20 research outputs found
Formalizing Euclidâs first axiom.
Formalizing Euclidâs first axiom. Bulletin of Symbolic Logic. 20 (2014) 404â5. (Coauthor: Daniel NovotnĂœ)
Euclid [fl. 300 BCE] divides his basic principles into what came to be called âpostulatesâ and âaxiomsââtwo words that are synonyms today but which are commonly used to translate Greek words meant by Euclid as contrasting terms.
Euclidâs postulates are specifically geometric: they concern geometric magnitudes, shapes, figures, etc.ânothing else. The first: âto draw a line from any point to any pointâ; the last: the parallel postulate.
Euclidâs axioms are general principles of magnitude: they concern geometric magnitudes and magnitudes of other kinds as well even numbers. The first is often translated âThings that equal the same thing equal one anotherâ.
There are other differences that are or might become important.
Aristotle [fl. 350 BCE] meticulously separated his basic principles [archai, singular archĂȘ] according to subject matter: geometrical, arithmetic, astronomical, etc. However, he made no distinction that can be assimilated to Euclidâs postulate/axiom distinction.
Today we divide basic principles into non-logical [topic-specific] and logical [topic-neutral] but this too is not the same as Euclidâs. In this regard it is important to be cognizant of the difference between equality and identityâa distinction often crudely ignored by modern logicians. Tarski is a rare exception. The four angles of a rectangle are equal toânot identical toâone another; the size of one angle of a rectangle is identical to the size of any other of its angles. No two angles are identical to each other.
The sentence âThings that equal the same thing equal one anotherâ contains no occurrence of the word âmagnitudeâ. This paper considers the problem of formalizing the proposition Euclid intended as a principle of magnitudes while being faithful to the logical form and to its information content
Microprofiles of oxygen around <i>Potamogeton malaianus</i> stems and leaves with and without periphyton.
<p>A, C, and E indicate thick periphyton; B, D, and F indicate periphyton removed; G indicates young leaves with little periphyton. Microprofiles were measured at three different points under quantum flux density of 300 ”mol photons·m<sup>â2</sup>·s<sup>â1</sup> on <i>P. malaianus</i> stems and leaves. The outer surfaces of the periphyton layer are indicated by horizontal bars. The leaf surfaces are indicated by 0. Microprofiles of oxygen around young leaves were not markedly different between the presence of little periphyton and periphyton removed.</p
The estimated O<sub>2</sub> fluxes (ÎŒmol·cm<sup>â2</sup>·min<sup>â1</sup>) through the broad diffusive boundary layer associated to the surface of <i>Potamogeton malaianus</i> according to Fick's first law (nâ=â3)
<p>Values represent means of triplicates and standard error, respectively. NA, non-applicable.</p
Schematic of oxygen microprofiles around submerged macrophyte leaves with periphyton.
<p>Schematic of oxygen microprofiles around submerged macrophyte leaves with periphyton.</p
Microprofiles of pH around <i>Potamogeton malaianus</i> stems and leaves with and without periphyton.
<p>A, C, and E, indicate thick periphyton; B, D, and F indicate periphyton removed; G indicates young leaves with a little periphyton. Microprofiles were measured at three different points under quantum flux density of 300 ”mol photons·m<sup>â2</sup>·s<sup>â1</sup> on <i>P. malaianus</i> stems and leaves. The outer surfaces of the periphyton layer are indicated by horizontal bars. The leaf surfaces are indicated by 0. The microprofiles of pH around young leaves were not markedly different between the presence of little periphyton and periphyton removed.</p
Rapid light curves of <i>Potamogeton malaianus</i> with different biomass densities of periphyton.
<p>Values with bars indicate standard deviations, nâ=â3.</p
The characteristics of periphyton on the leaves and stems of <i>Potamogeton malaianus</i>.
<p>Values represent means of triplicates and standard error, respectively. DW, dry weight;AW, ash weight; FADW, free ash dry weight; Chl a, chlorophyll a; DBL, diffusive boundary layer</p
Supplementary document for Femtosecond laser-induced phase transition in VO2 films - 6171202.pdf
Supplemental Documen
High Performance and Enhanced Durability of Thermochromic Films Using VO<sub>2</sub>@ZnO CoreâShell Nanoparticles
For
VO<sub>2</sub>-based thermochromic smart windows, high luminous transmittance
(<i>T</i><sub>lum</sub>) and solar regulation efficiency
(Î<i>T</i><sub>sol</sub>) are usually pursued as the
most critical issues, which have been discussed in numerous researches.
However, environmental durability, which has rarely been considered,
is also so vital for practical application because it determines lifetime
and cycle times of smart windows. In this paper, we report novel VO<sub>2</sub>@ZnO coreâshell nanoparticles with ultrahigh durability
as well as improved thermochromic performance. The VO<sub>2</sub>@ZnO
nanoparticles-based thermochromic film exhibits a robust durability
that the Î<i>T</i><sub>sol</sub> keeps 77% (from 19.1%
to 14.7%) after 10<sup>3</sup> hours in a hyperthermal and humid environment,
while a relevant property of uncoated VO<sub>2</sub> nanoparticles-based
film badly deteriorates after 30 h. Meanwhile, compared with the uncoated
VO<sub>2</sub>-based film, the VO<sub>2</sub>@ZnO-based film demonstrates
an 11.0% increase (from 17.2% to 19.1%) in Î<i>T</i><sub>sol</sub> and a 31.1% increase (from 38.9% to 51.0%) in <i>T</i><sub>lum</sub>. Such integrated thermochromic performance
expresses good potential for practical application of VO<sub>2</sub>-based smart windows