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Ternary pnictides semiconductors with II-IV-V2 stoichiometry hold potential as cost effective thermoelectric materials with suitable electronic transport properties, but their lattice thermal conductivities ($\kappa$) are typically too high. Gaining insight into their vibrational properties is therefore crucial to finding strategies to reduce $\kappa$ and achieve improved thermoelectric performance. We present a theoretical exploration of the lattice thermal conductivities for a set of pnictide semiconductors with ABX2 composition (A = Zn, Cd; B = Si, Ge, Sn; and X = P, As), using machine-learning based regression algorithms to extract force constants from a reduced number of density functional theory simulations, and then solving the Boltzmann transport equation for phonons. Our results align well available experimental data, decreasing the mean absolute error by ~3 Wm-1K-1 with respect to the best previous set of theoretical predictions. Zn-based ternary pnictides have, on average, more than double the thermal conductivity of the Cd-based compounds. Anisotropic behaviour increases with the mass difference between A and B cations, but while the nature of the anion does not affect the structural anisotropy, the thermal conductivity anisotropy is typically higher for arsenides than for phosphides. We identify compounds, like CdGeAs2, for which nanostructuring to an affordable range of particle sizes could lead to values low enough for thermoelectric applications., Comment: 24 pages, 8 figures

We characterize several stability properties, such as inverse or composition closedness, for ultraholomorphic function classes of Roumieu type defined in terms of a weight matrix. In this way we transfer and extend known results from J. Siddiqi and M. Ider, from the weight sequence setting and in sectors not wider than a half-plane, to the weight matrix framework and for sectors in the Riemann surface of the logarithm with arbitrary opening. The key argument rests on the construction, under suitable hypotheses, of characteristic functions in these classes for unrestricted sectors. As a by-product, we obtain new stability results when the growth control in these classes is expressed in terms of a weight sequence, or of a weight function in the sense of Braun-Meise-Taylor.

We construct optimal flat functions in Carleman-Roumieu ultraholomorphic classes associated to general strongly nonquasianalytic weight sequences, and defined on sectors of suitably restricted opening. A general procedure is presented in order to obtain linear continuous extension operators, right inverses of the Borel map, for the case of regular weight sequences in the sense of Dyn'kin. Finally, we discuss some examples (including the well-known $q$-Gevrey case) where such optimal flat functions can be obtained in a more explicit way., Comment: 29 pages. Important improvements, mainly in Section 3: a simplified concept of optimal flat function is introduced, and their general construction is provided for strongly non-quasianalytic weight sequences and in narrow enough sectors

While the asymptotic Borel mapping, sending a function into its series of asymptotic expansion in a sector, is known to be surjective for arbitrary openings in the framework of ultraholomorphic classes associated with sequences of rapid growth, there is no general procedure to construct extension operators in this case. We do provide such operators in complex sectors for some particular classes considered by S.~Pilipovi{\'c}, N.~Teofanov and F.~Tomi{\'c} in the ultradifferentiable setting. Although these classes are, in their words, "beyond Gevrey regularity", in some cases they keep the property of stability under differentiation, which is crucial for our technique, based on formal Borel- and truncated Laplace-like transforms with suitable kernels., Comment: 21 pages

We characterize the equality between ultradifferentiable function classes defined in terms of abstractly given weight matrices and in terms of the corresponding matrix of associated weight functions by using new growth indices. These indices, defined by means of weight sequences and (associated) weight functions, are extending the notion of O-regular variation to a mixed setting. Hence we are extending the known comparison results concerning classes defined in terms of a single weight sequence and of a single weight function and give also these statements an interpretation expressed in O-regular variation., Comment: 26 pages; some typos are corrected; this version has been accepted for publication in Res. Math

In this work we study the use of moderate deviation functions to measure similarity and dissimilarity among a set of given interval-valued data. To do so, we introduce the notion of interval-valued moderate deviation function and we study in particular those interval-valued moderate deviation functions which preserve the width of the input intervals. Then, we study how to apply these functions to construct interval-valued aggregation functions. We have applied them in the decision making phase of two Motor-Imagery Brain Computer Interface frameworks, obtaining better results than those obtained using other numerical and intervalar aggregations.

Ultra-high temperature ceramics, UHTCs, are a group of materials with high technological interest because their use in extreme environments. However, their characterization at high temperatures represents the main obstacle for their fast development. Obstacles are found from a experimental point of view, where only few laboratories around the world have the resources to test these materials under extreme conditions, and also from a theoretical point of view, where actual methods are extremely expensive. Here, a new theoretical high-throughput framework for the prediction of the thermoelastic properties of materials is introduced. This approach can be systematically applied to any kind of crystalline material, drastically reducing the computational cost of previous methodologies. Elastic constants for UHTCs have been calculated at a wide range of temperatures with excellent agreement with experimentally reported values. Moreover, other mechanical properties such a bulk modulus, shear modulus or Poisson ration have been also explored. Other frameworks with similar computational cost have been used only for predicting isotropic or averaged properties, however this new approach opens the door to the calculation of anisotropic properties at a very low computational cost.

We study the surjectivity of, and the existence of right inverses for, the asymptotic Borel map in Carleman-Roumieu ultraholomorphic classes defined by regular sequences in the sense of E. M. Dyn'kin. We extend previous results by J. Schmets and M. Valdivia, by V. Thilliez, and by the authors, and show the prominent role played by an index associated with the sequence and introduced by Thilliez. The techniques involve regular variation, integral transforms and characterization results of A. Debrouwere in a half-plane, steming from his study of the surjectivity of the moment mapping in general Gelfand-Shilov spaces., Comment: 18 pages. Some changes are related to an index shift in condition $(\beta_2)$, property (9) and the proof of Proposition 4.4. The example proving that (vii) does not imply (vi) in that Proposition has been changed. New proof, avoiding the use of condition (dc), for the implication from (i) to (ii) in Theorem 4.5. Some new comments added and some misprints corrected

The aim of this work is to generalize the ultraholomorphic extension theorems from V. Thilliez in the weight sequence setting and from the authors in the weight function setting (of Roumieu type) to a mixed framework. Such mixed results have already been known for ultradifferentiable classes and it seems natural that they have ultraholomorphic counterparts. In order to have control on the opening of the sectors in the Riemann surface of the logarithm for which the extension theorems are valid we are introducing new mixed growth indices which are generalizing the known ones for weight sequences and functions. As it turns out, for the validity of mixed extension results the so-called order of quasianalyticity (introduced by the second author for weight sequences) is becoming important., Comment: 32 pages

Unity is a software specifically designed for the development of video games. However, due to its programming possibilities and the polyvalence of its architecture, it can prove to be a versatile tool for stimuli presentation in research experiments. Nevertheless, it also has some limitations and conditions that need to be taken into account to ensure optimal performance in particular experimental situations. Such is the case if we want to use it in an experimental design that includes the acquisition of biometric signals synchronized with the broadcasting of video and audio in real time. In the present paper, we analyse how Unity (version 5.5.1f1) reacts in one such experimental design that requires the execution of audio-visual material. From the analysis of an experimental procedure in which the video was executed following the standard software specifications, we have detected the following problems desynchronization between the emission of the video and the audio; desynchronization between the temporary counter and the video; a delay in the execution of the screenshot; and depending on the encoding of the video a bad fluency in the video playback, which even though it maintains the total playback time, it causes Unity to freeze frames and proceed to compensate with little temporary jumps in the video. Finally, having detected all the problems, a compensation and verification process is designed to be able to work with audio-visual material in Unity (version 5.5.1f1) in an accurate way. We present a protocol for checks and compensations that allows solving these problems to ensure the execution of robust experiments in terms of reliability., Comment: 13 Pages

We consider r-ramification ultradifferentiable classes, introduced by J. Schmets and M. Valdivia in order to study the surjectivity of the Borel map, and later on also exploited by the authors in the ultraholomorphic context. We characterize quasianalyticity in such classes, extend the results of Schmets and Valdivia about the image of the Borel map in a mixed ultradifferentiable setting, and obtain a version of the Whitney extension theorem in this framework., Comment: 31 pages; this version has been accepted for publication in Monatsh. Math

The Stieltjes moment problem is studied in the framework of general Gelfand-Shilov spaces defined via weight sequences. We characterize the injectivity and surjectivity of the Stieltjes moment mapping, sending a function to its sequence of moments, in terms of growth conditions for the defining weight sequence. Finally, a related moment problem at the origin is studied., Comment: 18 pages

We introduce a general multisummability theory of formal power series in Carleman ultraholomorphic classes. The finitely many levels of summation are determined by pairwise comparable, nonequivalent weight sequences admitting nonzero proximate orders and whose growth indices are distinct. Thus, we extend the powerful multisummability theory for finitely many Gevrey levels, developed by J.-P. Ramis, J. \'Ecalle and W. Balser, among others. We provide both the analytical and cohomological approaches, and obtain a reconstruction formula for the multisum of a multisummable series by means of iterated generalized Laplace-like operators., Comment: 47 pages

A plethora of spaces in Functional Analysis (Braun-Meise-Taylor and Carleman ultradifferentiable and ultraholomorphic classes; Orlicz, Besov, Lipschitz, Lebesque spaces, to cite the main ones) are defined by means of a weighted structure, obtained from a weight function or sequence subject to standard conditions entailing desirable properties (algebraic closure, stability under operators, interpolation, etc.) for the corresponding spaces. The aim of this paper is to stress or reveal the true nature of these diverse conditions imposed on weights, appearing in a scattered and disconnected way in the literature: they turn out to fall into the framework of O-regular variation, and many of them are equivalent formulations of one and the same feature. Moreover, we study several indices of regularity/growth for both functions and sequences, which allow for the rephrasing of qualitative properties in terms of quantitative statements., Comment: 37 pages

We prove an extension theorem for ultraholomorphic classes defined by so-called Braun-Meise-Taylor weight functions and transfer the proofs from the single weight sequence case from V. Thilliez [28] to the weight function setting. We are following a different approach than the results obtained in [11], more precisely we are working with real methods by applying the ultradifferentiable Whitney-extension theorem. We are treating both the Roumieu and the Beurling case, the latter one is obtained by a reduction from the Roumieu case., Comment: 35 pages

We study the injectivity and surjectivity of the Borel map in three instances: in Roumieu-Carleman ultraholomorphic classes in unbounded sectors of the Riemann surface of the logarithm, and in classes of functions admitting, uniform or nonuniform, asymptotic expansion at the corresponding vertex. These classes are defined in terms of a log-convex sequence $\mathbb{M}$ of positive real numbers. Injectivity had been solved in two of these cases by S. Mandelbrojt and B. Rodr\'iguez-Salinas, respectively, and we completely solve the third one by means of the theory of proximate orders. A growth index $\omega(\mathbb{M})$ turns out to put apart the values of the opening of the sector for which injectivity holds or not. In the case of surjectivity, only some partial results were available by J. Schmets and M. Valdivia and by V. Thilliez, and this last author introduced an index $\gamma(\mathbb{M})$ (generally different from $\omega(\mathbb{M})$) for this problem, whose optimality was not established except for the Gevrey case. We considerably extend here their results, proving that $\gamma(\mathbb{M})$ is indeed optimal in some standard situations (for example, as far as $\mathbb{M}$ is strongly regular) and puts apart the values of the opening of the sector for which surjectivity holds or not., Comment: 34 pages