. Interstitial fluid fluids through the membrane where the cap cell and tubule cell interlock 2. Filtrate empties into the external environment Metanephridia: excretory organs that collect fluid directly from the coelom – each segment of an annelid has a pair of metanephridia, which are immersed in coelomic fluid and enveloped by a capillary network Malpighian Tubules: organs that remove nitrogenous wastes and that also function in osmoregulation; extend from dead-end tips immersed in hemolymph to openings into the digestive tract Excretory Organs 1. Kidneys: a pair of organs each about 10cm in length that transport and store urine 2. Ureter: Duct where urine produced by each kidney exit through (two ureters) 3. Urinary Bladder: two ureters drain into this common sac 4. Urethra: where urine is expelled from through this tube Kidney Structure Outer Renal Cortex/Inner Renal Medulla: Found in each kidney and both are supplied with blood by a renal artery and drained by a renal vein; within these structure there are tightly packed excretory tubules and blood vessels.  Tubules: carry and process a filtrate produced from the blood entering the kidney  Nearly all the fluid in the filtrate is reabsorbed through blood vessels and exits renal vein o Remaining fluid leaves excretory tubules as urine and is collected through inner renal pelvis, and exits via ureter Nephron Types Nephron: the functional units of the vertebrate kidney that weave back and forth across the renal cortex and medulla  Cortical Nephrons: (85%) which reach only a short distance into the medulla  Juxtamedullary Nephrons: remainder which extend deep into the medulla; are essential for production of urine that is hyperosmotic to body fluids, a key adaption for water conservation in mammals Nephron Organization Glomerulus: A single long tubule as well as a ball of capillaries that each nephron consists of Bowman’s Capsule: The blind end of the tubule that forms a cup- shaped swelling Processing Occurs through: 1. Proximal Tubule 2. Loop of Henle (a hairpin turn with a descending limb and an ascending limb) 3. Distal Tubule 4. Ends at the collecting duct which receives processed filtrate from many nephrons and transports to renal pelvis Afferent Arteriole: an offshoot of the renal artery that branches and forms the capillaries of the glomerulus Efferent Arteriole: when the capillaries converge as they leave the glomerulus Vasa Recta: hairpin-shaped capillaries that serve the renal medulla, including the long loop of Henle of juxtamedullary nephrons 44.4 1. Proximal Tube: critical for recapture of ions, water, and valuable nutrients from the huge volume of initial filtrate; NaCl enters through facilitated diffusion from the transport epithelium  Active transport: NaCl; H+; Nutrients  Passive Transport: NH ;3HCO ; 3 ; H O 2 2. Descending limb of the loop of Henle: Reabsorption of water continues as the filtrate moves into the descending limb of the loop of Henle; the interstitial fluid bathing the tubule must be hyperosmotic to the filtrate; as a result, the filtrate loses water and increases in solute concentration all along its journey down the descending limb a. Aquaporin: make the numerous water channels that makes transport epithelium freely permeable to water 3. Ascending limb of the loop of Henle: Filtrate reaches the tip of the loop and then returns to the cortex in the ascending limb; has a transport epithelium that lacks water channels; epithelial membrane is impermeable to water a. A thin segment near the loop tip – NaCl diffuses out of the permeable tubule into the interstitial fluid; helps maintain osmolarity of the interstitial fluid in the medulla b. A thick segment adjacent to the distal tube – movement of NaCl out of the filtrate continues however the epithelium actively transports NaCl into the interstitial fluid; the filtrate becomes progressively more dilute as it moves up to the cortex 4. Distal Tube: Regulates K and NaCl concentration of body fluids; involves variation in the amount of K secreted into the filtrate & NaCl reabsorbed 5. Collecting Duct: Carries the filtrate through the medulla to the renal pelvis Countercurrent Multiplier Systems: countercurrent systems which expend energy to create concentration gradients; involves the loop of Henle which maintains a high salt concentration in the interior of the kidney, enabling the kidney to form concentrated urine 44.5 Vasopressin: key hormone in the regulatory circuitry of the kidney, also known as antidiuretic hormone (ADH) Renin-angiotensin-aldosterone system (RAAS): A second regulatory mechanism that helps maintain homeostasis by acting on the kidney Juxtaglomerular Apparatus (JGA): a specialized tissue consisting of cells of and around the afferent arteriole, which supplies blood to the glomerulus  When blood pressure/volume drops in the afferent arteriole, the JGA releases the enzyme renin which initiates a sequence of steps that cleave a plasma protein Angiotensin II: The peptide that is yielded by angiotensinogen causes from the enzyme renin from JGA Aldosterone: Hormone that causes the nephrons’ distal tubules and + collecting duct to absorb more Na and water, increasing blood volume and pressure Atrial Natriuretic Peptide: ANP opposes the RAAS; released in response to an increase in blood volume and pressure

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Chapter 14, Problem 14.46 is Solved
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Textbook: Advanced Engineering Mathematics
Edition: 7
Author: Peter V. O'Neill
ISBN: 9781111427412

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In each of 23 through 28, compute the windowed Fourier transform of f for the given