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Joseph Rabinoff - One of the best experts on this subject based on the ideXlab platform.
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tropical Analytic Geometry newton polygons and tropical intersections
Advances in Mathematics, 2012Co-Authors: Joseph RabinoffAbstract:Abstract In this paper we use the connections between tropical algebraic Geometry and rigid-Analytic Geometry in order to prove two main results. We use tropical methods to prove a theorem about the Newton polygon for convergent power series in several variables: if f 1 , … , f n are n convergent power series in n variables with coefficients in a non-Archimedean field K, we give a formula for the valuations and multiplicities of the common zeros of f 1 , … , f n . We use rigid-Analytic methods to show that stable complete intersections of tropical hypersurfaces compute algebraic multiplicities even when the intersection is not tropically proper. These results are naturally formulated and proved using the theory of tropicalizations of rigid-Analytic spaces, as introduced by Einsiedler, Kapranov, and Lind (2006) [14] and Gubler (2007) [20] . We have written this paper to be as readable as possible both to tropical and arithmetic geometers.
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tropical Analytic Geometry newton polygons and tropical intersections
Advances in Mathematics, 2012Co-Authors: Joseph RabinoffAbstract:Abstract In this paper we use the connections between tropical algebraic Geometry and rigid-Analytic Geometry in order to prove two main results. We use tropical methods to prove a theorem about the Newton polygon for convergent power series in several variables: if f 1 , … , f n are n convergent power series in n variables with coefficients in a non-Archimedean field K, we give a formula for the valuations and multiplicities of the common zeros of f 1 , … , f n . We use rigid-Analytic methods to show that stable complete intersections of tropical hypersurfaces compute algebraic multiplicities even when the intersection is not tropically proper. These results are naturally formulated and proved using the theory of tropicalizations of rigid-Analytic spaces, as introduced by Einsiedler, Kapranov, and Lind (2006) [14] and Gubler (2007) [20] . We have written this paper to be as readable as possible both to tropical and arithmetic geometers.
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tropical Analytic Geometry newton polygons and tropical intersections
arXiv: Algebraic Geometry, 2010Co-Authors: Joseph RabinoffAbstract:In this paper we use the connections between tropical algebraic Geometry and rigid Analytic Geometry in order to prove two main results. We use tropical methods to prove a theorem about the Newton polygon for convergent power series in several variables: if f_1,...,f_n are n convergent power series in n variables with coefficients in a non-Archimedean field K, we give a formula for the valuations and multiplicities of the common zeros of f_1,...,f_n. We use rigid-Analytic methods to show that stable complete intersections of tropical hypersurfaces compute algebraic multiplicities even when the intersection is not tropically proper. These results are naturally formulated and proved using the theory of tropicalizations of rigid-Analytic spaces, as introduced by Einsiedler-Kapranov-Lind [EKL06] and Gubler [Gub07b]. We have written this paper to be as readable as possible both to tropical and arithmetic geometers.
Scott Shucheng Lin - One of the best experts on this subject based on the ideXlab platform.
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note on the derivation of eoq epq inventory models with two backorders costs using Analytic Geometry and algebra
Applied Mathematical Modelling, 2019Co-Authors: Scott Shucheng LinAbstract:Abstract This study examines the paper of Cardenas-Barron, entitled “The derivation of EOQ/EPQ inventory models with two backorders costs using Analytic Geometry and algebra.” that was published in Applied Mathematical Modelling at 2011 to point out it contains questionable results. The algebraic Geometry and algebra applied by Cardenas-Barron [2] violated the rule of the arithmetic-geometric mean (AGM) mentioned by Cardenas-Barron [74] . Moreover, we point out Sphicas [1] had already solved this kind of EOQ and EPQ models using algebraic methods.
Leopoldo Eduardo Cardenasbarron - One of the best experts on this subject based on the ideXlab platform.
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the derivation of eoq epq inventory models with two backorders costs using Analytic Geometry and algebra
Applied Mathematical Modelling, 2011Co-Authors: Leopoldo Eduardo CardenasbarronAbstract:The EOQ model will have a century of its discovery in two years, and recently still, many researchers have been using alternative approaches to model and solve inventory systems. The EOQ/EPQ models have been developed using different optimization methods. However, in many of the works that deal with the EOQ/EPQ with backorders only linear backorders cost is considered. This paper proposes another easy method which uses basic concepts of Analytic geometric and algebra. The proposed method finds the optimal lot size and backorders level considering both linear and fixed backorders costs. Additionally, this paper presents a review of the different optimization methods utilized in inventory theory.
Federico Bambozzi - One of the best experts on this subject based on the ideXlab platform.
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Analytic Geometry over f1 and the fargues fontaine curve
Advances in Mathematics, 2019Co-Authors: Federico Bambozzi, Oren Benbassat, Kobi KremnizerAbstract:Abstract This paper develops a theory of Analytic Geometry over the field with one element. The approach used is the Analytic counter-part of the Toen-Vaquie theory of schemes over F 1 , i.e. the base category relative to which we work out our theory is the category of sets endowed with norms (or families of norms). Base change functors to Analytic spaces over Banach rings are studied and the basic spaces of Analytic Geometry (e.g. polydisks) are recovered as a base change of Analytic spaces over F 1 . We conclude by discussing some applications of our theory to the theory of the Fargues-Fontaine curve and to the ring of Witt vectors.
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closed graph theorems for bornological spaces
Khayyam Journal of Mathematics, 2016Co-Authors: Federico BambozziAbstract:The aim of this paper is that of discussing closed graph theorems for bornological vector spaces in a self-contained way, hoping to make the subject more accessible to non-experts. We will see how to easily adapt classical arguments of functional analysis over $mathbb R$ and $mathbb C$ to deduce closed graph theorems for bornological vector spaces over any complete, non-trivially valued field, hence encompassing the non-Archimedean case too. We will end this survey by discussing some applications. In particular, we will prove De Wilde's Theorem for non-Archimedean locally convex spaces and then deduce some results about the automatic boundedness of algebra morphisms for a class of bornological algebras of interest in Analytic Geometry, both Archimedean (complex Analytic Geometry) and non-Archimedean.
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closed graph theorems for bornological spaces
arXiv: Functional Analysis, 2015Co-Authors: Federico BambozziAbstract:The aim of this paper is that of discussing Closed Graph Theorems for bornological vector spaces in a way which is accessible to non-experts. We will see how to easily adapt classical arguments of functional analysis over $\mathbb{R}$ and $\mathbb{C}$ to deduce Closed Graph Theorems for bornological vector spaces over any complete, non-trivially valued field, hence encompassing the non-Archimedean case too. We will end this survey by discussing some applications. In particular, we will prove de Wilde's Theorem for non-Archimedean locally convex spaces and then deduce some results about the automatic boundedness of algebra morphisms for a class of bornological algebras of interest in Analytic Geometry, both Archimedean (complex Analytic Geometry) and non-Archimedean.
As Kaddour - One of the best experts on this subject based on the ideXlab platform.
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The Tsai-Wu failure criterion rationalised in the context of UD composites
Composites Part A-applied Science and Manufacturing, 2017Co-Authors: Shuguang Li, Yuning Liang, Elena Sitnikova, As KaddourAbstract:This paper is to rationalise the empirical aspect of the Tsai-Wu failure criterion in the context of UD composites associated with the determination of the interactive strength property F12 based on the Analytic Geometry. It reveals that the condition of closed failure envelope cannot be satisfied by all UD composites and hence the restriction should be abandoned. Depending on the way the failure envelope opens, UD composites can be classified into two categories. (a) F12 can be determined uniquely using the conventional strength properties with an additional assumption that the material exhibits very high or infinite strength under triaxial compression at a specific stress ratio; or (b) The Tsai-Wu criterion leads to one of the two scenarios: either allowing infinite strength for an in-plane stress state or allowing infinite strength under triaxial stresses involving tension along fibres.