Search results for "Mathematica"
showing 10 items of 7971 documents
Water distribution network robust design based on energy surplus index maximization
2015
The aim of this paper is to show that energy surplus indices, such as resilience index, besides providing a very good indirect measure of water distribution network reliability to be adopted during the design phase, represent also a valuable and effective indicator of the robustness of the network in alternative network scenarios, and can thus be profitably used in condition of future demands uncertainty. The methodology adopted consisted of (I) multi-objective design optimization performed in order to minimize construction costs while maximizing the resilience index; (II) retrospective performance assessment of the alternative solutions of the Pareto front obtained, under demand conditions…
Surrogate-assisted multicriteria optimization: Complexities, prospective solutions, and business case
2017
Complexity in solving real-world multicriteria optimization problems often stems from the fact that complex, expensive, and/or time-consuming simulation tools or physical experiments are used to evaluate solutions to a problem. In such settings, it is common to use efficient computational models, often known as surrogates or metamodels, to approximate the outcome (objective or constraint function value) of a simulation or physical experiment. The presence of multiple objective functions poses an additional layer of complexity for surrogate-assisted optimization. For example, complexities may relate to the appropriate selection of metamodels for the individual objective functions, extensive …
Modeling of the sustainable development of multifunctional farms in Ukraine
2017
Dynamiczne optymalne planowanie i prognozowanie racjonalnego połączenia sektorów rolniczych pozwala przy najniższych kosztach i ryzyku dokonać przejścia od tradycyjnych form działalności do rolnictwa ekologicznego lub organicznego. Artykuł naświetla kwestię gradacji ekologiczności gospodarstwa rolnego, która obejmuje podstawowe kryteria zrównoważonych modeli rozwoju rolnictwa. Za pomocą programowania matematycznego udowodniono skuteczność zwiększenia poziomu ekologizacji. Przedstawiono zautomatyzowany model rozwoju gospodarstwa rolnego oraz sposoby zwiększenia bezpieczeństwa produkcji. Model jest uniwersalny i może być stosowany w przedsię-biorstwach lasostepu Ukrainy Lewobrzeżnej.
Organizational Wellness Modeling
2009
The aim of the present paper is to establish certain mathematical models for organizational wellness as well as to create some wellness optimization problems applicable to any type of organization (including universities) that might be mathematically solved resorting to aspects of operational research of mathematical analysis. The results obtained associated with a mathematical apparatus enable one to perform analyses, comparisons, interpretations, predictions. All of us have, consciously or not, a genuine curiosity in creating and shaping organizational wellness. This concept represents a highly topical issue since professional activity, irrespective of its field, holds a very significant …
Developing Primary School Students’ Formal Geometric Definitions Knowledge by Connecting Origami and Technology
2019
In this paper, we present opportunities with the uses of origami and technology, in our case GeoGebra, in teaching formal geometric definitions for fifth-grade primary school students (11-12yrs). Applying origami in mathematical lessons is becoming to be recognized as a valuable tool for improving students’ mathematical knowledge. In previous studies, we developed origami and technology activities for high-school mathematics, but we wanted to explore if such approach would work in primary school as well. For this reason, we chose a flat origami model оf the crane and we used this model to introduce students to basic geometrical notions and definitions, such as points, lines, intersections o…
Intrinsic Lipschitz Graphs and Vertical β-Numbers in the Heisenberg Group
2016
The purpose of this paper is to introduce and study some basic concepts of quantitative rectifiability in the first Heisenberg group $\mathbb{H}$. In particular, we aim to demonstrate that new phenomena arise compared to the Euclidean theory, founded by G. David and S. Semmes in the 90's. The theory in $\mathbb{H}$ has an apparent connection to certain nonlinear PDEs, which do not play a role with similar questions in $\mathbb{R}^{3}$. Our main object of study are the intrinsic Lipschitz graphs in $\mathbb{H}$, introduced by B. Franchi, R. Serapioni and F. Serra Cassano in 2006. We claim that these $3$-dimensional sets in $\mathbb{H}$, if any, deserve to be called quantitatively $3$-rectifi…
Gradient and Lipschitz Estimates for Tug-of-War Type Games
2021
We define a random step size tug-of-war game and show that the gradient of a value function exists almost everywhere. We also prove that the gradients of value functions are uniformly bounded and converge weakly to the gradient of the corresponding $p$-harmonic function. Moreover, we establish an improved Lipschitz estimate when boundary values are close to a plane. Such estimates are known to play a key role in the higher regularity theory of partial differential equations. The proofs are based on cancellation and coupling methods as well as an improved version of the cylinder walk argument. peerReviewed
Fixed Angle Inverse Scattering for Almost Symmetric or Controlled Perturbations
2020
We consider the fixed angle inverse scattering problem and show that a compactly supported potential is uniquely determined by its scattering amplitude for two opposite fixed angles. We also show that almost symmetric or horizontally controlled potentials are uniquely determined by their fixed angle scattering data. This is done by establishing an equivalence between the frequency domain and the time domain formulations of the problem, and by solving the time domain problem by extending the methods of [RS19] which adapts the ideas introduced in [BK81] and [IY01] on the use of Carleman estimates for inverse problems.
Limiting Carleman weights and conformally transversally anisotropic manifolds
2020
We analyze the structure of the set of limiting Carleman weights in all conformally flat manifolds, 3 3 -manifolds, and 4 4 -manifolds. In particular we give a new proof of the classification of Euclidean limiting Carleman weights, and show that there are only three basic such weights up to the action of the conformal group. In dimension three we show that if the manifold is not conformally flat, there could be one or two limiting Carleman weights. We also characterize the metrics that have more than one limiting Carleman weight. In dimension four we obtain a complete spectrum of examples according to the structure of the Weyl tensor. In particular, we construct unimodular Lie groups whose …
The Calderón problem for the fractional Schrödinger equation with drift
2020
We investigate the Calder\'on problem for the fractional Schr\"odinger equation with drift, proving that the unknown drift and potential in a bounded domain can be determined simultaneously and uniquely by an infinite number of exterior measurements. In particular, in contrast to its local analogue, this nonlocal problem does \emph{not} enjoy a gauge invariance. The uniqueness result is complemented by an associated logarithmic stability estimate under suitable apriori assumptions. Also uniqueness under finitely many \emph{generic} measurements is discussed. Here the genericity is obtained through \emph{singularity theory} which might also be interesting in the context of hybrid inverse pro…