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We establish a strong form of Littlewood's conjecture with inhomogeneous shifts, for a full‐dimensional set of pairs of badly approximable numbers on a vertical line. We also prove a uniform assertion of this nature, generalising a strong form of a result of Haynes et al. Finally, we establish a similar result involving inhomogeneously badly approximable numbers, making progress towards a problem posed by Pollington et al. [ABSTRACT FROM AUTHOR]

For two contacting rigid bodies, the friction force F is proportional to the normal load and independent of the macroscopic contact area and relative velocity V (Amonton’s law). With two mutually sliding polymer samples, the surface irregularities transmit deformation to the underlying material. Energy loss along the deformation cycles is responsible for the friction force, which now appears to depend strongly on V [see, e.g., N. Maeda et al., Science 297, 379 (2002)]. We base our theoretical interpretation on the assumption that polymer chains are mainly subjected to oscillatory “reptation” along their “tubes.” At high deformation frequencies—i.e., with a large sliding velocity V—the internal viscosity due to the rotational energy barriers around chain bonds hinders intramolecular mobility. As a result, energy dissipation and the correlated friction force strongly diminish at large V. Derived from a linear differential equation for chain dynamics, our results are basically consistent with the experimental data by Maeda et al. [Science 297, 379 (2002)] on modified polystyrene. Although the bulk polymer is below Tg, we regard the first few chain layers below the surface to be in the liquid state. In particular, the observed maximum of F vs V is consistent with physically reasonable values of the molecular parameters. As a general result, the ratio F/V is a steadily decreasing function of V, tending to V-2 for large velocities. We evaluate a much smaller friction for a cross-linked polymer under the assumption that the junctions are effectively immobile, also in agreement with the experimental results of Maeda et al. [Science 297, 379 (2002)]. [ABSTRACT FROM AUTHOR]

Turnover of information system (IS) personnel is a critical problem for organizations. To gain a better understanding of turnover, researchers have explored career orientations that characterize an employee's internal motivations and desires. The inability of an organization to match career desires is often related to measures indicative of turnover in IS employees, including intent to leave and career dissatisfaction, though empirical evidence is indirect and inconclusive. Using career orientations, this study explicitly models the impact of the discrepancy between the wants of employees and employee perceptions of how their organization satisfies those wants. The model is based on discrepancy theory and predicts the gap is closely related to the turnover indicators. Model predictions hold true for a sample of 153 IS personnel. These results indicate the importance of developing career plans that employees perceive as matching their wants. [ABSTRACT FROM AUTHOR]

This study examines procurement irregularities, as one of the most unexplored threats in the procurement process of construction projects. It also tests the suppositions associated with the contributions of irregularities to corruption in construction procurement. An expert survey is conducted with 62 construction-related practitioners selected via nonprobabilistic sampling in the context of a Ghana, to assess the criticalities of the irregularities. Eighteen irregularities were identified within the context selected for this study. A soft computing technique known as the Fuzzy Synthetic Evaluation (FSE) method is employed to examine the identified irregularities. Other relevant techniques including factor analyses, normalization, and descriptive tools are employed to factorize the identified irregularities and test the hypotheses. Out of the 18 irregularities, 11 were revealed to be critical. The findings reveal that the top three irregularities were: payments for uncompleted works, sourcing of proforma invoices from the same supplier and the lack of proper coordination among key departments. Moreover, four constructs were developed using the identified measurement items. They are administrativespecific, procedural, compliance and contract monitoring irregularities. Out of the four, the topmost critical construct turns out to be compliance irregularities. Theoretically, this study advances the scholarship of construction by shedding lights on the irregularities associated with the procurement processes of construction projects. It also contributes to an indepth understanding of the noted irregularities. In practical terms, this study contributes to the procurement planning and policy-making process, it assists decision makers in putting in place measures to prevent or extirpate the likelihood of any of the irregularities' occurrences. [ABSTRACT FROM AUTHOR]

Differential equations are used to model problems in science and engineering that involve the change of some variable with respect to another. In real-life problems, the differential equation that models the problem is too complicated to solve exactly for this reason, in recent years much attention has been devoted to deriving numerical methods for approximating their solution. In particular, in this paper we consider the use of Adams-Bashforth like a multi-step method. Adams-Bashforth method of different steps is constructed, and then we use the fourth-step one, on Mathematica Package for numerical approaches. The numerical results are compared with analytical ones, shown in different ways, tables and graphics, accompanied by examples of their use. [ABSTRACT FROM AUTHOR]

Abstract We study the weighted star discrepancy of the Halton sequence. In particular, we show that the Halton sequence achieves strong polynomial tractability for the weighted star discrepancy for product weights (γ j) j ≥ 1 under the mildest condition on the weight sequence known so far for explicitly constructive sequences. The condition requires sup d ≥ 1 max 0̸ ≠ u ⊆ [ d ] ∏ j ∈ u (j γ j) < ∞. The same result holds for Niederreiter sequences and for other types of digital sequences. Our results are true also for the weighted unanchored discrepancy. [ABSTRACT FROM AUTHOR]

Abstract Doubling and level permutation of factors are widely used in the construction of uniform designs and minimum aberration designs. Based on the viewpoint that double design is the orthogonal combination of all possible level permutations of its initial two-level design, a method of tripling for three-level design, which triples both the run size and number of factors of initial design, is proposed by orthogonally combining all possible level permutations of its initial design in this paper. The wrap-around L 2 -discrepancy of triple design is expressed by the wordlength pattern of its initial design, and a tight lower bound of the wrap-around L 2 -discrepancy of triple design is obtained. An efficient method for constructing uniform minimum aberration designs is proposed based on the projection of triple design. These constructed designs have better properties, such as minimum aberration and lower discrepancy, than existing uniform designs, and are recommended for use in practice. Highlights • A new concept named as triple design is proposed for fractional factorial design. • The WD of triple design is expressed by the wordlength pattern of its initial design. • A tight lower bound of the wrap-around L2-discrepancy of triple design is obtained. • Triple design has better properties, such as minimum aberration, lower discrepancy. [ABSTRACT FROM AUTHOR]

The irregularity of a graph G is defined as irr (G) = ∑ u v ∈ E (G) | d u − d v | , where d u denotes the degree of a vertex u ∈ V (G) and E (G) is the edge set of G. From the class of all n -vertex (molecular) trees, graphs with the first five minimal irr -values have already been characterized in the literature. The main purpose of this paper is to determine the graphs with the sixth, seventh and eighth minimal irr -values among all the members of the aforementioned class for n ≥ 7 , n ≥ 8 and n ≥ 8 , respectively. [ABSTRACT FROM AUTHOR]

The longitudinal dispersion coefficient (Kx) is fundamental to modeling of pollutant and sediment transport in natural rivers, but a general expression for Kx, with applicability in low or high flow conditions, remains a challenge. The objective of this paper is to develop a Pareto-Optimal-Multigene Genetic Programming (POMGGP) equation for Kx by analyzing 503 data sets of channel geometry and flow conditions in natural streams worldwide. In order to acquire reliable data subsets for training and testing, Subset Selection of Maximum Dissimilarity Method (SSMD), rather than the classical trial and error method, was used by a random manipulation of these data sets. A new hybrid framework was developed that integrates SSMD with Multigene Genetic Programming (MGP) and Pareto-front optimization to produce a set of selected dimensionless equations of Kx and find the best equation with wide applicability. The POMGGP-based final equation was evaluated and compared with 8 published equations, using statistical indices, graphical visualization of 95% confidence ellipse, Taylor diagram, discrepancy ratio (DR) distribution, and scatter plots. Besides being simple and applicable to a broad range of conditions, the proposed equation predicted Kx more accurately than did the other equations and can therefore be used for the prediction of longitudinal dispersion coefficient in natural river flows. [ABSTRACT FROM AUTHOR]

Researchers frequently use the Nielsen ‘bimonthly’ retail audit data as a measure of actual sales over a two-month period. The results of several simulations suggest that this practice can lead to parameter estimates that are biased by as much as 22%. A bias of this magnitude could seriously affect conclusions reached by researchers and lead managers to make incorrect marketing decisions. This discrepancy is due to the fact that different stores in the Nielsen sample are audited over different two-month periods. As a result, the aggregate Nielsen audit figure partially reflects sales over a three-month period. Several procedures for reducing the bias in the parameter estimates are suggested. [ABSTRACT FROM AUTHOR]

When scientists are asked to give expert advice on risk-related questions, such as the authorization of medical drugs, deliberation often does not eliminate all disagreements. I propose to model these remaining discrepancies as differences in risk assessments and/or in risk acceptability thresholds. The normative question I consider, then, is how the individual expert views should best be aggregated. I discuss what "best" could mean, with an eye to some robustness considerations. I argue that the majority rule, which is currently often used in expert panels, has significant drawbacks. [ABSTRACT FROM AUTHOR]

In 1959 Fejes Tóth posed a conjecture that the sum of pairwise nonobtuse angles between N unit vectors in Sd is maximized by periodically repeated elements of the standard orthonormal basis. We obtain new improved upper bounds for this sum, as well as for the corresponding energy integral. We also provide several new approaches to the only settled case of the conjecture: d = 1. [ABSTRACT FROM AUTHOR]

An edge irregular total k-labeling f : V U E → {1, 2, 3, ..., k} of a graph G = (V, E) is a labeling of vertices and edges of G in such a way that for any two different edges uv and u'v' their weights f (u) + f (uv) + f (v) and f (u') + f (u' v') + f (v') are distinct. The total edge irregularity strength tes(G) is defined as the minimum k for which the graph G has an edge irregular total k-labeling. In this paper, we study the total edge irregularity strength for shadow graph of cycle and path, total graph of cycle and path, lotus inside a circle, double wheel graph. [ABSTRACT FROM AUTHOR]

We consider the problem of deterministic load balancing of tokens in the discrete model. A set of n processors is connected into a d-regular undirected network. In every timestep, each processor exchanges some of its tokens with each of its neighbors in the network. The goal is to minimize the discrepancy between the number of tokens on the most-loaded and the least-loaded processor as quickly as possible. In this work, we identify some natural conditions on deterministic load-balancing algorithms to improve upon the long-standing results of Rabani et al. (1998). Specifically, we introduce the notion of cumulatively fair load-balancing algorithms where in any interval of consecutive timesteps, the total number of tokens sent out over an edge by a node is the same (up to constants) for all adjacent edges. We prove that algorithms that are cumulatively fair and where every node retains a sufficient part of its load in each step, achieve a discrepancy of O(d min &lbrace; &sqrt; log n/μ,&sqrt; n&rbrace;) in time O(T), where μ is the spectral gap of the transition matrix of the graph. We also show that, in general, neither of these assumptions may be omitted without increasing discrepancy. We then show, by a combinatorial potential reduction argument, that any cumulatively fair scheme satisfying some additional assumptions achieves a discrepancy of O(d) almost as quickly as the continuous diffusion process. This positive result applies to some of the simplest and most natural discrete load balancing schemes. [ABSTRACT FROM AUTHOR]

This paper examines how a regime of penalties or sanctions for breaching public financial management (PFM) laws and regulations can be designed to increase compliance with these laws. Financial irregularities can be as high as five to eight percent of GDP or more in some poorly administered countries. If a sanctions regime is to be effective, it should meet the three core principles of impartiality, proportionality, and transparency. An empirical analysis of sanctions regimes and recovery rates in 26 countries suggests that excessive use of "harsh" sanctions could negatively affect the level of compliance. The design of a sanctions regime should include both "soft" and "harsh" measures which are proportionate to the severity of financial irregularities. The paper describes three institutional models ("financial police," "risk‐based," and "sanctions coordinator") that countries have used to implement a sanctions regime. An approach targeting expenditure that is highly vulnerable to irregularities tends to achieve a better recovery rate than a regime based on a "mass investigation, mass sanctions" approach. A tailored approach based on the third model may be appropriate for low‐capacity countries. [ABSTRACT FROM AUTHOR]

In this paper, we consider a two-dimensional inverse boundary value problem for Poisson equation on annular domain, consisting of recovering boundary data on the inner boundary from temperature data on the outer circle. This problem is ill-posed in the sense of Hadamard, i.e., small errors in the data can lead to arbitrarily large perturbations in the solution. We establish an infinite singular value expansion for sought boundary data assuming noise-free temperature measurements. In the case of corrupted data, the truncated series is used as a regularized solution; i.e. ill-posedness is dealt with by filtering away high frequencies in the solution. The truncation parameter is determined by Morozov’s discrepancy principle and an error estimate to quantify the accuracy of the computed approximate solution is derived. The proposed regularization method is illustrated by numerical simulations using synthetic data. [ABSTRACT FROM AUTHOR]

Abstract In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to solve the inverse heat conduction problem in estimating the unknown inner wall surface geometry of a two-layer-wall furnace whose inner wall is made of functionally graded materials (FGMs). The unknown geometry is estimated from the temperature measurements taken within the furnace wall. The inverse solutions will be justified based on the numerical experiments in which two different geometry of inner surface are to be determined. The temperature data obtained from the direct problem are used to simulate the temperature measurements. The influence of measurement errors and measurement locations on the precision of the estimated results is also investigated. Results show that the unknown geometry of the inner wall surface can be predicted precisely by using the present approach for the test cases considered in this study. [ABSTRACT FROM AUTHOR]

The flux transport dynamo, in which the poloidal magnetic field is generated by the Babcock–Leighton mechanism and the meridional circulation plays a crucial role, has emerged as an attractive model for the solar cycle. Based on theoretical calculations done with this model, we argue that the fluctuations in the Babcock–Leighton mechanism and the fluctuations in the meridional circulation are the most likely causes of the irregularities of the solar cycle. With our increased theoretical understanding of how these irregularities arise, it can be possible to predict a future solar cycle by feeding the appropriate observational data in a theoretical dynamo model. [ABSTRACT FROM AUTHOR]

Most of the traditional pattern classifiers assume their input data to be well-behaved in terms of similar underlying class distributions, balanced size of classes, the presence of a full set of observed features in all data instances, etc. Practical datasets, however, show up with various forms of irregularities that are, very often, sufficient to confuse a classifier, thus degrading its ability to learn from the data. In this article, we provide a bird’s eye view of such data irregularities, beginning with a taxonomy and characterization of various distribution-based and feature-based irregularities. Subsequently, we discuss the notable and recent approaches that have been taken to make the existing stand-alone as well as ensemble classifiers robust against such irregularities. We also discuss the interrelation and co-occurrences of the data irregularities including class imbalance, small disjuncts, class skew, missing features, and absent (non-existing or undefined) features. Finally, we uncover a number of interesting future research avenues that are equally contextual with respect to the regular as well as deep machine learning paradigms. [ABSTRACT FROM AUTHOR]

A digraph is called irregular if its distinct vertices have distinct degree pairs. An irregular digraph is called minimal (maximal) if the removal of any arc (addition of any new arc) results in a non-irregular digraph. It is easily seen that the minimum sizes among irregular n-vertex whether digraphs or oriented graphs are the same and are asymptotic to (√2/3) n3/2; maximum sizes, however, are asymptotic to n² and n²/2, respectively. Let s stand for the sum of initial positive integers, s = 1, 3, 6, ... . An oriented graph Hs and a digraph Fs, both large (in terms of the size), minimal irregular, and on any such s vertices, s ≥ 21, are constructed in [Large minimal irregular digraphs, Opuscula Math. 23 (2003) 21-24], co-authored by Z. D-H. and three more of the present co-authors (Z.M., J.M., Z.S.). In the present paper we nearly complete these constructions. Namely, a large minimal irregular digraph Fn, respectively oriented graph Hn, are constructed for any of remaining orders n, n > 21, and of size asymptotic to n², respectively to n²/2. Also a digraph Φn and an oriented graph Gn, both small maximal irregular of any order n ≥ 6, are constructed. The asymptotic value of the size of Gn is at least (√2/3) n3/2 and is just the least if n = s → ∞, but otherwise the value is at most four times larger and is just the largest if n = s -1 → ∞. On the other hand, the size of Φn is of the asymptotic order Θ(n3/2). [ABSTRACT FROM AUTHOR]

A vertex irregular total k-labeling of a graph G with vertex set V and edge set E is an assignment of positive integer labels {1, 2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. The total vertex irregularity strength of G, denoted by tvs(G) is the minimum value of the largest label k over all such irregular assignment. In this paper, we study the total vertex irregularity strength of cycle quadrilateral snake, sunflower, double wheel, fungus, triangular book and quadrilateral book. [ABSTRACT FROM AUTHOR]

Objectives: Double reading in diagnostic radiology can find discrepancies in the original report, but a systematic program of double reading is resource consuming. There are conflicting opinions on the value of double reading. The purpose of the current study was to perform a systematic review on the value of double reading.Methods: A systematic review was performed to find studies calculating the rate of misses and overcalls with the aim of establishing the added value of double reading by human observers.Results: The literature search resulted in 1610 hits. After abstract and full-text reading, 46 articles were selected for analysis. The rate of discrepancy varied from 0.4 to 22% depending on study setting. Double reading by a sub-specialist, in general, led to high rates of changed reports.Conclusions: The systematic review found rather low discrepancy rates. The benefit of double reading must be balanced by the considerable number of working hours a systematic double-reading scheme requires. A more profitable scheme might be to use systematic double reading for selected, high-risk examination types. A second conclusion is that there seems to be a value of sub-specialisation for increased report quality. A consequent implementation of this would have far-reaching organisational effects.Key Points: • In double reading, two or more radiologists read the same images.• A systematic literature review was performed.• The discrepancy rates varied from 0.4 to 22% in various studies.• Double reading by sub-specialists found high discrepancy rates. [ABSTRACT FROM AUTHOR]

In this paper, we explore PD-type ILC schemes of fractional version with pulse compensation for single-input-single-output fractional differential systems. More precisely, we design a new type of pulse-based ILC schemes involving fractional derivative and sign function for a class of fractional order linear systems with initial state shift. In order to tracking discrepancy incurred by the initial state shift effectively, a new function of pulse compensation is introduced. The effectiveness of the result is illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

We show how to select an item with the majority color from n two-colored items, given access to the items only through an oracle that returns the discrepancy of subsets of k items (the absolute value of the difference between the numbers of items with each color). We use n/⌊k2⌋+O(k) queries, improving a previous method by De Marco and Kranakis that used n-k+k2/2 queries. We also prove a lower bound of n/(k-1)-O(n1/3) on the number of queries needed, both for discrepancy queries and to queries that return the partition of items into monochromatic subsets. This improves a lower bound of ⌊n/k⌋ by De Marco and Kranakis. [ABSTRACT FROM AUTHOR]

For expansive continuous maps with the specification property, we compute the topological entropy of the irregular set for the Birkhoff averages of a continuous function. This is the set of points for which the Birkhoff averages do not converge. The entropy is expressed in terms of a conditional variational principle. We also consider the general case of irregular sets obtained from ratios of Birkhoff averages of continuous functions. Moreover, we obtain a conditional variational principle for the topological entropy of the family of subsets of the irregular set formed by the points such that the set of accumulation points of the ratio of Birkhoff averages is a given interval. As nontrivial applications, we obtain conditional variational principles for the topological entropy of the level sets of local entropies, pointwise dimensions and Lyapunov exponents both on repellers and hyperbolic sets. [ABSTRACT FROM AUTHOR]

Four notions of distributional chaos, namely DC1, DC2, DC 2 1 2 and DC3, are studied within the framework of operators on Banach spaces. It is known that, for general dynamical systems, DC1 ⊂ DC2 ⊂ DC 2 1 2 ⊂ DC3. We show that DC1 and DC2 coincide in our context, which answers a natural question. In contrast, there exist DC 2 1 2 operators which are not DC2. Under the condition that there exists a dense set X 0 ⊂ X such that T n x → 0 for any x ∈ X 0 , DC3 operators are shown to be DC1. Moreover, we prove that any upper-frequently hypercyclic operator is DC 2 1 2 . Finally, several examples are provided to distinguish between different notions of distributional chaos, Li–Yorke chaos and irregularity. [ABSTRACT FROM AUTHOR]

We find natural and convenient conditions which allow us to produce classes of genuine real map germs with Milnor tube fibration, either with Thom regularity or without it. [ABSTRACT FROM AUTHOR]

A new graph characteristic, even modular edge irregularity strength of graphs is introduced. Estimation on this parameter is obtained and the precise values of this parameter are obtained for some families of graphs. [ABSTRACT FROM AUTHOR]

An intercalate in a Latin square is a 2 x 2 Latin subsquare. Let N be the number of intercalates in a uniformly random n x n Latin square. We prove that asymptotically almost surely N ≥ (1 - o(1)) n²/4, and that 피N ≤ (1 + o(1)) n²/2 (therefore asymptotically almost surely N ≤ fn² for any f → ∞). This significantly improves the previous best lower and upper bounds. We also give an upper tail bound for the number of intercalates in 2 fixed rows of a random Latin square. In addition, we discuss a problem of Linial and Luria on low-discrepancy Latin squares. [ABSTRACT FROM AUTHOR]

In this paper we investigate a special sequence related to the Halton sequence, namely the Halton sequence indexed by ⌊ n β ⌋ with β ∈ R , and prove a metric almost low-discrepancy result. [ABSTRACT FROM AUTHOR]

Let X be a variety over a field k and let X∞ be its space of arcs. We study the complete local ring  := OX∞,PeE, where PeE is the stable point defined by an integer e ≥ 1 and a divisorial valuation vE on X. Assuming char k = 0, we prove that embdim  = e(k̂E + 1), where k̂E is the Mather discrepancy of X with respect to vE. We also obtain that dim b  has as lower bound e(aMJ(E; X)), where aMJ(E; X) is the Mather–Jacobian log-discrepancy of X with respect to vE. For X normal and a complete intersection, we prove as a consequence that if PE has codimension 1 in X∞ then the discrepancy kE ≤ 0. [ABSTRACT FROM AUTHOR]

In this analysis we used a spatially explicit, simplified bottom-up approach, based on animal inventories, feed dry matter intake, and feed intake-based emission factors to estimate county-level enteric methane emissions for cattle and manure methane emissions for cattle, swine, and poultry for the contiguous United States. Overall, this analysis yielded total livestock methane emissions (8916 Gg/yr; lower and upper 95% confidence bounds of ±19.3%) for 2012 (last census of agriculture) that are comparable to the current USEPA estimates for 2012 and to estimates from the global gridded Emission Database for Global Atmospheric Research (EDGAR) inventory. However, the spatial distribution of emissions developed in this analysis differed significantly from that of EDGAR and a recent gridded inventory based on USEPA. Combined enteric and manure methane emissions from livestock in Texas and California (highest contributors to the national total) in this study were 36% lesser and 100% greater, respectively, than estimates by EDGAR. The spatial distribution of emissions in gridded inventories (e.g., EDGAR) likely strongly impacts the conclusions of top-down approaches that use them, especially in the source attribution of resulting (posterior) emissions, and hence conclusions from such studies should be interpreted with caution. [ABSTRACT FROM AUTHOR]

We are interested in the numerical solution of the ordinary differential equation y'(t) = f(t, y(t)) when f is smooth in y but lacks regularity in t. We describe a family of methods akin to the Runge-Kutta family. It involves Monte Carlo simulation of integrals. We focus on third-order schemes which use random samples in dimension three.We give error bounds in terms of the step size and the discrepancy of the set used for the Monte Carlo approximations. We solve a model problem in which f undergoes rapid time variations. It is shown for this example that, by using a quasi-random point set in place of pseudo-random samples, we are able to obtain reduced errors. [ABSTRACT FROM AUTHOR]

In this paper we investigate the convergence of Chebyshev type regularization strategy combined with the Morozov discrepancy principle, which is an a posteriori parameter choice rule and independent of the a priori information of exact solution. Compared with the standard Tikhonov regularization method, the Chebyshev type regularization method has no saturation restriction so that its convergence order holds for any υ ≥ 1 2 , where p = 2 υ + 1 2 υ in the H o ̈ l d e r type estimate. [ABSTRACT FROM AUTHOR]

Let be a graph. A total labeling is called totally irregular total -labeling of if every two distinct vertices and in satisfy and every two distinct edges and in satisfy where and The minimum for which a graph has a totally irregular total -labeling is called the total irregularity strength of , denoted by In this paper, we determined the total irregularity strength of disjoint union of isomorphic copies of generalized Petersen graph. [ABSTRACT FROM AUTHOR]

A procedure for extraction of variations in the ionospheric total electron content (TEC) caused by the presence of local regions containing small-scale irregularities of the electron concentration has been developed. The procedure employs the transionospheric sounding data obtained with the use of a double-frequency GPS/GLONASS receiver. The procedure is based on extraction of individual components of the TEC time series by applying to the series the procedure of simple sliding-window smoothing with the width of the window selected according to the period of the TEC variations caused by the various-scale ionospheric irregularities. The efficiency of the procedure is demonstrated by the actual measurement data. [ABSTRACT FROM AUTHOR]

We compute all irregular primes less than 231 = 2 147 483 648. We verify the Kummer-Vandiver conjecture for each of these primes, and we check that the ρ-part of the class group of Q(ζp) has the simplest possible structure consistent with the index of irregularity of ρ. Our method for computing the irregular indices saves a constant factor in time relative to previous methods, by adapting Rader's algorithm for evaluating discrete Fourier transforms. [ABSTRACT FROM AUTHOR]

Track irregularities generally viewed as weak stationary random processes are perhaps the most important excitations to the vehicle/track coupled system. To better clarify the random vibration characteristics and probabilistic relationships between track random irregularities and dynamic behaviors of vehicle/track systems, it is a necessity to consider the full properties of track irregularities on amplitude, frequency and probability in vehicle/track interactions. The purpose of this paper is to develop a probabilistic model to select representative and realistic track irregularity sets from numerous data with higher efficiency and accuracy. To establish the vehicle/track interaction model, the finite element method and vehicle/track coupled dynamics are adopted and effectively combined, which can be used to reveal the interaction mechanisms between the moving vehicles and the guiding tracks. Moreover, the probabilistic transmission relationships between track irregularities and system responses are addressed by introducing a probability density evolution method. Through detailed comparisons with the experimental measurements and other advanced models, this proposed model is proved to be fairly effective and highly efficient. [ABSTRACT FROM AUTHOR]

In this paper we evaluate the three main methods for correcting the susceptibility-induced artefact in diffusion-weighted magnetic-resonance (DW-MR) data, and assess how correction is affected by the susceptibility field’s interaction with motion. The susceptibility artefact adversely impacts analysis performed on the data and is typically corrected in post-processing. Correction strategies involve either registration to a structural image, the application of an acquired field-map or the use of additional images acquired with different phase-encoding. Unfortunately, the choice of which method to use is made difficult by the absence of any systematic comparisons of them. In this work we quantitatively evaluate these methods, by extending and employing a recently proposed framework that allows for the simulation of realistic DW-MR datasets with artefacts. Our analysis separately evaluates the ability for methods to correct for geometric distortions and to recover lost information in regions of signal compression. In terms of geometric distortions, we find that registration-based methods offer the poorest correction. Field-mapping techniques are better, but are influenced by noise and partial volume effects, whilst multiple phase-encode methods performed best. We use our simulations to validate a popular surrogate metric of correction quality, the comparison of corrected data acquired with AP and LR phase-encoding, and apply this surrogate to real datasets. Furthermore, we demonstrate that failing to account for the interaction of the susceptibility field with head movement leads to increased errors when analysing DW-MR data. None of the commonly used post-processing methods account for this interaction, and we suggest this may be a valuable area for future methods development. [ABSTRACT FROM AUTHOR]

As the integrated reflection of track substructure deformations and the most important excitation for vehicle–track interactions, track irregularities show random nature, and generally being regarded as weak stationary random processes. To better expose the full statistical characteristics of track random irregularities on amplitude and wavelength, a time–frequency transform and probability theory based model is developed to simulate representative and realistic track irregularity sets by combining with random sampling methods. Moreover, a three-dimensional (3-D) vehicle–track coupled model is established by finite element method and dynamic equilibrium equations, where the nonlinearity of wheel/rail interaction is considered. Finally, a probability density evolution method (PDEM) is introduced to solve the probabilistic transmission issues between track irregularity sets and dynamic responses of vehicle–track coupled systems. There is a clear demonstration that the results derived by proposed methods are comparable to the experimental measurements. Through effectively applying the above methodologies, the probabilistic and random characteristics of vehicle–track interaction can be properly revealed. [ABSTRACT FROM AUTHOR]

Multiple scattering of a plane electromagnetic wave by a layer with random one-dimensional rectangular irregularities of the permittivity is studied. The dependence of the mean scattered intensity on the parameters of the irregularities is obtained. It is established that the mean intensity of the field oscillates as a function of the mean width of irregularities. The conditions for a substantial increases or decrease in the mean intensity of the wave in the layer are determined. [ABSTRACT FROM AUTHOR]

In this paper, we in multiple dimensions. We present a stability estimate for determining the source term in the multiple dimensional heat equation in an unbounded domain, and the regularization parameter is chosen by a discrepancy principle. Error estimate between the exact solution and its regularization solution is given. Numerical experiments for the one-dimension and two-dimension cases show the effectiveness of the method. [ABSTRACT FROM AUTHOR]