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The establishment of a reference method for the determination of the allergen protein content in a processed food material has been explored. An analytical approach was developed to enable the comparability of food allergen measurement results expressed in a decision-relevant manner. A proof of concept is here presented, resulting in quantity values for the common measurand, namely ‘mass of total allergen protein per mass of food’. The quantities are determined with SI traceability to enable the comparability of reported results. A method for the quantification of total milk protein content in an incurred baked food at a concentration level clinically relevant is presented. The strategy on how to obtain the final analytical result is outlined. Challenges associated with this method are discussed, in particular the optimal extraction of the marker proteins, the complete digestion and release of the peptides in an equimolar fashion, the use of conversion factors to translate the amount of measured proteins into total milk protein and the estimation of the uncertainty contributions as well as of the combined uncertainty of the final result. The implementation of such a reference method for the determination of the total allergen content in a processed food is an important step, which will provide comparable measurement data of relevance to risk assessors. Graphical abstract Electronic supplementary material The online version of this article (10.1007/s00216-020-02959-0) contains supplementary material, which is available to authorized users.

This paper studies the one-to-one two-sided marriage model (Gale and Shapley 1962). If agents’ preferences exhibit mutually best (i.e., each agent is most preferred by her/his most preferred matching partner), there is a unique stable matching without rank gaps (i.e., in each matched pair the agents assign one another the same rank). We study in how far this result is robust for matching markets that are “close” to mutually best. Without a restriction on preference profiles, we find that natural “distances” to mutually best neither bound the size of the core nor the rank gaps at stable matchings. However, for matching markets that satisfy horizontal heterogeneity, “local” distances to mutually best provide bounds for the size of the core and the rank gaps at stable matchings., The first draft of this paper was written while F. Klijn was LFUI guest professor at Innsbruck University. He gratefully acknowledges the hospitality of Innsbruck University and support from AGAUR-Generalitat de Catalunya (2017-SGR-1359), Ministerio de Ciencia, Innovación y Universidades (ECO2017-88130-P), and the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2015-0563 and CEX2019-000915-S). C. Kah and M. Walzl thank the Austrian Science Foundation (FWF) for support through project P-28632-G27 and SFB63.

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 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.

Based on Bohr’s equivalence relation for general Dirichlet series, in this paper we connect the families of equivalent exponential polynomials with a geometrical point of view related to lines in crystal-like structures. In particular we characterize this equivalence relation, and give an alternative proof of Bochner’s property referring to these functions, through this new geometrical perspective. The first author’s research was partially supported by PGC2018-097960-B-C22 (MCIU/AEI/ERDF, UE).

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.

This paper presents a full generalization of Bohr’s equivalence theorem for the case of almost periodic functions, which improves a recent result that was uniquely formulated in the case of existence of an integral basis for the set of exponents of the associated Dirichlet series. J.M. Sepulcre research was partially supported by MICIU of Spain under Project Number PGC2018-097960-B-C22.

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

Two important issues characterize the design of bootstrap methods to construct confidence intervals for the correlation between two time series sampled (unevenly or evenly spaced) on different time points: (i) ordinary block bootstrap methods that produce bootstrap samples have been designed for time series that are coeval (i.e., sampled on identical time points) and must be adapted; (ii) the sample Pearson correlation coefficient cannot be readily applied, and the construction of the bootstrap confidence intervals must rely on alternative estimators that unfortunately do not have the same asymptotic properties. In this paper it is argued that existing proposals provide an unsatisfactory solution to issue (i) and ignore issue (ii). This results in procedures with poor coverage whose limitations and potential applications are not well understood. As a first step to address these issues, a modification of the bootstrap procedure underlying existing methods is proposed, and the asymptotic properties of the estimator of the correlation are investigated. It is established that the estimator converges to a weighted average of the cross-correlation function in a neighborhood of zero. This implies a change in perspective when interpreting the results of the confidence intervals based on this estimator. Specifically, it is argued that with the proposed modification of the bootstrap, the existing methods have the potential to provide a useful lower bound for the absolute correlation in the non-coeval case and, in some special cases, confidence intervals with approximately the correct coverage. The limitations and implications of the results presented are demonstrated with a simulation study. The extension of the proposed methodology to the problem of estimating the cross-correlation function is straightforward and is illustrated with a real data example. Related applications include the estimation of the autocorrelation function and the periodogram of a time series. This work was supported by Spain Ministry of Science, Innovation and Universities grant number RTI2018-093874-B-100.

Given a smooth complex toric variety we will compare real Lagerberg forms and currents on its tropicalization with invariant complex forms and currents on the toric variety. Our main result is a correspondence theorem which identifies the cone of invariant closed positive currents on the complex toric variety with closed positive currents on the tropicalization. In a subsequent paper, this correspondence will be used to develop a Bedford-Taylor theory of plurisubharmonic functions on the tropicalization., Final version, 50 pages, 1 figure, to appear in Mathematische Zeitschrift

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.

In this paper, we study flag codes on the vector space $${{\mathbb {F}}}_q^n$$ F q n , being q a prime power and $${{\mathbb {F}}}_q$$ F q the finite field of q elements. More precisely, we focus on flag codes that attain the maximum possible distance (optimum distance flag codes) and can be obtained from a spread of $${{\mathbb {F}}}_q^n$$ F q n . We characterize the set of admissible type vectors for this family of flag codes and also provide a construction of them based on well-known results about perfect matchings in graphs. This construction attains both the maximum distance for its type vector and the largest possible cardinality for that distance.

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.

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 $$\varOmega $$ .

This paper analyzes the Lipschitz behavior of the feasible set mapping associated with linear and convex inequality systems in $${\mathbb {R}}^{n}$$ R n . To start with, we deal with the parameter space of linear (finite/semi-infinite) systems identified with the corresponding sets of coefficient vectors, which are assumed to be closed subsets of $${\mathbb {R}} ^{n+1}$$ R n + 1 . In this framework the size of perturbations is measured by means of the (extended) Hausdorff distance. A direct antecedent, extensively studied in the literature, comes from considering the parameter space of all linear systems with a fixed index set, T, where the Chebyshev (extended) distance is used to measure perturbations. In the present work we propose an appropriate indexation strategy which allows us to establish the equality of the Lipschitz moduli of the feasible set mappings in both parametric contexts, as well as to benefit from existing results in the Chebyshev setting for transferring them to the Hausdorff one. In a second stage, the possibility of perturbing directly the set of coefficient vectors of a linear system leads to new contributions on the Lipschitz behavior of convex systems via linearization techniques.

Our paper is focused on spaces of generalized almost periodic functions which, as in classical Fourier analysis, are associated with a Fourier series with real frequencies. In fact, based on a pertinent equivalence relation defined on the spaces of almost periodic functions in Bohr, Stepanov, Weyl and Besicovitch’s sense, we refine the Bochner-type property by showing that the condition of almost periodicity of a function in any of these generalized spaces can be interpreted in the way that, with respect to the topology of each space, the closure of its set of translates coincides with its corresponding equivalence class. The first author’s research was supported by PGC2018-097960-B-C22 (MCIU/AEI/ERDF, UE).

Published 07 September 2021: Correction to: On the Convergence of Multi-Level Hermite&-Padé Approximants for a Class of Meromorphic Functions (Mediterr. J. Math. 18, 219 (2021). In the original publication, the surname of the Author "L. G. González Ricardo" was inadvertently swapped. The correct Author group has been provided below: L. G. González Ricardo, G. López Lagomasino and S. Medina Peralta The present paper deals with the convergence properties of multi-level Hermite-Padé approximants for a class of meromorphic functions given by rational perturbations with real coefficients of a Nikishin system of functions, and study the zero location of the corresponding multiple orthogonal polynomials.

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 give log-convexity properties for solutions to discrete Schrödinger equations with different discrete versions of Gaussian decay at two different times. For free evolutions, we use complex analysis arguments to derive these properties, while in a perturbative setting we use a preliminar log-convexity statement in order to conclude our result. The author was supported by the projects PGC2018-094528-B-I00 funded by (AEI/FEDER, UE) and acronym “IHAIP,” ERCEA Advanced Grant 669689-HADE, and the Basque Government IT641-13

In this paper we will give a short and elementary proof that critical relations unfold transversally in the space of rational maps., Comment: Published version (open access)

In this paper, we consider a confined physical scenario to prove the global existence of smooth solutions with bounded density and finite energy for the inviscid incompressible porous media (IPM) equation. The result is proved using the stability of stratified solutions, combined with an additional structure of our initial perturbation, which allows us to get rid of the boundary terms in the energy estimates., The authors are supported by Spanish National Research Project MTM2014-59488-P and ICMAT Severo Ochoa Projects SEV-2011-0087 and SEV-2015-556, the grant ERC Grant 7882250-NONFLU. AC was partially supported by the ERC Grant 307179-GFTIPFD and DL was supported by La Caixa-Severo Ochoa grant.

Weighted Sobolev spaces play a main role in the study of Sobolev orthogonal polynomials. The aim of this paper is to prove several important properties of weighted Sobolev spaces: separability, reflexivity, uniform convexity, duality and Markov-type inequalities. Francisco Marcellán: Supported in part by two Grants from Ministerio de Economía y Competitividad (MTM2012-36732-C03-01 and MTM2015-65888-C4-2-P), Spain. Yamilet Quintana: Supported in part by a Grant from Ministerio de Economía y Competitividad (MTM2012-36732-C03-01), Spain. José M. Rodríguez: Supported in part by three Grants from Ministerio de Economía y Competititvidad, Agencia Estatal de Investigacin (AEI) and Fondo Europeo de Desarrollo Regional (FEDER) (MTM2013-46374-P, MTM2016-78227-C2-1-P and MTM2015-69323-REDT), Spain, and a Grant from CONACYT (FOMIX-CONACyT-UAGro 249818), México.

This paper is concerned with the distributions of zeros of solutions to first order delay dynamic equations on time scales. The results are obtained using iterative sequences.

In this paper, we simultaneously estimate camera pose and non-rigid 3D shape from a monocular video, using a sequential solution that combines local and global representations. We model the object as an ensemble of particles, each ruled by the linear equation of the Newton’s second law of motion. This dynamic model is incorporated into a bundle adjustment framework, in combination with simple regularization components that ensure temporal and spatial consistency. The resulting approach allows to sequentially estimate shape and camera poses, while progressively learning a global low-rank model of the shape that is fed back into the optimization scheme, introducing thus, global constraints. The overall combination of local (physical) and global (statistical) constraints yields a solution that is both efficient and robust to several artifacts such as noisy and missing data or sudden camera motions, without requiring any training data at all. Validation is done in a variety of real application domains, including articulated and non-rigid motion, both for continuous and discontinuous shapes. Our on-line methodology yields significantly more accurate reconstructions than competing sequential approaches, being even comparable to the more computationally demanding batch methods., This work has been partially supported by the Spanish Ministry of Science and Innovation under project RobInstruct TIN2014-58178-R; by a scholarship FPU12/04886 from the Spanish MECD; and by the ERA-net CHISTERA projects VISEN PCIN-2013-047 and I-DRESS PCIN-2015-147.

In this paper, we consider the biharmonic problem of a partial differential inclusion with Dirichlet boundary conditions. We prove existence theorems for related partial differential inclusions with convex and nonconvex multivalued perturbations, and obtain an existence theorem on extremal solutions, and a strong relaxation theorem. Also we prove that the solution set is compact $R_{\delta}$ if the perturbation term of the related partial differential inclusion is convex, and its solution set is path-connected if the perturbation term is nonconvex.

In this paper, using fixed point index and the mixed monotone technique, we present some multiplicity and uniqueness results for the singular nonlocal boundary value problems involving nonlinear integral conditions. Our nonlinearity may be singular in its dependent variable and it is allowed to change sign.

This paper deals with the asymptotic stability and boundedness of the solution of a time-varying impulsive Volterra integro-dynamic system on time scales in which the coefficient matrix is not necessarily stable. We generalize to a time scale some known properties concerning the asymptotic behavior and boundedness from the continuous case.

In the ongoing discussion about combining rules and ontologies on the Semantic Web a recurring issue is how to combine first-order classical logic with nonmonotonic rule languages. Whereas several modular approaches to define a combined semantics for such hybrid knowledge bases focus mainly on decidability issues, we tackle the matter from a more general point of view. In this paper, we show how Quantified Equilibrium Logic (QEL) can function as a unified framework which embraces classical logic as well as disjunctive logic programs under the (open) answer set semantics. In the proposed variant of QEL, we relax the unique names assumption, which was present in earlier versions of QEL. Moreover, we show that this framework elegantly captures the existing modular approaches for hybrid knowledge bases in a unified way.

The purpose of this paper is to introduce the concept of general fuzzy multivalued variational inclusions and to study the existence problem and the iterative approximation problem for certain fuzzy multivalued variational inclusions in Banach spaces. Using the resolvent operator technique and a new analytic technique, some existence theorems and iterative approximation techniques are presented for these fuzzy multivalued variational inclusions.

From a Bayesian point of view, in this paper we discuss the influence of a subset of observations on the posterior distributions of parameters in a growth curve model with unstructured covariance. The measure used to assess the influence is based on a Bayesian entropy, namely Kullback-Leibler divergence (KLD). Several new properties of the Bayesian entropy are studied, and analytically closed forms of the KLD measurement both for the matrix-variate normal distribution and the Wishart distribution are established. In the growth curve model, the KLD measurements for all combinations of the parameters are also studied. For illustration, a practical data set is analyzed using the proposed approach, which shows that the diagnostics measurements are useful in practice.

Earth scientists and land managers often wish to group sampling sites that are both similar with respect to their properties and near to one another on the ground. This paper outlines the geostatistical rationale for such spatial grouping and describes a multivariate procedure to implement it. Sample variograms are calculated from the original data or their leading principal components and then the parameters of the underlying functions are estimated. A dissimilarity matrix is computed for all sampling sites, preferably using Gower's general similarity coefficient. Dissimilarities are then modified using the variogram to incorporate the form and extent of spatial variation. A nonhierarchical classification of sampling sites is performed on the leading latent vectors of the modified dissimilarity matrix by dynamic clustering to an optimum. The technique is illustrated with results of its application to soil survey data from two small areas in Britain and from a transect. In the case of the latter results of spatially weighted classifications are compared with those of strict segmentation. An appendix lists a Genstat program for a spatially constrained classification using a spherical variogram as an example. RESP-10421

Rotation scheduling implies a reduction in pipe flows and, consequently, in network cost. This kind of scheduling is considered rigid, but the recent development of new technologies, such as Supervisory Control And Data Acquisition systems (SCADA), has allowed high-frequency irrigation (1 day or less), making it an interesting option when either designing or managing an irrigation network. In this paper, simple formulas and relevant variables are presented to easily assess the relative flow reduction in networks under a rotation schedule. The flow reduction depends on the number of outlets supplied and the probability of these being opened. The presented equations were applied to different networks, and the results obtained were accurate, with an average error of only 5%. It was observed that the ratio between relative cost reduction and the relative flow reduction had a mean value of 0.50. This ratio might be used to roughly estimate the cost reduction from the calculated relative flow reduction. The flexibility of the networks under a rotation schedule was improved by adding just one outlet flow rate to those used to size the pipes. This research was partially funded by “Infraestructures.cat”.

I am afraid I disagree with Dr. Vajda's comments1 on the analysis of variance technique appropriate to two–way tables with unequal frequencies in the different sub-classes. As I pointed out in the paper referred to2, the expressions for the efficient estimates of the ‘main’ effects of the two variables are different according as interactions are assumed to exist or not. If interaction is assumed, the efficient estimate for the first variable in a 2 × 2 table, using Vajda's notation, is