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280
Infinitesimals and Pavelka logic
"... Rational Pavelka Logic does not admit infinitesimals. We argue that infinitesimals are important in logic and we present an alternative approach which admits them. It is built up in a similar style, but based on the Chang’s perfect MValgebra. We prove a partial result towards the completeness of t ..."
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Rational Pavelka Logic does not admit infinitesimals. We argue that infinitesimals are important in logic and we present an alternative approach which admits them. It is built up in a similar style, but based on the Chang’s perfect MValgebra. We prove a partial result towards the completeness
Infinitesimals: Intuition and Rigor
, 2006
"... The infinitesimal has played an interesting role in the history of analysis. It was initially used to support the work of Newton and Leibniz in the development of the calculus. However, by the end of the 1700s, it became an object of derision and was finally driven away by the development of the con ..."
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his calculus 1) infinitesimals 2) fluxions and 3) the method of prime and ultimate ratios (Cultural). He defined a fluxion as the speed with which a quantity changes over time and denoted the fluxion of a variable x with x . He used o to represent an infinitely small amount of time and specified
Sensitivity to Infinitesimal Delays in Neutral Equations
, 1998
"... In this paper we investigate the sensitivity of the stability of neutral functional differential equations with respect to changes in the delays. This sensitivity is caused by the behaviour of the essential spectrum which, in turn, is determined by the roots of an exponential polynomial. In [1], Ave ..."
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In this paper we investigate the sensitivity of the stability of neutral functional differential equations with respect to changes in the delays. This sensitivity is caused by the behaviour of the essential spectrum which, in turn, is determined by the roots of an exponential polynomial. In [1
Infinitesimally rigid polyhedra. I. Statics of frameworks
 Transactionsofthe American Mathematical Society
, 1984
"... Abstract. From the time of Cauchy, mathematicians have studied the motions of convex polyhedra, with the faces held rigid while changes are allowed in the dihedral angles. In the 1940s Alexandrov proved that, even with additional vertices along the natural edges, and with an arbitrary triangulation ..."
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Cited by 30 (4 self)
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Abstract. From the time of Cauchy, mathematicians have studied the motions of convex polyhedra, with the faces held rigid while changes are allowed in the dihedral angles. In the 1940s Alexandrov proved that, even with additional vertices along the natural edges, and with an arbitrary triangulation
SMOOTH INFINITESIMAL ANALYSIS BASED MODEL OF MULTIDIMENSIONAL GEOMETRY
"... Abstract. In this work a new approach to multidimensional geometry based on smooth infinitesimal analysis (SIA) is proposed. An embedded surface in this multidimensional geometry will look different for the external and internal observers: from the outside it will look like a composition of infinite ..."
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of infinitesimal segments, while from the inside like a set of points equipped by a metric. The geometry is elastic. Embedded surfaces possess dual metric: internal and external. They can change their form in the bulk without changing the internal metric.
Infinitesimal Variation of Harmonic Forms and Lefschetz Decomposition
, 2001
"... Let X be a compact Kähler manifold and let A(X)cl denote the space of all closed forms on X. Each choice of a Kähler form ω on X defines a Hodge decomposition of A(X)cl into the subspace of dexact forms and the subspace of harmonic forms Hω. How does the subspace Hω ⊂ A(X)cl depend on ω? In this pa ..."
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Cited by 1 (0 self)
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? In this paper we study the infinitesimal variation of Hω. The most interesting situation to which the results apply and which was the original motivation for this work is the following: Let X be a CalabiYau manifold and K 0 be the set of all Ricciflat Kähler forms. Due to Calabi and Yau, the natural
Nonstandard Analysis Applied to Special and General Relativity The Theory of Infinitesimal LightClocks
, 2009
"... Any portion of this monograph may be reproduced, without change and giving proper authorship, by any method without seeking permission and without the payment of any fees. ..."
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Cited by 1 (1 self)
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Any portion of this monograph may be reproduced, without change and giving proper authorship, by any method without seeking permission and without the payment of any fees.
Infinitesimal form boundedness and Trudinger’s subordination for the Schrödinger operator
"... Abstract. We give explicit analytic criteria for two problems associated with the Schrödinger operator H = − ∆ + Q on L 2 (R n) where Q ∈ D ′ (R n) is an arbitrary real or complexvalued potential. First, we obtain necessary and sufficient conditions on Q so that the quadratic form 〈Q·, · 〉 has zer ..."
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Cited by 10 (3 self)
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of the major steps here is the reduction to a similar inequality with nonnegative function ∇(1−∆) −1 Q  2 +(1−∆) −1 Q  in place of Q. This provides a complete solution to the infinitesimal form boundedness problem for the Schrödinger operator, and leads to new broad classes of admissible distributional
Multiintersection Traffic Light Control Using Infinitesimal Perturbation Analysis?
"... Abstract: We address the traffic light control problem for multiple intersections in tandem by viewing it as a stochastic hybrid system and developing a Stochastic Flow Model (SFM) for it. Using Infinitesimal Perturbation Analysis (IPA), we derive online gradient estimates of a cost metric with res ..."
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Cited by 3 (1 self)
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Abstract: We address the traffic light control problem for multiple intersections in tandem by viewing it as a stochastic hybrid system and developing a Stochastic Flow Model (SFM) for it. Using Infinitesimal Perturbation Analysis (IPA), we derive online gradient estimates of a cost metric
Structural Stability and Renormalization Group for Propagating Fronts
, 1994
"... A solution to a given equation is structurally stable if it suffers only an infinitesimal change when the equation (not the solution) is perturbed infinitesimally. We have found that structural stability can be used as a velocity selection principle for propagating fronts. We give examples, using nu ..."
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Cited by 12 (0 self)
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A solution to a given equation is structurally stable if it suffers only an infinitesimal change when the equation (not the solution) is perturbed infinitesimally. We have found that structural stability can be used as a velocity selection principle for propagating fronts. We give examples, using
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