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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]

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]