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INTERMEDIATE VALUES AND INVERSE FUNCTIONS ON Nonarchimedean Fields
"... Continuity or even differentiability of a function on a closed interval of a nonArchimedean field are not sufficient for the function to assume all the intermediate values, a maximum, a minimum or a unique primitive function on the interval. These problems are due to the total disconnectedness of ..."
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Cited by 8 (8 self)
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Continuity or even differentiability of a function on a closed interval of a nonArchimedean field are not sufficient for the function to assume all the intermediate values, a maximum, a minimum or a unique primitive function on the interval. These problems are due to the total disconnectedness
Constrained second order optimization on nonArchimedean fields
 Department of Physics and Astronomy, University of Manitoba
"... Communicated by Prof. T.A. Springer at the meeting of November 252002 Constrained optimization on nonArchimedean fields is presented. We formalize the notion of a tangent plane to the surface defined by the constraints making use of an implicit function Theorem similar to its real counterpart. Then ..."
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Cited by 6 (6 self)
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Communicated by Prof. T.A. Springer at the meeting of November 252002 Constrained optimization on nonArchimedean fields is presented. We formalize the notion of a tangent plane to the surface defined by the constraints making use of an implicit function Theorem similar to its real counterpart
Iteration Product of Nörlund Methods of Double Sequences in NonArchimedean Fields
"... The aim of the paper is to define the iteration product of Nörlund methods of double sequences in a complete, nontrivially valued, nonarchimedean field and prove a few inclusion theorems on the iteration product of Nörlund methods of double sequences in such fields. ..."
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The aim of the paper is to define the iteration product of Nörlund methods of double sequences in a complete, nontrivially valued, nonarchimedean field and prove a few inclusion theorems on the iteration product of Nörlund methods of double sequences in such fields.
Generalized power series on a nonArchimedean field
, 2006
"... Power series with rational exponents on the real numbers field and the LeviCivita field are studied. We derive a radius of convergence for power series with rational exponents over the field of real numbers that depends on the coefficients and on the density of the exponents in the series. Then we ..."
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Cited by 7 (7 self)
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Power series with rational exponents on the real numbers field and the LeviCivita field are studied. We derive a radius of convergence for power series with rational exponents over the field of real numbers that depends on the coefficients and on the density of the exponents in the series. Then we
Quasiinvariant and pseudodifferentiable measures on a nonArchimedean Banach space. II. Measures with values in nonArchimedean fields
, 2001
"... Quasiinvariant and pseudodifferentiable measures on a Banach space X over a nonArchimedean locally compact infinite field with a nontrivial valuation are defined and constructed. Measures are considered with values in nonArchimedean fields, for example, the field Qp of padic numbers. Theorems ..."
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Cited by 11 (9 self)
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Quasiinvariant and pseudodifferentiable measures on a Banach space X over a nonArchimedean locally compact infinite field with a nontrivial valuation are defined and constructed. Measures are considered with values in nonArchimedean fields, for example, the field Qp of padic numbers. Theorems
OneDimensional Optimization on NonArchimedean Fields. Journal of Nonlinear and Convex Analysis, 2:351–361
, 2001
"... Abstract. One dimensional optimization on nonArchimedean fields is presented. We derive first and second order necessary and sufficient optimality conditions. For first order optimization, these conditions are similar to the corresponding real ones; but this is not the case for higher order optimiz ..."
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Cited by 8 (8 self)
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Abstract. One dimensional optimization on nonArchimedean fields is presented. We derive first and second order necessary and sufficient optimality conditions. For first order optimization, these conditions are similar to the corresponding real ones; but this is not the case for higher order
Analysis on nonArchimedean Field Extensions of the Real Numbers and Applications
"... In this talk, we will give an overview of our work on nonArchimedean ordered field extensions of the real numbers that are real closed and complete in the order topology. The smallest such field, the LeviCivita field R [1], is small enough to allow for the calculus on the field to be implemented o ..."
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In this talk, we will give an overview of our work on nonArchimedean ordered field extensions of the real numbers that are real closed and complete in the order topology. The smallest such field, the LeviCivita field R [1], is small enough to allow for the calculus on the field to be implemented
Stochastic processes and their spectral representations over nonarchimedean fields
, 801
"... The article is devoted to stochastic processes with values in finiteand infinitedimensional vector spaces over infinite fields K of zero characteristics with nontrivial nonarchimedean norms. For different types of stochastic processes controlled by measures with values in K and in complete topolo ..."
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The article is devoted to stochastic processes with values in finiteand infinitedimensional vector spaces over infinite fields K of zero characteristics with nontrivial nonarchimedean norms. For different types of stochastic processes controlled by measures with values in K and in complete
Results 1  10
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8,604