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In this note, we point out several gaps in Gurudwan and Sharma (Appl. Math. Comput. 217(15):6748-6754, 2011) and Yang (Appl. Math. Comput. 218(21):10367-10369, 2012) and give the main results under weaker conditions. MSC: 47H10; 47H09; 46B20

Myocardial stiffness is a valuable clinical biomarker for the monitoring and stratification of heart failure (HF). Cardiac finite element models provide a biomechanical framework for the assessment of stiffness through the determination of the myocardial constitutive model parameters. The reported parameter intercorrelations in popular constitutive relations, however, obstruct the unique estimation of material parameters and limit the reliable translation of this stiffness metric to clinical practice. Focusing on the role of the cost function (CF) in parameter identifiability, we investigate the performance of a set of geometric indices (based on displacements, strains, cavity volume, wall thickness and apicobasal dimension of the ventricle) and a novel CF derived from energy conservation. Our results, with a commonly used transversely isotropic material model (proposed by Guccione et al.), demonstrate that a single geometry-based CF is unable to uniquely constrain the parameter space. The energy-based CF, conversely, isolates one of the parameters and in conjunction with one of the geometric metrics provides a unique estimation of the parameter set. This gives rise to a new methodology for estimating myocardial material parameters based on the combination of deformation and energetics analysis. The accuracy of the pipeline is demonstrated in silico, and its robustness in vivo, in a total of 8 clinical data sets (7 HF and one control). The mean identified parameters of the Guccione material law were \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_1=3000\pm 1700\,\hbox {Pa}$$\end{document}C1=3000±1700Pa and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =45\pm 25$$\end{document}α=45±25 (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_f=25\pm 14$$\end{document}bf=25±14, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_{ft}=11\pm 6$$\end{document}bft=11±6, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_{t}=9\pm 5$$\end{document}bt=9±5) for the HF cases and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_1=1700\,\hbox {Pa}$$\end{document}C1=1700Pa and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =15$$\end{document}α=15 (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_f=8$$\end{document}bf=8, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_{ft}=4$$\end{document}bft=4, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_{t}=3$$\end{document}bt=3) for the healthy case.

Correlation is ubiquitously used in gene expression analysis although its validity as an objective criterion is often questionable. If no normalization reflecting the original mRNA counts in the cells is available, correlation between genes becomes spurious. Yet the need for normalization can be bypassed using a relative analysis approach called log-ratio analysis. This approach can be used to identify proportional gene pairs, i.e. a subset of pairs whose correlation can be inferred correctly from unnormalized data due to their vanishing log-ratio variance. To interpret the size of non-zero log-ratio variances, a proposal for a scaling with respect to the variance of one member of the gene pair was recently made by Lovell et al. Here we derive analytically how spurious proportionality is introduced when using a scaling. We base our analysis on a symmetric proportionality coefficient (briefly mentioned in Lovell et al.) that has a number of advantages over their statistic. We show in detail how the choice of reference needed for the scaling determines which gene pairs are identified as proportional. We demonstrate that using an unchanged gene as a reference has huge advantages in terms of sensitivity. We also explore the link between proportionality and partial correlation and derive expressions for a partial proportionality coefficient. A brief data-analysis part puts the discussed concepts into practice. The authors were supported by CRG internal funds provided by the Catalan Government. I. E. was also paid by the Spanish Ministerio de Economía y Competitividad under Grant BFU2011-28575.

Motivated by the well-known result that stiffness of soft tissue is proportional to the stress, many of the constitutive laws for soft tissues contain an exponential function. In this work, we analyze properties of the exponential function and how it affects the estimation and comparison of elastic parameters for soft tissues. In particular, we find that as a consequence of the exponential function there are lines of high covariance in the elastic parameter space. As a result, one can have widely varying mechanical parameters defining the tissue stiffness but similar effective stress–strain responses. Drawing from elementary algebra, we propose simple changes in the norm and the parameter space, which significantly improve the convergence of parameter estimation and robustness in the presence of noise. More importantly, we demonstrate that these changes improve the conditioning of the problem and provide a more robust solution in the case of heterogeneous material by reducing the chances of getting trapped in a local minima. Based upon the new insight, we also propose a transformed parameter space which will allow for rational parameter comparison and avoid misleading conclusions regarding soft tissue mechanics.

In this paper we, firstly, review the main known results on systems of an arbitrary (possibly infinite) number of weak linear inequalities posed in the Euclidean space Rn (i.e., with n unknowns), and, secondly, show the potential power of this theoretical tool by developing in detail two significant applications, one to computational geometry: the Voronoi cells, and the other to mathematical analysis: approximate subdifferentials, recovering known results in both fields and proving new ones. In particular, this paper completes the existing theory of farthest Voronoi cells of infinite sets of sites by appealing to well-known results on linear semi-infinite systems. This research was partially supported by PGC2018-097960-B-C22 of the Ministerio de Ciencia, Innovación y Universidades (MCIU), the Agencia Estatal de Investigación (AEI), and the European Regional Development Fund (ERDF); by CONICET, Argentina, Res D No 4198/17; and by Universidad Nacional de Cuyo, Secretaría de Investigación, Internacionales y Posgrado (SIIP), Res. 3922/19-R, Cod.06/D227, Argentina.

The final version is published in Complex Analysis and Operator Theory, 13-No.6, (2019). Received: 8 May 2018 / Accepted: 24 December 2018 / Published online: 11 January 2019. Acknowledgment: The work of M. Ferreira, M.M. Rodrigues and N. Vieira was supported by Portuguese funds through CIDMA-Center for Research and Development in Mathematics and Applications, and FCT–Funda¸c˜ao para a Ciˆencia e a Tecnologia, within project UID/MAT/04106/2019. The work of the authors was supported by the project New Function Theoretical Methods in Computational Electrodynamics / Neue funktionentheoretische Methoden f¨ur instation¨are PDE, funded by Programme for Cooperation in Science between Portugal and Germany (“Programa de A¸c˜oes Integradas Luso-Alem˜as 2017” - DAAD-CRUP - Ação No. A-15/17 / DAAD-PPP Deutschland-Portugal, Ref: 57340281). N. Vieira was also supported by FCT via the FCT Researcher Program 2014 (Ref: IF/00271/2014). In this paper, we develop a time-fractional operator calculus in fractional Clifford analysis. Initially, we study the $L_p$-integrability of the fundamental solutions of the multi-dimensional time-fractional diffusion operator and the associated time-fractional parabolic Dirac operator. Then we introduce the time-fractional analogs of the Teodorescu and Cauchy-Bitsadze operators in a cylindrical domain, and we investigate their main mapping properties. As a main result, we prove a time-fractional version of the Borel-Pompeiu formula based on a time-fractional Stokes' formula. This tool in hand allows us to present a Hodge-type decomposition for the forward time-fractional parabolic Dirac operator with left Caputo fractional derivative in the time coordinate. The obtained results exhibit an interesting duality relation between forward and backward parabolic Dirac operators and Caputo and Riemann-Liouville time-fractional derivatives. We round off this paper by giving a direct application of the obtained results for solving time-fractional boundary value problems. UID/MAT/04106/2019. A-15/17 / DAAD-PPP IF/00271/2014 info:eu-repo/semantics/publishedVersion

This paper presents a DIRECT-type method that uses a filter methodology to assure convergence to a feasible and optimal solution of nonsmooth and nonconvex constrained global optimization problems. The filter methodology aims to give priority to the selection of hyperrectangles with feasible center points, followed by those with infeasible and non-dominated center points and finally by those that have infeasible and dominated center points. The convergence properties of the algorithm are analyzed. Preliminary numerical experiments show that the proposed filter-based DIRECT algorithm gives competitive results when compared with other DIRECT-type methods., The authors would like to thank two anonymous referees and the Associate Editor for their valuable comments and suggestions to improve the paper. This work has been supported by COMPETE: POCI-01-0145-FEDER-007043 and FCT - Fundac¸ao para a Ciência e Tecnologia within the projects UID/CEC/00319/2013 and ˆ UID/MAT/00013/2013., info:eu-repo/semantics/publishedVersion

This paper is concerned with the boundary stabilization problem of first-order hyperbolic equations with input delay. In our previous work, the same problem for parabolic equations with input delay was addressed. For the hyperbolic equation, the element of time lag is similarly replaced by a transport equation and a backstepping method is employed. However, unlike in the case of the parabolic equation, it is difficult to obtain the eigenvalues and eigenfunctions of the system operator for the hyperbolic equation. Hence, we cannot construct the target system and the controller by using the finite-dimensional control theory together. In this paper, using $$C_0$$ -semigroups for hyperbolic equations with nonlocal boundary condition, we show that the proposed controller is expressed by an abstract form in a Hilbert space so-called a predictor, and that the predictor makes sense under a condition. Further, for the inverse integral transformation, we obtain an interesting result on its continuity under the same condition. A numerical algorithm is also proposed for solving a non-standard hyperbolic equation appearing in our controller design.

The aim of this paper is to deal with the boundedness of the Hardy-Littlewood maximal operator on variable exponent Morrey spaces of an integral form. As an application of the boundedness of the maximal operator, we establish Sobolev-type inequalities for Riesz potentials $$I_{\alpha (\cdot )}f$$ of variable order $$\alpha (\cdot )$$ of functions f in variable exponent Morrey spaces of an integral form.

The paper deals with systems of linear differential equations with coefficients depending on the Markov process. Equations for particular density and the moment equations for given systems are derived and used in the investigation of solvability of initial problems and stability. Results are illustrated by examples. The paper deals with systems of linear differential equations with coefficients depending on the Markov process. Equations for particular density and the moment equations for given systems are derived and used in the investigation of solvability of initial problems and stability. Results are illustrated by examples.

This paper deals with functional equations in the form of $f(x) + g(y) = h(x,y)$ where $h$ is given and $f$ and $g$ are unknown. We will show that if $h$ is a Borel measurable function associated with characterizations of the uniform or Cauchy distributions, then there is no measurable solutions of the equation. Our proof uses a characterization of the Dirac measure and it is also applicable to the arctan equation., Comment: 7 pages, to appear in Aequationes mathematicae

In the research of optimization problems, optimality conditions play an important role. By using some derivatives, various types of necessary and/or sufficient optimality conditions have been introduced by many researchers. Especially, in convex programming, necessary and sufficient optimality conditions in terms of the subdifferential have been studied extensively. Recently, necessary and sufficient optimality conditions for quasiconvex programming have been investigated by the authors. However, there are not so many results concerned with Karush–Kuhn–Tucker type optimality conditions for non-differentiable quasiconvex programming. In this paper, we study a Karush–Kuhn–Tucker type optimality condition for quasiconvex programming in terms of Greenberg–Pierskalla subdifferential. We show some closedness properties for Greenberg–Pierskalla subdifferential. Under the Slater constraint qualification, we show a necessary and sufficient optimality condition for essentially quasiconvex programming in terms of Greenberg–Pierskalla subdifferential. Additionally, we introduce a necessary and sufficient constraint qualification of the optimality condition. As a corollary, we show a necessary and sufficient optimality condition for convex programming in terms of the subdifferential.

In this paper, D-optimal chemical balance weighing designs with three objects are considered. The error terms are assumed to form a first-order autoregressive process, which implies that the covariance matrix of the vector of errors depends on the known parameter $$\rho $$ . It is shown that the designs constructed by Katulska and Smaga (Metrika 76:393–407, 2013) are still D-optimal weighing designs with three objects under a wider interval of possible values for parameter $$\rho $$ than that considered in that paper. Those designs are also proved to be highly D-efficient designs, when D-optimal design is not known.

The purpose of this paper is to introduce the concept of fuzzy variational- like inequalities and to study the existence problem and the iterative approximation problem for solutions of certain kinds of fuzzy variational- like inequalities in Hilbert spaces. By using the general auxiliary principle technique, Ky Fan's KKM theorem, Nadler's fixed point theorem, and some new analytic techniques, some existence theorems and some iterative approximation schemes for solving this kind of fuzzy variational- like inequalities are established. The results presented in this paper are new and they generalize, improve, and unify a number of recent results.

This paper provides new characterizations for the subdifferential of the pointwise supremum of an arbitrary family of convex functions. The main feature of our approach is that the normal cone to the effective domain of the supremum (or to finite-dimensional sections of it) does not appear in our formulas. Another aspect of our analysis is that it emphasizes the relationship with the subdifferential of the supremum of finite subfamilies, or equivalently, finite weighted sums. Some specific results are given in the setting of reflexive Banach spaces, showing that the subdifferential of the supremum can be reduced to the supremum of a countable family. The research of the first author is supported by ANID-Fondecyt 1190012, Proyecto/Grant PIA AFB-170001, MICIU of Spain and Universidad de Alicante (Contract Beatriz Galindo BEA- GAL 18/00205). The second author is supported by the Research Project PGC2018-097960-B-C21 from MICINN, Spain, and by the Australian ARC—Discovery Projects DP 180100602.

In this paper we first extend from normed spaces to locally convex spaces some characterizations of denting points in convex sets. On the other hand, we also prove that in an infrabarreled locally convex space a point in a convex set is denting if and only if it is a point of continuity and an extreme point of the closure of such a convex set under the strong topology in the second dual. The version for normed spaces of the former equivalence is new and contains, as particular cases, some known and remarkable results. We also extend from normed spaces to locally convex spaces some known characterizations of the weak property (π) of cones. Besides, we provide some new results regarding the angle property of cones and related. We also state that the class of cones in normed spaces having a pointed completion is the largest one for which the vertex is a denting point if and only if it is a point of continuity. Finally we analyse and answer several problems in the literature concerning geometric properties of cones which are related with density problems into vector optimization. The authors Fernando García-Castaño and M. A. Melguizo Padial have been supported by MINECO and FEDER (MTM2017-86182-P).

We consider a fractional order viscoelasticity problem modelled by a power-law type stress relaxation function. This viscoelastic problem is a Volterra integral equation of the second kind with a weakly singular kernel where the convolution integral corresponds to fractional order differentiation/integration. We use a spatial finite element method and a finite difference scheme in time. Due to the weak singularity, fractional order integration in time is managed approximately by linear interpolation so that we can formulate a fully discrete problem. In this paper, we present a stability bound as well as a priori error estimates. Furthermore, we carry out numerical experiments with varying regularity of exact solutions at the end., Accepted by Advances in Computational Mathematics

In this paper we have given conditions on exponential polynomials $$P_{n}(s)$$ of Dirichlet type to be attained the equality between each of two pairs of bounds, called essential bounds, $$a_{P_{n}(s)}$$ , $$\rho _{N}$$ and $$b_{P_{n}(s)}$$ , $$\rho _{0}$$ associated with $$P_{n}(s)$$ . The reciprocal question has been also treated. The bounds $$a_{P_{n}(s)}$$ , $$b_{P_{n}(s)}$$ are defined as the end-points of the minimal closed and bounded real interval $$I= [ a_{P_{n}(s)},b_{P_{n}(s)} ] $$ such that all the zeros of $$P_{n}(s)$$ are contained in the strip $$I\times {\mathbb {R}}$$ of the complex plane $${\mathbb {C}}$$ . The bounds $$\rho _{N}$$ , $$\rho _{0}$$ are defined as the unique real solutions of Henry equations of $$P_{n}(s)$$ . Some applications to the partial sums of the Riemann zeta function have been also showed.

We analyse the performance of well-known evolutionary algorithms (1+1)EA and (1+$\lambda$)EA in the prior noise model, where in each fitness evaluation the search point is altered before evaluation with probability $p$. We present refined results for the expected optimisation time of the (1+1)EA and the (1+$\lambda$)EA on the function LeadingOnes, where bits have to be optimised in sequence. Previous work showed that the (1+1)EA on LeadingOnes runs in polynomial expected time if $p = O((\log n)/n^2)$ and needs superpolynomial expected time if $p = \omega((\log n)/n)$, leaving a huge gap for which no results were known. We close this gap by showing that the expected optimisation time is $\Theta(n^2) \cdot \exp(\Theta(\min\{pn^2, n\}))$ for all $p \le 1/2$, allowing for the first time to locate the threshold between polynomial and superpolynomial expected times at $p = \Theta((\log n)/n^2)$. Hence the (1+1)EA on LeadingOnes is much more sensitive to noise than previously thought. We also show that offspring populations of size $\lambda \ge 3.42\log n$ can effectively deal with much higher noise than known before. Finally, we present an example of a rugged landscape where prior noise can help to escape from local optima by blurring the landscape and allowing a hill climber to see the underlying gradient. We prove that in this particular setting noise can have a highly beneficial effect on performance., Comment: This is an extended version of a paper that appeared in the Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2018), https://doi.org/10.1145/3205455.3205595

In this paper we study vakonomic dynamics on contact systems with nonlinear constraints. In order to obtain the dynamics, we consider a space of admisible paths, which are the ones tangent to a given submanifold. Then, we find the critical points of the Herglotz action on this space of paths. This dynamics can be also obtained through an extended Lagrangian, including Lagrange multiplier terms. This theory has important applications in optimal control theory for Herglotz control problems, in which the cost function is given implicitly, through an ODE, instead of by a definite integral. Indeed, these control problems can be considered as particular cases of vakonomic contact systems, and we can use the Lagrangian theory of contact systems in order to understand their symmetries and dynamics., M. de León and M. Lainz acknowledge the partial finantial support from MINECO Grants MTM2016-76-072-P and the ICMAT Severo Ochoa project SEV-2015-0554. M. Lainz wishes to thank MICINN and ICMAT for a FPI-Severo Ochoa predoctoral contract PRE2018-083203. M.C. Muñoz-Lecanda acknowledges the financial support from the Spanish Ministerio de Ciencia, Innovación y Universidades project PGC2018-098265-B-C33 and the Secretary of University and Research of the Ministry of Business and Knowledge of the Catalan Government project 2017-SGR-932.

First-exit problems for the Brownian motion (W(t)) or general diffusion processes, have important applications. Given a boundary b(t), the distribution of the first-exit time $$\tau $$ τ has to be computed, in most cases numerically. In the inverse first-passage-time problems, the distribution of $$\tau $$ τ is given and the boundary b has to be found. The boundary and the density of $$\tau $$ τ satisfy a Volterra integral equation. Again numerical methods approximate the solution b for given distribution of $$\tau $$ τ . We propose and analyze estimators of b for a given sample $$\tau _1,\ldots ,\tau _n$$ τ 1 , … , τ n of first-exit times. The first estimator, the empirical estimator, is the solution of a stochastic version of the Volterra equation. We prove that it is strongly consistent and we derive an upper bound for its asymptotics convergence rate. Finally, this estimator is compared to a Bayesian estimator, which is based on an approximate likelihood function. Monte Carlo experiments suggests that the empirical estimator is simple, computationally manageable and outperforms the alternative procedure considered in this paper.

In this paper we will get a class of functional equations involving a countable set of terms, summed by the well known Bochner–Fejér summation procedure, which are closely associated with the set of almost periodic functions. We will show that the zeros of a prefixed almost periodic function determine analytic solutions of such a functional equation associated with it, and we will obtain other solutions which are analytic or meromorphic on a certain domain. J. M. Sepulcre was supported by PGC2018-097960-B-C22 (MCIU/AEI/ERDF, UE).

The radius of robust feasibility provides a numerical value for the largest possible uncertainty set that guarantees robust feasibility of an uncertain linear conic program. This determines when the robust feasible set is non-empty. Otherwise the robust counterpart of an uncertain program is not well-defined as a robust optimization problem. In this paper, we address a key fundamental question of robust optimization: How to compute the radius of robust feasibility of uncertain linear conic programs, including linear programs? We first provide computable lower and upper bounds for the radius of robust feasibility for general uncertain linear conic programs under the commonly used ball uncertainty set. We then provide important classes of linear conic programs where the bounds are calculated by finding the optimal values of related semidefinite linear programs (SDPs), among them uncertain SDPs, uncertain second-order cone programs and uncertain support vector machine problems. In the case of an uncertain linear program, the exact formula allows us to calculate the radius by finding the optimal value of an associated second-order cone program., 25 pages

In this paper we prove the existence of solutions of regularized set-valued variational inequalities involving Brezis pseudomonotone operators in reflexive and locally uniformly convex Banach spaces. By taking advantage of this result, we approximate a general set-valued variational inequality with suitable regularized set-valued variational inequalities, and we show that their solutions weakly converge to a solution of the original one. Furthermore, by strengthening the coercivity conditions, we can prove the strong convergence of the approximate solutions.

In this paper we consider a finite-dimensional vector space $${\mathcal {P}}$$ P over the Galois field $${\text {GF}}(2),$$ GF ( 2 ) , and the family $${\mathcal {B}}_k$$ B k (respectively, $${\mathcal {B}}_k^*$$ B k ∗ ) of all the k-sets of elements of $$\mathcal {P}$$ P (respectively, of $${\mathcal {P}}^*= {\mathcal {P}} \setminus \{0\}$$ P ∗ = P \ { 0 } ) summing up to zero. We compute the parameters of the 3-design $$({\mathcal {P}},{\mathcal {B}}_k)$$ ( P , B k ) for any (necessarily even) k, and of the 2-design $$({\mathcal {P}}^{*},{\mathcal {B}}_k^{*})$$ ( P ∗ , B k ∗ ) for any k. Also, we find a new proof for the weight distribution of the binary Hamming code. Moreover, we find the automorphism groups of the above designs by characterizing the permutations of $${\mathcal {P}}$$ P , respectively of $${\mathcal {P}}^*$$ P ∗ , that induce permutations of $${\mathcal {B}}_k$$ B k , respectively of $${\mathcal {B}}_k^*.$$ B k ∗ . In particular, this allows one to relax the definitions of the permutation automorphism groups of the binary Hamming code and of the extended binary Hamming code as the groups of permutations that preserve just the codewords of a given Hamming weight.

The authors would like to correct the errors caused by a wrong equation (A=B+z), at the end of the proof of Lemma 2.1 in the original article, which affects this lemma, two subsequent examples, as well as other statements spread along the paper.

The performance of turbo codes at the error floor region is largely determined by the effective free distance, which corresponds to the minimum Hamming weight among all codeword sequences generated by input sequences of weight two. In this paper, we study turbo codes of dimension one obtained from the concatenation of two equal codes and present an upper bound on the effective free distance of a turbo code with these parameters defined over any finite field. We do that making use of the so-called (A, B, C, D) state-space representations of convolutional codes and restrict to the case where A is invertible. A particular construction, from a linear systems point of view, of a recursive systematic convolutional code of rate 1/n so that the effective free distance of the corresponding turbo code attains this upper bound is also presented. D. Napp was partially supported by the the Universitat d’Alacant (Grant No. VIGROB-287) and Generalitat Valenciana (Grant No. AICO/2017/128). V. Herranz and C. Perea were supported by the Ministerio de Economa, Industria y Competitividad within project TIN2016-80565-R.

The coherent systems are basic concepts in reliability theory and survival analysis. They contain as particular cases the popular series, parallel and k-out-of-n systems (order statistics). Many results have been obtained for them by assuming that the component lifetimes are independent. In many practical cases, this assumption is unrealistic. In this paper, we study them by assuming a time-transformed exponential model for the joint distribution of the component lifetimes. This model is equivalent to the frailty model which assumes that they are conditionally independent given a common risk parameter (which represents the common environment risk). Under this model, we obtain explicit expressions for the system reliability function and comparison results for the main stochastic orders. We obtain both expressions from minimal path sets and those from minimal survival signatures. Some aging classes and the system residual lifetime (under different assumptions) are studied as well. JN and JM acknowledge the support received from Ministerio de Economía, Industria y Competitividad of Spain under grant MTM2016-79943-P (AEI/ FEDER,UE). JM also acknowledges the support received from the Conselleria d’Educació, Investigació, Cultura i Esport (Generalitat de la Comunitat Valenciana) under grant GV/2017/015.

In this paper it is shown that the complex functional equation $$F(z)+F(2z)=0$$ , $$z\in \varOmega :=\mathbb {C}\setminus ( -\infty ,0 ] $$ , is stable in the strong sense of Ulam. It means that given an analytic and bounded function f(z) on $$\varOmega $$ satisfying $$\left| f(z)+f(2z)\right| 0$$ , there exists an analytic solution F(z) of the above functional equation such that $$\left| f(z)-F(z)\right| 0$$ , not necessarily bounded on $$\varOmega $$ .

A real orthogonal matrix representing a rotation in four dimensions can be decomposed into the commutative product of a left- and a right-isoclinic rotation matrix. This operation, known as Cayley’s factorization, directly provides the double quaternion representation of rotations in four dimensions. This factorization can be performed without divisions, thus avoiding the common numerical issues attributed to the computation of quaternions from rotation matrices. In this paper, it is shown how this result is particularly useful, when particularized to three dimensions, to re-orthonormalize a noisy rotation matrix by converting it to quaternion form and then obtaining back the corresponding proper rotation matrix. This re-orthonormalization method is commonly implemented using the Shepperd–Markley method, but the method derived here is shown to outperform it by returning results closer to those obtained using the singular value decomposition which are known to be optimal in terms of the Frobenius norm., Fuding was provided by Ministerio de Economía y Competitividad (Grant no. DPI2017-88282-P), Ministerio de Economía y Competitividad (Grant no. MDM-2016-0656) and National Science Foundation (Grant no. 1208385).

In this paper, we consider cash management systems with multiple bank accounts described by a given particular relationship between accounts and by a linear state transition law. Since cash managers may simultaneously consider a number of possibly conflicting goals, we provide a general stochastic goal programming model that is able to handle multiple goals and also the inherent uncertainty introduced by expected cash flows. We describe in detail an instance of our general model that considers the optimization of three different criteria such as cost, risk and cash balance stability. We claim that cash balance stability is an interesting goal to deal with the inherent uncertainty of expected cash flows. We also provide useful instructions for cash managers to set the main parameters of our model in practice. Our model provides a systematic approach to multiobjective cash management that is ready to be implemented in decision support systems for cash management., This work has been partially funded by Generalitat de Catalunya (2017 SGR 172), AI4EU (H2020-825619), LOGISTAR (H2020-769142).

In this paper, we extend the vertical modeling approach for the analysis of survival data with competing risks to incorporate a cure fraction in the population, that is, a proportion of the population for which none of the competing events can occur. The proposed method has three components: the proportion of cure, the risk of failure, irrespective of the cause, and the relative risk of a certain cause of failure, given a failure occurred. Covariates may affect each of these components. An appealing aspect of the method is that it is a natural extension to competing risks of the semi-parametric mixture cure model in ordinary survival analysis; thus, causes of failure are assigned only if a failure occurs. This contrasts with the existing mixture cure model for competing risks of Larson and Dinse, which conditions at the onset on the future status presumably attained. Regression parameter estimates are obtained using an EM-algorithm. The performance of the estimators is evaluated in a simulation study. The method is illustrated using a melanoma cancer data set.

Inspired by the papers by Abbas, Aczel and by Chudziak and Tabor, we consider the problem of existence and uniqueness of extensions for the generalized Pexider equation $$k(x+y)=l(x)+m(x)n(y) \;\;\; {\rm for} \;\;\; (x,y)\in D,$$ where D is a nonempty open subset of a normed space. We show that the connectedness of D, assumed in the mentioned above papers, can be weakened.