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In this work, we propose an adaptive variation on the classical Heavy-ball method for convex quadratic minimization. The adaptivity crucially relies on so-called “Polyak step-sizes”, which consists of using the knowledge of the optimal value of the optimization problem at hand instead of problem parameters such as a few eigenvalues of the Hessian of the problem. This method happens to also be equivalent to a variation of the classical conjugate gradient method, and thereby inherits many of its attractive features, including its finite-time convergence, instance optimality, and its worst-case convergence rates.The classical gradient method with Polyak step-sizes is known to behave very well in situations in which it can be used, and the question of whether incorporating momentum in this method is possible and can improve the method itself appeared to be open. We provide a definitive answer to this question for minimizing convex quadratic functions, an arguably necessary first step for developing such methods in more general setups.

We consider the problem of linearizing a pseudo-Boolean function $f : \lbrace 0,1\rbrace ^n \rightarrow \mathbb{R}$ by means of $k$ Boolean functions. Such a linearization yields an integer linear programming formulation with only $k$ auxiliary variables. This motivates the definition of the linearization complexity of $f$ as the minimum such $k$. Our theoretical contributions are the proof that random polynomials almost surely have a high linearization complexity and characterizations of its value in case we do or do not restrict the set of admissible Boolean functions. The practical relevance is shown by devising and evaluating integer linear programming models of two such linearizations for the low auto-correlation binary sequences problem. Still, many problems around this new concept remain open.

Automatic test paper design is critical in education to reduce workloads for educators and facilitate an efficient teaching process. However, current designs fail to satisfy the realistic teaching requirements of educators, including the consideration of both test quality and efficiency. This is the main reason why teachers still manually construct tests in most teaching environments. In this paper, the quality of tests is quantitatively defined while considering multiple objectives, including a flexible coverage of knowledge points, cognitive levels, and question difficulty. Then, a model based on the technique of linear programming is delicately designed to explore the optimal results for this newly defined problem. However, this technique is not efficient enough, which cannot obtain results in polynomial time. With the consideration of both test quality and generation efficiency, this paper proposes a genetic algorithm (GA) based method, named dynamic programming guided genetic algorithm with adaptive selection (DPGA-AS). In this method, a dynamic programming method is proposed in the population initialization part to improve the efficiency of the genetic algorithm. An adaptive selection method for the GA is designed to avoid prematurely falling into the local optimal for better test quality. The question bank used in our experiments is assembled based on college-level calculus questions from well-known textbooks. The experimental results show that the proposed techniques can construct test papers with both high effectiveness and efficiency. The computation time of the test assembly problem is reduced from 3 hours to 2 seconds for a 5000-size question bank as compared to a linear programming model with similar test quality. The test quality of the proposed method is better than the other baselines.

This study investigates the surface characteristics of printing papers using fractal geometry, focusing on surface roughness and surface friction as independent properties. The fractal dimension (FD) was analyzed using the power spectral density method, which provided a more distinct characterization of paper surfaces compared to the variogram method. Surface roughness and friction were measured using a stylus-based contact profilometer, and mean absolute deviation (MAD) parameters, such as the mean absolute deviation of surface roughness (RMAD) and friction, were calculated to capture surface variability. The results revealed that while conventional parameters, such as roughness average (Ra) and the average coefficient of friction, are highly sensitive to measurement conditions, MAD-based parameters demonstrate greater robustness and stability. For instance, the regression equation for RMAD vs. Ra showed a strong correlation, with an R² value close to 1.0. However, the slopes were significantly less than one. Furthermore, FD exhibited weak correlations with surface roughness and friction, with R² values of 0.342 and 0.016, respectively, highlighting its unique ability to characterize autocorrelation or complexity of surface. Additionally, the effects of coating on paper surfaces were evaluated, revealing reduced flocculation of surface profiles but a 5% increase in FD, indicating enhanced surface complexity. These findings underscore the complementary role of FD in providing a comprehensive understanding of surface properties, with potential applications in quality control and the design of paper products.

Background:Understanding fractions in mathematics often poses greater complexity compared to integral numbers. The primary difficulty lies in students' inadequate grasp of fractional basics, notably in comparing and sequencing fractions. Aim: This research seeks to create and evaluate a learning pathway's effect on fourth graders' comprehension of fractions, with a focus on their comparison and sequencing. Method: Employing a design research validation study approach, the research progresses through preliminary design, experimental design, and retrospective analysis. Conducted in a Palembang school involving six fourth graders recommended by their teacher, data collection encompassed essay-based pre and post-tests, Student Activity Sheets, observations, interviews, and documentations. The data analysis was retrospectively carried out, anchored on HLT as the benchmark. Result: Findings reveal a student learning trajectory encompassing three principal activities. Initially, students used folding and gluing of paper to discern fraction values. Subsequently, they engaged in coloring and illustrating folds for fraction comparison. The final activity involved drawing, coloring boxes, and fraction comparison and sequencing. Overall, students showed proficiency in understanding and determining fraction values and comparing them, yet struggled with ordering certain fractions. Conclusion: The structured learning path facilitated students' understanding of basic fraction concepts, especially in comparing them. Nevertheless, reinforcing methods or approaches for teaching fraction ordering is essential.

In this paper we extend the SuperHyperAlgebra, SuperHyperGraph, SuperHyperTopology, SuperHyperSoft Set, endowed with SuperHyperOperations, SuperHyperAxioms, and SuperHyperFunctions, to the most general form of structure, from our real world, called SuperHyperStructure in any field of knowledge. A practical application of the SuperHyperStructure is presented at the end. The prefix “Hyper” [Marty, 1934] stand for the codomain of the functions and operations to be P(H), or the powerset of the set H. While the prefix “Super” [Smarandache, 2016] stands for using the Pn (H), n ≥ 2, or the n-th PowerSet of the Set H {because the set (or system) 𝐻 (that may be a set of items, a company, institution, country, region, etc.) is organized in sub-systems, which in their turn are organized in sub-sub-systems, and so on} in the domain and/or codomain of the functions and operations.

This Special Issue comprises the second collection of papers submitted by both the Editorial Board Members (EBMs) of the journal Mathematical and Computational Applications (MCA) and the outstanding scholars working in the core research fields of MCA [...]

In 1921 Mellin published a Comptes Rendu paper computing the principal solution of a polynomial using generalized hypergeometric functions of its coefficients. He used an integral transform nowadays bearing his name. Slightly over three pages, the paper is written in French in a terse style befitting the language. This article makes Mellin’s landmark result accessible to people who are not experts in hypergeometric functions and complex analysis by deriving detailed proofs that were omitted in Mellin’s paper.

In this paper, we consider a robust combinatorial optimization problem with uncertain weights and propose an uncertainty set that generalizes interval uncertainty by imposing lower and upper bounds on deviations of subsets of items. We prove that if the number of such subsets is fixed and the family of these subsets is laminar, then the robust combinatorial optimization problem can be solved by solving a fixed number of nominal problems. This result generalizes a previous similar result for the case where the family of these subsets is a partition of the set of items.

Predicting stock prices is contained in the basic approach is fundamental and technical analysis which is needed by entrepreneurs who invest their capital, this analysis is to determine the company's financial performance and must continue to be carried out, to carry out this analysis we use the help of several financial ratios where several types of ratios Return on Assets, Debt to Equity Ratio, Return on Equity, and Book Value per Share are some examples. The authors applied a quantitative descriptive approach to companies listed on the Indonesia Stock Exchange in the Pulp & Paper sector for this study. According to the Correlation and Regression tables, all of the variables ROA, ROE, DER, and BVS have an effect on stock prices, but the stock session obtained on the variables ROA, ROE, and DER has a very significant effect on stock prices but has no significant effect on stock prices on the BVS variable. So in the long term the company must implement one of two policies, namely low solvency means using less debt than own capital and a low solvency policy will not cause high interest expenses to be borne by the company so that it will affect growth.

In an era overwhelmed by academic big data, students grapple with identifying academic papers that resonate with their learning objectives and research interests, due to the sheer volume and complexity of available information. This study addresses the challenge by proposing a novel academic paper recommendation system designed to enhance personalized learning through the nuanced understanding of academic social networks. Utilizing the theory of social homogeneity, the research first constructs a sophisticated academic social network, capturing high-order social relationships, such as co-authorship and advisor–advisee connections, through hypergraph modeling and advanced network representation learning techniques. The methodology encompasses the development and integration of a hypergraph convolutional neural network and a contrastive learning framework to accurately model and recommend academic papers, focusing on aligning with students’ unique preferences and reducing reliance on sparse interaction data. The findings, validated across multiple real-world datasets, demonstrate a significant improvement in recommendation accuracy, particularly in addressing the cold-start problem and effectively mapping advisor–advisee relationships. The study concludes that leveraging complex academic social networks can substantially enhance the personalization and precision of academic paper recommendations, offering a promising avenue for addressing the challenges of academic information overload and fostering more effective personalized learning environments.

Frank and Wolfe’s celebrated conditional gradient method is a well-known tool for solving smooth optimization problems for which minimizing a linear function over the feasible set is computationally cheap. However, when the objective function is nonsmooth, the method may fail to compute a stationary point. In this work, we show that the Frank–Wolfe algorithm can be employed to compute Clarke-stationary points for nonconvex and nonsmooth optimization problems consisting of minimizing upper-$C^{1,\alpha }$ functions over convex and compact sets. Furthermore, under more restrictive assumptions, we propose a new algorithm variant with stronger stationarity guarantees, namely directional stationarity and even local optimality.

We construct a two discrete parameter family of compact minimal surfaces embedded in the Berger sphere which may be considered as the analogue of the helicoidal Karcher-Scherk surfaces.

Standards are a set of guidelines or criteria used to ensure consistency, quality, safety, and compatibility in products, services, and processes [...]

Abstract Very recently Jain et al. (J. Inequal. Appl. 2022:73, 2022) introduced the concept of multivalued F-contraction with altering distance function and investigated the existence of best proximity points for this class of mappings. In this article we prove that the existence of best proximity points for multivalued F-contraction non-self mappings can be obtained from the corresponding fixed point result for multivalued F-contraction self mappings, and so the main conclusion due to Jain et al. is not a real generalization of fixed point theory.

A scheme for the integration of $ \, {}^{C} \mathit{\boldsymbol{{D}}}^{(1/n)} $-type fractional differential equations (FDEs) is presented in this paper. The approach is based on the expansion of solutions to FDEs via fractional power series. It is proven that $ \, {}^{C} \mathit{\boldsymbol{{D}}}^{(1/n)} $-type FDEs can be transformed into equivalent $ \left(\, {}^{C} \mathit{\boldsymbol{{D}}}^{(1/n)}\right)^n $-type FDEs via operator calculus techniques. The efficacy of the scheme is demonstrated by integrating the fractional Riccati differential equation.

This study aims at understanding the role of the tools chosen throughout the processes of solving a non-routine mathematical problem and communicating its solution. In assuming that problem-solving is a synchronous activity of mathematization and expression of mathematical thinking we take our proposed Mathematical Problem Solving with Technology (MPST) model to analyze the processes of solving-and-expressing-problems. Resorting to qualitative methods for data collection and analysis, we report on the case of an 8th grader working on a covariation problem to examine the role that paper-and-pencil and digital tools play in the development of a conceptual model of the situation. We found that the resources used throughout the solving-and-expressing activity influenced the depth of the conceptual model developed, within a process of progressive mathematization. Whereas paper-and-pencil led to the emergence of a conceptual model based on exploring particular cases, the digital transformation of the solution was triggered by the process of communicating its mathematical justification and expanded the previous model. Moreover, the complexity of this activity is evidenced by its multiple sequences of processes. Finally, the integration process seems crucial as the concomitant use of technological and mathematical resources precedes major advancements in the expansion of the conceptual model.

From time to time, we hear in the news about a breach or attack on some well-known companies as just news, but it is a serious problem because it is the privacy of citizens, their money in trade and managing their businesses and projects. In this paper, we offer a review of the honey encryption planner. Honey Encryption is the encryption system that ensures flexibility versus the brute-force attack through the provision of plain reasonable text, but false for each key is invalid utilized by a trespasser to decrypt a message, two key areas are open it is difficult to create a compelling message trap that's perfect enough to deceive the striker even when he believes that he has the message in its original form. The next problem, the typo issue, where a valid phony plain text seem to a lawful user when he accidentally enters the wrong key. Our goal is to have more satisfaction disguised tricks that are perfect enough to prevent a trespasser from getting the original message, We also need new security methods because the attackers are looking for new ways to attack the systems, so we proposed a new way to protect messages and passwords well and difficult to break and take all the possibilities of attack, including the brute-force, and then the data is hidden in an image with a public secret key.

This contribution focuses on paper models of architectural surfaces, in particular on some roofing systems describable by developable ones. Drawing on an interdisciplinary approach, between Architecture and Mathematics, potentialities and criticalities of these models in explicitly conveying Geometry are investigated, in relation to educational and communicative tasks, both when they are used in a direct, tangible way, and when the use is mediated by images generated by them (thus indirect); we discuss on the possibility for models and images to communicate their explicit and implicit Geometries. The main issue discussed is that a material or analytical description unequivocally allows to grasp all the peculiarities of geometrical shapes, while other representations are subject to critical selection of data and are therefore affected by subjective interpretations; similarly, the translation of the physical model into images is the result of choices which emphasize certain object peculiarities over others and is thus less objective. Hence the importance of the physical model (as well as its digital counterparts) which, even if not used directly, can be complementary to a content that, alone, would be partial and/or misleading.

Recently, the systems of e-learning are improved technologically and the led to the emergence of e-learning systems that reached the level of adaptation to students. Through which, it changed the entire education system during the Internet era. Nonetheless, the use of rule-based, assumption-based, and network-based method have some vital methodologies used to implement learner models across adaptive learning systems. The so common way to structure the learner models approaches rely on the personalization and user modelling. However, personalization and user modeling found out to be the best approaches-not only in developing students' talents but also in allowing students to take their own learning direction and making sure that they are using their potential to the fullest. The mismatching in viewpoints and perceptions between teachers and technicians along with a lack of appropriate technical knowledge have been identified as some of the major challenges affecting the learner model development. the main objective of this article is to show the use of different approaches through the recent scholars’ in implementing learner models within adaptive e-learning systems. Moreover, approaches and challenges in implementing learner models are also described

Let $ R $ be a ring with identity. The commuting graph of $ R $ is the graph associated to $ R $ whose vertices are non-central elements in $ R $, and distinct vertices $ A $ and $ B $ are adjacent if and only if $ AB = BA $. In this paper, we completely determine the automorphism group of the commuting graph of $ 2\times 2 $ matrix ring over $ \mathbb{Z}_{p^{s}} $, where $ \mathbb{Z}_{p^{s}} $ is the ring of integers modulo $ p^{s} $, $ p $ is a prime and $ s $ is a positive integer.

The human capability to react or adapt to upcoming changes strongly relies on the ability to forecast them [...]

Simonas Vainbergas, a teacher of Jewish primary schools in prewar Lithuania (1894?), was one of few his colleagues that actively collaborated with Lithuanian pedagogical journals. He published in them 11 papers in didactics of mathematics about teaching mathematics at primary schools. The said papers helped young teachers of primary schools to improve their qualification. There is a great probability that S. Vainbergas was a victim of holocaust.

Abstract In a recently published theorem on the split common fixed point problem for strict pseudocontractive and asymptotically nonexpansive mappings, Tang et al. (J. Inequal. Appl. 2015:305, 2015) studied a uniformly convex and 2-uniformly smooth real Banach space with the Opial property and best smoothness constant κ satisfying the condition 0 < κ < 1 2 $0

Perception is an individual's ability to respond, interpret, and distinguish a view of any information to a stimulus. So the aims of this study was to find out: (1) students' perceptions of the use of an equation editor in writing mathematical notation as assignments for calculus class I papers, (2) students' perceptions of writing calculus I paper assignments using the manual method (handwriting). The research subjects consisted of 16 students majoring in Extension Informatics Engineering (afternoon class) Semester I. The type of research was descriptive qualitative. Data collection techniques are interviews. The analysis stage is to analyze the results of the interviews. The results of the study concluded that: (1) 11 (eleven) students agreed to use the equation editor in writing calculus I paper assignments,the rest were still confused about the use of the equation editor; and (2) all students do not agree if the paper is written using the manual method (handwriting) because the results are not neat and take a long time.

Investigating the research trends within a scientific domain by analyzing semantic information extracted from scientific journals has been a topic of interest in the natural language processing (NLP) field. A research trend evaluation is generally based on the time evolution of the term occurrence or the term topic, but it neglects an important aspect—research publication latency. The average time lag between the research and its publication may vary from one month to more than one year, and it is a characteristic that may have significant impact when assessing research trends, mainly for rapidly evolving scientific areas. To cope with this problem, the present paper is the first work that explicitly considers research publication latency as a parameter in the trend evaluation process. Consequently, we provide a new trend detection methodology that mixes auto-ARIMA prediction with Mann–Kendall trend evaluations. The experimental results in an electronic design automation case study prove the viability of our approach.

This Special Issue comprises the first collection of papers submitted by the Editorial Board Members (EBMs) of the journal Mathematical and Computational Applications (MCA), as well as outstanding scholars working in the core research fields of MCA [...]

Theprocess in which waste paper is collected and then reprocessed for reuse iscalled paper recycling. Paper recycling is very often routine of human life.Paper recycling is very important to reduce deforestation and pollution. It hasbeen analyzed that scrap dealer plays a vital role in this cycle that collectswaste paper from distributor and customer and then sent it to the paperindustry, so the effect of scrap dealers is observed here. This waste paperrecycling model is divided into four compartments namely paper industry,distributor, customer and scrap dealer. The model is proposed as a system ofnon-linear differential equation. The basic reproduction number is computed tosee the impact of scrap dealer.

Nowadays, forecasting applications are receiving unprecedent attention thanks to their capability to improve the decision-making processes by providing useful indications [...]

Paper waste in the mockups design with regular, irregular, and amorphous patterns is a critical problem in digital printing presses. Paper waste reduction directly impacts production costs, generating business and environmental benefits. This problem can be mapped to the two-dimensional irregular bin-packing problem. In this paper, an iterated local search algorithm using a novel neighborhood structure to detect overlaps between amorphous shapes is introduced. This algorithm is used to solve the paper waste problem, modeled as one 2D irregular bin-packing problem. The experimental results show that this approach works efficiently and effectively to detect and correct the overlaps between regular, irregular, and amorphous figures.

We correct the proof of Theorem 2 in the mentioned paper concerning finite-difference equilibrium solutions.

Environmental pollution has become an important obstacle on the path of ecological civilization construction, and it is urgent to control environmental pollution. By establishing an evolutionary game model, this thesis focuses on analyzing how paper-making enterprises choose their own emission reduction strategies under the reward and punishment mechanism. It further analyzes how social welfare changes under the reward and punishment mechanism, and finally through simulation research, this thesis analyzes the evolutionary paths of paper-making enterprises’ pollution emission strategies under the reward and punishment mechanism. The results of the reward and punishment mechanism are as follows: under the static reward and punishment mechanism, the game system will repeatedly oscillate around a point. There is no stable equilibrium point at this time. However, under the dynamic reward and punishment mechanism, the game system will tend to a stable equilibrium point. The results of social welfare analysis show that high-intensity rewards will reduce the amount of pollution discharged by paper-making enterprises, thereby maximizing social welfare. On the contrary, when paper-making enterprises discharge a large amount of pollution, they will be subject to high-intensity penalties. When facing high-intensity punishments, paper-making enterprises will tend to not to discharge. So social welfare is also maximized. The simulation research results show that reasonable punishment strategies are more effective than reward ones. Based on this, the author proposes countermeasures, such as establishing a reasonable reward and punishment mechanism, reasonably determining the reward and punishment intensity for polluting enterprises. The emission reduction strategies of paper-making enterprises will be affected by the government’s reward and punishment mechanism. A deep study of its internal mechanism is not only of great significance for pollution control but also of great significance for the development of a green economy.

Aiming at the problem of easy tampering and difficult integrity authentication of paper text documents, this paper proposes a robust content authentication method for printed documents based on text watermarking scheme resisting print-and-scan attack. Firstly, an authentication watermark signal sequence related to content of text document is generated based on the Logistic chaotic map model; then, the authentication watermark signal sequence is embedded into printed paper document by using a robust text watermarking scheme; finally, the watermark information is extracted from scanned image of paper document, and compared with the authentication watermark information calculated in real time by the text document content obtained by OCR technology, thereby performing content integrity authentication of the paper text documents. Experimental results show that our method can achieve the robust content integrity authentication of paper text documents, and can also accurately locate the tampering position. In addition, the document after embedding the watermark information has a good visual effect, and the text watermarking scheme has a large information capacity.

This paper proposes the use of notebooks for the design documentation and tool interaction in the rigorous design of embedded systems. Conventionally, a notebook is a sequence of cells alternating between (textual) code and prose to form a document that is meant to be read from top to bottom, in the spirit of literate programming. We extend the use of notebooks to embedded systems specified by pCharts. The charts are visually edited in cells inline. Other cells can contain statements that generate code and analyze the charts qualitatively and quantitatively; in addition, notebook cells can contain other instructions to build the product from the generated code. This allows a notebook to be replayed to re-analyze the design and re-build the product, like a script, but also allows the notebook to be used for presentations, as for this paper, and for the inspection of the design. The interaction with the notebook is done through a web browser that connects to a local or remote server, thus allowing a computationally intensive analysis to run remotely if needed. The pState notebooks are implemented as an extension to Jupyter. The underlying software architecture is described and the issue of proper placement of transition labels in charts embedded in notebooks is discussed.

The administration of A/B exams usually involves the use of items. Issues arise when the pre-establishment of a question bank is necessary and the inconsistency in the knowledge points to be tested (in the two exams) reduces the exams ‘fairness’. These are critical for a large multi-teacher course wherein the teachers are changed such that the course and examination content are altered every few years. However, a fair test with randomly participating students should still be a guaranteed subject with no item pool. Through data-driven decision-making, this study collected data related to a term test for a compulsory general course for empirical assessments, pre-processed the data and used item response theory to statistically estimate the difficulty, discrimination and lower asymptotic for each item in the two exam papers. Binary goal programing was finally used to analyze and balance the fairness of A/B exams without an item pool. As a result, pairs of associated questions in the two exam papers were optimized in terms of their overall balance in three dimensions (as the goals) through the paired exchanges of items. These exam papers guarantee their consistency (in the tested knowledge points) and also ensure the fairness of the term test (a key psychological factor that motivates continued studies). Such an application is novel as the teacher(s) did not have a pre-set question bank and could formulate the fairest strategy for the A/B exam papers. The model can be employed to address similar teaching practice issues.

In this paper we correct an inaccuracy that appears in the proof of Theorem 1. in Czerwik [1].

Coinduction occurs in two guises in Horn clause logic: in proofs of self-referencing properties and relations, and in proofs involving construction of (possibly irregular) infinite data. Both instances of coinductive reasoning appeared in the literature before, but a systematic analysis of these two kinds of proofs and of their relation was lacking. We propose a general proof-theoretic framework for handling both kinds of coinduction arising in Horn clause logic. To this aim, we propose a coinductive extension of Miller et al's framework of uniform proofs and prove its soundness relative to coinductive models of Horn clause logic.

RedPRL is an experimental proof assistant based on Cartesian cubical computational type theory, a new type theory for higher-dimensional constructions inspired by homotopy type theory. In the style of Nuprl, RedPRL users employ tactics to establish behavioral properties of cubical functional programs embodying the constructive content of proofs. Notably, RedPRL implements a two-level type theory, allowing an extensional, proof-irrelevant notion of exact equality to coexist with a higher-dimensional proof-relevant notion of paths.

The first sentence in the abstract should be replaced with the sentence "A sequence $(x_{k})$ is called arithmetically convergent if for each $\varepsilon > 0$ there is an integer $n_{0}$ such that $|x_{m} - x_{}| \geq n_{0}$, where the symbol $< m, n >$ denotes the greatest common divisor of the integers $m$ and $n$".

The purpose of this short note is to present a correction of the proof of the main result given in the paper “Equivalence of the existence of best proximity points and best proximity pairs for cyclic and noncyclic nonexpansive mappings,” Demonstr. Math. 53 (2020), 38–43.

The Abbreviated Math Anxiety Scale (AMAS) is one of the most popular instruments measuring math anxiety (MA). It has been validated across several linguistic and cultural contexts. In this study, we investigated the extent of administration method invariance of the AMAS by comparing results (average scores, reliabilities, factorial structure) obtained online with those from paper-and-pencil. We administered the online version of the AMAS to Polish students. Results indicate that psychometric properties of the AMAS do not differ between online and paper-and-pencil administration. Additionally, average scores of the AMAS did not differ considerably between administration forms, contrary to previous results showing that computerized measurement of MA leads to higher scores. Therefore, our results provide evidence for the usefulness of the AMAS as a reliable and valid MA measurement tool for online research and online screening purposes across cultures and also large similarity between administration forms outside an American-English linguistic and cultural context. Finally, we provide percentile and standard norms for the AMAS for adolescents and adults (in the latter case for both online and paper-and-pencil administration) as well as critical differences for the comparison of both subscales in an individual participant for practical diagnostic purposes.

In this paper, we improve some recent coupled fixed point results for single-valued operators in the framework of ordered b-metric spaces established by Bota et al. [M-F. Bota, A. Petrusel, G. Petrusel and B. Samet, Coupled fixed point theorems for single-valued operators in b-metric spaces, Fixed Point Theory Appl. (2015) 2015:231]. Also, we prove that Perov-type fixed point theorem in ordered generalized $b$-metric spaces is equivalent with Ran-Reurings-type theorem in ordered b-metric spaces.

In this short note we indicate some improvement of an article published in this journal by Crespo, Ivorra and Ramos [6]. The techniques used are connected with several smoothing effects associated with linear partial differential operators which give rise to some accretive operators in $L^1(\Omega )$, as well as with some $H^2(\Omega )$ estimates independent on time.

The formation index of filter paper is one of the most important characteristics used in industrial quality control. Its estimation is often based on subjective comparison chart rating or, even more objective, on the power spectrum of the paper structure observed on a transmission light table. It is shown that paper formation can be modeled as Gaussian random fields with a well defined class of correlation functions, and a formation index can be derived from the density of the Bartlett spectrum estimated from image data. More precisely, the formation index is the mean of the Bessel transform of the correlation taken for wave lengths between 2 and 5 mm.

This paper examines the added value of a digital tool that constitutes a new model to introduce students to multiplication. Drawing on the theory of semiotic mediation, the semiotic potential of this new model is analysed with respect to the same task that can be solved in two different settings (the digital tool and pencil and paper). The analysis shows that the task solutions undergo significant changes depending on to the technological settings. Even though the end product of the model–task dyads might look the same in both settings, the product emerges from the different processes that would mediate quite different meanings for multiplication. This suggests that while designing tasks that involve mathematical models, rather than focusing only on the end product, considering the whole process would reveal the extensive potential meanings the model–task dyad can mediate.

Some recent analytical papers have explored limiting behaviors of Landaude Gennes models for liquid crystals in certain extreme ranges of the model parameters: limits of “vanishing elasticity” (in the language of some of these papers) and “low-temperature limits.” We use simple scaling analysis to show that these limits are properly interpreted as limits in which geometric length scales (such as the size of the domain containing the liquid crystal material) become large compared to intrinsic length scales (such as correlation lengths or coherence lengths, which determine defect core sizes). This represents the natural passage from a mesoscopic model to a macroscopic model and is analogous to a “London limit” in the Ginzburg-Landau theory of superconductivity or a “large-body limit” in the Landau-Lifshitz theory of ferromagnetism. Known relevant length scales in these parameter regimes (nematic correlation length, biaxial coherence length) can be seen to emerge via balances in equilibrium Euler-Lagrange equations associated with well-scaled Landau-de Gennes free-energy functionals.

We answer a question posed by S.G. Kim in [3] and show that some of the results of his paper are immediate consequences of known results.

Creativity is recognized nowadays as a basic skill. However, the educational system fails in promoting their development. On the other hand, a growing acknowledgement of the importance of geometry emerges. Conceptual renewal, namely on isometries, requires new approaches based on mathematically significant tasks. The digital revolution has brought powerful tools but demands changes in the educational process. The use of Dynamic Geometry Environments (DGE), complementing ‘paper and pencil’, can contribute to provide rich learning environments, enhanced by Classroom Management Systems (CMS) such as iTALC. Indeed, the qualitative case study we carried out suggests that: the creation of an “atmosphere” of cooperation, collaboration and sharing seems to increase creativity dimensions; the use of DGE can facilitate the emergence of more creative productions; development of knowledge and geometrical capabilities seems to benefit from a complementary approach that combines DGE and ‘paper and pencil’ environments. Different approaches, with a more technological and exploratory nature seem to promote more favourable attitudes towards mathematics in general, and geometry, in particular.

This appendix gives a lower bound of the Billingsley-Hausdorff dimension of a level set related to Birkhoff average in the “non-compact” symbolic space $\mathbb{N}^{\mathbb{N}}$, defined by Gibbs measure.