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from article Tangent
Line L tangent to curve C at P.
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from article Heterocyclic polymer
Structural units in linear polymers. (a) Simple linear polymer. (b) Stepladder polymer. (c) Ladder polymer.
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from article Heterocyclic polymer
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from article Intermolecular forces
Schematic diagram of intermolecular interaction. (a) There is negligible interaction between atoms that are 1 nm apart. (b) For atoms separated by about 0.8 nm or less, attractive dispersion forces result from correlated fluctuations of the electron…
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from article Masking of sound
Three psychophysical tuning curves, showing the tonal masking effects for tonal signals of 300, 1000, or 3000 Hz. (After F. L. Wightman et al. Factors influencing frequency selectivity in normal and hearing-impaired listeners, in E. F. Evans and J.…
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from article Masking of sound
Width of the critical band in hertz as a function of signal frequency.
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from article Masking of sound
Relative amount of masking obtained in forward, simultaneous, and backward masking. (After W. A. Yost, Fundamentals of Hearing: An Introduction, 4th ed., Academic Press, New York, 2000)
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from article Masking of sound
Masking of a 1000-Hz pure-tone signal in forward masking when the masker is a two-tone complex consisting of a 1000-Hz masker and a second tone. (a) Threshold of signal for the two-tone masker relative to that obtained when only the 1000-Hz tone…
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from article Nitrogen oxides
Nitrogen-oxide structures. Blue = nitrogen. Red = oxygen.
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from article Star tracker
Strapdown satellite star tracker. (a) Mounting of system on the satellite. (b) Star tracker in housing. (Northrop Grumman Corp.)
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from article Star tracker
Silicon focal-plane arrays. (Northrop Grumman Corp.)
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from article Hyperbola
Hyperbola as a conic section.
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from article Hyperbola
Hyperbola as a locus of points.
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from article Alicyclic hydrocarbon
Internal bond angles (α) for (a–c) planar rings and (d) a tetrahedral carbon atom.
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from article Alicyclic hydrocarbon
Nonplanar (a) chair and (b) boat structures of cyclohexane.
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from article Alcohol
Ethanol production plant. (Credit: Julie Kendall/Getty Images)
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from article Alcohol
E85 is a gasoline-ethanol blend containing 51 to 83% ethanol. It is used in flexible-fuel vehicles, which can operate on gasoline or blends of gasoline and ethanol. About 20 million flexible-fuel vehicles are operating in the United States. (Credit:…
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from article Fluids
Probability of finding molecular centers at various separations in gases, liquids, and solids.
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from article Fluids
Conditions of pure-component phase behavior.
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from article Fluids
Behavior of pure-component pressures with density at various temperatures.
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from article Fluids
Behavior of pure-component compressibility factors with pressure at various temperatures.
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from article Biosynthesis
Biosynthetic relationships of some natural products. Specific examples which belong to the various classes are given in brackets.
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from article Thulium
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from article Chemistry
Periodic table. (Jaap Hart/Getty Images)
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from article Mercury (element)
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from article Mercury (element)
Mercury droplets exhibiting non-wetting of the surface. (Credit: A. Cerar/Getty Images)
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from article Mercury (element)
Tooth with a silver-amalgam filling. (Credit: Szasz-Fabian Jozsef/Shutterstock.com)
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from article Bipolar disorder
Prevalence of bipolar disorder in adults. The bar graph shows the percent of the U.S. adult population affected by bipolar disorder as it relates to age. (Credit: National Institute of Mental Health)
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from article Organic conductor
Structures of organic conductors. (a) Electron donors. (b) Acceptor molecule (TCNQ) and two monovalent anions. Abbreviations are explained in the text.
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from article Organic conductor
Stacking of charge-transfer compounds. (a) Segregated stacking of TTF-TCNQ-like materials. (b) Typical zigzag stacking of the (TMTSF)2X series.
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from article Organic conductor
Comparison of the range of electrical conductivities of some AsF5-doped conducting polymers with some metals, semiconductors, and nonconducting polymers.
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from article Organic conductor
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from article Geometrization theorem
Making a 2-D torus.
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from article Geometrization theorem
Life in Seifert-Weber dodecahedral space. (Courtesy of Geometry Center, University of Minnesota)
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from article Geometrization theorem
Hyperbolic dodecahedron of infinite diameter. The infinite spikes are rounded off “chimneys,” which are here triangular rather than rectangular. (Courtesy of Paul Nylander fromhttp://bugman123.com/)
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from article Geometrization theorem
Neck pinching, resulting in infinite curvature.
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from article Geometrization theorem
Ricci flow with surgery.
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from article Neuroeconomics
Neuroeconomics applies neuroscientific tools and methodologies to investigate the decision making that occurs inside the brain. (Credit: James Steidl/SuperStock)
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from article Doppler VOR
Collocation of Doppler VOR and TACAN beacons installed on 100-foot high (30-m) tower with a counterpoise of 119-ft (36-m) diameter in forest near Frankfurt, Germany. Circular array consists of 39 loop antennas fed by solid-state commutator. Center…
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from article Doppler VOR
Principle of Doppler VOR beacon. Reference signal R and bearing signal V which is generated by dipole d are shown as they would be measured in aircraft to the north, east, south, and west of the beacon. (a) Dipole d at 180°. (b) Dipole d at 270°.…
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from article Doppler VOR
Comparison of radial flight recordings. (a) From VOR installation. (b) From DVOR installation. Both experimental beacons were located at same unfavorable site. Plane is flying constant course at bearing of 133° from beacons at 4000-ft (1.2-km)…
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from article Matrix theory
Vector rotation that rotates any vector v in the plane counterclockwise through 45° to a new vector Tv.
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from article Psychological resilience
Psychological resilience refers to positive adaptation among individuals at risk for maladjustment. There are three classes of protective factors that help people to thrive in the face of significant adversities: support from close family and…
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from article Psychological resilience
The strongest predictor of resilient adaptation is the quality of an individual's close, personal relationships. In general, positive relationships help individuals to combat adversity through collective problem solving and through the sharing of…
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from article Calculus of variations
Weierstrass condition. Symbols explained in text.
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from article Calculus of variations
Example of an area-minimizing surface that cannot be written as the graph of a single function. (a) Nonconvex domain C. (b) Minimal graph over C that is not area-minimizing. (c) Second surface over C that has less area. (After F. Morgan, Geometric…
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from article Calculus of variations
Comparison of surfaces. (a) Surface with no handles. (b) Surface with one handle and less area. (c) Surface with two handles and still less area. (d, e, f) These three surfaces are deformed to show that they do have zero, one, and two handles,…
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from article Calculus of variations
Examples of surfaces minimizing the integral of a nonelliptic integrand among all bodies having the same volume (the surface at upper left) and among all surfaces having the same boundary (the saddle-shaped surface). Surfaces were computed as part…
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from article Suicide
Methods of suicide in (left) males and (right) females. The three most prevalent methods of suicide involve firearms, suffocation, and poisoning. Males are much more likely to use firearms, whereas the preferred method in females is poisoning.…
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from article Suicide
Age-adjusted suicide rates in males and females from 1999 to 2017 in the United States. (Credit: National Vital Statistics System, National Center for Health Statistics, Centers for Disease Control and Prevention)
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from article Linear algebra
Geometric representation of a vector OP.
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from article Hydrido complexes
Structure of ReH92−.
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from article Hydrido complexes
Structure of [HMn(CO)5].
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from article Hydrido complexes
Structure of [HRe(C5H5)2]. The aromatic C5H5 groups are represented by pentagons.
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from article Hydrido complexes
Hydridophosphine structures, with the C6H5 groups not shown. (a) [HRuCl(P{C6H5 }3)3]. (b) [H3Ir(P{C6H5 }3)3].
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from article Hydrido complexes
Reaction scheme for hydrogenation of an olefin using Wilkinson's catalyst.
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from article Hydrido complexes
Structure of [HCr2(CO)10]−.
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from article Hydrido complexes
Structure of [H2W2(CO)8]2−.
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from article Hydrido complexes
Core of the [H8Re2(P{C2H5 }2C6H5)4] molecule. All organic groups are omitted for clarity.
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from article Hydrido complexes
Structure of [H2Th(C5 {CH3 }5)2]2. The hydrogen atoms of the methyl groups are omitted for clarity.
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from article Liquid
Phase diagram of a pure substance.
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from article Periodic table
Periodic table of the elements.
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from article Cotton effect
Behavior of the ORD and CD curves in the vicinity of an absorption band at wavelength λ0 (idealized). (a) Positive Cotton effect. (b) Negative Cotton effect.
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from article Cotton effect
Curves used to determine relative rotatory intensities. (a) Partial ORD curve. (b) Partial CD curve.
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from article Cotton effect
Structural formula of (+)-trans-9-methyl-1,4,9,10- tetrahydronaphthalene.
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from article Cotton effect
Schematic representation of the twisted diene chromophore showing the two possible handednesses; the numbering is as indicated in Fig. 3 (a) Right-handed. (b) Left-handed.
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from article Sextant
Marine sextant.
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from article Sextant
Periscopic sextant for use in aircraft.
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from article Electrochemistry
Electrolysis of aqueous potassium bromide. (Copyright © McGraw-Hill Education/Stephen Frisch)
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from article Osmium
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from article Osmium
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from article Luminescence analysis
Typical photoluminescence excitation and emission spectra for molecules in solution.
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from article Luminescence analysis
Components of instrumentation for luminescence measurements.
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from article Psychosis
A colorized magnetic resonance imaging (MRI) scan of a human brain. Psychosis is a defective mental state in which there is a critical derangement of the mind (brain) involving abnormal contact with reality. (Credit: Govind Bhagavatheeshwaran and…
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from article Camphor
Camphor tree. (Credit: Gyro Photography/amanaimagesRF/Getty Images)
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from article Conic section
Four conic sections. (a) Circle. (b) Ellipse. (c) Parabola. (d) Hyperbola.
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from article Copper
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from article Copper
Chalcopyrite (CuFeS2), a copper-iron sulfide mineral, is an important copper-containing ore. (Credit: Linnas/Getty Images)
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from article Copper
Electrical wiring cable. (Credit: Shutterstock/Sydeen)
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from article Fullerene
Buckyball structure.
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from article Fullerene
Some of the more stable members of the fullerene family. (a) C28. (b) C32. (c) C50. (d) C60. (e) C70.
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from article Fullerene
Comparison of the structure of fullerene-60 with that of two giant fullerenes. (a) C60. (b) C240. (c) C540.
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from article Fullerene
Structure of the molecule C60Br6.
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from article Fullerene
A section of a carbon nanotube showing the concentric graphene tubes composing it.
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from article Drug delivery systems
A transdermal nicotine patch is a noninvasive method of controlled drug delivery. (Copyright © Plush Studios/Bill Reitzel/Blend Images)
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from article Drug delivery systems
Three levels of polymer drug delivery. (a) A polymer is used as carrier of drugs. (b) The drugs are connected to the polymer via cleavable peptide linkers. (c) A homing device is added to target specific tissue types. (Credit: Jan van Hest;…
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from article Half-life
The decay chain of uranium, which has a half-life of approximately 4.5 billion years and is the most common uranium isotope in nature. The alpha symbol (α) indicates alpha decay, while the beta symbol (β) indicates beta decay. Alpha decay emits an…
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from article Catenary
Catenary and force triangle which keeps a portion of the string in equilibrium.
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from article Catenary
Relation of catenary to the tractrix which is its involute.
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from article Narcotic
Heroin is an extremely addictive narcotic. (Credit: FotoMaximum/Getty Images)
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from article Narcotic
Chemical structure of a morphine alkaloid. Two important natural alkaloids are morphine and codeine. Heroin is synthesized from morphine by acetylation.
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from article Catalytic antibody
Schematic structure of an antibody molecule. The protein consists of two heavy chains and two light chains.
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from article Catalytic antibody
Early highlights of the first antibody-catalyzed reaction of ester hydrolysis. Stable tetrahedral phosphonate was used as the transition-state analog.
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from article Catalytic antibody
Mechanism of trapping the essential ε-amino group of a lysine residue in the antibody's binding pocket by using the 1,3-diketone hapten.
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from article Catalytic antibody
Prodrug activation via a tandem retro-aldol-retro-Michael reaction. X stands for heteroatoms N, O, or S (nitrogen, oxygen, or sulfur).
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from article Catalytic antibody
Generation of bispecific antibody originating from a catalytic antibody and a targeting antibody.
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from article Catalytic antibody
Chemotherapy targeted specifically to a tumor cell. The prodrug is prodoxorubicin, which is transformed to the active drug doxorubicin by the catalytic arm of the bifunctional antibody. The other arm binds to an antigen on a tumor cell.
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from article Air-traffic control
Terminal radar controller's plan view display. Aircraft positions are shown by radar returns. Display is centered on primary airport with parallel and intersecting runways. Range rings are spaced 5 mi (9 km) apart. Airspace within boundary and above…
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from article Legendre functions
Legendre polynomials Pn(x), n = 2, 3, 4, 5.
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from article Legendre functions
Legendre functions of the second kind, Qn(x). (After E. Jahnke and F. Emde, Tables of Functions with Formulae and Curves, 4th ed., Dover Publications, 1945)
