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Solutio Singularis Casus Circa Tautochronismum, Leonhard Euler

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No abstract provided.

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Problematis Isoperimetrici In Latissimo Sensu Accepti Solutio Generalis, Leonhard Euler

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No abstract provided.

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De Solutione Problematum Diophanteorum Per Numeros Integros, Leonhard Euler

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Euler searches for integer solutions to axx+bx+c=yy and considers some applications to figurate numbers.

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De Summatione Innumerabilium Progressionum, Leonhard Euler

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This paper concerns the sum of reciprocal squares, which equals π²/6. Euler does not yet have the tools to find this value directly, but instead approximates it as 1.644934. He says this follows from E25 and E19, and also refers us forward to E736. Then Euler brings in the harmonic series: letting f(x) denote the xth partial sum of the harmonic series, he approximates it as an integral and defines his constant γ as the limit of f(x) – log(x).

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Constructio Aequationis Differentialis AxN Dx = Dy + Y2 Dx, Leonhard Euler

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De Progressionibus Transcendentibus Seu Quarum Termini Generales Algebraice Dari Nequeunt, Leonhard Euler

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No abstract provided.

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Quomodo Data Quacunque Curva Inveniri Oporteat Aliam Quae Cum Data Quodammodo Iuncta Ad Tautochronismum Producendum Sit Idonea, Leonhard Euler

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No abstract provided.

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De Formis Radicum Aequationum Cuiusque Ordinis Coniectatio, Leonhard Euler

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For an equation of degree n, Euler wants to define a "resolvent equation" of degree n-1 whose roots are related to the roots of the original equation. Thus, by solving the resolvent one can solve the original equation. In sections 2 to 7 he works this out for quadratic, cubic, and biquadratic equations. In section 8 Euler says that he wants to try the same approach for solving the quintic equation and general nth degree equations. In the rest of the paper he tries to figure out in what cases resolvents will work.

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Von Der Gestalt Der Erden, Leonhard Euler

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No abstract provided.

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Methodus Generalis Summandi Progressiones, Leonhard Euler

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This paper leads to Bernoulli numbers from an integral of an infinite series and is called a beautiful triumph by Euler.

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Observationes De Theoremate Quodam Fermatiano Aliisque Ad Numeros Primos Spectantibus, Leonhard Euler

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Euler shows that the fifth Fermat number, 2^2⁵ +1 = 4,294,967,297, is not prime because it is divisible by 641, though he does not give any clues about how he discovered this fact. He also tacks on a few "theorems" but says that he does not yet know how to prove them.

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Specimen De Constructione Aequationum Differentialium Sine Indeterminatarum Separatione, Leonhard Euler

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In this paper, Euler investigates a differential equation that he encountered in finding the arc length of an ellipse. This differential equation cannot be solved by separation of variables, as is indicated in the title of the article. Euler first develops a formula for the arc length of an ellipse by cleverly manipulating a binomial series, then shows that this formula satisfies the desired differential equation. Integrating factors make a brief appearance.

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Curva Tautochrona In Fluido Resistentiam Faciente Secundum Quadrata Celeritatum, Leonhard Euler

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No abstract provided.

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De Innumerabilibus Curvis Tautochronis In Vacuo, Leonhard Euler

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No abstract provided.

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Solutio Problematis Astronomici Ex Datis Tribus Stellae Fixae Altitudinibus Et Temporum Differentiis Invenire Elevationem Poli Et Declinationem Stellae. Auct. L. Eulero, Leonhard Euler

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No abstract provided.

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Constructio Aequationum Quarundam Differentialium, Quae Indeterminatarum Separationem Non Admittunt, Leonhard Euler

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Solutio Problematis De Invenienda Curva, Quam Format Lamina Utcunque Elastica In Singulis Punctis A Potentiis Quibuscunque Sollicitata, Leonhard Euler

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No abstract provided.

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Nova Methodus Innumerabiles Aequationes Differentiales Secundi Gradus Reducendi Ad Aequationes Differentiales Primi Gradus, Leonhard Euler

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No abstract provided.

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De Linea Brevissima In Superficie Quacunque Duo Quaelibet Puncta Iungente, Leonhard Euler

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This article arose out of a homework assignment that Euler did for Johann Bernoulli. Bernoulli asked Euler to find the shortest line between two points on a surface. This work provided some of the first analytical foundations for the calculus of variations.

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Problematis Traiectoriarum Reciprocarum Solutio, Leonhard Euler

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This article contains Euler's first published use of complex numbers and a many-axis geometric construction. Euler also defines even functions f(x) as those for which f(x) = f(-x), perhaps the first use of this term.

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Dissertatio De Novo Quodam Curvarum Tautochronarum Genere, Leonhard Euler

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According to Eneström: "Intrigued by a clock invented by D. Sully, Euler busied himself with the construction of curves which cause a pendulum to swing isochronally."

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Tentamen Explicationis Phaenomenorum Aeris, Leonhard Euler

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No abstract provided.

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Methodus Inveniendi Traiectorias Reciprocas Algebraicas, Leonhard Euler

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No abstract provided.

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Constructio Linearum Isochronarum In Medio Quocunque Resistente, Leonhard Euler

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Human Complement Protein C8: The “Hole” Story, James M. Sodetz

Journal of the South Carolina Academy of Science

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Irrigated Agriculture Significantly Modifies Seasonal Boundary Layer Atmosphere And Lower Tropospheric Convective Environment, E. Lachenmeier, R. Mahmood, C. Phillips, U. Nair, E. Rappin, R. Pielke Sr., W. Brown, S. Oncley, J. Wurman, K. Kosiba, A. Kaulfus, J. Santanello Jr., E. Kim, P. Lawston-Parker, Michael Hayes, T. Franz

School of Natural Resources: Faculty Publications

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Wearable Electrochemical Sensors For Monitoring Performance Athletes, Kevin J. Fraser, Vincenzo F. Curtin, Shirley Coyle, Benjamin Schazmann, Robert Byrne, Fernando Benito-Lopez, Roisin M. Owens, George C. Malliaras, Dermot Diamond

Conference Papers

Nowadays, wearable sensors such as heart rate monitors and pedometers are in common use. The use of wearable systems such as these for personalized exercise regimes for health and rehabilitation is particularly interesting. In particular, the true potential of wearable chemical sensors, which for the real-time ambulatory monitoring of bodily fluids such as tears, sweat, urine and blood has not been realized. Here we present a brief introduction into the fields of ionogels and organic electrochemical transistors, and in particular, the concept of an OECT transistor incorporated into a sticking-plaster, along with a printable “ionogel” to provide a wearable biosensor …

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Full-Text Articles in Entire DC Network

Solutio Singularis Casus Circa Tautochronismum, Leonhard Euler

All Works by Eneström Number

Problematis Isoperimetrici In Latissimo Sensu Accepti Solutio Generalis, Leonhard Euler

All Works by Eneström Number

De Solutione Problematum Diophanteorum Per Numeros Integros, Leonhard Euler

All Works by Eneström Number

De Summatione Innumerabilium Progressionum, Leonhard Euler

All Works by Eneström Number

Constructio Aequationis Differentialis AxN Dx = Dy + Y2 Dx, Leonhard Euler

All Works by Eneström Number

De Progressionibus Transcendentibus Seu Quarum Termini Generales Algebraice Dari Nequeunt, Leonhard Euler

All Works by Eneström Number

Quomodo Data Quacunque Curva Inveniri Oporteat Aliam Quae Cum Data Quodammodo Iuncta Ad Tautochronismum Producendum Sit Idonea, Leonhard Euler

All Works by Eneström Number

De Formis Radicum Aequationum Cuiusque Ordinis Coniectatio, Leonhard Euler

All Works by Eneström Number

Von Der Gestalt Der Erden, Leonhard Euler

All Works by Eneström Number

Methodus Generalis Summandi Progressiones, Leonhard Euler

All Works by Eneström Number

Observationes De Theoremate Quodam Fermatiano Aliisque Ad Numeros Primos Spectantibus, Leonhard Euler

All Works by Eneström Number

Specimen De Constructione Aequationum Differentialium Sine Indeterminatarum Separatione, Leonhard Euler

All Works by Eneström Number

Curva Tautochrona In Fluido Resistentiam Faciente Secundum Quadrata Celeritatum, Leonhard Euler

All Works by Eneström Number

De Innumerabilibus Curvis Tautochronis In Vacuo, Leonhard Euler

All Works by Eneström Number

Solutio Problematis Astronomici Ex Datis Tribus Stellae Fixae Altitudinibus Et Temporum Differentiis Invenire Elevationem Poli Et Declinationem Stellae. Auct. L. Eulero, Leonhard Euler

All Works by Eneström Number

Constructio Aequationum Quarundam Differentialium, Quae Indeterminatarum Separationem Non Admittunt, Leonhard Euler

All Works by Eneström Number

Solutio Problematis De Invenienda Curva, Quam Format Lamina Utcunque Elastica In Singulis Punctis A Potentiis Quibuscunque Sollicitata, Leonhard Euler

All Works by Eneström Number

Nova Methodus Innumerabiles Aequationes Differentiales Secundi Gradus Reducendi Ad Aequationes Differentiales Primi Gradus, Leonhard Euler

All Works by Eneström Number

De Linea Brevissima In Superficie Quacunque Duo Quaelibet Puncta Iungente, Leonhard Euler

All Works by Eneström Number

Problematis Traiectoriarum Reciprocarum Solutio, Leonhard Euler

All Works by Eneström Number

Dissertatio De Novo Quodam Curvarum Tautochronarum Genere, Leonhard Euler

All Works by Eneström Number

Tentamen Explicationis Phaenomenorum Aeris, Leonhard Euler

All Works by Eneström Number

Methodus Inveniendi Traiectorias Reciprocas Algebraicas, Leonhard Euler

All Works by Eneström Number

Constructio Linearum Isochronarum In Medio Quocunque Resistente, Leonhard Euler

All Works by Eneström Number

Human Complement Protein C8: The “Hole” Story, James M. Sodetz

Journal of the South Carolina Academy of Science

School of Natural Resources: Faculty Publications

Wearable Electrochemical Sensors For Monitoring Performance Athletes, Kevin J. Fraser, Vincenzo F. Curtin, Shirley Coyle, Benjamin Schazmann, Robert Byrne, Fernando Benito-Lopez, Roisin M. Owens, George C. Malliaras, Dermot Diamond

Conference Papers