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Dalén's 1910 patent describes gas entering a diaphragm chamber. When its pressure overcomes a spring and magnetic restraint, a valve opens and the pilot ignites the burner. Escape of gas lowers the pressure, letting the valve close. A ratchet and cam alter an additional feed to create groups of flashes. This specification describes a pressure-driven flashing mechanism, rather than the sun valve's daylight sensor.^[ref]

The patent is evidence of the proposed mechanism, not an independent endurance or fuel-consumption test. For a simple original budget, suppose the pilot consumes gas at a steady rate $q_p$, the main burner consumes $q_m$ while lit, daylight shutoff permits operation for fraction $f$ of the day, and flashes occupy fraction $d$ of that permitted time. Then the daily mean consumption isFor stipulated $f=1/2$, $d=0.10$ and $q_p=0.02q_m$, this is $0.07q_m$, compared with $1.02q_m$ for a continuously lit main burner with the same pilot. The calculated saving is about $93.1\%$. The arithmetic explains the two independent opportunities for saving fuel; it does not establish those fractions or that performance for an actual lighthouse.

For the cylinder-plane image charges geometry, the attractive force is the displayed quantity per unit length. One derivation uses the effective energy including the voltage source: at fixed cylinder voltage $V$, the force toward increasing centre height is $F_d=V^2(d{C}^{\prime }/dd)/2$. Since $C^{\prime }=2\pi {\epsilon }_0/\mathrm{arcosh}(d/a)$ decreases with $d$, this force points toward the plane. For $d\gg a$, $\lambda \simeq 2\pi {\epsilon }_{0}V/\ln (2d/a)$ and $f\simeq \pi {\epsilon }_0{V}^2/[d{\ln }^2(2d/a)]$. A total force additionally requires the cable length.

Unsigned lecture notes in CS 4820: Algorithms, Spring 2011. The masthead identifies Cornell University and dates the document 2 May 2011. No individual author or course instructor is established. Cornell University is the institutional issuer and web host.

Online text: www.cs.cornell.edu/courses/cs4820/2011sp/handouts/approx_algs.pdf

Cited passages: Printed p. 1, heading and §1.1: institutional issuer, course, explicit date, independent random vertex placement and half-total-weight expectation.; §1.1.2, printed pp. 2–3: partial-assignment expectation, Algorithms 1–2, nondecreasing expectation, half-total-edge-weight guarantee and linear-time adjacency-list implementation..

Unsigned lecture in CS 312 at Cornell University, hosted by Cornell University’s Department of Computer Science. No individual author or publication date is credited on the inspected page.

Lecture notes: www.cs.cornell.edu/courses/cs312/2008sp/lectures/lec20.html

Cited passages: Resizable hash tables and amortized analysis; Amortized analysis.

Unsigned institutional lecture notes in CS 2112 Fall 2019. No individual author, editor or transcriber is credited, and no publication or revision date is established.

Online text: www.cs.cornell.edu/courses/cs2112/2019fa/lectures/loopinv/

Cited passages: opening definition; Using loop invariants to show code is correct, Establishment, Preservation, Postcondition and Termination; Binary search loop invariant; Debugging and choosing loop invariants.

The characteristic outward shape of a crystal; distinct from its internal crystal structure.

An atomic basis of a crystal is the motif of chemical species $s_j$ and relative positions $r_j$ attached identically to every lattice point $R$ of a Bravais lattice $\Lambda$. The ideal periodic structure is the labeled setThe primitive lattice translation vectors generate $R$ by integer combinations; the atomic basis lists what is repeated at $R$. These are different meanings of the word basis. In particular, the offsets $r_j$ need not be linearly independent vectors, and one of them may be zero. A primitive unit cell represents $N$ motif sites, even though it represents only one lattice point.

Changing the origin, choosing another primitive unit cell, or moving a motif site by a Bravais lattice translation changes the coordinates used to describe the same infinite crystal structure. The grouping into a motif does not, by itself, identify bonded molecules. In solid sodium chloride, grouping one sodium cation and one chlorine anion into an atomic basis does not create a collection of discrete NaCl molecules; the ionic crystal has an extended network of equivalent neighboring ions.

A lattice plane is a plane containing a two-dimensional periodic array of lattice points. Parallel lattice planes form equally spaced geometrical sheets; an atomic basis can place chemical atoms between them.

With primitive lattice translation vectors $a_i$, write $r=x{a}_1+y{a}_2+z{a}_3$. For integers $h,k,l$ with greatest common divisor one, the plane equationsgive a complete family labeled by Miller indices $(hkl)$. In a primitive cubic lattice, $(110)$ means $x+y=m$, parallel to $a_3$.^[ref]