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This paper presents a numerical method for the optimal tailoring of volume fraction distributions of reinforcement materials (pillars) within FGM (functionally graded material) sandwich beams with FG-CNTRC (functionally graded CNT-reinforced composite) facesheets. Since the mechanical behaviors of sandwich beams vary depending on the distribution pattern of reinforcement materials (CNT and ceramic in this paper) through the thickness, the tailoring of these distribution patterns is important to enhance the mechanical performance. In the present study, the thickness-wise distributions of CNT in the facesheets and ceramic in the core are optimized to maximize the fundamental natural frequency of sandwich beams, based on the exterior penalty-function method and the golden section method. The developed optimization method is verified and the resulting optimum distributions of CNT and ceramic are compared with the primitive functionally graded distribution patterns which are widely adopted in the literature. Moreover, the volume fraction distributions of CNT and ceramic are also individually optimized, and the optimum results between simultaneous (SO) and individual optimizations (IO) are compared. [ABSTRACT FROM AUTHOR]

Kaihua paper is a type of precious hand-made paper in China that has been used throughout Chinese history. Due to its extraordinary whiteness and fine texture, it was adopted by the imperial palace in the reign of Emperor Kang Xi and Yong Zheng of the Qing Dynasty of China in the 17th and 18th century. It is stained by a special type of yellowish-brown spot after years of storage, which is called a "peachy spot." The formation of such spots remains unclear, although complicated physicochemical processes or microbial activities might be involved. We performed nondestructive sampling and high-throughput sequencing on peachy spot surfaces, unstained areas, and air samples in the stack room to analysis the the bacterial and fungal communities, and performed prediction of functional genes of the bacterial communities. The results showed that peachy spot formation was mainly related to bacterial communities rather than fungal communities. Significantly more potential acid-producing, acidophilic or cellulase-producing bacteria, such as, Streptococcus, Staphylococcus, and Lysinibacillus, and pigment-producing bacteria, such as Methylobacterium and Rubrobacter, were identified in the peachy spot samples. Prediction of the functional genes of the bacterial community also suggested the production of acidic substance pigments. These findings provide new insights into the pigment formation mechanism in ancient paper and open an opportunity to develop new strategies to preserve the ancient paper documents. [ABSTRACT FROM AUTHOR]

This article introduces a nonparametric methodology combining the strengths of binary regression and latent variable formulations, while overcoming their disadvantages. The mathematical results are implemented through a novel Bayesian Hierarchical estimation methodology called Latent Adaptive Hierarchical Expectation Maximization Like algorithm. Requiring minimal assumptions, it extends extant methodologies, and in simulation studies gives better prediction and inference performances for asymmetric data generating processes. A new classification statistic, called Adjusted Receiver Operating Curve Statistic is also introduced. Utilizing it we demonstrate better overall model fit, inference and prediction performance of the proposed methodology over widely used existing methods in the sciences. In addition, the methodology can be used to perform model diagnostics for any model specification. This is a highly useful result, and it extends existing work for categorical model diagnostics broadly across the sciences. Furthermore, the mathematical results also highlight important new findings regarding the interplay of statistical significance and scientific significance. Finally, the methodology is applied to identifying highly-cited papers in the social sciences in a joint estimation framework. The results indicate that the methodology outperforms widely used existing artificial intelligence and machine learning models with very few Monte Carlo iterations. In Scientometric application, it finds Journal Impact Factor to be more important than Keyword Popularity parameters for explaining citation outcomes in select social science fields. It further finds that the percentage change in Published Popularity may also help to explain citation outcomes in the field. The findings appear to be new to the Scientometric field. • Introduces new statistical method for regressions requiring few assumptions. • Outperforms existing artificial intelligence/machine learning algorithms. • Introduces ARS: A general statistic for predication/comparison of models. • Applies methodology to identify highly-cited papers in the social sciences. • JIF more important than keywords for getting cited in some social science fields. [ABSTRACT FROM AUTHOR]

Under the premise of resource constraint, it is crucial to identify the product innovation opportunities contained in failed patents through external search in order to compensate for the shortcomings of enterprises' own technology. Due to the cost of patent research and development and the risk of infringement, this paper constructs a product innovation identification path that integrates the FOS and BERTopic model from the perspective of invalid patents. The path consists of three stages, including the identification of the problem to be solved by the product based on functional analysis, the extraction of the subject matter elements based on the core failed patent technology, and the generation and evaluation of innovative solutions based on TRIZ theory and the best- worst method (BWM). Finally, the feasibility of the path constructed in this paper is verified by taking a slurry pump as an example. The application results show that the product innovation identification path constructed in this paper can provide theoretical support for enterprises to carry out technological innovation activities efficiently. [ABSTRACT FROM AUTHOR]

Legal discourse has long been classified among those genres that defy generic changes the most (Gocić 2012). Recently, however, hybrid legal genres have been challenging this generic stability by imposing their own norms to coin a novel kind of 'legal culture' (Goźdź-Roszkowski 2011: 11). The law review article is a case in point for it combines both legal and academic standards of writing which make it "far richer in intertextuality and interdiscursivity" (Bhatia 2006: 6) than the traditional set of legal genres. This generic subversion can be traced in the lexico-grammatical choices made by the authors to turn their papers into influential legal sources rather than mere descriptions of the law. In this context, this study aspires to scrutinize the use of adverbial clauses as one specific lexico-grammatical choice in a corpus of 44 accredited law review papers with the aim of showing how this hybrid genre strives to evolve beyond the stagnation of what is termed 'language of the law'. Specifically, a Systemic Functional Linguistics analysis of the semantic, structural and thematic uses of these structures is conducted to demonstrate how the hybridity of contexts in a single genre can make for unprecedented generic breaches. The quantitative and qualitative analyses revealed an uneven distribution of adverbial patterns in favor of non-finite purpose and finite condition, concession and reason clauses. Additionally, the positional distribution of these patterns is manipulated whenever the need arises to hedge claims as a form of allegiance to the communal demands of the law and academia. These choices are found to comply with the authors' needs to balance both legal and academic rituals of writing while observing at the same time their personal needs to be highly acclaimed as legal scholars and to "publish or perish" (Christensen & Oseid 2008: 1). [ABSTRACT FROM AUTHOR]

Highlights: [•] We prepared a polyamide paper coating containing paraffin–DEET composites. [•] The polyamide film was directly prepared using interfacial polymerization. [•] The functional paper containing paraffin released DEET for a long period. [•] DEET release from the functional paper had a low temperature dependence. [•] Paraffin was important in achieving the sustained release of DEET. [ABSTRACT FROM AUTHOR]

Abstract: Complementing the work of T.-S. Liu and A.C.M. van Rooij we show that the existence of non-zero translation invariant operators between certain function spaces on a locally compact group implies its amenability. [Copyright &y& Elsevier]

• Robust functional form contains true parameters far more often than popular models. • Matches/outperforms widely used regression and Neural Network models. • Finds appropriate balance between Model Fit, Inference and Prediction (MIPs). • Introduces new large-sample DGP test; can use to improve A.I. models. • For MIS field finds Popularity Parameter to be important for predicting citations. This article introduces a versatile functional form for Generalized Linear Models (GLMs) through a simple, yet effective, transformation of the current framework. The models are applied through a new hierarchical bayesian estimation procedure for logistic regression to highly-cited papers in the Management Information Systems (MIS) field. The results are uniformly better, in regards to model fit and inference for in-sample and out-of-sample data, for simulation studies and real-world data applications, requiring very little time to convergence to true population parameters. In simulation studies, I show that the method contains the true parameters nearly three times as often as widely used existing GLMs, and does so while having confidence intervals that are 54.50% smaller, while requiring around two-thirds the number of MCMC iterations as existing bayesian methods. In Scientometric applications the methodology is shown to be highly robust with predictive/classification accuracy, either equaling or exceeding existing methods for identifying highly-cited articles including Artificial Neural Networks (ANN). Thus, the method is shown to be robust to the amount of asymmetry (or symmetry) of the probability of success (or failure) and robust to unbalanced samples and varying Data Generating Processes. Further, the methodology is equivalent to current methods if the data support them and is therefore complementary to existing methods, without loss of interpretability of model parameters. For the MIS field it finds that Popularity Parameter (PP) of an article Keywords can predict whether a paper will be highly-cited (top 25% of highly-cited articles) between two to three years after publication and beyond. Furthermore, given the small number of iterations needed for convergence, the methodology can also be used as a baseline method in Big Data (BD) settings for both Artificial Intelligence (AI) and Machine Learning (ML) contexts as well. [ABSTRACT FROM AUTHOR]

This document is a special issue of the journal Axioms titled "Topology and Functional Analysis" in honor of María Jesús Chasco's 65th birthday. It includes papers on topological groups, topological semi-groups, and topological vector spaces, highlighting the interaction between topology and functional analysis. The papers cover various topics such as factorization of groups into thin subsets, extensions of characters defined on subgroups, distinguished subgroups of compact Abelian groups, preservation of min-subgroup structure under aggregation functions, bounded sets in topological spaces subject to the action of a monoid, and the distinguished property in tensor products and weak* dual spaces. María Jesús Chasco is recognized for her contributions to mathematics, particularly in the field of duality in topological groups. [Extracted from the article]

In response to the analysis of the functional status of forearm blood vessels, this paper fully considers the orientation of the vascular skeleton and the geometric characteristics of blood vessels and proposes a blood vessel width calculation algorithm based on the radius estimation of the tangent circle (RETC) in forearm near-infrared images. First, the initial infrared image obtained by the infrared camera is preprocessed by image cropping, contrast stretching, denoising, enhancement, and initial segmentation. Second, the Zhang–Suen refinement algorithm is used to extract the vascular skeleton. Third, the Canny edge detection method is used to perform vascular edge detection. Finally, a RETC algorithm is developed to calculate the vessel width. This paper evaluates the accuracy of the proposed RETC algorithm, and experimental results show that the mean absolute error between the vessel width obtained by our algorithm and the reference vessel width is as low as 0.36, with a variance of only 0.10, which can be significantly reduced compared to traditional calculation measurements. [ABSTRACT FROM AUTHOR]

This research focuses on developing models to estimate the system reliability of Unmanned Ground Vehicles using knowledge and data from similar systems. Reliability is often a stand‐alone requirement and not always fully included in performance and life cycle cost models. Traditional reliability approaches require detailed knowledge of a system and are used in later design sta ges as well as development, operational test and evaluation, and operations. The critical role of reliability and its impact on acquisition program performance, cost, and schedule motivates the need for improved system reliability models in the early design stages. This research seeks to integrate reliability, performance, and cost models in a trade‐off analysis framework in the early acquisition stages. This research uses functional analysis methods to estimate reliability Pre‐Milestone A and assess the impact of reliability on performance and cost models of early system concepts. This research us es technology readiness level (TRL), which is indexed, to assess different levels of reliability for design. An integrated cost and performance model will inform decision ‐makers on the impact of reliability before choosing a system concept for further development. [ABSTRACT FROM AUTHOR]

With this note, we want to open a discussion on the duality theory for Interval Optimization. We begin by showing that some duality results Wu ( J Optim Theory Appl 144:615-628, ) are useless. [ABSTRACT FROM AUTHOR]

Unbalanced and insufficient development is a prominent problem in China's period of economic transformation, and an accurate grasp of the current situation and evolutionary trend of innovation and economic development is of great significance in finding a solution and promoting regional coordinated development. This paper introduces the framework of functional data analysis to the study of both innovation and economic development in China, examining its spatial dynamic distribution and convergence characteristic in greater depth. Empirical results revealed the following. (1) Significant regional differences exist in the absolute level of China's innovation development, with a balanced improvement in the development speed and growth potential. Significant differences exist in the absolute level and speed of economic development, but not in the potential energy of development as reflected by acceleration. (2) The σ(t) function of nationwide and regional innovation development shows a downward trend. There is σ(t) convergence in economic development nationwide and in the northeastern, eastern, and western regions, but the regional disparities in economic development within the six central provinces have not yet been effectively mitigated. (3) Nationwide and regional innovation development are in a state of β(t) convergence. There is significant β(t) convergence in the nationwide economic development, with a transition point from divergence to convergence in the northeastern, eastern, and western regions. However, the β(t) function of economic development in the central region shows a region-wide divergence. The findings of this paper have important policy implications for recognizing the balance and disparities in innovation and economic development among regions in China and promoting coordinated regional development. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we provide a computational approach to the shape of curves which are rational in polar coordinates, i.e. which are defined by means of a parametrization where both , are rational functions. Our study includes theoretical aspects on the shape of these curves, and algorithmic results which eventually lead to an algorithm for plotting the “interesting parts” of the curve, i.e. the parts showing the main geometrical features. [Copyright &y& Elsevier]

Recent years have witnessed noticeable expansion of new technologies related to distributed ledger technology (DLT) and blockchain networks in financial markets. As developments unfold, the key question that emerges is whether these technologies would work to foster traditional services or, conversely, would challenge their existence. Similar reflections exist for specific parts of the financial system. In particular for central counterparties (CCPs), proof-of-concepts and theoretical exercises have been conducted aiming at responding to such questions. While empirical experiences are yet to mature, theoretical exercises have suggested the impact on CCPs could be substantial, if not detrimental. The objective of this paper is to contribute to the literature and investigate the impact of DLTs on CCPs. Different from previous exercises, the paper resorts to the economic theory of financial service intermediation to substantiate the assessment. Using functional analysis and good type categorisation, the main conclusion of the paper is that under the current offering it seems challenging to foresee a scenario where any of the main services provided by a CCP would disappear or become fully disintermediated. The supporting argument is that the core functions of a CCP orbit around risk management, provided either as private or club type of good. Until now new technologies do not seem able to change the nature of these services and, therefore, render fundamental changes to CCPs less likely. [ABSTRACT FROM AUTHOR]

The article focuses on the Computational Optimization and Applications (COAP) 2008 Best Paper Award-winning work of Martin Weiser, Tobias Gënzler, and Anton Schiela at the Zuse Institute Berlin in Germany. It notes that their paper entitled "A control reduced primal interior point method for a class of control constrained optimal control problems" aims to establish function space oriented algorithms which work directly in the infinite-dimensional setting.

Let G be a semisimple linear algebraic group and X a nodal curve. We show that if ρ : G → On(ℂ)(Spn(ℂ)) is a faithful representation and if δ⋙ 0, then any δ-semistable singular G-bundle is actually a principal G-bundle away from the node of X. Furthermore, we considerably simplify the notion of δ-(semi)stability. [ABSTRACT FROM AUTHOR]

Copyright of Military Technical Courier / Vojnotehnicki Glasnik is the property of Military Technical Courier / Vojnotehnicki Glasnik and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The article discusses the 1913 paper "Sur les fonctionnelles continues et les fonctionnelles analytiques," by René Gâteaux. Focus is given on the modern concept of functional analysis based from the ideas of Gâteaux in the paper. Also provided is information on Gâteaux derivative and influence function in estimation theory.

Abstract: Ahn, Lee, Park and Yoo proved that the best constrained degree reduction of a polynomial f in -norm equals the best weighted Euclidean approximation of the Bernstein–Bézier coefficients of f in a paper, published in the journal, Computer Aided Geometric Design 21 (2) (2004) 181–191. In this note, we point out an error in their paper and give the correct result. [Copyright &y& Elsevier]

Recent technological advances have renewed the research interest in current-source inverters (CSIs). Nonetheless, CSI research still falls behind its voltage-source counterpart with regards to topologies, modulation, and control. Acknowledging the above, this paper presents a novel single-phase five-level CSI topology. The proposed circuit utilises eight switches and two inductors for the generation of five distinct output levels while maintaining low output voltage THD and d v / d t . Furthermore, by offsetting the inductor currents from a binary 1:2 to a trinary 1:3 ratio, the proposed inverter can generate seven current levels at its output. The inverter offers built-in short-circuit protection and can boost a low input DC voltage to a higher peak AC output voltage. These merits, alongside an electrolytic-capacitor-free design, simple current balancing mechanism, and fault-tolerant characteristics, make it a promising candidate for PV module-integrated inverter (MII) systems. The current topology utilises two inductors but is fully functional with single-inductor operation. The paper provides a functional analysis of the inverter topology alongside the inverter switching states and corresponding conduction paths. A detailed analysis of the inductor current dynamics as well as a current-balancing algorithm for dual- and single-inductor operations are given. The theoretical analysis of the proposed circuit and its functional operation are verified using simulations and experimental results carried out on a laboratory prototype. [ABSTRACT FROM AUTHOR]

This paper is dedicated to the memory of the esteemed Serbian mathematician Slaviša B. Prešić (1933–2008). The primary aim of this survey paper is to compile articles on Prešić-type mappings published since 1965. Additionally, it introduces a novel class of symmetric contractions known as Prešić–Menger and Prešić–Ćirić–Menger contractions, thereby enriching the literature on Prešić-type mappings. The paper endeavors to furnish young researchers with a comprehensive resource in functional and nonlinear analysis. The relevance of Prešić's method, which generalizes Banach's theorem from 1922, remains significant in metric fixed point theory, as evidenced by recent publications. The overview article addresses the growing importance of Prešić's approach, coupled with new ideas, reflecting the ongoing advancements in the field. Additionally, the paper establishes the existence and uniqueness of fixed points in Menger spaces, contributing to the filling of gaps in the existing literature on Prešić's works while providing valuable insights into this specialized domain. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the influence of past citations ki on papers' attachment rate Π(k, t) and propose a method to consider these influences by assigning different weights to ki. The correlation r between Π(k, t) and ki decrease rapidly with time, which suggests the different influences of past citations on the preferential attachment in citation networks. According to the different influences of ki on Π(k, t), we put different weights to ki and find a good linear dependence between Π(k, t) and the weighted past citations in three actual citation networks. [ABSTRACT FROM AUTHOR]

In this paper on a basis of functional analysis methods we justified theoretically the possibility of different orders root-polynomial functions application for interpolation and approximation of the boundary trajectory of an electron beam in case of its propagation in ionized gas with compensation of the space charge of the beam electrons. It is shown, that the root-polynomial functions satisfy to the second-order differential equation, describing the boundary trajectory of the beam electrons under such physical conditions. The results of interpolation and approximation of the boundary trajectory of the electron beam by root-polynomial functions from the second to the fifth order under the following physical conditions are presented. The interpolation results are compared with the corresponded results of the differential equation solution for the boundary trajectory of the electron beam using Runge-Kutta numerical method of the fourth order. These results are considered as reference ones for the interpolation task. To solve the approximation problem, in this paper an iterative algorithm based on the calculation of both values of the function and its derivatives at reference points is proposed. The approximation task is solved for a sample of numerical data obtained by experimental electron-beam equipment for real processes of current electron-beam technologies, which led to a rather large value of the experimental measurement error due to the effect of random factors associated with thermal treatment of products with electron beam. Test calculations show that the error of interpolation and approximation of numerical data, describing the boundary trajectory of electron beam in case of its propagation in ionized gas, does not exceed a few percent. The theoretical and practical results obtained in this paper are interesting for a wide range of specialists who are engaged in the physics of electron beams, the development of electron-beam technological equipment and implementation of current electron-beam technologies into industry. [ABSTRACT FROM AUTHOR]

In this paper, some properties of locally antisymmetrically connected spaces which are the localized version of the antisymmetrically connected T0-quasi-metric spaces constructed as the natural counterparts of connected complementary graphs, are presented in terms of asymmetric norms. According to that, we investigated some different aspects and examples of local antisymmetric connectedness in the framework of asymmetrically normed real vector spaces. Specifically, it is proved that the structures of antisymmetric connectedness and local antisymmetric connectedness coincide for the T0-quasi-metrics induced by the asymmetric norms which associate the theory of quasi-metrics with functional analysis. [ABSTRACT FROM AUTHOR]

Climate change has become increasingly important in recent years. It is the outcome of the burning of fossil fuels that increased the concentration of atmospheric carbon dioxide (CO 2 ), over the last century. Mitigating the impacts of climate change requires a better understanding and assessment of the countries' economic decisions on the amount of CO 2 emissions. This paper assesses the variability between the different countries in the trends of CO 2 emissions and electricity consumption from 1975 to 2014, while identifying clusters of countries of similar trends over time. The novel methodology applied in this paper enables us to assess long-debated issues in climate literature. The temporal dynamic effects of electricity consumption and economic growth on CO 2 emissions across countries are studied using functional data analysis (FDA) methods. The latter have proven to be useful tools for visualising similarities and differences in the non-linear trends of CO 2 emissions without forcing linear trends and stationary relationships which can be unrealistic and misleading. The results indicate the possibility of identifying changes in the trends of CO 2 emissions and electricity consumption for a wide range of heterogeneous countries over the study period. The findings also reveal that economic growth puts a strain on the environment, where many high-income countries are still away from attaining economic-energy sustainability. [ABSTRACT FROM AUTHOR]

Copyright of Automotive Digest is the property of Automotive Digest Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

U-statistics represent a fundamental class of statistics arising from modeling quantities of interest defined by multi-subject responses. U-statistics generalize the empirical mean of a random variable X to sums over every m-tuple of distinct observations of X. Stute [182] introduced a class of so-called conditional U-statistics, which may be viewed as a generalization of the Nadaraya-Watson estimates of a regression function. Stute proved their strong pointwise consistency to: r(m)(φ, t) ≔ 피[φ(F1,..., Ym)|(X1,..., Xm) = t], for t ∈ Xm. In this paper, we are mainly interested in the study of the kNN conditional U-processes in a functional mixing data framework. More precisely, we investigate the weak convergence of the conditional empirical process indexed by a suitable class of functions and of the kNN conditional U-processes when the explicative variable is functional. We treat the uniform central limit theorem in both cases when the class of functions is bounded or unbounded satisfying some moment conditions. The second main contribution of this study is the establishment of a sharp almost complete Uniform consistency in the Number of Neighbors of the constructed estimator. Such a result allows the number of neighbors to vary within a complete range for which the estimator is consistent. Consequently, it represents an interesting guideline in practice to select the optimal bandwidth in nonparametric functional data analysis. These results are proved under some standard structural conditions on the Vapnik-Chervonenkis classes of functions and some mild conditions on the model. The theoretical results established in this paper are (or will be) key tools for further functional data analysis developments. Potential applications include the set indexed conditional U-statistics, Kendall rank correlation coefficient, the discrimination problems and the time series prediction from a continuous set of past values. [ABSTRACT FROM AUTHOR]

It is considered best practice to conduct a functional analysis and visually inspect data collected to determine the function of problem behavior, which then informs the intervention approaches applied. Visual inspection has been described as a "subjective" process that may be affected by factors unrelated to the data. Structured decision-making guidelines have been established to address some of these shortcomings. The current paper is a follow-up to earlier work describing positive outcomes related to the viability of a decision support system based on structured criteria from Roane et al. Here, we demonstrate important improvements in a computer script's interpretation of functional analysis data, including improvement in agreement between the updated computer script version and experienced human raters (89%) compared to our original agreement outcomes (81%). This paper further supports the use of decision support systems for functional analysis interpretation. [ABSTRACT FROM AUTHOR]

This paper proposes the concept of green institutional environment, and constructs China's green institutional environmental system from the three dimensions of green supervision and public institution, green standardized institution and green accounting institution. Based on the relevant data from 2007 to 2017, this paper simulates China's green institutional environmental index through the Functional Data Analysis method and the functional entropy weight method. The results show that, first, there is a general upward trend in China's green institutional environmental index, with a range of [0.2–0.8]; the minimum value of this index is 0, and there is no maximum value. The larger the value, the higher the level of green institutional environment. Second, at the present stage, China's green standardized institution is relatively well-developed, accounting for the largest weight (i.e., [0.932–0.940]) in the green institutional environmental index system; the green accounting institution plays a supporting role, with a weight of [0.030–0.040], due to the fact that the Chinese government has made great efforts to implement policies at this level; the development of green supervision and public institution is under-developed and has little influence on the green institutional environmental index, with a weight of [0.0285–0.0305]. Finally, the proposed green institutional environmental index remains robust when equalizing the weights of the three dimensions. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel model to analyze serially correlated two-dimensional functional data observed sparsely and irregularly on a domain which may not be a rectangle. Our approach employs a mixed effects model that specifies the principal component functions as bivariate splines on triangles and the principal component scores as random effects which follow an auto-regressive model. We apply the thin-plate penalty for regularizing the bivariate function estimation and develop an effective EM algorithm along with Kalman filter and smoother for calculating the penalized likelihood estimates of the parameters. Our approach was applied on simulated datasets and on Texas monthly average temperature data from January year 1915 to December year 2014. Supplementary materials accompanying this paper appear online. [ABSTRACT FROM AUTHOR]

In many studies on disease progression, biomarkers are restricted by detection limits, hence informatively missing. Current approaches ignore the problem by just filling in the value of the detection limit for the missing observations for the estimation of the mean and covariance function, which yield inaccurate estimation. Inspired by our recent work [Liu and Houwing-Duistermaat (2022), 'Fast Estimators for the Mean Function for Functional Data with Detection Limits', Stat, e467.] in which novel estimators for mean function for data subject to detection limit are proposed, in this paper, we will propose a novel estimator for the covariance function for sparse and dense data subject to a detection limit. We will derive the asymptotic properties of the estimator. We will compare our method to the standard method, which ignores the detection limit, via simulations. We will illustrate the new approach by analysing biomarker data subject to a detection limit. In contrast to the standard method, our method appeared to provide more accurate estimates of the covariance. Moreover its computation time is small. [ABSTRACT FROM AUTHOR]

Xylan, one of the most important structures and polysaccharides, plays critical roles in plant development, growth, and defense responses to pathogens. Glucuronic acid substitution of xylan (GUX) functions in xylan sidechain decoration, which is involved in a wide range of physiological processes in plants. However, the specifics of GUXs in trees remain unclear. In this study, the characterization and evolution of the GUX family genes in E. grandis, a fast-growing forest tree belonging to the Myrtaceae family, were performed. A total of 23 EgGUXs were identified from the E. grandis genome, of which all members contained motif 2, 3, 5, and 7. All GUX genes were phylogeneticly clustered into five distinct groups. Among them, EgGUX01~EgGUX05 genes were clustered into group III and IV, which were more closely related to the AtGUX1, AtGUX2, and AtGUX4 members of Arabidopsis thaliana known to possess glucuronyltransferase activity, while most other members were clustered into group I. The light-responsive elements, hormone-responsive elements, growth and development-responsive elements, and stress-responsive elements were found in the promoter cis-acting elements, suggesting the expression of GUX might also be regulated by abiotic factors. RNA-Seq data confirmed that EgGUX02, EgGUX03, and EgGUX10 are highly expressed in xylem, and EgGUX09, EgGUX10, and EgGUX14 were obviously responses to abiotic stresses. The results of this paper will provide a comprehensive determination of the functions of the EgGUX family members, which will further contribute to understanding E. grandis xylan formation. [ABSTRACT FROM AUTHOR]

This paper investigates the vibration characteristics, both linear and non‐linear, of beams made from functional gradient materials (FGMs) with layers of Terfenol‐D attached to the top and bottom surfaces. Given the porosities that can occur during the manufacture of FGMs, the study examines the vibrational behaviour of beams with porosities. Euler–Bernoulli beam theory and the von‐Kármán non‐linear deformation field are used to formulate a fundamental equation predicting the free dynamic vibration of Terfenol‐D FGM structures with porosities. To complete this analysis, the paper also presents the application of two advanced methods. The first method involves employing the generalised finite element method (GFEM) associated with the reduced quadrature finite element method (RQFEM). GFEM offers a versatile and powerful approach, while RQFEM provides a specific method for studying dynamic phenomena. The second method utilises a semi‐analytical approach, the variational iteration method (VIM), which examines and complements the first method. Furthermore, we have demonstrated substantial alignment between the proposed solution and the results of finite element analysis, as well as with the existing literature, underscoring the effectiveness and accuracy of our analytical approach. The study also explores the influences of material property distribution, thermal loading, and porosity volume fraction on the linear and non‐linear behaviour of Terfenol‐D FGM beams. This comprehensive exploration furnishes valuable information on the intricate interplay of factors affecting vibration dynamics and control mechanisms in these advanced composite structures, offering insightful perspectives into the potential application of Terfenol‐D FGM beams in various fields. [ABSTRACT FROM AUTHOR]

Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of certain set-valued mappings between function spaces. This paper deals with the computational properties of these accretive and (generalized) monotone set-valued operators. In particular, we develop (and extend) for this field the theoretical framework of proof mining, a program in mathematical logic that seeks to extract computational information from prima facie "non-computational" proofs from the mainstream literature. To this end, we establish logical metatheorems that guarantee and quantify the computational content of theorems pertaining to accretive and (generalized) monotone set-valued operators. On the one hand, our results unify a number of recent case studies, while they also provide characterizations of central analytical notions in terms of proof theoretic ones on the other, which provides a crucial perspective on needed quantitative assumptions in future applications of proof mining to these branches. [ABSTRACT FROM AUTHOR]