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Assume that A and G are finite groups of coprime orders such that A acts on G via automorphisms. Let p be a prime. The following coprime action version of a well-known theorem of Ito about the structure of a minimal non-p-nilpotent groups is proved: if every maximal A-invariant subgroup of G is p-nilpotent, then G is p-soluble. If, moreover, G is not p-nilpotent, then G must be soluble. Some earlier results about coprime action are consequences of this theorem.

We complete a gap in the proof that exceptional polynomials are complete orthogonal systems in the associated Hilbert spaces.

Transformation plays a significant role in solving hydrological problems. In response to the comment on Singh and Das (2015) by Deng et al. (2015) regarding the transformation, boundary conditions and subsequent analytical solution of advection dispersion equation in semi-infinite heterogeneous porous media, it is argued that the transformation used by Singh and Das (2015) for finding the analytical solution is correct and mathematically valid. Also, the different expression of f ( mt ) used to obtain the solution are explained with their physical relevance in the field.

The Kalman-Yakubovich-Popov (KYP) Lemma, giving the frequency-domain criteria for solvability of LQR problems and feasibility of related LMIs and Lur'e-Riccati equations, is undoubtedly one of the cornerstone results in modern control theory. Numerous applications of the KYP lemma in nonlinear and robust control motivated its extension to systems with distributed parameters. Unlike the finite-dimensional case, where the KYP lemma admits elegant proofs by means of algebraic techniques and methods from convex analysis, a prerequisite for its infinite-dimensional extensions is feasibility of the corresponding LQR problem, resulting on assumptions of exponential or L 2 -stabilizability. This property is restrictive and not easily verifiable for general infinite-dimensional systems. Being quite natural in the problems of absolute stability, it seems unnecessary in other applications of the KYP lemma which require only solvability of the operator inequality, but not positivity of its solution, such as e.g. instability or dichotomy criteria. In the present paper we show, that in the “strict” or coercive case the KYP lemma retains its validity, replacing stabilizability assumption with some technical assumption which holds, for instance, whenever the linear system is exponentially dichotomic.

A Galerkin-based family of numerical formulations is presented for solving nonlinear optimal control problems. This paper introduces a family of direct methods that calculate optimal trajectories by discretizing the system dynamics using Galerkin numerical techniques and approximate the cost function with Gaussian quadrature. In this numerical approach, the analysis is based on L 2 -norms. An important result in the theoretical foundation is that the feasibility and consistency theorems are proved for problems with piecewise continuous controls. Galerkin methods may be formulated in a number of ways that allow for eficiency and/or improved accuracy while solving a wide range of optimal control problems with a variety of state and control constraints. Numerical formulations using Legendre test functions are derived. One formulation allows for a weak enforcement of boundary conditions, which imposes end conditions only up to the accuracy of the numerical approximation itself. Finally, a numerical example is shown to demonstrate the exponential convergence of Galerkin optimal control.

Adaptive Posicast Controller that is robust to delay-mismatch is introduced in this paper. Inspired from a recent result on guaranteed delay margins in adaptive control, the original adaptive laws of the above mentioned controller are modified using projection to compensate the uncertainty in the input delay. It is conjectured and shown in simulations that even though the assumed upper bound for the delay value is exceeded, Adaptive Posicast Controller with projection algorithm keeps all the system signals bounded.

In this paper, weighted stochastic gradient (WSG) algorithms for ARX models are proposed by modifying the standard stochastic gradient identification algorithms. In the proposed algorithms, the correction term is a weighted term of the correction terms of the standard SG algorithm in the current and last recursive steps. In addition, a latest estimation based WSG (LE-WSG) algorithm is also established. The convergence performance of the proposed LE-WSG algorithm is then analyzed. It is shown by a numerical example that both the WSG and LE-WSG algorithms can possess faster convergence speed and higher convergence precision compared with the standard SG algorithms if the weighting factor is appropriately chosen.

A generalized approach to design a proportional and derivative system faults fuzzy observer for continuous-time nonlinear systems described in the Takagi-Sugeno descriptor statespace form is presented in the paper. Considering measurable premise variables, the problem addressed is formulated as an enhanced concept to descriptor systems design, implying the asymptotic convergence both the state observer error as fault estimate error. Presented in the sense of the second Lyapunov method, an associated structure of linear matrix inequalities is outlined to possess the global observer asymptotic dynamic properties with compiling the local insiders by inference through the membership functions equal those of the system model. The proposed design conditions are verified by simulations in the numerical illustrative example.

The problem of assigning in part common left eigenvector assignment by the state feedback control of linear multi-input systems is considered in the paper. Based on linear matrix inequalities characterization, the exposition of the problem is formulated to handle a common left eigenvector for switched modes. Limited by preexisting degrees of freedom, which factually makes mutually contingent subsets of the closed-loop eigenvalue spectrum of each mode, the design conditions for in part common left eigenvector assignment of all modes are derived in the terms of linear matrix inequalities. The procedure provides a way available in linear switched control system design while the state-space control structures take standard forms. An example is included to assess the properties of the technique and its application.

RD is absent from the dimensional Eqs. (1)–(6) in Ref. [1], which we included in Ref. [1] as reference to the study of the related flow behaviors of the nanofluid. These equations constitute the governing flow equations of nanofluid over a stretching sheet in Ref. [1], and these dimensional equations are independent from the entropy generation Eq. (1) from Ref. [1] with RD as mentioned above. Entropy generation measures the degree or level of available (existing) irreversibilities within a process. The entropy generation equation is an extension from the governing flow Eqs. (1)–(6).

In this note we show that the presented proof of [1, th. 12] , being based on a false statement appearing in this proof, is not viable for all of the proclaimed values of the involved parameters. We also determine necessary and sufficient conditions for those parameters, which provides that the considered statement, and therefore [1, th. 12] itself, still remains valid.

It seems that the results obtained by the so-called Khater method contain computational or print errors. We look at this issue from a different point of a view, namely, from a theoretical side. We prove our claim by a formal direct approach instead of back substitution (trial and error) approach.

In the paper the second order half-linear delay differential equation ( r ( t ) | u ' ( t ) | α - 1 u ' ( t ) ) ' + p ( t ) | u ( ? ( t ) ) | α - 1 u ( ? ( t ) ) = 0 , α 1 is studied under the condition ? ∞ r - 1 / α ( t ) d t < ∞ . The oscillation criterion proved by Sun and Meng (2006, Theorem 2.2) is carefully examined and improved by simplifying and sharpening the estimates used in the original proof and removing unnecessary assumptions. Among others, using elementary arguments we show that an arbitrary positive nondecreasing function ? from this criterion can be safely and with no loss of generality replaced by a constant function. An extension to other related equations, such as neutral equations is also provided.

This paper presents a new method to calculate the feedback control gain for a class of multivariable bilinear system, and also applied this method on the control of two sections of paper-making process with disturbance. The robust H∞ control problem is to design a state feedback controller such that the robust stability and a prescribed H∞ performance of the resulting closed-loop system are ensured. The controller turns out to be robust with respect to the disturbance in the plant. Utilizing the Schur complement and some variable transformations, the stability conditions of the multivariable bilinear systems are formulated in terms of Lyapunov function via the form of linear matrix inequality (LMI). The gain of controller will be calculated via LMI. Finally, the application examples of a headbox section and a dryer section of paper-making process are used to illustrate the applicability of the proposed method.

In the present work, the analytical potential of laser induced breakdown spectroscopy (LIBS) for the discrimination of paper types and prints made by digital printers on these papers was assessed. Six different paper types (including standard office papers, color paper and non-bleached paper), and eight printers (including laser and inkjet, as well as color and black printers) were included in the study. Only one or two laser shots were delivered to each sample in order to cause minimal sample destruction and provide maximum spatial resolution. The statistical evaluation of LIBS spectra was performed by multiple methods including three comparative functions (linear correlation, sum of squared deviations and overlapping integral) as well as two advanced statistical methods (multivariate curve resolution alternating least squares (MCR-ALS) combined with classification tree and discriminant analysis (DA)). The best classification results were obtained with the newly introduced MCR-ALS/DA approach, which proved to be 96.3% accurate in the identification of the paper type and 83.3% accurate in the identification of the printer type, based on the LIBS spectrum collected from just a single laser shot to the sample. It was found that the UV part of the LIBS spectrum can be used most efficiently for the discrimination.

Aiming at the problem that paper smoothness cannot be measured on line, a new method for soft measurement of paper smoothness is put forward on the basis of studying paper quantization distribution. A soft measurement system is established, by which, paper quantization noise is processed by time–frequency analysis and non-linear transformation, so that online paper smoothness can be obtained through a Radial Basis Function Neural Networks (RBFNNs). The results show that this soft computing method is a feasible way with high measuring accuracy.

This paper provides a corrected formulation to the mixed integer programming model proposed by Aydogan et al. (2012) 1. They proposed a genetic algorithm to learn fuzzy rules for a fuzzy rule-based classification system and developed a Mixed Integer Programming model (MIP) to prune the generated rules by selecting the best set of rules to maximize predictive accuracy. However, their proposed MIP formulation contains errors, which are described in this technical note. We develop corrections and improvements to the original formulation and test it with non-parametric statistical tests on the same data sets used to evaluate the original model. The statistical analysis shows that the results of the correction formulation are significantly different from the original model.

We use Regev's double centralizer theorem from [7] to study invariants of matrices with group actions. This theory then has applications to trace identities and Poincare series.

Finite horizon anisotropy-based multicriteria filtering problem for the linear varying discrete time system has been solved. Multidimensional input disturbance consists of groups of signals, each group is characterized by its inaccurately given information theory properties. For that mathematical model, the bounded real lemma for an anisotropic norm has been proved. If the subsystem norms are limited to specific values, a sufficient condition for multicriteria estimator existence has been obtained. An estimation algorithm is based on recursion solving of linear difference matrix inequalities simultaneously with the inequality of a special type.

The problem of synthesizing time optimal “feedback” control for a single input linear time invariant system with constrained control input is considered. It is well known that the optimal open loop control is bang-bang and the switching takes place according to some switching surfaces in the state space. A parametric representation of the switching surfaces using Pontryagins’ minimum principle (PMP) is first computed. This parametric representation is in general not semi-algebraic. For such situations, Chebyshev polynomials are used to approximate the switching surfaces. Then, a Grobner basis based elimination algorithm is used to find an implicit representation for approximated switching surfaces. The computed representation is used to construct a state feedback based nested switching logic which will achieve a near time optimal state transfer of system states to the origin.

Computation of the stability limit of systems with time delay is essential in many research and industrial applications. Most of the computational methods consider the exact model of the system, and do not take into account the uncertainties. However, the stability charts are highly sensitive to the change of input parameters, such as eigenfrequency and timedelay. A method has been developed to determine the robust stability limits of delayed dynamical systems, which is insensitive to the parameter fluctuations of the dynamic system. The method is combined with an eficient numerical method, the so-called Multi-Dimensional Bisection Method and the resultant robust stability limits are compared by analytical results.

Control-Relevant Identification (CRI) proposes to generate models that are suitable to the control problem at hand, creating synergy between the control and identification algorithms. For model predictive control (MPC), it is recommended to use a model obtained by the minimization of a multi-step ahead prediction error cost function. One way of minimizing the cost function is applying the Levemberg-Marquardt (LM) optimization algorithm, provided the identification data set is not ill-conditioned. A second and more interesting approach is the line search method known as PLS-PH. In this work, a regularization-based line search method denoted as EN-PH is proposed to perform the minimization of the identification cost function. Two examples are presented to compare the predictive performance of models obtained using Least Squares, LM, PLS-PH and EN-PH. The examples have shown that the models fitted with EN-PH outperform the other models.

In this paper, we introduce some notions of invariancy for the Ricci tensor on real hypersurfaces in complex two-plane Grassmannians G 2 ( C m + 2 ) , namely, F -invariant and invariant Ricci tensor. Using these notions, we give non-existence theorem and characterization for the special case among the real hypersurfaces of Type ( A ) in G 2 ( C m + 2 ) , respectively. Here the distribution F is defined by F = [ ξ ] ∪ D ⊥ where D ⊥ = Span { ξ 1 , ξ 2 , ξ 3 } and [ ξ ] = Span { ξ } .

In this paper we introduce a notion of a t-filter on residuated lattices which is a generalization of several special types of filters. We provide some basic properties of t-filters and show how particular results about special types of filters (e.g. Extension property, Triple of equivalent characteristics, and Quotient characteristics) are uniformly covered by this simple general framework.

We show that the main results in the recent paper [4] by Sadiq Basha (2012) are not real generalizations but particular cases of existing fixed point theorems in the literature.

This paper outlines Binomial and Poisson distributions which are both used to measure the occurrence of a number of random events within a certain period.

This work seeks to obtain valuable products through an integral exploitation of lignocellulosic residues generated by agriculture, such as olive tree prunings. These sorts of residues are studied as alternative sources for lignocellulosic raw material in the paper industry and the black liquors generated could be used for several purposes, including the production of bioethanol. To reach these goals, a central composite factorial design was used to study the influence of operational variables [temperature (155, 170 and 185 ◦C), cooking time (40, 65 and 90min) and soda concentration (10, 14 and 18%)], on pulps and paper sheets properties obtained from olive tree prunings, likewise black liquors generated in these pulping processes were set up to enable both yeast strains (Saccharomyces cerevisiae CECT 1170 and Pichia stipitis CECT 1922) to be capable of doing an alcoholic fermentation at 30 and 26 ◦C respectively, 5.5 pH, and under 150 rpm shaking. The results were similar to those obtained with other agricultural residues which are alternative sources for the paper industry. The best values of the physicochemical properties of cellulose pulps, such as Kappa number (31.98) or viscosity (716.11mL/g) and the paper sheets, such as tensile index (608m) or tear index (1.655mNm2/g), were reached operating to high values of soda concentration and temperature and slight cooking times. However, the black liquors of this study were not an optimal medium for the bioethanol production. It might be due to the important presence of inhibitors in the fermentation processes, such as 5hydroxymethyl-furfural.

In the present paper we studied the Voronovskaya type theorem for modified Gamma operators presented by A. Izgi in the paper ''Voronovskaya type asymptotic approximation by modified Gamma operators'' [Applied Mathematics and Computation 217 (2011) 8061-8067]. We show that this theorem is not true. We present a correct form of this theorem and its proof. Furthermore, we obtain an error estimate for modified Gamma operators.

Five ratios R H , R T , S H , S T and S Z derived from the three-part division of a set of sources in h -core, h -tail and uncited sources are defined. Dynamic changes in the three independent ratios R H , S H and S Z are studied for six selected topics. Data about these topics are obtained from the Web of Science for scientific papers and Derwent Innovations Index for technical patents. It is observed that all R H - and S H -values decrease when the time span widens, while S Z stays the same or increases; and that all R H - and S H -values for papers are larger than the corresponding values for patents. The shifted Lotka distribution is used in a theoretical interpretation of these empirical phenomena.

The citation distribution of papers of selected individual authors was analyzed using five mathematical functions: power-law, stretched exponential, logarithmic, binomial and Langmuir-type. The former two functions have previously been proposed in the literature whereas the remaining three are novel and are derived following the concepts of growth kinetics of crystals in the presence of additives which act as inhibitors of growth. Analysis of the data of citation distribution of papers of the authors revealed that the value of the goodness-of-the-fit parameter R 2 was the highest for the empirical binomial relation, it was high and comparable for stretched exponential and Langmuir-type functions, relatively low for power law but it was the lowest for the logarithmic function. In the Langmuir-type function a parameter K , defined as Langmuir constant, characterizing the citation behavior of the authors has been identified. Based on the Langmuir-type function an expression for cumulative citations L relating the extrapolated value of citations l 0 corresponding to rank n = 0 for an author and his/her constant K and the number N of paper receiving citation l ≥ 1 is also proposed.

We illustrate the Efficient Forward Filtering Backward Smoothing (EFFBS) algorithm proposed by Khreich et al. (2010) for estimation of hidden Markov models. The algorithm is aimed at reducing the amount of memory required by the Baum-Welch recursions, while having the same complexity in terms of number of operations. In implementing the EFFBS algorithm we found a numerical problem that limits its applicability. We discuss this problem in detail, providing some possible explanations of the causes of the error, together with two illustrative examples.

This appendix collects some material on the cohomology of discrete subgroups of Lie groups and the theory of their representation varieties to provide background for the results of Sin and Thompson (2010, 2013) in [22,23] .

Singh and Arnab (2010) presented a bias adjustment to the jackknife variance estimator of Rao and Sitter (1995) in the presence of non-response. In their paper, they obtained a second-order approximation of the bias of the Rao-Sitter variance estimator and then proposed a bias-adjusted estimator based on this approximation. To compare their proposed variance estimator to various other variance estimators, they performed a simulation study and showed that their variance estimator is superior to the Rao-Sitter variance estimator. In fact they showed that the Rao-Sitter variance estimator suffers from severe underestimation. These results contradict those in the literature, which indicate that the Rao-Sitter variance estimator suffers from a positive bias if the sampling fractions are not negligible; see Rao and Sitter (1995) , Lee et al. (1995) and Haziza and Picard (2011) . Because of this contradiction, we felt that a further investigation was warranted. In this paper, we attempt to recreate the results of Singh and Arnab (2010) and, in fact, show that their second order approximation to the bias of the Rao-Sitter variance estimator is incorrect and that their simulation results are also questionable.

In this paper, an observer-based fault detection scheme is developed for one special kind of distributed parameter systems (DPS) of hyperbolic type. An alternative order reduction approach is utilized to handle the infinite-dimensional nature of DPS for fault detection purpose, compared with the existing modal analysis based method which relies on the existence of eigen-decomposition of the spatial differential operator. The developed fault detection scheme is finally implemented on a simulation model of the paper drying process in paper production industry, and the achieved results demonstrate the effectiveness of the proposed scheme.

Isocode card and IsoCode ID Sample Registration Matrix (Schleicher and Schuell BioScience Inc.) are different paper devices chemically treated that keep sample DNA safe from degradation, allowing for the indefinite storage of DNA at ambient temperatures. In this study, blood was collected on Isocode card while saliva, sperm were collected on IsoCode ID. We also tried to verify the effect of collecting urine on Isocode ID. All samples (belonging to the same male donor) were analyzed after 1 day, 1-5 months since their application on the paper.

This paper examines zero-sum games that are based on a cyclic preference relation defined over undistinguished actions. For each of these games, the set of Nash equilibria is characterized. When the number of actions is odd, a unique Nash equilibrium is always obtained. On the other hand, in the case of an even number of actions, every such game exhibits an infinite number of Nash equilibria. Our results give some insights as to the robustness of Nash equilibria with respect to perturbations of the action set.

In this paper, we examine and correct various results relating to estimation of a Pareto distribution in the presence of outliers according to a model introduced by Dixit and Jabbari Nooghabi (2011) [1] and further studied by Dixit and Jabbari Nooghabi (2011) [2] . In particular, Dixit and Jabbari Nooghabi (2011) [2] state that the maximum likelihood estimators for the parameters appearing in their model do not exist. We show that these estimators can in fact exist, and we present and illustrate a method for determining them when they do. Two numerical illustrations using actual insurance data are included.

We show that paper folding words contain arbitrarily large abelian powers.

In this paper, we determine the modularities of asymptotically optimal towers found by Maharaj and Wulftange in 2005. This is also a continuation of the work of Elkies in 2002.

A left canonical factorization theorem for rational matrix functions relative to the unit circle is presented. The result is a time invariant version of a recent strict LU factorization theorem for certain semi-separable operators, due to Dewilde (2012) [6]. Explicit formulas for the factors are also given. The theorem is proved, first by using the state space method of Dewilde (2012) [6], and next by using an operator theory approach. In both cases the main part of the proof concerns rational matrix functions that are unitary on the unit circle. © 2012 Royal Dutch Mathematical Society (KWG).

In this paper, we describe the development of a system for evaluating an specific quality characteristic of recycled paper sheets using techniques of image analysis and pattern recognition. We call Bumpiness the phenomenon of interest, which is new in the literature on paper quality. This phenomenon is characterized by the appearance of macroscopic undulations on the paper sheet surface that may emerge shortly or some time after its production. We explore the detection and measurement of this defect by means of computer vision and statistical pattern recognition techniques that may allow early detection at the production site. Our goal is to give an scalar continuous measure of Bumpiness. We propose features computed from Gabor filter banks (GFB) and discrete wavelet transforms (DWT) for the characterization of paper sheet surface Bumpiness in recycled paper images. The starting point is to state the problem as a classification of the paper sheet images into two classes: low and high Bumpiness. In this setting we obtain, with both proposed texture modelling approaches (GFB and DWT), classification accuracies comparable to the agreement between human observers. The best performance is obtained using DWT features. Finally, we propose as the scalar index of Bumpines the fisher discriminant analysis (FDA) function defined on the space of the best features for the classification task. We perform an innovative validation process of this Bumpiness index, based on the ordering of random pairs of images, obtaining a very high agreement with the human observers.

The paper deals with a statistical study on the thermal degradation of some old paper supports. The experimental data permit establishment of some regression models, which describe the dependence between the half time and the temperature at which the paper support is kept and, respectively, between the exposure time of the paper supports to a certain temperature and the absorbency value of a characteristic peak, representative for the paper support.

Using advanced machine learning techniques as an alternative to conventional double-entry volume equations known as classical allometric models , regression models of the inside-bark volume (dependent variable) for standing Eucalyptus globulus trunks (or main stems) have been built as a function of the following three independent variables: age, height and outside-bark diameter at breast height ( D ). The allometric models of volume, biomass or carbon support the estimation of carbon storage in forests and agroforestry systems. On one hand, this paper presents the construction of allometric models of the inside-bark volume for E. globulus trees. On the other hand, the experimental observed data (age, height, D and inside-bark volume) for 142 trees ( E. globulus ) were measured and a nonlinear model was built using a data-mining methodology based on multivariate adaptive regression splines (MARS) technique and multilayer perceptron networks (MLP) for regression problems. Coefficients of determination and Furnival’s indices indicate the superiority of the MARS technique over the allometric regression models and the MLP network. The agreement of the MARS model with observed data confirmed the good performance of the same one. Finally, conclusions of this innovative research are exposed.

In a recent paper, K. Soundararajan showed, roughly speaking, that the integers smaller than x whose prime factors are less than y are asymptotically equidistributed in arithmetic progressions to modulus q, provided that y^{4\sqrt{e}-\delta} \geq q and that y is neither too large nor too small compared with x. We show that these latter restrictions on y are unnecessary, thereby proving a conjecture of Soundararajan. Our argument uses a simple majorant principle for trigonometric sums to handle a saddle point that is close to 1., Comment: 18 pages

We introduce an algorithm for approximating a 2-manifold 3D mesh by a set of developable surfaces. Each developable surface is a generalized cylinder represented as a strip of triangles not necessarily taken from the original mesh. Our algorithm is automatic, creates easy-to-assemble pieces, and provides L"@K global error bounds. The algorithm consists of three stages. In the first stage, the mesh is segmented into meaningful components. The second stage approximates each of the mesh components in 3D by a set of triangle strips with smooth (non-jagged) boundaries that guarantee a maximal user-defined error relative to the original mesh. Finally, these strips are unfolded to the plane, resulting in flat patterns, which may be cut and assembled from paper. The approximation quality is controlled by a user-supplied parameter specifying the allowed Hausdorff distance between the input mesh and its piecewise-developable approximation. The strips generated by our algorithm may be parameterized to conform with the parameterization of the original mesh, if given, to facilitate texture mapping. We demonstrate this by physically assembling paper-craft models from the strips generated by our algorithm when run on several polygonal 3D mesh data sets.

In this paper, we focus on the proposed algorithms to solve a linear programming problem with the convex combination of the max–min and the max–average composition and the max–star composition, respectively. They have been proposed by Ghodousian and Khorram [A. Ghodousian, E. Khorram, Solving a linear programming problem with the convex combination of the max–min and the max–average fuzzy relation equations, Appl. Math. Comput. 180 (2006) 411–418] and Khorram et al. [E. Khorram, A. Ghodousian, A. Abbasi Molai, Solving linear optimization problems with max–star composition equation constraints, Appl. Math. Comput. 179 (2006) 654–661], respectively. Firstly, we show that the “Tabular method algorithm” in the first paper and the “First procedure” in the second paper may not lead to the optimal solutions of the two models in some cases. Secondly, we generalize the proposed algorithm by Abbasi Molai and Khorram [A. Abbasi Molai, E. Khorram, A modified algorithm for solving the proposed models by Ghodousian and Khorram and Khorram and Ghodousian, Appl. Math. Comput. 190 (2007) 1161–1167] to solve the two models. In fact, it modifies the presented algorithms in the two papers. Finally, some numerical examples are given to illustrate the purposes.

The present comment concerns some doubtful results included in the above papers.