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In electrical engineering, the power factor of an AC power system is defined as the ratio of the real power absorbed by the load to the apparent power flowing in the circuit, and is a dimensionless number in the closed interval of −1 to 1. A power factor magnitude of less than one indicates the voltage and current are not in phase, reducing the average product of the two. Real power is the instantaneous product of voltage and current and represents the capacity of the electricity for performing work. Apparent power is the product of RMS current and voltage. Due to energy stored in the load and returned to the source, or due to a non-linear load that distorts the wave shape of the current drawn from the source, the apparent power may be greater than the real power. A negative power factor occurs when the device (which is normally the load) generates power, which then flows back towards the source.

In an electric power system, a load with a low power factor draws more current than a load with a high power factor for the same amount of useful power transferred. The higher currents increase the energy lost in the distribution system, and require larger wires and other equipment. Because of the costs of larger equipment and wasted energy, electrical utilities will usually charge a higher cost to industrial or commercial customers where there is a low power factor.

Power-factor correction increases the power factor of a load, improving efficiency for the distribution system to which it is attached. Linear loads with low power factor (such as induction motors) can be corrected with a passive network of capacitors or inductors. Non-linear loads, such as rectifiers, distort the current drawn from the system. In such cases, active or passive power factor correction may be used to counteract the distortion and raise the power factor. The devices for correction of the power factor may be at a central substation, spread out over a distribution system, or built into power-consuming equipment.

Franklin Delano Roosevelt (, ROH-zə-velt; January 30, 1882 – April 12, 1945), often referred to by his initials FDR, was an American politician and attorney who served as the 32nd president of the United States from 1933 until his death in 1945. A member of the Democratic Party, he won a record four presidential elections and became a central figure in world events during the first half of the 20th century. Roosevelt directed the federal government during most of the Great Depression, implementing his New Deal domestic agenda in response to the worst economic crisis in U.S. history. As a dominant leader of his party, he built the New Deal Coalition, which defined modern liberalism in the United States throughout the middle third of the 20th century. His third and fourth terms were dominated by the Second World War, which ended shortly after he died in office.

Born into the Roosevelt family in Hyde Park, New York, he graduated from both Groton School and Harvard College, and attended Columbia Law School, which he left after passing the bar exam to practice law in New York City. In 1905, he married his fifth cousin once removed, Eleanor Roosevelt. They had six children, of whom five survived into adulthood. He won election to the New York State Senate in 1910, and then served as Assistant Secretary of the Navy under President Woodrow Wilson during the First World War. Roosevelt was James M. Cox's running mate on the Democratic Party's 1920 national ticket, but Cox was defeated by Republican Warren G. Harding. In 1921, Roosevelt contracted a paralytic illness, believed at the time to be polio, and his legs became permanently paralyzed. While attempting to recover from his condition, Roosevelt founded a polio rehabilitation center in Warm Springs, Georgia. Although unable to walk unaided, Roosevelt returned to public office after his election as governor of New York in 1928. He served as governor from 1929 to 1933, promoting programs to combat the economic crisis besetting the United States.

In the 1932 presidential election, Roosevelt defeated Republican incumbent Herbert Hoover in a landslide. He took office in the midst of the Great Depression and during the first 100 days of the 73rd U.S. Congress, Roosevelt spearheaded unprecedented federal legislation and issued a profusion of executive orders that instituted the New Deal—a variety of programs designed to produce relief, recovery, and reform. He created numerous programs to provide relief to the unemployed and farmers while seeking economic recovery with the National Recovery Administration and other agencies. He also instituted major regulatory reforms related to finance, communications, and labor, and presided over the end of Prohibition. He used radio to speak directly to the American people, giving 30 "fireside chat" radio addresses during his presidency and became the first American president to be televised. With the economy having improved rapidly from 1933 to 1936, Roosevelt won a landslide reelection in 1936. After the election, he sought passage of the Judicial Procedures Reform Bill of 1937 (or "court packing plan"), which would have expanded the size of the Supreme Court. The bill was blocked by the newly formed bipartisan Conservative Coalition. The economy then relapsed into the recession of 1937–1938. Other major 1930s legislation and agencies implemented under Roosevelt include the Securities and Exchange Commission, the National Labor Relations Act, the Federal Deposit Insurance Corporation, Social Security, and the Fair Labor Standards Act.

He was reelected in 1940 for his third term, making him the only U.S. president to serve for more than two terms. With World War II looming after 1938, the U.S. remained officially neutral, but Roosevelt gave strong diplomatic and financial support to China, the United Kingdom, and eventually the Soviet Union. Following the Japanese attack on Pearl Harbor on December 7, 1941, an event he called "a date which will live in infamy", Roosevelt obtained a congressional declaration of war on Japan. When Germany and Italy declared war on the US in response, the US formally entered the European theater of the war. Assisted by his top aide Harry Hopkins and with very strong national support, he worked closely with British Prime Minister Winston Churchill, Soviet General Secretary Joseph Stalin and Chinese Generalissimo Chiang Kai-shek in leading the Allied Powers against the Axis Powers. Roosevelt supervised the mobilization of the U.S. economy to support the war effort and implemented a Europe first strategy, initiating the Lend-Lease program and making the defeat of Germany first a priority over that of Japan. His administration oversaw the construction of The Pentagon, initiated the development of the world's first atomic bomb, and worked with other Allied leaders to lay the groundw reference

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Reverse osmosis (RO) is a water purification process that uses a partially permeable membrane to separate ions, unwanted molecules and larger particles from drinking water. In reverse osmosis, an applied pressure is used to overcome osmotic pressure, a colligative property that is driven by chemical potential differences of the solvent, a thermodynamic parameter. Reverse osmosis can remove many types of dissolved and suspended chemical species as well as biological ones (principally bacteria) from water, and is used in both industrial processes and the production of potable water. The result is that the solute is retained on the pressurized side of the membrane and the pure solvent is allowed to pass to the other side. To be "selective", this membrane should not allow large molecules or ions through the pores (holes), but should allow smaller components of the solution (such as solvent molecules, e.g., water, H2O) to pass freely.

In the normal osmosis process, the solvent naturally moves from an area of low solute concentration (high water potential), through a membrane, to an area of high solute concentration (low water potential). The driving force for the movement of the solvent is the reduction in the Gibbs free energy of the system when the difference in solvent concentration on either side of a membrane is reduced, generating osmotic pressure due to the solvent moving into the more concentrated solution. Applying an external pressure to reverse the natural flow of pure solvent, thus, is reverse osmosis. The process is similar to other membrane technology applications.

Reverse osmosis differs from filtration in that the mechanism of fluid flow is by osmosis across a membrane. The predominant removal mechanism in membrane filtration is straining, or size exclusion, where the pores are 0.01 micrometers or larger, so the process can theoretically achieve perfect efficiency regardless of parameters such as the solution's pressure and concentration. Reverse osmosis instead involves solvent diffusion across a membrane that is either nonporous or uses nanofiltration with pores 0.001 micrometers in size. The predominant removal mechanism is from differences in solubility or diffusivity, and the process is dependent on pressure, solute concentration, and other conditions.

Reverse osmosis is most commonly known for its use in drinking water purification from seawater, removing the salt and other effluent materials from the water molecules.