A positive resistive electrical load obeys Ohm's law, $V_L=I{R}_L$. Its resistive load line intersects the Thévenin terminal response atprovided $R_{\mathrm{th}}+R_L\ne 0$. For the Thévenin divider example, $R_L=1\mathrm{k\Omega }$ gives $I=24/7\mathrm{mA}$ and $V_L=24/7\mathrm{V}$; $R_L=4\mathrm{k\Omega }$ gives $I=1.5\mathrm{mA}$ and $V_L=6\mathrm{V}$. At $R_L=R_{\mathrm{th}}=\frac{4}{3}\mathrm{k\Omega }$, the voltage is $4\mathrm{V}$, half the open-circuit voltage.

For this positive $R_{\mathrm{th}}$, increasing $R_L$ reduces the drawn electric current and raises $V_L$ toward $V_{\mathrm{oc}}$. This explains voltmeter loading: a voltmeter itself is an electrical load. The equivalence also applies to a nonlinear electrical load through intersection with its terminal relation, but an arbitrary load need not give a unique operating point. If negative $R_{\mathrm{th}}$ cancels positive $R_L$, the displayed formula is singular; a real active circuit's limits and dynamics must then be considered.

To determine the Thévenin resistance, remove the external electrical load and set each independent electrical source to zero in the circuit model. A zero ideal voltage source enforces zero electric potential difference, so replace it by a short connection. A zero ideal current source enforces zero electric current, so replace it by an open connection. Retain every resistor, including any explicitly modeled supply electrical resistance. Turning an actual power supply's front-panel control to zero is not evidence that it physically becomes an ideal wire.

Retain every dependent electrical source and its controlling variable: its response to an electrical test source is part of the network's electrical resistance. Impose terminal voltage $v_t$ with an electrical test source and calculate $j_t$ entering the suppressed network at $a$. For a nonzero test yielding a finite ratio,Alternatively inject a known entering electric current and solve for $v_t$. The test electric current is opposite to the delivered-current convention of the original Thévenin terminal response. ^[ref]

For an original illustration, put a positive resistor $R$ across $a,b$ and a dependent electrical source in parallel that injects electric current $g{v}_t$ from $b$ toward $a$, where $g$ has units of electrical conductance. Its control is the same terminal voltage $v_t$. Kirchhoff's current law givesWith $R=1\mathrm{k\Omega }$ and $g=0.5\mathrm{mS}$, a $1\mathrm{V}$ test draws $0.5\mathrm{mA}$, giving $R_{\mathrm{th}}=2\mathrm{k\Omega }$. Removing the dependent electrical source would falsely give $1\mathrm{k\Omega }$. With $g=2\mathrm{mS}$, the model instead has $R_{\mathrm{th}}=-1\mathrm{k\Omega }$; with $g=1\mathrm{mS}$ it draws zero test electric current for any imposed voltage and has no finite ratio. An active physical realization requires a supply and has a limited operating range.

For a finite nonzero $R_{\mathrm{th}}$ and a well-defined short-circuit response, $I_{\mathrm{sc}}=V_{\mathrm{oc}}/R_{\mathrm{th}}$. Thus $R_{\mathrm{th}}=V_{\mathrm{oc}}/I_{\mathrm{sc}}$ is usable when $I_{\mathrm{sc}}\ne 0$. A source-free positive resistor has both $V_{\mathrm{oc}}=0$ and $I_{\mathrm{sc}}=0$, so this quotient cannot reveal its electrical resistance; an electrical test source can.

In the pictured original linear resistive circuit, the ideal voltage source keeps its upper node at $12\mathrm{V}$ relative to $b$. Let $R_1=2\mathrm{k\Omega }$ connect that node to $a$, and $R_2=4\mathrm{k\Omega }$ connect $a$ to $b$. With the external electrical load removed, the voltage divider givesTo find the Thévenin resistance, Thévenin source suppression replaces the ideal $12\mathrm{V}$ voltage source by a wire. Both resistors now join $a$ to $b$ in parallel, givingThis is the electrical resistance looking into the original network with its independent electrical source suppressed; the external electrical load is excluded.

An independent check uses Kirchhoff's current law at $a$, without suppressing anything:The Thévenin terminal response thus follows directly from the original topology. Shorting $a$ to $b$ in this ideal calculation gives $I_{\mathrm{sc}}=6\mathrm{mA}$: the lower resistor has zero voltage and the upper resistor limits the electric current. All numerical values here and in the figures are stipulated model values, not laboratory data.

With the passive sign convention applied to the network, its entering electric current is $J=-I$, and the same relation becomes $V=V_{\mathrm{oc}}+J{R}_{\mathrm{th}}$. The electrical load uses the passive sign convention with entering electric current $I$, so it absorbs power $VI$. A positive delivered electric current therefore produces a voltage drop for positive $R_{\mathrm{th}}$; changing the reference direction without changing the equation would give the wrong sign.

The reason is linearity of Ohm's law, Kirchhoff's current law, Kirchhoff's voltage law, and the constitutive relations of any linear dependent electrical sources. Solve once at $I=0$ with the independent electrical sources present. Subtract this solution from a solution with prescribed delivered electric current $I$: the fixed independent electrical sources cancel, leaving a homogeneous linear network whose terminal voltage change is proportional to $I$. This is a short superposition principle argument for an affine function; the fixed offset need not vanish.

The qualification about a well-defined response matters. An ideal voltage source alone has $R_{\mathrm{th}}=0$. An ideal nonzero current source alone constrains $I$ and does not have a finite open-circuit voltage or a representation $V=V_{\mathrm{oc}}-I{R}_{\mathrm{th}}$ with finite coefficients. Linear dependent electrical sources can give negative resistance, and singular ideal networks may fail to have a unique finite response. Neither a finite nor a strictly positive passive $R_{\mathrm{th}}$ follows merely from calling an electrical circuit linear. ^[ref]

An abstract machine specifies a computational state and rules for advancing that state without requiring one particular physical implementation. A Turing machine and a stack machine give different ways to organize the state and its transitions.

A comparison using a logarithm of two powers is expressed as $10{\log }_{10}(P_2/P_1)\mathrm{dB}$. Positive loss instead uses $10{\log }_{10}(P_{\mathrm{in}}/P_{\mathrm{out}})\mathrm{dB}$. For wave amplitudes, a factor twenty is appropriate only when the corresponding power ratio equals the square of the amplitude ratio.

A substituent is an attached chemical atom or group considered relative to a chosen molecular framework. Testing whether two substituents are identical may require comparing their full chemical bond connectivity and stereochemistry.

Conformational isomerism concerns spatial arrangements interconverted by internal motion, such as turning about a single chemical bond. Moving the entire molecule or applying a rotation changes its position or viewing direction, not its internal arrangement.

Absolute configuration records a spatial arrangement without leaving its handedness relative to its mirror unspecified. R and S configuration is one naming convention; optical rotation is a measured response.

Stereoisomers have the same chemical bond connectivity but different spatial arrangements. A mirror pair of distinct stereoisomers comprises enantiomers; diastereomers have no mirror-pair relation.

A spreadsheet tabular model assigns a consistent meaning to each row and column. For an original example, let rows 2–4 describe three items, with quantity in column A, unit price in column B, subtotal in column C, and total including tax in column D. Put the single shared tax rate in F1. The chosen rate $1/5$ is an illustrative assumption. Quantities, unit prices and F1 are inputs; columns C and D hold spreadsheet formulas and display their computed values as outputs.

Enter decimal inputs 2.5, 1.75, 4.5 for the unit prices and 0.2 for the tax rate. The following table expresses those values as exact fractions so that the arithmetic is easy to check. It does not require typing a fraction into an input spreadsheet cell or assume that all software calculates with exact rational numbers.

Start with C2 containing =A2*B2 and D2 containing =C2*(1+$F$1). Here * requests multiplication, and 1+$F$1 adds the tax fraction to one. Copy these two spreadsheet formulas down into rows 3 and 4, a fill operation. The relative spreadsheet references change with the destination row: C3 becomes =A3*B3 and D3 becomes =C3*(1+$F$1); C4 becomes =A4*B4 and D4 becomes =C4*(1+$F$1). The absolute spreadsheet reference $F$1 continues to read the shared rate. Copying spreadsheet formulas adjusts relative coordinates while retaining absolute coordinates. ^[ref]

The same mathematical expression applies to every item. Writing $q_i$ for quantity, $p_i$ for unit price and $t$ for the shared tax rate givesFor row 2, the exact arithmetic is $(3\cdot 5/2)(1+1/5)=(15/2)(6/5)=9$. The subtotals add to $47/2$, so the totals add to $(47/2)(6/5)=141/5$, agreeing with $9+42/5+54/5$. The spreadsheet formulas encode the relationship; the displayed numbers are its results for these particular inputs.

This separation is useful for forecasting and sensitivity analysis. Keeping quantities and unit prices fixed while changing only F1 from $1/5$ to $1/4$ gives exact totals $75/8$, $35/4$, and $45/4$. More generally, a rate change $\Delta t$ changes each total byThis follows by expanding the two mathematical expressions and cancelling $s_i(1+t)$. Here $\Delta t=1/20$, so the increases are $3/8$, $7/20$, and $9/20$, adding to $47/40$. One shared input makes the assumption visible and consistent across all rows. Overwriting a computed total with a number would instead remove that spreadsheet formula; its value would cease to follow the model when the rate changes.

// Target: computer-science.bigb

A family of light-sensing proteins with interconvertible red-absorbing and far-red-absorbing forms. Phytochrome links light perception to plant development, including the lettuce red and far-red germination experiment.^[ref]

The width of a frequency range assigned to a signal. Exact spectral support and widths defined by a retained-power fraction or amplitude threshold must be distinguished.

Recovering two orthogonal components of a signal by averaging its products with sine and cosine reference signals at the chosen frequency.

Signal distortion is an unwanted change in a signal's shape or information-bearing relationships. A nonlinear response $y=ax+b{x}^2$ driven by a sinusoid produces DC and a second harmonic, introducing frequencies absent from the input. A linear system can also distort a waveform when its gain or phase response varies across the signal bandwidth, changing the relation between existing components. Distortion differs from additive noise, although both can degrade a measurement. The relevant comparison is to the intended signal transformation; an intentional filter is not faulty merely because it changes the waveform.

An analog multiplier produces an output proportional to the product of two input signals, often $v_o=v_x{v}_y/V_s$ for a specified scale voltage $V_s$. Multiplying two sinusoids generates sum and difference frequencies by the product-to-sum identity. This supports modulation, synchronous detection and frequency mixing. Real devices have limits on input range, bandwidth, offset and feedthrough, so an unwanted output can remain when one nominal input is zero. A four-quadrant multiplier accepts either sign on both inputs; more restricted devices implement fewer sign combinations.

A protein obtained from cattle serum and widely used as a reference sample in biochemistry. It serves as a protein standard for assays such as the bicinchoninic acid assay, and as a model protein in dialysis experiments.

Cohesin is a multisubunit chromosome-associated protein complex involved in sister-chromatid cohesion and chromosome organization. Cleavage of a cohesin component helps permit sister separation at anaphase. Cohesin also contributes to chromosomal loop organization: acute removal can eliminate loop domains without implying that every aspect of gene expression changes immediately. Its segregation and interphase-organization roles are related but experimentally separable. ^[ref][ref]

A program written in the input notation of a compiler or interpreter, before the particular translation being discussed.

Polystyrene is a polymer with repeating units $-\mathrm{C}{\mathrm{H}}_2-\mathrm{CH}({\mathrm{C}}_6{\mathrm{H}}_5)-$, placing a phenyl side group on alternate backbone carbons. Addition polymerization retains the monomer's phenyl group while converting its carbon-carbon double bond into backbone bonds.

Polystyrene standards are used for organic-solvent size-exclusion chromatography. Their hydrodynamic size supplies a conditional SEC molar mass calibration; a different polymer of equal molar mass need not have the same coil size or elution volume.^[ref]