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AbstractIn a recent paper, Baker and Oliver Lorscheid showed that Descartes’s Rule of Signs and Newton’s Polygon Rule can both be interpreted as multiplicities of polynomials over hyperfields. Hyperfields are a generalization of fields which encode things like the arithmetic of signs or of absolute values. By looking at multiplicities of polynomials over such algebraic structures, Baker and Lorscheid showed that you can recover the rules of Descartes and Newton. In this paper, we define tropical extensions for idylls. Such extensions have appeared for semirings with negation symmetries in the work of Akian-Gaubert-Guterman and for hypergroups and hyperfields in the work of Bowler-Su. Examples of tropical extensions are extending the tropical hyperfield to higher ranks, or extending the hyperfield of signs to the tropical real hyperfield by including a valuation. The results of this paper concern the interaction of multiplicities and tropical extensions. First, there is a lifting theorem from initial forms to the entire polynomial from which we will show that multiplicities for a polynomial are equal to the corresponding multiplicity for some initial form. Second, we show that tropical extensions preserve the property that the sum of all multiplicities is bounded by the degree. Consequentially, we have this degree bound for every stringent hyperfield. This gives a partial answer to a question posed by Baker and Lorscheid about which hyperfields have this property. [ABSTRACT FROM AUTHOR]

Shame we are told is as intense as it is unrelenting. Shame we are told, further still, is as contagious as it is transmittable. By fastidiously attending to clinical reports and theoretical depictions of shame's totalizing character, I argue in this paper that we can notice something that has broadly gone unnoticed: shame assumes for itself absolute value. To bear this out, I contrast my view with that of the dominant one: that shame has an instrumental value. I show some limitations of the dominant view by reflecting on the role of shame in psychoanalytic training. The picture that emerges may seem quaintly commonsensical, and even commonplace, but it has, I think, vast clinical implications. I believe that it certainly has the potential to open some new horizons. The arguments for such a bold claim will occupy the concluding section of my paper. [ABSTRACT FROM AUTHOR]

The Capra operation is a graph theoretical operation that transforms the given graph into a structurally different and larger graph. It is commonly used in statistical analysis, data processing, and scientific research to compare and analyze data. The Capra operation involves subtracting the reference value from each numerical value, taking the absolute value of the resultand raising it to a specified power. This operation is used to create a new set of values that are more sensitive to differences between numerical values and can help to identify outliers and other anomalous data points. The Capra operation has numerous applications in fields such as finance, engineering, and biology, where it is used to analyze data and make predictions about future trends. Its ability to transform data and highlight differences between values makes it a valuable tool for researchers and analysts seeking to gain deeper insights into the patterns and structures within their data. In this paper, we studied the distance-based topological indices of some graphs under the Capra operation. [ABSTRACT FROM AUTHOR]

In multiple linear regressions, it is known that least-squares estimates of the parameters are likely to be too large in absolute value and possibly of wrong sign, if explanatory variables are correlated. To reduce the undesirable effects of collinearity, the ridge estimator has been proposed as an alternative method to the least squares estimator. The biggest debate with the ridge estimator is the selection of the regularization parameter. Several methods for the selection of the regularization parameter have been discussed. Although most of these methods are based on minimizing the mean square error of the ridge estimator, bootstrap resampling method is also proposed to provide an optimal regularization parameter which gives an estimate of mean square error of prediction. The purpose of this paper is to provide a comprehensive study of regularization parameter selection methods which consider bootstrap approach as well as estimation and prediction approaches. The paper concludes with application of these procedures to simulation studies and real data. [ABSTRACT FROM AUTHOR]

This paper presents an Accounting and Valuation (AV) method within the scope of Integrated Resource Planning (IRP) to analyze social impacts when implementing new energy resources. The method is based on a critical analysis from existing assessments regarding the IRP and its design is based on algorithms that convert qualitative information of social attributes into absolute values. These values feed the subsequent stages of the IRP to select the best energy resource (among available options) to be implemented. The method has been applied and tested as a pilot case in a rural region in Peru. This work provides extremely valuable information for decision-makers to assess, with real and quantitative data, investment decisions regarding energy planning. [ABSTRACT FROM AUTHOR]

In the process of coal preparation, large particles are often misplaced into the flotation feedings due to poor classification, and thus bring about negative effects on flotation results. In this paper, batch flotation tests of 0.5–2.5 mm were carried out at different reagent dosage to quantitatively analyze the effect of particle size and density on flotation. Flotation partition curves in corresponding conditions were plotted based on sizing analysis and float-and-sink tests of flotation products. Generalized skew-normal distribution model based on quartile was used to fit the experimental data and the variation rules of separation density, probable error and skewness, etc. with particle size and reagents were obtained, and the density-size partition surface mathematical model was established. The results show that floating ratio decreases with density and particle size. The separation density and probable error both decreases with particle size. The values of skewness were negative and tended to 0 with the decreasing of particle size. As the dosage of reagents increased, the separation density increased, the probable error increased slightly, and the difference of absolute values of skewness decreased. The research results put forward the theoretical instruction of expanding the upper limit of floatable size of particles and improving flotation efficiency. [ABSTRACT FROM AUTHOR]

In this paper, by transforming the vertical linear complementarity problem (VLCP) as a certain absolute value equation, we design a class of modulus-based matrix splitting iteration methods for solving the VLCP. The convergence properties of the proposed methods are discussed in depth. By making use of some numerical experiments, we confirm the efficiency of the proposed methods. Numerical results show that the proposed methods are superior to the classical modulus-based matrix splitting iteration methods. [ABSTRACT FROM AUTHOR]

This paper deals with the finite-time and fixed-time bipartite consensus tracking (FFBCT) problems for multi-agent systems (MASs) , in which both cooperative and competition exist. Using Lyapunov stability methods, distributed nonlinear protocols are provided to ensure all agents reach agreement. Its absolute value is the same but it might be different in direction. Besides, the second protocol can make the system reach bipartite consensus in fixed time regardless of the initial state of agents. Moreover, boundaries for settling times are estimated. Some numerical examples are finally presented to prove the validity of our designs. [ABSTRACT FROM AUTHOR]

A node is a structurally balanced (respectively, unbalanced) node if and only if the absolute value of its corresponding entry in the right eigenvector associated with the zero eigenvalue of the Laplacian matrix is equal to (respectively, is less than) one. The corresponding entry in the right eigenvector is called the algebraic trait for the structurally balanced property of a node. This paper aims to explore the algebraic trait for the structurally balanced property of a node under a signed digraph with a spanning tree by using a geometric-based method. Such a geometric point of view reveals the relationships of the links in a network for structurally balanced and structurally unbalanced nodes. The structurally balanced property of a node is determined by its parent nodes, and the connections between itself and its parent nodes. First of all, a hierarchical structure of its parent nodes is proposed, based on which the Laplacian matrix of the underlying topology can be written as a lower triangular matrix. Then, according to the lower triangular Laplacian matrix, the mathematical expression of the right eigenvector associated with the zero eigenvalue is derived. Based on this, as well as the definition of the structurally balanced node, the algebraic trait for the structurally balanced property of a node is obtained. Finally, a numerical example is provided to verify theoretical results. [ABSTRACT FROM AUTHOR]

A new class of statistics obtained by ordering the absolute values of the observations arising from absolutely continuous distributions which are symmetrically distributed about zero is introduced in this paper. The statistics generated by the above method are named as absolved order statistics (AOS) of the given sample. The association of the distribution of these statistics with the distribution of order statistics arising from the folded form of the parental density about zero is outlined. The vector of AOS is proved to be a minimal sufficient statistic for the class F θ (1) of all absolutely continuous distributions which are symmetrically distributed about zero. A method of estimation of the scale parameter of any distribution belonging to F θ (1) using AOS is described. Illustration on the advantage of the above method of estimation is described for the distributions such as (i) logistic, (ii) normal, and (iii) double Weibull. A more realistic censoring scheme involving AOS as well is discussed in this paper. We have derived the U-statistic estimator based on AOS for the scale parameter σ of any distribution f (x , σ) ∈ F θ (1) using the best linear unbiased estimate (BLUE) based on AOS of a preliminary sample as kernel. We have illustrated the performance of this estimator with an U-statistic generated from BLUE based on order statistics for each of (i) logistic (ii) normal and (iii) double Weibull distributions. [ABSTRACT FROM AUTHOR]

Let G be a graph. The energy of G, E (G) , is defined as the sum of absolute values of its eigenvalues. Here, it is shown that if G is a graph and { H 1 , ... , H k } is an edge partition of G, such that H 1 , ... , H k are spanning; then E (G) = ∑ i = 1 k E (H i) if and only if A i A j = 0 , for every 1 ⩽ i , j ⩽ k and i ≠ j , where A i is the adjacency matrix of H i . It was proved that if G is a graph and H 1 , ... , H k are subgraphs of G which partition edges of G, then E (G) ⩽ ∑ i = 1 k E (H i). In this paper we show that if G is connected, then the equality is strict, that is E (G) < ∑ i = 1 k E (H i). [ABSTRACT FROM AUTHOR]

In this paper, we propose a modified generalized SOR-like (MGSOR) method for solving an absolute value equation (AVE), which is obtained by reformulating equivalently AVE as a two-by-two block nonlinear equation and by introducing the transformation P y := | x | with a general nonsingular matrix P. The convergence results of the MGSOR method are obtained under certain assumptions imposed on the involved parameters. Furthermore, the optimal parameters minimizing the convergence rate of the MGSOR method for solving AVE are studied in detail. Numerical experiments further illustrate that the MGSOR method is efficient and has better performance than some existing iteration methods in aspects of the number of iteration steps and CPU time. [ABSTRACT FROM AUTHOR]

This paper investigates the attenuation behavior of flexural waves in functionally graded and disordered piezoelectric metamaterials. These structures are expediently designed by tuning the shunted piezoelectric electrical circuit. The transfer matrix method is employed to calculate the dispersive relationship of one-dimensional graded piezoelectric meta beams. It is found that the attenuation zone of the graded arrangement becomes wider compared with the result of the corresponding periodic structures. Moreover, the attenuation zone becomes wider by increasing the capacitance ratio's absolute value in a specific region. We demonstrate that the graded system generating the rainbow effect can slow down the flexural wave propagation in the host structure and increase the interaction time between elastic waves and local electrical circuits through the time-domain analysis. Besides, we study further the two-dimensional graded and disordered piezoelectric meta plates. Numerical results show that the bandwidth of the latter on average is broader than that of the former. Moreover, the disordered system can keep the continuity of the dominant attenuation zone and further increase the attenuation bandwidth within the larger capacitance ratio. These graded and disorder configuration concepts may pave a new way for elastic wave manipulation to realize broadband vibration suppressions and frequency selective spatial separations. [ABSTRACT FROM AUTHOR]

In this paper, a new three-term spectral conjugate subgradient method is presented to solve an absolute value equation. The new method is constructed based on conjugate gradient method proposed by Dai & Yuan and Barzilai & Borwein technique. In each iteration, a descent direction is generated. The global convergence of the new method is established under some mild assumptions. The numerical results are reported, showing the efficiency of our method. [ABSTRACT FROM AUTHOR]

Two graphs having the same spectrum are said to be cospectral. A pair of singularly cospectral graphs is formed by two graphs such that the absolute values of their nonzero eigenvalues coincide. Clearly, a pair of cospectral graphs is also singularly cospectral but the converse may not be true. Two graphs are almost cospectral if their nonzero eigenvalues and their multiplicities coincide. In this paper, we present necessary and sufficient conditions for a pair of graphs to be singularly cospectral, giving an answer to a problem posted by Nikiforov. In addition, we construct an infinite family of pairs of noncospectral singularly cospectral graphs with unbounded number of vertices. It is clear that almost cospectral graphs are also singularly cospectral but the converse is not necessarily true, we present families of graphs where both concepts: almost cospectrality and singularly cospectrality agree. [ABSTRACT FROM AUTHOR]

The eccentricity matrix ϵ (G) of a connected graph G is obtained from the distance matrix of G by retaining the largest distance in each row and each column and setting the remaining entries as 0. The eccentricity matrices of graphs are closely related to the distance matrices of graphs, nevertheless a number of properties of eccentricity matrices are substantially different from those of the distance matrices. The eccentricity matrices of trees need not be invertible though the distance matrices of trees are invertible. In this paper, we establish a necessary and sufficient condition for the eccentricity matrix of a tree to be invertible. The largest eigenvalue of ϵ (G) is called the ε-spectral radius, and the eccentricity energy (or the ε-energy) of G is the sum of the absolute values of the eigenvalues of ϵ (G). We obtain some bounds for the ε-spectral radius and characterize the extreme graphs. Two graphs are said to be ε-equienergetic if they have the same ε-energy. For any n ≥ 5 , we construct a pair of ε-equienergetic graphs on n vertices, which are not ε-cospectral. [ABSTRACT FROM AUTHOR]

The energy of a graph is defined as the sum of the absolute values of all eigenvalues with respect to its adjacency matrix. Denote by Gn,m the set of all connected graphs having n vertices and m edges. Caporossi et al. [Caporossi G, Cvetkovi D, Gutman I, et al. Variable neighbourhood search for extremal graphs. 2. Finding graphs with external energy. J Chem Inf Comput Sci. 1999;39:984–996] conjectured that among all graphs in Gn,m, n ≥ 6 and n − 1 ≤ m ≤ 2(n − 2), the graphs with minimum energy are the star Sn with m−n + 1 additional edges all connected to the same vertices for m ≤ n + ⌊ (n − 7) / 2 ⌋ , and the bipartite graph with two vertices on one side, one of which is connected to all vertices on the other side, otherwise. In this paper, we provide a new approach to investigate the conjecture above. Especially, we determine the unique tetracyclic graph having minimum energy. [ABSTRACT FROM AUTHOR]

Let S(G) be the Seidel matrix of a graph G. The Seidel energy of G, denoted by ES(G), is defined to be the sum of absolute values of all eigenvalues of the Seidel matrix S(G) of G. In this paper, we consider the change of Seidel energy of graphs due to edge deletion. It is proved that the Seidel energy of the tripartite Turán graph T(n, 3) of order n ≥ 9 is always increased when an edge is deleted. [ABSTRACT FROM AUTHOR]

Given a duopoly of firms that produce differentiated outputs maximizing profits and emitting pollution, this paper introduces an emission charge as an environmental policy and analyses its static and dynamic effects on emission reductions. Among other results, it is shown that the emission charge effectively controls the aggregate emission level. Although increasing an emission charge could increase the individual emissions, it is also shown that such adverse response is limited to the case where the own-market size elasticity is larger than the cross-market size elasticity in absolute value. From a dynamic point of view, it is demonstrated that the emission charge has double stabilizing effects; increasing the charge is, first, to enlarge the stability region and second, to stabilize unstable oscillations through a period-halving bifurcation. [ABSTRACT FROM AUTHOR]

In spatially varying coefficient models, there has been a common assumption of homoscedasticity. In many practical situations, however, rarely can we know a priori whether this assumption is true or not. In this paper, we propose a simple test for detecting spatial heteroscedasticity in spatially varying coefficient models. Specifically, the testing procedure is constructed based on the square root of the absolute value of the residuals obtained by the local linear geographically weighted estimation. Simulation experiments are conducted to evaluate the performance of the proposed method and the results demonstrate that the method in the paper is quite robust to the types of the error distributions and is more powerful in some cases, especially when the sample size is not very large. A real-world data set is analyzed to demonstrate the application of the proposed test method and the paper is ended with a final remark. [ABSTRACT FROM AUTHOR]

This paper examines the impact of a set of corporate governance provisions (CGI) as provided in the Zimbabwe Corporate Governance Code (Zimcode) and financial performance using a sample of 48 companies listed on the Zimbabwe Stock Exchange between 2013 to 2018. The Zimcode was introduced in 2015 in Zimbabwe and its main purpose was to curtail corporate scandals that had ravaged listed companies as a result of inadequate corporate governance compliance and was meant to augment the outdated colonial-era Companies Act of 1951. The study uses a market-based measure (Tobin's Q) and an accounting-based measure (ROA) as proxies for financial performance. A CGI is constructed using three dimensions: board, directors and ownership; accounting and auditing; and risk management. Least Absolute Value (LAV), Ordinary least Squares (OLS) with heteroscedasticity consistent standard errors and Fixed Effects estimators are used to examine if the introduction of the Zimcode has improved the financial performance of companies. The results show that the corporate governance reform in Zimbabwe through the introduction of the Zimcode did not significantly affect the financial performance of Zimbabwean companies. This might be a signal that the regulators need to overhaul the code or gravitate toward mandatory compliance. [ABSTRACT FROM AUTHOR]

Let G be a graph and S (G) be the Seidel matrix of G. The Seidel energy E s (G) is defined to be the sum of the absolute value of all eigenvalues of the Seidel matrix of G. In this paper, we study some properties of the Seidel eigenvalues of G. Moreover, we present some lower and upper bounds for the Seidel energy of G. [ABSTRACT FROM AUTHOR]

In this paper, silicon-based Asymmetric-Elevated-Source-Drain Tunnel Field-Effect Transistor (AESD-TFET), for gate lengths (LGs), viz. 70, 45, 32, 22, and 13 nm, is investigated for the first time to find its suitability in sub-400-mV low-stand-by-power (LSTP) digital operation, followed by finding its reliability and stability against the adverse effect of Positive Bias Temperature Instability (PBTI) for LG = 13 nm corresponding to the (recent) state-of-the-art technology node for the "More Moore" options in realizing LSTP digital functions. The whole work is executed with the help of 2-D numerical methods, via a model-calibration against a couple of experimental works on Elevated-Drain TFET (ED-TFET) and Elevated-Source TFET (ES-TFET), respectively, followed by a comparison of performances between the three, in terms of threshold voltage (VT), average subthreshold swing (SSavg), OFF-state current (IOFF), ION/IOFF ratio, OFF-state leakage power, and drain-induced barrier lowering (DIBL), and then a measurement of shifts in VT, IOFF, ION/IOFF, and SSavg for different PBTI stress conditions for temperature ≥ 300 K. For the optimum value of LG (i.e. 13 nm), a reduction of 56% and 66% in DIBL, a drop of 15.84% and 45.74% in SSavg, a reduction of about 1 decade and 3 decades in IOFF, and an improvement of nearly 1 decade and 2 decades in ION/IOFF have been obtained for the AESD-TFET against the ES- and ED-TFET devices, respectively. The same has also been found to show maximum stability against the PBTI effect under the two-temperature conditions (i.e. 300 K and 398 K) in terms of IOFF, ION/IOFF and SSavg with the lowest possible shifts in VT (∼ 0%) and SSavg (9%), besides maintaining the most excellent absolute values of the aforesaid parameters. [ABSTRACT FROM AUTHOR]

In the remote sensing community, HyperSpectral (HS) images (HSI) are becoming increasingly popular as the advancement of technology and the consequent reduction of cost make them financially more accessible. The reason for their success is the higher capability they can offer, with respect to multispectral data, to discriminate classes that are spectrally similar. A series of pre-processing steps such as geometric, radiometric and atmospheric corrections are carried out on raw data captured by HS sensors. The processed data is then passed to the data analyst, whose work generally relies on the assumption that the received HS data is 'clean,' as all possible corrections have already been implemented; however, corrections are hardly perfect and residual disturbances can still bias the quality of results. At this stage, however, all corrections based on ancillary information have already been made and the possibilities for 'exogenous' correction of data are exhausted. More could be possibly done by sourcing additional information from the data itself. In this paper, we propose a simple yet effective additional step for error suppression through energy scaling, termed 'Error Removal by Energy Scaling' (ERES). In classification problems, the absolute value of wavelength λ is often overlooked, except for, e.g. removal of strong absorption bands; yet the λ value can actually further support the classification process if their physical meaning is tapped. The proposed ERES method is indeed a non-linear scaling method, derived from physical phenomena linked with radiation extinction properties. In ERES, each band is associated with an energy level, that is inversely related to its own wavelength. The associated nonlinear energy information in HSI, neglected in most classification strategies, prevents optimal separation of class-specific spectral signatures, that are generated by the physics of wave-matter interaction. This is especially true for linear classifiers such as Support Vector Machines (SVM). Removing this physics-linked information makes data more suitable to be classified with physics-unaware classification strategies, typically used in down stream remotely sensed data processing. The relevance of the issue, and the benefits of ERES, are discussed and validated in this work over three different datasets, using accuracy improvements on the popular Spectral Angle Mapper and SVM classifiers as a means to gauge the effectiveness of the correction strategy. Results clearly reveal the positive impact of applying ERES to the data before proceeding to classification. [ABSTRACT FROM AUTHOR]

Rutherford developed his revolutionary model of the atom based on experiments using helium nuclei scattered by a thin gold foil. In this paper, we review the measurements of the size of the helium nucleus, focusing on spectroscopic techniques. We touch on the 'proton radius puzzle' that has incited a great deal of interest in high-resolution spectroscopy of the most fundamental atoms. We find that for an absolute value of the size of the helium nucleus, the theoretical advance that will give a new determination is just around the corner. [ABSTRACT FROM AUTHOR]

In this paper, the multi-dimensional control optimisation problem involving first-order PDE constraints is considered. The absolute value penalty function method is used to solve the considered problem. Further, the saddle point of the Lagrange functional defined for the aforesaid control optimisation problem is discussed. Thereafter, the exactness property of the absolute value penalty function method is studied with the help of saddle-point theory. Then, the relationship between a minimiser of the penalised multi-dimensional control optimisation problem and a saddle point of the aforesaid control problem is established under the convexity assumption. Moreover, we have verified the theoretical results with applications. [ABSTRACT FROM AUTHOR]

The paper analyses the possibility of increasing efficiency of the Iterative Weighted Similarity Transformation (IWST) method, which is a prototype of classic robust methods, using global optimisation approach instead of classical one, available in the literature. For the purpose of solving the optimisation problem of the IWST method, in addition to the Iterative Reweighted Least Squares (IRLS) method, the Genetic algorithm (GA) and Generalised Particle Swarm Optimisation (GPSO) algorithm were applied, in order to overcome some flaws of IRLS method. Experimental research was performed based on the Monte Carlo simulation using the mean success rate (MSR) on the example of the geodetic control network for monitoring the Šelevrenac dam in the Republic of Serbia. By using the GA and GPSO algorithms, the overall efficiency of the IWST method has been increased by about 18% compared to the IRLS method. Also, it has been determined that the efficiency of the IRLS method significantly reduces with the increase in the number of displaced potential reference points (PRPs), while the GA and GPSO algorithms' efficiency does not change significantly. The values of overall absolute true errors due to the increased number of displaced PRPs in the GA and GPSO algorithms did not change notably while with the IRLS method their values increased significantly. [ABSTRACT FROM AUTHOR]

Fault detection is essential for monitoring of various biological processes and becomes even more important in that context. This paper, therefore, presents an enhanced tool that merges state estimation with fault detection (FD) methods to improve monitoring of biological processes. The proposed technique, so-called particle filter (PF)-based maximum double adaptive exponential weighted moving average (EWMA) chart, involves two steps. First, the states of the biological processes are estimated using the PF method. In the second step, the faults are detected using the maximum double adaptive EWMA chart. The proposed method is based on the maximum of the absolute values of the EWMA statistics, one monitoring adaptively the variance and the other controlling the mean. The FD performance is studied utilising a wastewater treatment model. The detection performances are assessed in terms of missed detection rate, false alarm rate, detection speed, sensibility to fault sizes and robustness to noise levels. [ABSTRACT FROM AUTHOR]

The theory of symmetric functions has many applications in the investigation of fixed points, estimation of absolute values of some integrals and obtaining the results of the type of Cartan’s uniqueness theorem. In this paper, we solve some differential subordinations and superordinations involving analytic functions with respect to the symmetric points and also derive some sandwich results under certain assumptions on the parameters involved. The various results presented in this paper are shown to apply to yield the corresponding (new or known) results for many simpler function classes. [ABSTRACT FROM AUTHOR]

In this paper, we present an inequality of characteristic functions for ψ-mixing random vectors, and derive an upper bound for the supremum of the absolute value of the difference of two multivariate probability density functions based on ψ-mixing random vectors. For its application, we discuss the Berry-Esseen type bounds for conditional value-at-risk estimator based on ψ-mixing sequences, by the suitable choice of some constants, the Berry-Esseen type bounds of the estimator can attain O ( n − 1 / 6 ). [ABSTRACT FROM AUTHOR]

The k-generalized Fibonacci sequence F (k) := (F n (k) ) n ≥ − (k − 2) is the linear recurrent sequence of order k, whose first k terms are 0 , ... , 0 , 1 and each term afterwards is the sum of the preceding k terms. In this paper, we extend F (k) to negative indices and give an upper bound on the absolute value of its largest zero in terms of k. In particular, we find that the zero-multiplicity of the k-generalized Fibonacci sequence is exactly k (k − 1) / 2 for all k ∈ [ 4 , 500 ]. We prove that the zero multiplicity of the k-generalized Fibonacci sequence is at least k (k − 1) / 2 for all k ≥ 2. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of estimating the quantile of a two-parameter exponential distribution with respect to an arbitrary strictly convex loss function under progressive type II censoring. Inadmissibility of the best affine equivariant (BAE) estimator is established through a conditional risk analysis. In particular we provide dominance results for quadratic, linex and absolute value loss functions. Further, a class of dominating estimators is derived using the IERD (integral expression of risk difference) approach of Kubokawa (1994). In sequel the generalized Bayes estimator is shown to improve the BAE estimator. [ABSTRACT FROM AUTHOR]

The energy E (G) of a graph G is the sum of the absolute values of all eigenvalues of G. More recently, the authors of Wong, Wang and Chu [Lower bounds of graph energy in terms of matching number. Linear Algebra Appl. 2018;549:276–286] obtained a lower bound for graph energy. They proved that, for a connected graph G apart from K 1 , K 3 and K p , q with 1 ≤ p q ≤ 4 , the energy of G is at least 2 5 . In the present paper, we aim to improve the lower bound from 2 5 to 6. The extreme graphs with energy 6 are characterized. [ABSTRACT FROM AUTHOR]

In this paper, we study spectral properties of complex weighted digraphs. We show that a complex weighted digraph D is balanced if and only if D and | D | have the same spectrum, where | D | is the absolute value weighted digraph of D, that is, the digraph obtained by replacing the weight of each arc by its absolute value. We extend the concept of real energy to complex weighted digraphs and obtain extremal energy unicyclic complex weighted digraphs with cycle-weight in the punctured disk Δ = { z ∈ C : | z | ≤ 1 } ∖ { 0 }. We consider a family of complex weighted digraphs D n , h , in which each digraph has order n and cycles of length h ≥ 2 only with constant complex weight c = a + ι ˙ b. We show that for each D ∈ D n , h , the real energy of D is related to the real energy of unweighted cycle of length h and in some special cases real energy can be compared using quasi-order relation on coefficients of the characteristic polynomial. Finally, we obtain upper bounds on the real energy which generalize those known for unweighted digraphs and signed digraphs. [ABSTRACT FROM AUTHOR]

Since the early 1990s, global trade has doubled, with a corresponding increase in emissions embodied in trade. Standard accounting of emissions counts the 'territorial' emissions that occur within a country, but there has also been discussion about the need for 'consumption-based' carbon accounting (CBCA) that counts the carbon emissions required to produce the goods and services consumed in a country (in short: the Country Carbon Footprint (CCF)). Global multi-regional input-output (GMRIO) databases form the method of choice to calculate carbon footprints. Due to the need to combine different data sources to construct GMRIOs, and incompleteness and inconsistencies in data sources, estimations and balancing procedures have to be applied. Such construction procedures are not uniform. This leads to hesitation over using CCF results in policy formulation. The empirical analysis reviewed in this paper synthesizes the few simple measures that can already lead to robust CCF results, even with different GMRIO models. The single most important point is to use harmonized territorial carbon emissions in different GMRIO models. Then, differences between databases for most countries are less than 10% between GMRIOs, and considerably lower than 10% for large countries with a high GDP compared to imports. When investigating the trends in CCF as opposed to the absolute value, the differences become even smaller. Hence, harmonizing data already used in classical production-based accounts and related policy making appears to be the most relevant factor also for CBCA and calculating CCFs. Key policy insights Country Carbon Footprints (CCFs) are best calculated with Global Multi Regional Input Output (GMRIO) databases. Compared to territorial carbon accounting, the additional use of GMRIOs for calculating CCFs in principle leads to higher uncertainties. However, trends in CCFs – that is, relative change over time – calculated with different GMRIOs are already very robust. Harmonizing territorial emissions across GMRIOs is the single most important factor that reduces uncertainty in CCFs, followed by the use of an official national Environmentally Extended Input-Output model for the country for which a CCF is calculated. Working towards an internationally accepted GMRIO, such as the OECD's inter-country input-output (ICIO) table, is recommended. [ABSTRACT FROM AUTHOR]

This paper introduces a new class of Hadamard matrix-based mixed-level foldover designs (MLFODs) and an algorithm which facilitates the construction of MLFODs. Our new MLFODs were constructed by converting some 2-level columns of a Hadamard matrix to 3-level ones. Like the 2-level foldover designs (FODs), each new MLFOD was constructed by a half fraction and its foldover. Our Hadamard-matrix based MLFODs are compared with the conference matrix-based FODs of Jones & Nachtsheim (2013) in terms of the D-efficiencies and the maximum of the absolute values of the correlation coefficients among the columns of the model matrix. Like the latter, our designs are also definitive in the sense that the estimates of all main effects are unbiased with respect to any active second order effects. In addition, they require fewer runs and can be used to study the presence of the second-order effects more efficiently. Examples illustrating the use of our new MLFODs are given. [ABSTRACT FROM AUTHOR]

Mapping of the distribution of individual seagrass species is essential for any attempts to manage seagrass ecosystems. It is therefore important to understand how the spectra of different seagrass species vary, in order to establish their unique absorption features and how these can be utilised for mapping by making use of remote-sensing images. This paper presents measurements of the reflectance spectra between 400 and 900 nm for nine tropical species of seagrass. Continuum removal and multispectral resampling procedures were applied to the spectra. Dendrogram analysis was carried out to identify species clustering as the basis for a mapping scheme. Spectral Angle Mapper (SAM) and Spectral Information Divergence (SID) approaches were employed for the classification of seagrass species using WorldView-2 images and measured spectra as the input endmember. Classification Tree Analysis (CTA) and an image segmentation approach using CTA (Object-Based Image Analysis – OBIA) were performed as a means of comparison. The results indicate that the absorption features and overall shape of the spectra for all seagrass species are relatively similar, and implied that the major differences are attributable to the absolute reflectance values. Consequently, SAM and SID produced results of low accuracy (<30%), whereas, CTA and OBIA delivered results exhibiting higher accuracy (60–92%). The use of a spectral-based classification algorithm was ineffective for the classification and mapping of seagrass species using multispectral images. The utilisation of absolute reflectance values was beneficial for the classification of seagrass species having similar spectral shape. [ABSTRACT FROM AUTHOR]

In this paper, a new method for the interpretation of magnetic sources is developed using magnetic gradient tensor data. The total magnetisation direction of each magnetic source is estimated, and the magnetic gradient tensor is transformed into tensor data, which would be produced by the same sources with vertical magnetisation. Furthermore, the horizontal edges of the broad steep-sided magnetic sources are estimated from the ratio of the sum of absolute values of the eigenvalues (SAE) and Bzz of the transformed magnetic gradient tensor. The depth estimation of the magnetic sources is obtained using a modified Euler deconvolution method that eliminates the structural index from the equations. The process was tested on both synthetic and measured magnetic data. The results show that this method reduces considerably the effects of total magnetisation and is tolerant to the noise of the data. In addition, this method calculates vertical locations without any prior information about the structural index of the source. [ABSTRACT FROM AUTHOR]

In this paper, we propose a model based on multivariate decomposition of multiplicative – absolute values and signs – components of asset returns. In the m-variate case, the marginals for the m absolute values and the binary marginals for the m directions are linked through a 2m-dimensional copula. The approach is detailed in the case of a bivariate decomposition. We outline the construction of the likelihood function and the computation of different conditional measures. The finite-sample properties of the maximum likelihood estimator are assessed by simulation. An application to predicting bond returns illustrates the usefulness of the proposed method. [ABSTRACT FROM AUTHOR]

For every real matrix A having as an eigenvector e, the all-ones vector, an upper bound is obtained for the absolute value of its eigenvalues except, in some cases, the one associated with e. Comparisons are made between this bound and some existing bounds for stochastic matrices as well as other types of matrices such as Laplacian matrices and Randić matrices. Other examples and results are also provided. An interesting recent article 'An eigenvalue localization theorem for stochastic matrices and its application to Randić matrices', Linear Algebra Appl. 2016;505:85-96, by A. Banerjee and R. Mehatari, is useful for this present paper. [ABSTRACT FROM AUTHOR]

Dot mapping is a cartographic representation method to visualise discrete absolute values and their spatial distribution. To achieve this, dots equal in size and represented value are used. According to the dot value, a certain number of dots are used to depict a data value. These dots usually form dot clusters. The data value needs to be rounded to a multiple of the dot value. It is possible to roughly determine the visualised data value by counting the dots and multiplying this number with the dot value. As there are many parameters – dot size, dot value, map scale – to consider when designing a dot map, the manual way is very complex and time consuming. This paper presents a method to automatically create a dot representation of a dot map from given statistical data that needs no cartographic expertise. The dot representation may be combined with other elements, such as a topographic background, to form a complete map. So the algorithm can easily be integrated into the map design process. The paper refines the basic approach of automated dot mapping published earlier. The dot placement and arrangement have been improved compared to the basic method. [ABSTRACT FROM AUTHOR]

Due to Godambe (1985), one can obtain the Godambe optimum estimating functions (EFs) each of which is optimum (in the sense of maximizing the Godambe information) within a linear class of EFs. Quasi-likelihood scores can be viewed as special cases of the Godambe optimum EFs (see, for instance, Hwang and Basawa, 2011). The paper concerns conditionally heteroscedastic time series with unknown likelihood. Power transformations are introduced in innovations to construct a class of Godambe optimum EFs. A “best” power transformation for Godambe innovation is then obtained via maximizing the “profile” Godambe information. To illustrate, the KOrea Stock Prices Index is analyzed for which absolute value transformation and square transformation are recommended according to the ARCH(1) and GARCH(1,1) models, respectively. [ABSTRACT FROM AUTHOR]

Existing measures in the literature that are specifically concerned with testing and measuring independence between two continuous variables are all based on examining the definition of independence, i.e.,  FXY(x,y) =FX(x)FY(y). A new measure is constructed uniquely in this paper that uses the absolute value of first difference on adjacent ranks of one variable with respect to the other. This measure captures the degree of functional dependence attributable to the amount of randomness and the complexity of the underlying bivariate dependence structure in a commensurate way that existing coefficients are incapable of. As a test statistic of independence, this measure is shown to have comparable or better power than existing statistics against a wide range of alternative hypotheses that consist of functional and multivalued relational dependence with additive noise. [ABSTRACT FROM PUBLISHER]

In this paper, we show that the total number of distinct basic solutions generated by the simplex method using Tardos' basic algorithm is polynomially bounded in the number of constraints, the number of variables, and the maximum absolute value determinant of submatrices of a coefficient matrix. Tardos' basic algorithm generates auxiliary LP problems whose right-hand side vectors are scaled and rounded to integers. If the coefficient matrix is totally unimodular and all the auxiliary problems are nondegenerate, then the proposed simplex method is strongly polynomial. In the analysis of the algorithm, we use the recent results by Kitahara and Mizuno. [ABSTRACT FROM PUBLISHER]

Understanding graphical representations of algebraic equations, particularly graphical representations of absolute value equations, significantly improves students’ mathematical comprehension and ignites within them an appreciation of the beauty and aesthetics of mathematics. In this paper, we focus on absolute value equations of linear and quadratic expressions, by examining various cases, presenting different methods of solving them by graphical representation, exhibiting the advantage of using dynamic software such as GeoGebra in solving them, and illustrating some examples of interesting graphical solutions. We recommend that teachers take advantage of the rapid development in technology to help learners tangibly visualize the solutions of absolute value equations before proceeding to the analytical solutions. [ABSTRACT FROM PUBLISHER]