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AbstractQuantum computing, grounded in the principles of quantum mechanics, has ushered in a new era of intriguing possibilities and fresh scientific insights. In this document, we present an innovative algorithm tailored for the encryption and decryption of images. This algorithm harnesses the quasi-probability values extracted from each state within the quantum system, represented as |ψ〉. These numerical values are seamlessly integrated with conventional data to facilitate image encryption and decryption processes. Our methodology undergoes comprehensive validation and evaluation through extensive simulations performed on the IBM Qiskit Aer simulator. We subject the generated numerical sequence to rigorous statistical scrutiny using the NIST SP 800-22 suite, ensuring its authenticity and reliability. Employing a quantum system comprising 3 qubits and uniform rotation gates, our algorithm produces a dataset consisting of 41,943,040 binary digits. Additionally, we conduct a thorough assessment encompassing both visual and statistical analyses to ascertain the effectiveness and robustness of our proposed algorithm. Furthermore, we emphasize the critical importance of achieving a quasi-probability error rate of 10−6 for real-world implementation, highlighting the practical viability and scalability of our approach. Through comparative analysis and meticulous examination of correlation patterns, our study provides invaluable insights into the distinctive characteristics and efficacy of our encryption scheme. [ABSTRACT FROM AUTHOR]

The Huneke-Wiegand conjecture is a decades-long open question in commutative algebra. García-Sánchez and Leamer showed that a special case of this conjecture concerning numerical semigroup rings k [ Γ ] can be answered in the affirmative by locating certain arithmetic sequences within the numerical semigroup Γ. In this paper, we use their approach to prove the Huneke-Wiegand conjecture in the case where Γ is generated by a generalized arithmetic sequence and showcase how visualizations can be leveraged to find the requisite arithmetic sequences. [ABSTRACT FROM AUTHOR]

In a pre-service mathematics methods class I taught, in which we mathematized political districting (first horizontally, then vertically), student questions led to engaging mathematics, in particular, the development of a new number sequence. [ABSTRACT FROM AUTHOR]

This paper explores the specialized knowledge mobilized by a mathematics teacher in the selection and use of examples for teaching sequences. Taking an experimental case study approach, we analyse the examples deployed in a series of third-year secondary level lessons on sequences and identify the different knowledge subdomains activated according to the mathematics teachers' specialized knowledge analytical model. We will analyse active and passive examples, pointing out the mathematical entity that is being exemplified and the aspect of this entity which is being emphasized by the example. The results identify the different subdomains and categories which are drawn on in the selection and use of examples, along with the various interconnections across knowledge subdomains which interact in the process. [ABSTRACT FROM AUTHOR]

The aim of this note is to give a general theorem related to the divergence of series. A direct consequence of this theorem is the divergence of harmonic series. Furthermore, we show that this theorem can imply the divergence of some other familiar divergent series. [ABSTRACT FROM AUTHOR]

An m-sequence is the one of the largest period among those produced by a linear feedback shift register. It possesses several desirable features of pseudorandomness such as balance, uniform pattern distribution and ideal autocorrelation for applications to communications. However, it also possesses undesirable features such as low linear complexity. Here we prove a nontrivial upper bound on its arithmetic autocorrelation, another figure of merit introduced by Mandelbaum for error-correcting codes and later investigated by Goresky and Klapper for FCSRs. The upper bound is close to half of the period and hence rather large, which gives an undesirable feature. [ABSTRACT FROM AUTHOR]

Over the past decades, the Multi-Task Learning (MTL) problem has attracted much attention in the artificial intelligence and machine learning communities. However, most published work in this area focuses on point estimation; that is, estimating model parameters and/or making predictions. This article studies another important aspect of the MTL problem: uncertainty quantification for model choices and predictions. To be more specific, this article approaches the MTL problem with multivariate regression and develops a novel method for deriving a probability density function on the space of all potential regression models. With this density function, point estimates, as well as confidence and prediction ellipsoids, can be obtained for quantities of interest, such as future observations. The proposed method, termed GMTask, is based on the generalized fiducial inference (GFI) framework and is shown to enjoy desirable theoretical properties. Its promising empirical properties are illustrated via a sequence of numerical experiments and applications to two real datasets. for this article are available online. [ABSTRACT FROM AUTHOR]

An extension of the Laplace transform obtained by using the Laguerre-type exponentials is first shown. Furthermore, the solution of the Blissard problem by means of the Bell polynomials gives the possibility to associate to any numerical sequence a Laplace-type transform depending on that sequence. Computational techniques for the corresponding transform of analytic functions, involving Bell polynomials, are derived. [ABSTRACT FROM AUTHOR]

We illustrate the identity C n , n + 2 = C n + 2 , n + 1 , where C k , n denotes the n th k-gonal number. [ABSTRACT FROM AUTHOR]

This paper considers the problem of sequencing mixed-model assembly lines (MMALs). Our goal is to determine the sequence of products to minimise work overload. This problem is known as the MMAL sequencing problem with work overload minimisation: we explicitly use task operation times to find the product sequence. This paper is based on an industrial case study of a truck assembly line. In this industrial context, as a reaction to work overloads, operators at the workstations finish their tasks before the product reaches the next workstation, but at the expense of fatigue. Furthermore, there are different types of operators, each with different task responsibilities. The originality of this work is to model this new way of reacting against work overloads, to integrate three operator types in the sequencing model and to apply the developed methods in a real industrial context. To solve this problem, we propose three meta-heuristic procedures: genetic algorithm, simulated annealing and a combination of these two meta-heuristics. All the methods proposed are tested on industrial data and compared to the solutions obtained using a mixed-integer linear programme. The results show that the proposed methods considerably improve the results of the current procedure used in the case study. [ABSTRACT FROM AUTHOR]

The measurement of the line impedance in long lines is adversely affected by fault and system parameters such as, the type and location of the fault, fault resistance, short circuit MVA of the source (presence of weak source), power transfer angle etc. This paper proposes a new technique to measure the line impedance during fault condition accurately, considering wide variations in the aforementioned variables. It is based on the mathematical analysis of the sequence network diagram of a non-homogeneous 400 kV, 50 Hz double infeed line, considering a single line-to-ground fault. Instead of using voltage and current vectors for the analysis, the impedance vectors are used to calculate the new impedance seen at the time of fault. The technique is verified using MATLAB/SIMULINK software. The simulation results conclude that the new measuring technique is precise, simple to understand, and rigid to the changes in all the system and fault parameters considered in this paper. [ABSTRACT FROM AUTHOR]

Bioinformatics in the present day has been firmly established as a regulator in genomics. In recent times, applications of Signal processing in exon prediction have gained a lot of attention. The exons carry protein information. Proteins are composed of connected constituents known as amino acids that characterize the specific function. Conversion of the nucleotide character string into a numerical sequence is the gateway before analyzing it through signal processing methods. This numeric encoding is the mathematical descriptor of nucleotides and is based on some statistical properties of the structure of nucleic acids. Since the type of encoding extremely affects the exon detection accuracy, this paper is devised for the review of existing encoding (mapping) schemes. The comparative analysis is formulated to emphasize the importance of the genetic code setting of amino acids considered for application related to computational elucidation for exon detection. This work covers much helpful information for future applications. [ABSTRACT FROM AUTHOR]

This article considers a single-machine due-window assignment scheduling problem based on a common flow allowance (i.e. all jobs have slack due window (SLKW)). We assume that the actual processing time of a job is a function of its position in a sequence (learning effect) and its continuously divisible and non-renewable resource allocation. The problem is to determine the optimal due windows, the optimal resource allocation and the processing sequence simultaneously to minimise costs for earliness, tardiness, the window location, window size, makespan and resource consumption. For a linear or a convex function of the amount of a resource allocated to the job, we provide a polynomial time algorithm, respectively. Some extensions of the problem are also shown. [ABSTRACT FROM PUBLISHER]

This study is concerned with the manufacturing model that has a common machine at stage one and two parallel dedicated machines at stage two. All jobs need to be processed on the stage-one common machine. After the stage-one processing, the jobs of type 1 (type 2) will route to the first (second) dedicated machine at stage two. We first elaborate several published works on makespan minimisation which are not known to other streams of recent works. While the minimisation of maximum lateness is strongly NP-hard, we develop a linear-time algorithm to solve the case where two sequences of the two job types are given a priori. [ABSTRACT FROM PUBLISHER]

ABSTRACTIn human-computer interactions, higher-level visuospatial function is likely needed to effectively use the interface. The aim of this study is to clarify whether individuals with visuospatial defects can use electronic devices effectively. We quantitatively and qualitatively analyzed the ability of seven individuals with Bálint syndrome and seven individuals with left-unilateral spatial neglect (USN) to input a digit sequence into a flat touch interface. Control groups consisted of seven individuals with memory deficits and 11 healthy individuals. Participants with Bálint syndrome took longer and had more hesitations than the USN group and the two control groups to input numerical sequences (Steel-Dwass test, p < .01). In addition, participants with Bálint syndrome had a high percentage of hesitations for exploration of the button array on the interface relative to USN and the memory deficit group (Fisher's exact test, p < .05). Regarding neuropsychological data, participants with Bálint syndrome had a lower score for visuospatial working memory than participants with USN and the memory deficits control group (Steel-Dwass test, p < .01). The results shed some light on the relation between visuospatial working memory deficits and the spatial perception of interface layouts and spatial control during electronic device operation. [ABSTRACT FROM AUTHOR]

We study a scheduling problem with the operations that require renewable as well as non-renewable resources. After an operation has been completed, the non-renewable resource is depleted whereas the renewable resource can be made available for the next operation. Of both the renewable and the non-renewable resources limited amounts are available and they need to be transported to the locations where they are needed. The operations have deadlines, and the availability of the renewable resources depends on the sequence of the operations. Such operations scheduling problems are commonly encountered in the practices of emergency logistics that deliver medical services to the affected areas after a disaster, where renewable resources typically refer to medical teams and non-renewable resources refer to medical supplies. We present a complexity classification for our problem and show where the borderline lies between NP-hardness and polynomial time solvability. We analyse the structural properties of our problem, provide strongly polynomial-time solutions for four special cases and list the cases that are computationally intractable. Finally, we propose a framework of heuristic procedures for solving more general versions of this problem. [ABSTRACT FROM AUTHOR]

Evolutionary information is essential for the protein annotation. The number of homologs of a protein retrieved is correlated with the annotations related to the protein structure or function. With the continuous increase in the number of available sequences, fast and effective homology detection methods are particularly important. To increase the efficiency of homology detection, a novel method named CONVERT is proposed in this paper. This method regards homology detection as a translation task and presents a concept of representative protein. Representative proteins are not real proteins. A representative protein corresponds to a protein family, it contains the characteristics of the family. Our method employs the seq2seq model to establish the many-to-one relationship between proteins and representative proteins. Based on the many-to-one relationship, CONVERT converts protein sequences into fixed-length numerical representations, so as to increase the efficiency of homology detection by using numerical comparison instead of sequence alignment. For alignment results, our method adopts ranking to obtain a sorted list. We evaluate the proposed method on two benchmark datasets. The experimental results show that the performances of our method are comparable with the state-of-the-art methods. Meanwhile, our method is ultra-fast and can obtain results in hundreds of milliseconds. [ABSTRACT FROM AUTHOR]

Benford's law is an empirical "law" governing the frequency of leading digits in numerical data sets. Surprisingly, for mathematical sequences the predictions derived from it can be uncannily accurate. For example, among the first billion powers of 2, exactly 301029995 begin with digit 1, while the Benford prediction for this count is 10 9 log 10 2 = 301029995.66 ... . Similar "perfect hits" can be observed in other instances, such as the digit 1 and 2 counts for the first billion powers of 3. We prove results that explain many, but not all, of these surprising accuracies, and we relate the observed behavior to classical results in Diophantine approximation as well as recent deep conjectures in this area. [ABSTRACT FROM AUTHOR]

Algebra is a key course in the high school mathematics sequence. Despite its prominence, large-scale examinations of algebra instruction are rare and it is not clear whether and how instructional practices that support students' learning of algebra content manifest in classroom instruction. Drawing on video from 108 ninth-grade algebra lessons from 5 districts recorded as part of the Measures of Effective Teaching (MET) Project, I describe instruction using scores from a newly developed, algebra-focused observation tool to ground the description of instructional practice in the content being taught. I present the range of instructional formats and the nature and quality of algebra-focused instructional features related to the teaching of procedures and to the ways in which teachers leverage connections to support students' algebra learning. To illustrate these descriptive results, I present case studies of 2 lessons: 1 rated typical and 1 rated high-quality. I find that although the majority of lessons in the sample follow traditional formats, specific instructional features that benefit student learning in algebra are present to a modest degree across lessons, though not often at high levels of quality. The case lessons demonstrate both glimmers of promise and missed opportunities to engage in instruction that benefits student learning of algebra. I discuss the implications of these results for improving the quality of algebra teaching and argue for the affordances of a content-focused observation tool as a lens for instructional improvement efforts. [ABSTRACT FROM AUTHOR]

In this paper, we develop a formulation for the economic lot scheduling problem (ELSP) wherein products with sequence-dependent setups are to be scheduled on a single facility to minimise the average sum of inventory holding and setup costs. We show that our formulation, based on the time varying lot size approach, always provides feasible schedules for any given sequence and is independent of the setups being sequence-independent or sequence-dependent. We compare our schedule with the schedule proposed by Dobson (1992) and reveal the infeasibility associated with Dobson's formulation. A numerical example evaluating schedules with both cases of setups: sequence-independent and sequence-dependent, demonstrates our assertion. [ABSTRACT FROM AUTHOR]

Lotsizing in capacitated pure flow shop with sequence-dependent setups has been considered in this paper. An exact formulation of the problem is provided as a mixed-integer program. It is well known that the capacitated lotsizing and scheduling problem (CLSP) is NP-hard. The introduction of serially arranged machines and sequence-dependent setups makes the problem even more complicated. Five MIP-based heuristics based on iterative procedures are provided. The first three heuristics are based on the original model but to solve non-small instances of problem, the last two heuristics are based on permutation flow shop problem which ignores the majority of combinations. To test the accuracy of heuristics, two lower bounds are developed and compared against the optimal solution. The trade-offs between solution quality and computational times of heuristics are also provided. [ABSTRACT FROM AUTHOR]

A mixed-model assembly line is commonly used in the automobile industry. When there are multiple departments on an assembly line, there are usually different sequencing considerations from various departments. Intentional sequence alteration to accommodate a different sequencing consideration can be needed for a downstream department. Unintentional sequence alteration may also take place due to rework or equipment breakdowns. There is also an increasingly common practice in automobile assembly to have parts sequenced before delivering to the final assembly line. To achieve sequenced parts delivery, the sequence needs to be known in advance. Thus, addressing sequence alteration and restoration becomes more relevant for an automobile mixed-model assembly line. A number of sequence alteration methods to accommodate a downstream department's sequencing considerations are presented. One method easily supports sequence restoration of the sequence altered by the method. Two sequence restoration methods for restoring the sequence altered by unintentional reasons are discussed; the proper sizing of the two restoration methods are also addressed. These sequence alteration and restoration approaches mainly address the design and control aspects of the mixed-model assembly line. A case study based on an automobile assembly plant is presented to demonstrate the use of these methods. [ABSTRACT FROM AUTHOR]

The input-weighted average standard processing time for a multi-item machine is discussed in this paper. For practical purposes it is important to have a short average processing time. It is shown that the input-weighted average processing time does not depend on the scheduling, sequencing and lot-sizing; it is only influenced by the total input and by the individual standard processing times. Furthermore, the relationship between the individual standard processing time and the average standard processing time is investigated. It is proven that the input-weighted average standard processing time is a convex function of the standard processing time of one certain item. An interesting consequence of the convexity is the fact that a decrease of the standard processing time of an item with a standard processing time less than half of the input-weighted average standard processing time causes an increase of the input-weighted average processing time. [ABSTRACT FROM AUTHOR]

Based on zigzag and contour-offset methods for cutting layers described in pixel maps, three unified tool path generation modules for NC rough cutting of sculptured surfaces are presented. The zigzag-stack-without-island module generates the tool path for a to-be-machined area without any inside island. The zigzag-stack-with-islands module is for a to-be-machined area with single or multiple inside islands. For small corners or to-be-machined areas left by the first cutter in a cutting sequence, the boundary-offset-for-corners module is used. An obstacle avoidance module that generates rapid traversal tool paths between adjacent cutting layers or different cutting tool path segments in the same cutting layer is also developed. These modules are easy to implement and robust. When combined with the divide-and-conquer machining method, unnecessary lifts can be avoided and the generated tool paths will be more effective in terms of total machining time for the best cutting sequence (Tao 1999). [ABSTRACT FROM AUTHOR]

Process capability indices such as Cp, Cpk and Cpm have been widely used in manufacturing for process assessment and for evaluation of purchasing decisions. Quality engineers and process operators are often asked to summarize the quality of a process by combining a sequence of Cpkor Cpm. This paper compares three different methods for combining the estimates of the process capability indices Cpk, Cpm and Cpmk from a sequence of independent samples. The criterion of minimum mean-squared-error (MSE) is applied. We find that, in general, methods for the combination of sample process capability indices based on the overall sample mean and pooled sample variance give smaller MSE than those based on weighted averages of the estimates of process capability indices. [ABSTRACT FROM AUTHOR]

Machine sequencing is an essential step towards the physical layout of machines as it determines the relative positions of machines in a layout. Linear machine sequencing is most popular due to its efficient flow structure and its ability to arrange machines in various flow layouts. For example, in a conveyor or an AGV system, the layout can be a straight line, a U-shape line, a serpentine line, or a loop. This paper addresses the problem of determining a common linear machine sequence (also known as a linear flowline) for multi-products with different operation sequences. Each machine type has a limited number of duplicates available for use. The objective is to minimize the total flow distance travelled by the products on this linear flowline. The flows of products are allowed in the forward direction, either in-sequence or by-pass (i.e. no backtrack movements are allowed). To solve this problem, we first construct a feasible flow network that satisfies all operation sequences and then transform it into a linear machine sequence. To improve the solution, a modified simulated annealing is utilized. The new algorithm was tested on several examples in the literature. [ABSTRACT FROM AUTHOR]

This paper presents the derivation and evaluation of two new MILP models for the SDST flowshop sequencing problem. The first model, TS1, was derived directly from the assignment-problem-based MILP model for the regular flowshop that Stafford modified from the original Wagner three-machine all-integer model. The second model, TS2, combined the properties of model TS1 with the looser constraints approach of Srikar and Ghosh, as modified by Stafford and Tseng (model SG*). Three experiments were used to compare both new models to the SG* model. Both new models were found to use significantly less computation time than the SG* model, especially for problem sizes of 6 or more jobs and 5 or more machines. The TS1 model used significantly less computation time than the TS2 model, making it the current best MILP model in the SDST flowshop literature. [ABSTRACT FROM AUTHOR]

This paper focuses on the operation sequencing problem in process planning, which is the problem of determining the sequence of operations required for producing a part with the objective of minimizing the sum of machine, set-up and tool change costs. In general, operation sequencing in process planning has been a difficult optimization problem, since it has combinatorial characteristics and complex precedence relations. This paper first suggests a precedence-directed graph to describe the precedence relations among operations with a compact form. Then, using the directed graph, the authors develop optimal and heuristic branch and fathoming algorithms that can give optimal and near optimal solutions respectively. Application of the two algorithms is illustrated using an example part. Also, to show the performance of the suggested algorithms, computational experiments were done on randomly generated problems and the results show that the heuristic algorithm gives optimal solutions for all the generated problems with much shorter computation time. [ABSTRACT FROM AUTHOR]

The paper focuses on the modelling and evaluating product end-of-life options, which is the problem of representing products and determining disassembly sequences with the objective of maximizing revenue. For the problem considered here, three algorithms were developed. The first is the algorithm to generate the product recovery graph semi-automatically for a given product liaison graph. Then, using the generated product recovery graph, another algorithm is developed to obtain optimal disassembly plans that maximize revenue. This algorithm is based on the backward calculation so that the hyperedges of the recovery graph are visited only once. Finally, to cope with uncertainties of the end-of-life products, a recovery graph questioning algorithm is suggested to find the margin of allowed revenue reduction of a given target edge that maintains the same optimal plan. Application of the three algorithms is illustrated using an example. [ABSTRACT FROM AUTHOR]

In this paper, we propose a modelling approach for the medium term planning of manufacturing systems characterized by coexisting large volume and small volume products, in which changeovers play a critical role in achieving maximum efficiency. Although the model is based upon the large time bucket paradigm, it is capable of representing start-ups by sequencing the lots of items produced in long sequences. Specifically, we consider a capacitated lot-sizing problem with parallel machines, in which the products have a three-level hierarchical structure: end items are aggregated into families, which in turn are aggregated into types. Minor set-ups and major changeovers take place when switching between families within a type or between types, respectively. The resulting mathematical programming problem is decomposed via Lagrangean relaxation, leading to sub-problems that can be solved in polynomial time. The whole approach has been validated by applying it to large size case studies drawn from the textile industry. [ABSTRACT FROM AUTHOR]

Given a finite set of positive integers G and polynomials , , with degree of equal to g, we associate to them a sequence of Charlier type polynomials defined from the Charlier polynomials by using certain Casoratian determinants (whose entries are the polynomials). Charlier type polynomials are eigenfunctions of higher order difference operators. When , the polynomials are also orthogonal, and then satisfy a three term recurrente relation. In this paper, we prove that whatever the polynomials 's are, the Charlier type polynomials always satisfy higher order recurrence relations. We also introduce and characterize the algebra of difference operators associated to the recurrence relations satisfied by the sequence. Our characterization is constructive and surprisingly simple. As a consequence, we prove that is, essentially, the unique choice such that the polynomials are orthogonal with respect to a measure. [ABSTRACT FROM AUTHOR]

Let be the set of sequences (L1,... , Ln), , admitting a minimal partial realisation of order d. To each , we associate two sequences of integers with r1 ≥ r2 ≥ ... ≥ rβ > 0 = rβ+1 = ... = rn and with s1 ≥ s2 ≥ ... ≥ sα > 0 = sα+1 = ... = sn called the partial Brunovsky column and row indices of L, respectively. Let be the subset of formed by the sequences L for which α + β ≤ n. Let Σco be the set of matrix triples with (F, G) controllable and (H, F) observable. We denote by Σco ≤ the subset of Σco formed by the triples which are minimal partial realisations of the sequences. For every ξ ∈ Σco ≤, we obtain a versal deformation of ξ corresponding to the action of the group , we show a method for obtaining a minimal partial realisation ξ of , and we derive a versal deformation of L from the obtained versal deformation of ξ. [ABSTRACT FROM AUTHOR]

Let a word be a sequence of n i.i.d. integer random variables. The perimeter P of the word is the number of edges of the word, seen as a polyomino. In this paper, we present a probabilistic approach to the computation of the moments of P. This is applied to uniform and geometric random variables. We also show that, asymptotically, the distribution of P is Gaussian and, seen as a stochastic process, the perimeter converges in distribution to a Brownian motion. [ABSTRACT FROM AUTHOR]

In this note, we study the logarithmic derivation module of a non-free arrangement. We prove a generalized addition theorem for all arrangements. This addition theorem allows us to find various relationships between non-free arrangements, free arrangements, and restriction counts. For graphic arrangements, we can use these results to find a lower bound for the maximal degree generator in terms of triangles in the associated graph. We also apply these results to the case of hypersolvable arrangements where we define hyperexponents and use them to find a lower bound for their maximal degree generator. [ABSTRACT FROM AUTHOR]

It is well established that random practice compared to blocked practice enhances motor learning. Additionally, while information in the environment may be incidental, learning is also enhanced when an individual performs a task within the same environmental context in which the task was originally practiced. This study aimed to disentangle the effects of practice schedule and incidental/environmental context on motor learning. Participants practiced three finger sequences under either a random or blocked practice schedule. Each sequence was associated with specific incidental context (i.e., color and location on the computer screen) during practice. The participants were tested under the conditions when the sequence-context associations remained the same or were changed from that of practice. When the sequence-context association was changed, the participants who practiced under blocked schedule demonstrated greater performance decrement than those who practiced under random schedule. The findings suggested that those participants who practiced under random schedule were more resistant to the change of environmental context. [ABSTRACT FROM AUTHOR]

This study contributes to a multifaceted picture of young children's emergent number knowledge by focusing on the variety of ways in which children express and use quantitative information. The authors' aims are to (a) explore the extent to which quantifying collections 1–5 and using that information pose different levels of difficulty to children from 33 to 47 months old, (b) identify intra- and intertask response patterns, and (c) analyze the influence of socioeconomic status and age on these response patterns. Sixty-six children from two contrasting socioeconomic status groups (very low and middle) were asked to solve tasks with 1–5 elements in the context of a game. Using quantitative information turned out to be more complex than quantification. Intra- and intertask response patterns showed that children gradually come to understand the first five numerical values according to the numerical sequence in a much less strict way than that proposed by the cardinal-knowers model that posits that children progress in an orderly way in their number knowledge. Children in different ages and socioeconomic status groups were found to be more similar to each other when the whole arc of responses provided was considered than when solely correct performance was measured. [ABSTRACT FROM AUTHOR]

Affiliation network is one kind of two-mode social network with two different sets of nodes (namely, a set of actors and a set of social events) and edges representing the affiliation of the actors with the social events. The connections in many affiliation networks are only binary weighted between actors and social events that can not reveal the affiliation strength relationship. Although a number of statistical models are proposed to analyze affiliation binary weighted networks, the asymptotic behaviors of the maximum likelihood estimator (MLE) are still unknown or have not been properly explored in affiliation weighted networks. In this paper, we study an affiliation model with the degree sequence as the exclusively natural sufficient statistic in the exponential family distributions. We derive the consistency and asymptotic normality of the maximum likelihood estimator in affiliation finite discrete weighted networks when the numbers of actors and events both go to infinity. Simulation studies and a real data example demonstrate our theoretical results. [ABSTRACT FROM AUTHOR]

This paper introduces an optimization algorithm for finding the sequence of stock sheets to use in a two-dimensional bill-of-materials layout problem, when there is more than one size of stock sheet to choose from and when the method for laying each single sheet is already chosen. To reduce computer time and memory requirements for solving this problem, two other heuristic approaches are also proposed. Tests on data from a Wisconsin manufacturer show that the use of multiple sheet sizes can materially reduce the trim losses achieved from a layout system that uses only a single sheet size. The heuristic methods introduced represent progressive stages in the trade-off between layout quality and the computer time and memory required to achieve the layout. [ABSTRACT FROM AUTHOR]

The COVERT job shop dispatching rule was tested extensively twenty years ago with impressive results, however, since then it has been included in only one comparative analysis with other sequencing rules, and, reported instances of its application have been infrequent. In this paper, the COVERT rule is examined in detail relative to its applicability, its sensitivity to various operating parameters and performance measures, and its performance compared to several other sequencing rules including truncated SPT rules, dynamic slack rules and modified duedate rules. The performance of COVERT is examined for a variety of tardiness measures. The examination is conducted within the context of a simulation model of a machine-constrained job shop with serial jobs and random routings. The results indicate that COVERT performs well as a sequencing rule and in most instances was superior to the other sequencing rules tested both directly and across varying degrees of due-date tightness. [ABSTRACT FROM AUTHOR]

This paper initiates a structure for analysing problems involved in sequencing the operations that must be performed by a robot to tend machines in a cell. The sequence of operations is shown to be important in determining the feasibility of assigning a robot to tend machines and achieve specified production rates. Various cases, defined by the parameters that describe the system, are identified and analysed. Optimal sequencing procedures are described for several fundamental cases. Models are developed to prescribe solutions in more advanced cases, and the computational complexity of these cases is defined. [ABSTRACT FROM AUTHOR]

Statistical analysis of machine utilization has shown that about 45% of machine time is spent in tool changes between jobs. Reducing job change-over costs can therefore make a big difference in machine utilization. Job change-over costs depend greatly on the job sequence chosen for a given job collection and this paper shows that systematic job sequencing can reduce machine setting time by as much as 80%. Apart from the direct benefit accruing from systematic job sequencing, there can be indirect benefits through a continuing programme of tool and tooling standardization. The methods available in both a manual version and a computerized version, and a demonstration is given. [ABSTRACT FROM AUTHOR]

The flow-shop sequencing problem with no wait in process and with jobs requiring dissimilar technological order for machine processing is formulated in this paper. A systematic method is suggested for obtaining the optimum solution to the sequencing problem. An example of four jobs with four technological orderings for machine processing and four machines is solved to illustrate the suggested method. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a concept of A-sequences of Halpern type where A is an averaging infinite matrix. If A is the identity matrix, this notion become the well-know sequence generated by Halpern's iteration. A necessary and sufficient condition for the strong convergence of A-sequences of Halpern type is given whenever the matrix A satisfies some certain concentrating conditions. This class of matrices includes two interesting classes of matrices considered by Combettes and Pennanen [J. Math. Anal. Appl. 2002;275:521-536]. We deduce all the convergence theorems studied by Cianciaruso et al. [Optimization. 2016;65:1259-1275] and Muglia et al. [J. Nonlinear Convex Anal. 2016;17:2071-2082] from our result. Moreover, these results are established under the weaker assumptions. We also show that the same conclusion remains true under a new condition. [ABSTRACT FROM AUTHOR]

Symbolic dynamic is an important model of a general systems. This paper is devoted to the study of hyperspace dynamical systems of such systems. More precisely, we investigate the expansivity, topological entropy of the induced hyperspace dynamical system of a symbolic dynamical system . [ABSTRACT FROM AUTHOR]

In this paper, using geometric polynomials, we obtain a generating function of p-Bernoulli numbers in terms of harmonic numbers. As consequences of this generating function, we derive closed formulas for the finite summation of Bernoulli and harmonic numbers involving Stirling numbers of the second kind. We also give a relationship between the p-Bernoulli numbers and the generalized Bernoulli polynomials. [ABSTRACT FROM AUTHOR]

By means of the symmetric summation theorem on polynomial differences due to Chu and Magli [Summation formulae on reciprocal sequences. European J Combin. 2007;28(3):921-930], we examine Bernoulli and Euler polynomials of higher order. Several reciprocal relations on Bernoulli and Euler numbers and polynomials are established, including some recent ones obtained by Agoh Shortened recurrence relations for generalized Bernoulli numbers and polynomials. J Number Theory. 2017;176:149-173. [ABSTRACT FROM AUTHOR]

The convergence of iterated Boolean sums for different sequences of operators has been studied keeping fixed the number M of iterations or recently letting for a fixed operator. Here we consider some convergence properties of iterated Boolean-type sums of the classical Bernstein and Bernstein-Durrmeyer operators in the case where both the operators and their order of iterations are not fixed. In the case of Bernstein-Durrmeyer operators, we obtain a general solution of this problem. We can also state some alternative expressions of the semigroups and resolvent operators associated with the Voronovskaja’s formula for these sequences of operators. [ABSTRACT FROM AUTHOR]

In this article, by using the hybrid projection method or the shrinking projection method, we introduce two strong convergence theorems for finding a common fixed point of a finite family of sequences of nearly nonexpansive mappings in Hilbert spaces. [ABSTRACT FROM AUTHOR]

We consider the longest run of either successes or failures in a sequence of Bernoulli trials. The exact distribution of this random variable is obtained using probability generating function techniques. We consider approximating the tail areas of this random variable using a partial fraction approximation and a saddlepoint approximation with various continuity corrections. We investigate and compare the performance of the approximations for various values of sequence length and various values of the probability of success. [ABSTRACT FROM AUTHOR]

In this study, we identify a generalization of q-Bernstein type operators and investigate approximation properties of a sequence of these operators. We estimate rate of approximation by modulus of continuity. We prove Voronovskaya type theorem for these operators. [ABSTRACT FROM AUTHOR]