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from article Branched polymer
Steps in the synthesis of a starburst polymer. s = surface. o = interior. fr = reactive group. fp = protected group.
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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 Nitrogen oxides
Nitrogen-oxide structures. Blue = nitrogen. Red = oxygen.
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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 Physical science
An astronaut conducts a physical science experiment aboard the International Space Station involving buoyancy-driven convection and sedimentation, which as force-dependent phenomena occur differently in a microgravity environment. (Credit: NASA)
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from article Model theory
Conceptual model of a system.
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from article Model theory
Model of a regional population system.
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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 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 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 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 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 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 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 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)
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from article Frequency counter
Block diagram of a reciprocal frequency counter.
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from article Circle
A circle, with radius, diameter, and circumference indicated. (Credit: McGraw-Hill Education)
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from article Circle
Nine-point circle and Euler line PMH.
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from article Sonobuoy
Launch of a sonobuoy from an antisubmarine warfare (ASW) aircraft. (a) In flight. (b) Buoy strikes the water in a nearly vertical attitude. (c) Antenna and hydrophone are positioned automatically.
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from article Blowpipe
Glassblower blowing into a blowpipe to shape molten glass. (Credit: Hero Images/Getty Images)
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from article Trihedron
Trihedron and trihedral angles.
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from article Trihedron
Spherical triangle ABC formed by intersection of sphere with a trihedron. The center of the sphere is at the vertex of the trihedron.
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from article Tin
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from article Tin
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from article Isoelectric point
Titration of alanine with sodium hydroxide (NaOH), showing the course of pH with added fractional equivalents. The four arrows show, from left to right, the pKa [½ cations: NH3+(CH3)COOH, and ½ zwitterions: NH3+(CH3)CHCOO−], the pl (all…
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from article Isoelectric point
Course of the charges carried by lysine (pKa = 2.18) molecules in dilute aqueous solution with pH during a titration with alkali. Shown are the net charge, going from +2 at low pH to +1 between pH 4.5 and 6.5, the isoelectric point at pH 9.74, the…
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from article Iridium
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from article Gamma function
Depiction of gamma function Γ(z) for real values of z.
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from article Biofuel cell
Schematic of a biofuel cell with a microbial catalyst at the bioanode, an enzymatic catalyst at the biocathode, and a polymer electrolyte membrane (PEM) separator between the two compartments. (Reproduced with permission from ACS Publications from…
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from article Biofuel cell
Top: Direct electron transfer of oxygen-reduction by a multicopper oxidase. Bottom: Mediated electron transfer of oxygen reduction by the same multicopper oxidase. (Reproduced with permission from ACS Publications from R. D. Milton, T. Wang, K. L.…
