Modified Ostrowski’s method with eighth-order convergence and high efficiency index

In this paper, based on Newton’s method, we derive a modified Ostrowski’s method with an eighth-order convergence for solving the simple roots of nonlinear equations by Hermite interpolation methods. Per iteration this method requires three evaluations of the function and one evaluation of its first derivative, which implies that the efficiency index of the developed method is 1.682, which is optimal according to Kung and Traub’s conjecture Kung and Traub (1974) [2]. Numerical comparisons are made to show the performance of the derived method, as shown in the illustrative examples.     

Asymptotic efficiency analysis on the modified Paulson’s procedure with a PAC guarantee

While solving large-scale ranking-and-selection (R&S) problems, the statistical validities of many existing fully-sequential R&S procedures may no longer hold. With a few modifications on a classical fully-sequential procedure, Paulson’s procedure, it can provide the probably approximately correct (PAC) guarantee which is a good fit for large-scale R&S problems. To provide the PAC guarantee, the modified procedure loses some efficiency on the total sample size. In this paper, we show, both theoretically and numerically, that the efficiency loss is tolerable.     

The training institution efficiency of the semiconductor institute programme in Taiwan—application of spatiotemporal ICA with DEA approach

Despite the fact that Taiwan’s high-tech industry has gradually secured a leading position in the world, enterprises in Taiwan have striven to strengthen their technical advancement by providing employees with various internal or external training programmes. These institutional training programmes are designed to sustain competitive advantage, enhance the quality of manpower and improve operational efficiency. Much literature assesses the efficiency of an internal training programme that is initiated by a firm, but only a little literature studies the efficiency of an external training programme that is led by a government. Various efficiency measurement tools, such as conventional statistical methods and non-parametric methods, have been successfully developed in the literature. Among these tools, the data envelopment analysis (DEA) approach is one of the most widely discussed. However, the DEA's capability to discriminate efficient decision-making units from inefficient decision-making units requires much improvement (Adler and Yazhemsky). In this paper, a two-stage approach of integrating spatiotemporal independent component analysis (stICA) and DEA is developed for efficiency measurement. stICA is used to search for latent source signals where no relevant signal mixture mechanisms are available; and DEA is used to measure the relative efficiencies of decision-making units (DMUs). We suggest using stICA first to extract the input variables for generating independent components (IC), then selecting the ICs representing the independent sources of input variables, and finally inputting the selected ICs as new variables in the DEA model. To find the effects of environmental variables on the estimated efficiency scores, the Tobit–Bayes (censored) regression is applied. A simulated dataset and the training institution dataset provided by the Semiconductor Institute in Taiwan is used for analysis. The empirical result shows that the proposed method can not only separate performance differences between the training institutions but also improve the discriminatory capability of the DEA's efficiency measurement. The study results can serve as a reference for training institutions wishing to enhance their training efficiency.     

Finite-time stability analysis of fractional order time-delay systems: Gronwall’s approach

In this paper, a stability test procedure is proposed for linear nonhomogeneous fractional order systems with a pure time delay. Some basic results from the area of finite time and practical stability are extended to linear, continuous, fractional order time-delay systems given in state-space form. Sufficient conditions of this kind of stability are derived for particular class of fractional time-delay systems. A numerical example is given to illustrate the validity of the proposed procedure.     

A Quasi-isometric embedding into the group of Hamiltonian diffeomorphisms with Hofer’s metric

We construct an embedding Φ of [0, 1]^∞ into Ham(M, ω), the group of Hamiltonian diffeomorphisms of a suitable closed symplectic manifold (M, ω). We then prove that Φ is in fact a quasi-isometry. After imposing further assumptions on (M, ω), we adapt our methods to construct a similar embedding of ? ⊕ [0, 1]^∞ into either Ham(M, ω) or

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, the universal cover of Ham(M, ω). Along the way, we prove results related to the filtered Floer chain complexes of radially symmetric Hamiltonians. Our proofs rely heavily on a continuity result for barcodes (as presented in [28]) associated to filtered Floer homology viewed as a persistence module.

     

Modeling the interaction of an electromagnetic field with a two-dimensional surface in the framework of symanzik’s approach

Symanzik’s approach to the construction of models for the interaction between quantum fields and macroobjects allows finding the general form of the action functional with a Chern-Simons potential up to an arbitrary dimensionless constant; it is used to describe the interaction of a material surface with the electromagnetic field. We discuss results obtained in static models of such a type. We also consider a simple dynamic model of the interaction of a massless scalar field with moving planes.     

A generalization of Kendall’s tau and the asymptotic efficiency of the corresponding independence test

We consider a generalization of Kendall’s rank correlation coefficient proposed by Kochar and Gupta in 1987. This generalization is a nondegenerate U-statistic with a special kernel. We calculate Bahadur’s local efficiency for the independence test based on this statistic. It is shown that this test is locally efficient for alternatives described by the Woodworth dependence function. Bibligraphy: 29 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 244, 1997, pp. 227–237. Translated by S. Yu. Pilyugin.     

Transformation of urban public transport financing and its effect on operators’ efficiency: evidence from the Czech Republic

The purpose of this study is to analyze changes in the efficiency of urban public transport in the Czech Republic. Network data envelopment analysis and cluster analysis were applied to data from 19 urban public transport systems during 2004–2016. The series structure of the network was considered, including production and consumption stages with three external inputs (employees, rolling stock, and energy), one final output (passengers), and two intermediate products (vehicle-kilometres and seat-kilometres). The relationship between changes in efficiency and the method of financing for the operation of transport services was explored through standard statistical methods. One of the main findings was that the efficiency of smaller transport systems with complicated access to sources of funding were systematically less efficient, particularly in the consumption stage. These trends were even more significant after the reorganization of urban public transport funding in 2010.     

Bahadur’s efficiency of a test of exponentiality based on the loss-of-memory property

A test of exponentiality of Kolmogorov-Smirnov type based on the loss-of-memory characterization property is under study. The large-deviation asymptotics under the null-hypothesis is calculated. Local Bahadur efficiencies for commonly used parametric alternatives are found. Conditions of the Bahadur local optimality are obtained. Bibliography: 13 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 244, 1997, pp. 315–329. Translated by S. Yu. Pilyugin     

Sequences of 0’s and 1’s: Special sequence spaces with the separable Hahn property

As pointed out in [4] the paper [2], authored by G. Bennett, J. Boos and T. Leiger, contains a nontrivial gap in the argumentation of the proof of Theorem 5.2 which is one of main results of that paper and has been applied three times. Till now neither the gap is closed nor a counterexample has been stated. That is why the authors have examined in [4] the situation around the ‘gap’ aiming to a better understanding for the gap. The aim of this paper is to prove the mentioned applications of the theorem in doubt by using gliding hump arguments (quite similar to the classical proofs of the Theorems of Schur and Hahn in the first case (cf. [3]) and a very technical and artful construction, being of independent mathematical interest, in the second case). Research of T. Leiger supported by Estonian Science Foundation Grant 5376.     

Applying a hybrid DEA model to evaluate the influence of marketing activities to operational efficiency on Taiwan’s international tourist hotels

This study uses the hybrid DEA model, in which the proportionate inputs are evaluated with a radial measure and the non-proportionate inputs are evaluated with a non-radial measure in order to evaluate the impact of marketing expense on the efficiency of Taiwan's international tourist hotels. We further introduce the hybrid DEA into the technology gap measurement to evaluate the technology gaps of marketing expense utilization between different operating types. The empirical results indicate that the inefficiency caused from excess marketing expense is the main reason for lower efficiency in many tourist hotels, especially to chain-operated hotels and hotels that cater to domestic clients. Through the hybrid technology gap measurement, we find that the utilization of marketing resources is more effective for independent, city type hotels, as well as those that cater to international clients.     

Developing the roots of modelling conceptions: ‘mathematical modelling is the life of the world’

A study conducted with 25 Year 6 primary school students investigated the potential for a short classroom intervention to begin the development of a Modelling conception of mathematics on the way to developing a sense of mathematics as a way of thinking about life. The study documents the developmental roots of the cognitive activity, actions and conceptions of both modelling and mathematics that these beginners to modelling displayed. Understanding the conceptions of mathematics that students might hold or be developing and how these can be influenced in early schooling are essential ingredients in any plans for introducing modelling seriously into primary school classrooms. The majority of the students (22/25) were identified as displaying a developing conception of modelling as a way of problem handling. The three other students displayed the developmental roots of a way of understanding the world conception of modelling. These three students also displayed a Modelling conception of mathematics with one showing indications of developing towards a Life conception of mathematics.     

Convergence analysis of Oja’s iteration for solving online PCA with nonzero-mean samples

Principal component analysis(PCA)is one of the most popular multivariate data analysis techniques for dimension reduction and data mining,and is widely used in many fields ranging from industry and biology to finance and social development.When working on big data,it is of great necessity to consider the online version of PCA,in which only a small subset of samples could be stored.To handle the online PCA problem,Oja(1982)presented the stochastic power method under the assumption of zero-mean samples,and there have been lots of theoretical analysis and modified versions of this method in recent years.However,a common circumstance where the samples have nonzero mean is seldom studied.In this paper,we derive the convergence rate of a nonzero-mean version of Oja’s algorithm with diminishing stepsizes.In the analysis,we succeed in handling the dependency between each iteration,which is caused by the updated mean term for data centering.Furthermore,we verify the theoretical results by several numerical tests on both artificial and real datasets.Our work offers a way to deal with the top-1 online PCA when the mean of the given data is unknown.     

Fractal and multifractal analysis of the rise of oxygen in Earth’s early atmosphere

The rise of oxygen in Earth’s atmosphere that occurred 2.4–2.2 billion years ago is known as the Earth’s Great Oxidation, and its impact on the development of life on Earth has been profound. Thereafter, the increase in Earth’s oxygen level persisted, though at a more gradual pace. The proposed underlying mathematical models for these processes are based on physical parameters whose values are currently not well-established owing to uncertainties in geological and biological data. In this paper, a previously developed model of Earth’s atmosphere is modified by adding different strengths of noise to account for the parameters’ uncertainties. The effects of the noise on the time variations of oxygen, carbon and methane for the early Earth are investigated by using fractal and multifractal analysis. We show that the time variations following the Great Oxidation cannot properly be described by a single fractal dimension because they exhibit multifractal characteristics. The obtained results demonstrate that the time series as obtained exhibit multifractality caused by long-range time correlations.     

Bolzano’s Argument for the Existence of Substances: a Formalization with Two Types of Predication

The topic of our analysis is the argument for the existence of substances given by Bernard Bolzano in Athanasia (1827), where he essentially employs two ontological categories: substance and adherence. Bolzano considers the real and conditioned Inbegriff of all adherences, which are wirklich and nicht selbst bestehen. He claims that the formed collection is dependent on something external and non-adherential, which therefore is a substance. Bolzano’s argumentation turns out to be structurally similar to his argument for the existence of God from Lehrbuch der Religionswissenschaft (1834), but in each of these reasonings, we find different plausible interpretations of the key concept “Inbegriff”. The latter argumentation refers to the mereological totality of existentially conditioned objects. We propose the explication of the Bolzanian Inbegriff of all adherences using two types of predication: we consider its extension as composed of certain intensional counterparts of adherences. In our approach, we use a fragment of the theory of abstract objects formulated by E. Zalta (1983), describing two different relations between individuals and properties: extensional exemplification and intensional encoding. We put our reconstruction in a wider context of Bolzano’s ontology, formulating the needed axioms with two primitive predicates of second order ... is an adherence, ... is conditioned by something real as well as the conditionally introduced first order predicate constant \(\mathfrak {In}\) for Inbegriff of all adherential ideas. Finally, we sketch a model for our theory.     

The operator approach to Il’yushin’s models of viscoelastic media under the isothermal processes of deformation

Three Il’yushin’s models of viscoelastic media are considered. The theorems of strong unique solvability of the corresponding initial boundary-value problems are proved. All models are uniformly reduced to the Cauchy problems for differential first-order equations in some Hilbert space under some restrictions on physical parameters. Using these equations, we pose the problems of a spectrum of various viscoelastic media.