Mathematics

4679 KiB

Open AccessArticle

The Catastrophe of Electric Vehicle Sales

by Timothy Sands

Mathematics 2017, 5(3), 46; https://doi.org/10.3390/math5030046 - 17 Sep 2017

Viewed by 4484

Electric vehicles have undergone a recent faddy trend in the United States and Europe, and several recent publications trumpet the continued rise of electric vehicles citing steadily-climbing monthly vehicle sales. The broad purpose of this study is to examine this optimism with some [...] Read more.

Electric vehicles have undergone a recent faddy trend in the United States and Europe, and several recent publications trumpet the continued rise of electric vehicles citing steadily-climbing monthly vehicle sales. The broad purpose of this study is to examine this optimism with some degree of mathematical rigor. Specifically, the methodology will use catastrophe theory to explore the possibility of a sudden, seemingly-unexplainable crash in vehicle sales. The study begins by defining optimal system equations that well-model the available sales data. Next, these optimal models are used to investigate the potential response to a slow dynamic acting on the relatively faster dynamic of the optimal system equations. Catastrophe theory indicates a potential sudden crash in sales when a slow dynamic is at-work. It is noteworthy that the prediction can be made even while sales are increasing. Full article

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361 KiB

Open AccessArticle

Fusion Estimation from Multisensor Observations with Multiplicative Noises and Correlated Random Delays in Transmission

by Raquel Caballero-Águila, Aurora Hermoso-Carazo and Josefa Linares-Pérez

Mathematics 2017, 5(3), 45; https://doi.org/10.3390/math5030045 - 4 Sep 2017

Cited by 13 | Viewed by 3544

Abstract

In this paper, the information fusion estimation problem is investigated for a class of multisensor linear systems affected by different kinds of stochastic uncertainties, using both the distributed and the centralized fusion methodologies. It is assumed that the measured outputs are perturbed by [...] Read more.

In this paper, the information fusion estimation problem is investigated for a class of multisensor linear systems affected by different kinds of stochastic uncertainties, using both the distributed and the centralized fusion methodologies. It is assumed that the measured outputs are perturbed by one-step autocorrelated and cross-correlated additive noises, and also stochastic uncertainties caused by multiplicative noises and randomly missing measurements in the sensor outputs are considered. At each sampling time, every sensor output is sent to a local processor and, due to some kind of transmission failures, one-step correlated random delays may occur. Using only covariance information, without requiring the evolution model of the signal process, a local least-squares (LS) filter based on the measurements received from each sensor is designed by an innovation approach. All these local filters are then fused to generate an optimal distributed fusion filter by a matrix-weighted linear combination, using the LS optimality criterion. Moreover, a recursive algorithm for the centralized fusion filter is also proposed and the accuracy of the proposed estimators, which is measured by the estimation error covariances, is analyzed by a simulation example. Full article

(This article belongs to the Special Issue Stochastic Processes with Applications)

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479 KiB

Open AccessArticle

Topics of Measure Theory on Infinite Dimensional Spaces

by José Velhinho

Mathematics 2017, 5(3), 44; https://doi.org/10.3390/math5030044 - 29 Aug 2017

Cited by 3 | Viewed by 5330

Abstract

This short review is devoted to measures on infinite dimensional spaces. We start by discussing product measures and projective techniques. Special attention is paid to measures on linear spaces, and in particular to Gaussian measures. Transformation properties of measures are considered, as well [...] Read more.

This short review is devoted to measures on infinite dimensional spaces. We start by discussing product measures and projective techniques. Special attention is paid to measures on linear spaces, and in particular to Gaussian measures. Transformation properties of measures are considered, as well as fundamental results concerning the support of the measure. Full article

457 KiB

Open AccessArticle

On Minimal Covolume Hyperbolic Lattices

by Ruth Kellerhals

Mathematics 2017, 5(3), 43; https://doi.org/10.3390/math5030043 - 22 Aug 2017

Cited by 2 | Viewed by 4264

Abstract

We study lattices with a non-compact fundamental domain of small volume in hyperbolic space

H^{n}

. First, we identify the arithmetic lattices in

{Isom}^{+} H^{n}

of minimal covolume for even n up to 18. Then, we discuss the related problem [...] Read more.

We study lattices with a non-compact fundamental domain of small volume in hyperbolic space

H^{n}

. First, we identify the arithmetic lattices in

{Isom}^{+} H^{n}

of minimal covolume for even n up to 18. Then, we discuss the related problem in higher odd dimensions and provide solutions for

n = 11

and

n = 13

in terms of the rotation subgroup of certain Coxeter pyramid groups found by Tumarkin. The results depend on the work of Belolipetsky and Emery, as well as on the Euler characteristic computation for hyperbolic Coxeter polyhedra with few facets by means of the program CoxIter developed by Guglielmetti. This work complements the survey about hyperbolic orbifolds of minimal volume. Full article

(This article belongs to the Special Issue Geometry of Numbers)

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768 KiB

Open AccessArticle

On the Uniqueness Results and Value Distribution of Meromorphic Mappings

by Rahman Ullah, Xiao-Min Li, Faiz Faizullah, Hong-Xun Yi and Riaz Ahmad Khan

Mathematics 2017, 5(3), 42; https://doi.org/10.3390/math5030042 - 17 Aug 2017

Cited by 1 | Viewed by 2928

Abstract

This research concentrates on the analysis of meromorphic mappings. We derived several important results for value distribution of specific difference polynomials of meromorphic mappings, which generalize the work of Laine and Yang. In addition, we proved uniqueness theorems of meromorphic mappings. The difference [...] Read more.

This research concentrates on the analysis of meromorphic mappings. We derived several important results for value distribution of specific difference polynomials of meromorphic mappings, which generalize the work of Laine and Yang. In addition, we proved uniqueness theorems of meromorphic mappings. The difference polynomials of these functions have the same fixed points or share a nonzero value. This extends the research work of Qi, Yang and Liu, where they used the finite ordered meromorphic mappings. Full article

932 KiB

Open AccessArticle

On the Duality of Regular and Local Functions

by Jens V. Fischer

Mathematics 2017, 5(3), 41; https://doi.org/10.3390/math5030041 - 9 Aug 2017

Cited by 5 | Viewed by 4174

Abstract

In this paper, we relate Poisson’s summation formula to Heisenberg’s uncertainty principle. They both express Fourier dualities within the space of tempered distributions and these dualities are also inverse of each other. While Poisson’s summation formula expresses a duality between discretization and periodization, [...] Read more.

In this paper, we relate Poisson’s summation formula to Heisenberg’s uncertainty principle. They both express Fourier dualities within the space of tempered distributions and these dualities are also inverse of each other. While Poisson’s summation formula expresses a duality between discretization and periodization, Heisenberg’s uncertainty principle expresses a duality between regularization and localization. We define regularization and localization on generalized functions and show that the Fourier transform of regular functions are local functions and, vice versa, the Fourier transform of local functions are regular functions. Full article

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347 KiB

Open AccessFeature PaperReview

Integral Representations of the Catalan Numbers and Their Applications

by Feng Qi and Bai-Ni Guo

Mathematics 2017, 5(3), 40; https://doi.org/10.3390/math5030040 - 3 Aug 2017

Cited by 42 | Viewed by 8741

Abstract

In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi function, discuss equivalent relations between these integral representations, supply alternative and new proofs of several integral representations, collect applications of some integral representations, and present sums of several [...] Read more.

In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi function, discuss equivalent relations between these integral representations, supply alternative and new proofs of several integral representations, collect applications of some integral representations, and present sums of several power series whose coefficients involve the Catalan numbers. Full article

793 KiB

Open AccessArticle

Confidence Intervals for Mean and Difference between Means of Normal Distributions with Unknown Coefficients of Variation

by Warisa Thangjai, Suparat Niwitpong and Sa-Aat Niwitpong

Mathematics 2017, 5(3), 39; https://doi.org/10.3390/math5030039 - 28 Jul 2017

Cited by 17 | Viewed by 3974

Abstract

This paper proposes confidence intervals for a single mean and difference of two means of normal distributions with unknown coefficients of variation (CVs). The generalized confidence interval (GCI) approach and large sample (LS) approach were proposed to construct confidence intervals for the single [...] Read more.

This paper proposes confidence intervals for a single mean and difference of two means of normal distributions with unknown coefficients of variation (CVs). The generalized confidence interval (GCI) approach and large sample (LS) approach were proposed to construct confidence intervals for the single normal mean with unknown CV. These confidence intervals were compared with existing confidence interval for the single normal mean based on the Student’s t-distribution (small sample size case) and the z-distribution (large sample size case). Furthermore, the confidence intervals for the difference between two normal means with unknown CVs were constructed based on the GCI approach, the method of variance estimates recovery (MOVER) approach and the LS approach and then compared with the Welch–Satterthwaite (WS) approach. The coverage probability and average length of the proposed confidence intervals were evaluated via Monte Carlo simulation. The results indicated that the GCIs for the single normal mean and the difference of two normal means with unknown CVs are better than the other confidence intervals. Finally, three datasets are given to illustrate the proposed confidence intervals. Full article

2118 KiB

Open AccessArticle

Variable Shape Parameter Strategy in Local Radial Basis Functions Collocation Method for Solving the 2D Nonlinear Coupled Burgers’ Equations

by Hananeh Nojavan, Saeid Abbasbandy and Tofigh Allahviranloo

Mathematics 2017, 5(3), 38; https://doi.org/10.3390/math5030038 - 21 Jul 2017

Cited by 3 | Viewed by 4221

Abstract

This study aimed at investigating a local radial basis function collocation method (LRBFCM) in the reproducing kernel Hilbert space. This method was, in fact, a meshless one which applied the local sub-clusters of domain nodes for the approximation of the arbitrary field. For [...] Read more.

This study aimed at investigating a local radial basis function collocation method (LRBFCM) in the reproducing kernel Hilbert space. This method was, in fact, a meshless one which applied the local sub-clusters of domain nodes for the approximation of the arbitrary field. For time-dependent partial differential equations (PDEs), it would be changed to a system of ordinary differential equations (ODEs). Here, we intended to decrease the error through utilizing variable shape parameter (VSP) strategies. This method was an appropriate way to solve the two-dimensional nonlinear coupled Burgers’ equations comprised of Dirichlet and mixed boundary conditions. Numerical examples indicated that the variable shape parameter strategies were more efficient than constant ones for various values of the Reynolds number. Full article

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731 KiB

Open AccessArticle

Elimination of Quotients in Various Localisations of Premodels into Models

by Rémy Tuyéras

Mathematics 2017, 5(3), 37; https://doi.org/10.3390/math5030037 - 9 Jul 2017

Viewed by 4055

Abstract

The contribution of this article is quadruple. It (1) unifies various schemes of premodels/models including situations such as presheaves/sheaves, sheaves/flabby sheaves, prespectra/

Ω

-spectra, simplicial topological spaces/(complete) Segal spaces, pre-localised rings/localised rings, functors in categories/strong stacks and, to some extent, functors from a [...] Read more.

The contribution of this article is quadruple. It (1) unifies various schemes of premodels/models including situations such as presheaves/sheaves, sheaves/flabby sheaves, prespectra/

Ω

-spectra, simplicial topological spaces/(complete) Segal spaces, pre-localised rings/localised rings, functors in categories/strong stacks and, to some extent, functors from a limit sketch to a model category versus the homotopical models for the limit sketch; (2) provides a general construction from the premodels to the models; (3) proposes technics that allow one to assess the nature of the universal properties associated with this construction; (4) shows that the obtained localisation admits a particular presentation, which organises the structural and relational information into bundles of data. This presentation is obtained via a process called an elimination of quotients and its aim is to facilitate the handling of the relational information appearing in the construction of higher dimensional objects such as weak

(ω, n)

-categories, weak

ω

-groupoids and higher moduli stacks. Full article

(This article belongs to the Special Issue Homological and Homotopical Algebra and Category Theory)

269 KiB

Open AccessArticle

Lattices and Rational Points

by Evelina Viada

Mathematics 2017, 5(3), 36; https://doi.org/10.3390/math5030036 - 9 Jul 2017

Cited by 1 | Viewed by 3428

Abstract

In this article, we show how to use the first and second Minkowski Theorems and some Diophantine geometry to bound explicitly the height of the points of rank

N - 1

on transverse curves in

E^{N}

, where E is an elliptic [...] Read more.

In this article, we show how to use the first and second Minkowski Theorems and some Diophantine geometry to bound explicitly the height of the points of rank

N - 1

on transverse curves in

E^{N}

, where E is an elliptic curve without Complex Multiplication (CM). We then apply our result to give a method for finding the rational points on such curves, when E has

Q

-rank

\leq N - 1

. We also give some explicit examples. This result generalises from rank 1 to rank

N - 1

previous results of S. Checcoli, F. Veneziano and the author. Full article

(This article belongs to the Special Issue Geometry of Numbers)

243 KiB

Open AccessArticle

Banach Subspaces of Continuous Functions Possessing Schauder Bases

by Sergey V. Ludkowski

Mathematics 2017, 5(3), 35; https://doi.org/10.3390/math5030035 - 24 Jun 2017

Viewed by 2953

Abstract

In this article, Müntz spaces

M_{Λ, C}

of continuous functions supplied with the absolute maximum norm are considered. An existence of Schauder bases in Müntz spaces

M_{Λ, C}

is investigated. Moreover, Fourier series approximation of functions in Müntz spaces [...] Read more.

In this article, Müntz spaces

M_{Λ, C}

of continuous functions supplied with the absolute maximum norm are considered. An existence of Schauder bases in Müntz spaces

M_{Λ, C}

is investigated. Moreover, Fourier series approximation of functions in Müntz spaces

M_{Λ, C}

is studied. Full article

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Mathematics, Volume 5, Issue 3 (September 2017) – 12 articles

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