# Non-nonstandard analysis: Real infinitesimals

## Related Articles

- infinitesimal. // Hutchinson Dictionary of Scientific Biography;2005, p1
Number that is not zero but is less than any finite number. Infinitesimal numbers clearly do not exist in the conventional system of real numbers, but modern developments in logic allow the use of an extended system of numbers that includes infinitesimal numbers. Calculations with these adhere...

- Case 4. // Journal of Endourology;Sep2008, Vol. 22 Issue 9, p1873
A 55-Year-Old Male Is to Undergo a Percutaneous Nephrolithotomy for a Complete Staghorn Calculus Involving All Calices. At the Onset of the Procedure How Should the Nephostomy Tract(s) Be Established

- barycentric calculus. // Hutchinson Dictionary of Scientific Biography;2005, p1
Coordinate geometry calculations using a coordinate system devised by August MÃ¶bius in which numerical coefficients are assigned to points on a plane, giving the position of a general point by reference to four or more noncoplanar points. Described in this way, the general point thus...

- Description and exact maximum and minimum values of the remainder in the problem of the distribution of fractional parts. Krasil'shchikov, V. V.; Shutov, A. V. // Mathematical Notes;Feb2011, Vol. 89 Issue 1/2, p59
We obtain a description of the maximum and minimum values of the remainder in the problem of the distribution of fractional parts. The exact maximum and minimum values of the remainder are calculated; they are independent of the length of the bounded remainder interval. It is shown that these...

- Multiplicity of Solutions for a Nonlinear Degenerate Problem in Anisotropic Variable Exponent Spaces. STANCU-DUMITRU, DENISA // Bulletin of the Malaysian Mathematical Sciences Society;2013, Vol. 36 Issue 1, p117
We study a nonlinear elliptic problem with Dirichlet boundary condition involving an anisotropic operator with variable exponents on a smooth bounded domain Î© âŠ‚ RN. For that equation we prove the existence of at least two nonnegative and nontrivial weak solutions. Our main result is...

- A cut-free sequent calculus for relevant logic RW*. Ilić, Mirjana; Boričić, Branislav // Logic Journal of the IGPL;Aug2014, Vol. 22 Issue 4, p673
A right-handed cut-free sequent calculus GRW for the contraction-less relevant logic RW is presented. Based on GRW, the disjunction property and the decidability, the properties which both had been proved for RW earlier, are obtained by a pure proofâ€“theoretical method.

- A NATURAL GEOMETRIC FRAMEWORK FOR THE SPACE OF INITIAL DATA OF NONLINEAR PDES. MORENO, GIOVANNI // Proceedings of the Annual International Conferences on Geometry,;2012, Vol. 13, p245
The modern geometrical approach to nonlinear PDEs is the out-come of a nontrivial synthesis of differential calculus over commutative al-gebras and cohomological algebra in the context of infinite jet spaces. In this paper we propose a very natural generalization of the notion of a jet space,...

- infinitesimal calculus. // Hutchinson Dictionary of Scientific Biography;2005, p1
Original name for "calculus," that is, differential and integral calculus, and so called because it was thought to rely on "infinitely small" quantities. (It is now seen to be based upon a precise theory of limits.)

- Calculus Method for Optimizing the Balance in Rod Pumping Units. Rusu, Liliana; Eparu, Ion // Petroleum - Gas University of Ploiesti Bulletin, Technical Serie;2012, Vol. 64 Issue 3, p29
It is presented a calculus method for balancing optimization of rod pumping units. The computer program having this mathematic model as base, it is flexible and allows any input parameter and provides the exact weight values of counterbalance for pumping units with direct schema.