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Abstract data types (ADTs) provide a way to define data structures and the operations allowed on them, independent of the specific implementation details. Choosing the appropriate data type is for many applications the most important step in their development that affects their performance. To investigate the most suitable stack implementation for evaluating arithmetic expressions with complex numbers, we developed an Android application. These expressions may contain a larger number of complex numbers, for example, 25, which can be enclosed in parentheses arbitrarily. The Android application uses an array and linked-list implementation of a stack ADT to evaluate these expressions in its methods, as well as a simple stack implementation that uses none ADT. We determined a more efficient implementation of a stack ADT and the most efficient implementation at all by analysing the execution times of these methods, which were evaluating the same arithmetic expressions with complex numbers. In the paper we also analyse the functioning of both these stack ADT implementations and a simple stack implementation that does not use an ADT. [ABSTRACT FROM AUTHOR]

In [17], we introduced an extensional variant of generic realizability [22], where realizers act extensionally on realizers, and showed that this form of realizability provides inner models of $\mathsf {CZF}$ (constructive Zermelo–Fraenkel set theory) and $\mathsf {IZF}$ (intuitionistic Zermelo–Fraenkel set theory), that further validate $\mathsf {AC}_{\mathsf {FT}}$ (the axiom of choice in all finite types). In this paper, we show that extensional generic realizability validates several choice principles for dependent types , all exceeding $\mathsf {AC}_{\mathsf {FT}}$. We then show that adding such choice principles does not change the arithmetic part of either $\mathsf {CZF}$ or $\mathsf {IZF}$. [ABSTRACT FROM AUTHOR]

The biggest challenge associated with a renewable energy source (RES) based microgrids is to maintain their frequency stability. In solving this challenge, virtual inertia control (VIC) could be viewed as an unavoidable part of alternating current (AC) microgrids. For VIC, a phase-locked loop (PLL) is essential for obtaining information regarding the changes in the frequency of the microgrid. However, implementation of PLL might cause greater oscillation in frequency because of its system dynamics. Such type of issues can be resolved by using a multistage proportional integral derivative (PID) controller which restricts the undesirable frequency measurement and thus helps in improving the stability of the microgrid. In this paper, a novel Sine augmented scaled arithmetic optimization algorithm is proposed in purpose to tune the parameters of the aforementioned controller. The effectiveness of the proposed methodology is validated through contrastive simulation results, and the impact of a few standard strategies such as a change in system boundaries and various steps of RESs penetration are also demonstrated. • The concept of virtual inertia control (VIC) is proposed for frequency control in an AC microgrid. • Impact of RESs on virtual inertia control-based AC microgrid is investigated. • By altering the original AOA algorithm, a Sine augmented scaled AOA algorithm is created. • SCA-AOA algorithm is compared with AOA and other algorithms in terms of fitness function. • A MSPID controller is designed with the SCA-AOA algorithm for the VIC-based AC microgrid. [ABSTRACT FROM AUTHOR]

This paper proposes a fault-tolerant distributed Bayesian filter for multi-sensor state estimation using a peer-to-peer sensor network with incoherent local estimates problems. The proposed approach uses a Gaussian mixture rather than a single Gaussian distribution to represent the fusion result, which can effectively reduce the negative impact of corrupted local estimates on the fusion results. The resulting filter performs Bayesian recursion via Gaussian mixture. To accommodate a heterogeneous sensor network, we develop a novel arithmetic average fusion employing a set of covariance-dependent weighting coefficients, where the fusion error covariance is effectively reduced in the case of fusing information with different qualities. For intersensor communication, a partial flooding scheme is investigated, in which only valid-likely Gaussian components are disseminated and fused between neighbor sensors. Theoretically, it is shown that under reasonable assumptions, the presented fault-tolerant distributed estimator can guarantee local stability with the exponentially bounded estimation error in the mean square. The effectiveness and superiority of our approach are validated through both simulation and experiment scenarios. • The first-ever fault-tolerant distributed Bayesian filter. • Efficient fault-tolerant Bayesian filter for resolving inconsistent local estimates. • Novel arithmetic average fusion adapted to heterogeneous sensor networks. • The stability of the proposed distributed estimator can be guaranteed. • Real-world experimental validation. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to define novel kind of operations on trapezoidal fuzzy numbers that is totally different from the existing operations. Significance of the proposed operations is that the transportation cost is even reduced while the same problem solved by existing operations. To validate this, two real-life examples are solved. [ABSTRACT FROM AUTHOR]

This paper proposes an improved variant of the arithmetic optimization algorithm (AOA), called LMRAOA, which is used to solve numerical and engineering problems. Various strategies are proposed to improve AOA. First, Multi-Leader Wandering Around Search Strategy (MLWAS) is proposed to improve the exploration ability of the algorithm on global scale. Then, Random High-Speed Jumping Strategy (RHSJ) is proposed, and the search agent performs high-speed search in the current neighborhood to improve the exploitation ability. Finally, in order to avoid local optima, adaptive lens opposition-based learning strategy is proposed, and linear changes are proposed in its parameters to further satisfy the dynamic changes. 27 classic benchmark functions, 6 engineering optimization problems, and CEC2014, CEC2019 and CEC2020 competition functions are tested by LMRAOA algorithm and comparison algorithm. The experimental results show that, in most cases, the LMRAOA outperforms other algorithms in solving engineering and numerical problems, and can provide effective solutions. [ABSTRACT FROM AUTHOR]

The new operations based on the Aczel–Alsina t-norm and t-conorm show the advantage of flexible operations by adjusting different parameter values. Motivated based on the new operations, we propose the Aczel–Alsina operations and weighted aggregation operators of neutrosophic Z-numbers (NZNs) to solve the flexible decision-making problem by adjusting different parameter values depending on the decision maker's preference under the environment of NZNs. To do so, this paper first proposes the Aczel–Alsina t-norm and t-conorm operations of NZNs and develops the NZN Aczel–Alsina weighted arithmetic averaging (NZNAAWAA) and NZN Aczel–Alsina weighted geometric averaging (NZNAAWGA) operators to aggregate NZNs. Then, a multiple attribute decision-making (MADM) method is developed by the NZNAAWAA and NZNAAWGA operators under the NZN environment. Finally, a numerical example is provided to verify the influence of different parameter values on decision-making results. Compared with existing MADM methods, the new MADM method shows its feasibility and flexibility in MADM applications. Moreover, the new MADM approach can not only extend the existing MADM methods, but also overcome the lack of decision-making flexibility of the existing MADM methods. [ABSTRACT FROM AUTHOR]

This paper proposes new symmetric cryptography algorithms of Residue Number System and its Modified Perfect Form. According to the first method, ciphertext is regarded as a set of residues to the corresponding sets of modules (keys) and decryption or decimal number recovery from its residues takes place according to the Chinese Remainder Theorem. To simplify the calculations, it is proposed to use a Modified Perfect Form of Residue Number System, which leads to a decrease in the number of arithmetic operations (in particular, finding the inverse and multiplying by it) during the decryption process. Another method of symmetric encryption based on the Chinese Remainder Theorem can be applied when fast decryption is required. In this algorithm, the plaintext block is divided into sub-blocks that are smaller than the corresponding module and serve as remainders on dividing some number, which is a ciphertext, by these modules. Plaintext recovery is based on finding the ciphertext remainders to the corresponding modules. Examples of cryptography algorithms implementation and their encryption schemes are given. The security of the proposed methods is estimated on the basis of the Prime number theorem and the Euler function. It is investigated which bitness and a number of modules are required for the developed symmetric security systems to ensure the same security level as the largest length key of the AES algorithm does. It is found that as the number of modules increases, their bitness decreases. Graphical dependencies of cryptanalysis complexity on bitness and a number of modules are built. It is shown that with the increase of specified parameters, the security of the developed methods also increases. [ABSTRACT FROM AUTHOR]

A 3D mesh can be reconstructed from multiple viewpoint images or from a single structured light image. Lossy compression of such images by standard techniques such as JPEG at high compression ratios lead to 3D reconstruction being adversely affected by artifacts and missing vertices. In this paper we demonstrate an improved algorithm capable of high compression ratios without adversely affecting 3D reconstruction and with minimum data loss. The compression algorithm starts by applying block DCT over the input image, and the transformed data being quantized using an optimized quantization matrix. The quantized coefficients of each block are arranged as a 1D array and saved with other block's data in a larger matrix of coefficients. The DC coefficients are subject to a first order difference whose values are referred to as residual array. The AC coefficients are reduced by eliminating zeros and saving the non-zero values in a reduced coefficients array using a mask of 0 (for a block of zeros) and 1 (for a block of non-zeros). Finally, arithmetic coding is applied to both coefficients and residual arrays. At decompression stage, the coefficients matrix is regenerated by scanning the coefficients array and examining the headers to substitute zero and non-zero data. This matrix is then added to the residual array to obtain the original DC values. The IDCT is then applied to obtain the original image. The proposed algorithm has been tested with images of varying sizes in the context of 3D reconstruction. Results demonstrate that our proposed algorithm is superior to traditional JPEG at higher compression ratios with high perceptual quality of images and the ability to reconstruct the 3D models more effectively, both for structured light images and for sequences of multiple viewpoint images. [ABSTRACT FROM AUTHOR]

This paper presents a design of digital control based on a fixed-point model for an application of a single phase AC-DC boost Converter with a high power factor and low current distortion. The system uses a simple closed-loop control with a slow voltage loop (outer loop) to stabilize the output DC bus voltage at the required level and a fast current loop (inner loop) to achieve input power factor correction. The digital control uses a fixedpoint structure that improves the control accuracy without increasing the number of arithmetic operations and does not require specific running conditions. The behavior of the system is fully verified by using a digital simulation under Matlab/Simulink environment and experimentally with an implementation in real-time using Xilinx ISE 14.7 software, hardware description language VHDL, Xilinx FPGA ML605 board, and EVAL-AD7656 evaluation board for high-speed analog-to-digital conversion. The obtained results show a good agreement between experiments and simulations for steadystate and transient-responses. [ABSTRACT FROM AUTHOR]

Arithmetic optimization algorithm (AOA) is a meta -heuristic algorithm inspired by mathematical operations. AOA has been diffusely used for optimization issues on continuous domains, but few scholars have studied discrete optimization problems. In this paper, we proposed Binary AOA (BAOA) based on two strategies to handle the feature selection problem. The first strategy used S-shaped and V-shaped shift functions to map continuous variables to discrete variables. The second strategy was to combine four logical operations (AND, OR, XOR, XNOR) on the basis of the transfer function, and constructed a parameter model based on the sine and cosine function. An enhanced logic binary sine–cosine function arithmetic optimization algorithm (LBSCAOA) was proposed to realize the position update of variables. Its purpose was to improve the algorithm's global search capabilities and local exploitation capabilities. In the simulation experiments, 20 datasets were selected to testify the capability of the proposed algorithm. Since KNN had the advantages of easy understanding and low training time complexity, this classifier was selected for evaluation. The performance of the improved algorithm was comprehensively evaluated by comparing the average classification accuracy, the average number of selected features, the average fitness value and the average running time. Simulation results showed LBSCAOA with V-Shaped "V4" stood out among many improved algorithms. On the other hand, LBSCAOA with V-Shaped "V4" was used as a representative to compare with other typical feature selection algorithms to verify its competitivenes. [ABSTRACT FROM AUTHOR]

An earlier paper on formulating arithmetic in a connexive logic ended with a conjecture concerning C#, the closure of the Peano axioms in Wansing's connexive logic C. Namely, the paper conjectured that C# is Post consistent relative to Heyting arithmetic, i.e., is nontrivial if Heyting arithmetic is nontrivial. The present paper borrows techniques from rele- vant logic to demonstrate that C# is Post consistent simpliciter, rendering the earlier conjecture redundant. Given the close relationship between C and Nelson's paraconsistent N4, this also supplements Nelson's own proof of the Post consistency of N4#. Insofar as the present technique allows infinite models, this resolves Nelson's concern that N4# is of interest only to those accepting that there are finitely many natural numbers. [ABSTRACT FROM AUTHOR]

Résumé Dans cette revue de la littérature, nous faisons état des connaissances scientifiques concernant la relation entre l'usage des doigts dans des tâches numériques et les performances et comportements des individus dans ces mêmes tâches. Nous nous interrogeons notamment sur l'universalité de l'usage des doigts pour représenter des quantités ou pour faire des calculs arithmétiques. Dans une première partie, nous présentons les travaux sur l'adulte qui témoignent d'usages conscients et inconscients des doigts dans des tâches numériques. La seconde partie de l'article s'intéresse aux travaux menés auprès d'enfants et la question principale à laquelle nous tentons de répondre est celle du rôle des doigts dans la construction des savoirs numériques. Abstract In this literature review, we describe the state of the art of the scientific knowledge about the relationship between the use of fingers in numerical tasks and individuals' performance in those tasks. One of the questions we want to answer is related with the universality of finger use in order to represent quantities on fingers or to achieve arithmetic calculations. In a first part of the paper, we report the results of studies highlighting the conscious and unconscious use of fingers in adults when they perform simple numerical tasks. In the second part of the manuscript, we adopt a more developmental point of view and our main question is whether finger use in children shapes their mental representations of numbers. In order to answer this question, we review the literature concerning the use of fingers for counting collection of objects through pointing, for representing quantities through finger rising and for calculating through finger manipulations. One crucial issue addressed in this part of the paper is the role of finger use for a possible transition between non-symbolic and symbolic number mental representations. In the last part of the paper, we discuss whether fingers are important, necessary or useless for the construction of numerical knowledge and conclude that, despite their possible influence on adults' and children's behaviors and number understanding, they are not indispensable for developing accurate number mental representations. Finally, our review allows us to conclude that an innate view of the relationship between fingers and numbers is not fully supported in the literature and that a more functionalist view wherein fingers can support numerical acquisitions is more plausible. [ABSTRACT FROM AUTHOR]

This paper describes the development of encryption algorithms using the magic square of order 5 and Multi-level keys with the addition of Matrix keys to increase implementation speed and complexity. This work relied mainly on the magic sum and some equations that were added as an improvement on previous work. Multi-level keys were used for three different message sizes, and an additional key matrix with size 5×5 was used to add more complexity. The proposed work was performed using both GF(P) and GF(28). Results were compared with the MS3, they have been found good, with acceptable speed and high complexity where it was (P)9 × (256)16 in the first algorithm, (P)9 × (256)16 × 3 in the second algorithm, and (P)9 × (256)16 × 3 × (P)25 in the third algorithm, the complexity changed according to the chosen value of N randomness, in addition to speed, complexity, NIST calculations have been performed for texts and histogram calculations for different images were calculated and compared as well. [ABSTRACT FROM AUTHOR]

This study aims to examine the differences in numerosity estimation on a right-to-left number line between second- to fourth-grade students and undergraduate students, together with whether number-line estimation is related to basic arithmetic tasks (addition and subtraction). Hence, 53 Arabic-speaking children and 63 Arabic-speaking adults performed a paper-based number-line estimation task and also an arithmetic task. Number-line estimation was represented either by the percentage of absolute errors in positing the quantities on the line, by the accuracy, or by the r score for linearity of representation. The results show that, although children's addition (but not subtraction) performance resembles that of adults, the correlations vary between number line and arithmetic scores. Addition scores are positively correlated with error percentages in the children's number-line tasks, while subtraction is negatively correlated with adults' error percentages. These differences are assumed to be attributed to various uses of recall and procedural strategies. [ABSTRACT FROM AUTHOR]

This paper presents a vector relation-centric algorithm for solving arithmetic word problems (AWPs), which uses vector relation acquisition and scene knowledge to ensure the performances of problem understanding and symbolic solver correspondingly. The vector relation acquisition procedure builds on the synergy of the vector syntax-semantics method and the deep neural miner. Compared with the syntax-semantics method, the vector syntax-semantics method decreases not only the number of models but also semantic ambiguities and computational costs. For the scene knowledge, this paper proposes a scene-aware symbolic solver which infers relations obeying scene rules to decrease the occurrences of unwanted operations. Experimental results show that the proposed algorithm is superior to the high-performance baseline algorithm in both accuracy and computational cost. In accuracy, the proposed algorithm increased the accuracy by 3.9% on the sum of the three scene subsets due to the use of the scene knowledge and vector computing; as a result, it increased the accuracy by 0.5% on the sum of six authoritative datasets. In computational cost, the proposed algorithm decreased the computing cost by more than 50%. Thus, this paper makes a significant contribution to developing instruments for solving AWPs. [ABSTRACT FROM AUTHOR]

The pandemic of Covid-19 has caused a shift of paradigm of education, from face-to-face to e-learning. E-learning leads to an escalation in digitalization of handwritten documents because it requires submission of homework and assignments through online. To help teachers in checking digitalized handwritten homework, this paper proposes an automatic checking system based on a convolutional neural network (CNN) for handwritten numeral recognition. The CNN is used to recognize four arithmetic operations in mathematical questions consisting of addition, deduction, multiplication and division. The performance CNN in handwritten numeral recognition have been optimized in terms of activation function and gradient descent algorithm. The proposed CNN is also trained and tested with the MNIST handwritten data set. The experimental results show that the recognition accuracy the improved CNN improves to a certain extent as compared to before optimization. [ABSTRACT FROM AUTHOR]

The paper discusses multidimensional fuzzy RDM-arithmetic and its application to solving linear fuzzy equation systems. Such arithmetic can also be used to test whether the found solution satisfies condition of nestedness and thus initially verify its correctness. The presented methods are illustrated with three examples coming from the literature. [ABSTRACT FROM AUTHOR]

This paper explores the influence of product type and arithmetic task complexity on users' perceived mental effort and satisfaction in the context of online grocery shopping. A two-factor within-subject experiment was conducted with 32 participants. Results show that experience products and complex arithmetic tasks are associated with higher perceived mental effort compared to search products and simple arithmetic tasks. Perceived mental effort and satisfaction are negatively related. The more cognitive effort users need to invest in their online shopping tasks, the less satisfied they are likely to be with their online experience. Our results suggest that cognitive absorption mediates the relationship between cognitive effort and satisfaction. The study contributes to our understanding of online grocery shopping by explaining the effect of arithmetic complexity and product type on user satisfaction. It also offers shopping website designers a way to improve consumers' online grocery shopping experience by implementing simple technology features in their websites to help users reduce their mental effort. [ABSTRACT FROM AUTHOR]

In recent days we can see that multicore computers have the ability to easily manipulate digit numbers however as numbers get bigger the computation becomes more complex, the reason is that the size of both CPU registers and buses is limited. As a result, the arithmetic operations such as addition, subtraction, multiplication, and division for CPU become more complex to perform. For solving the problem of how to do computation on big digit numbers, a number of algorithms have been developed. However, the existing algorithms are noticeably slow because they operate on bits individually and are designed to run over single-core computers only. In this paper, an AI model is presented that performs a computation on tokens of 8-digit numbers to assist boost the CPU computation performance. [ABSTRACT FROM AUTHOR]

The hardware implementation of optimization algorithms has gained significant attention due to its potential for augmenting performance and efficiency. This paper presents the hardware implementation of a Chaotic Opposition-Based Arithmetic Optimization Algorithm (COAOA). COAOA is inspired by integrating chaotic dynamics and opposition-based learning (OBL) principles in the original AOA algorithm. Inspired by chaotic maps, COAOA amplifies exploration and exploitation capabilities, while OBL enhances the search process by considering both positive and negative solution counterparts. Our proposed hardware implementation of COAOA harnesses Field-Programmable Gate Arrays (FPGAs) to accelerate optimization processes. Leveraging FPGA's parallel processing capabilities, the COAOA algorithm is efficiently parallelized and mapped onto the hardware architecture, streamlining arithmetic operations and governing algorithmic execution flow. To assess its efficacy, a comparison was made between the performance of the suggested structure and five alternative algorithms: opposition-based learning AOA (OAOA), Chaotic AOA, the original AOA, PSO and GA. Statistical analyses and tests were performed using benchmark functions like Rosenbrock, Rastrigin, Six-Hump Camel-Back, and Zirilli functions. The empirical findings indicate the substantial acceleration achieved through the hardware implementation of COAOA compared to the original AOA algorithm and its variants. This compelling outcome positions COAOA as a viable solution for real-time optimization challenges, signifying its potential to significantly expedite optimization tasks in practical applications. • An enhanced AOA variant, COAOA, is introduced with chaotic maps and OBL. • Chaotic map and OBL boost AOA's search efficiency, avoiding local minima. • COAOA's hardware design is executed on FPGA, achieving faster speed than software. • COAOA is benchmarked against AOA versions using the Xilinx Virtex-7 Pro Kit. [ABSTRACT FROM AUTHOR]

This paper reports on the research on year five pupils' understanding of generalised arithmetic, which aimed to investigate the understanding of year five pupils' commutative property and the property of zero together with its correlation with their mathematical achievement. Data for the study were collected via paper and pencil assessment answers for two items. Findings showed moderate achievement for both of the tasks. The pupils' explanation illustrated their poor conceptual understanding of commutative property and the property of zero. However, this understanding is not correlated with their mathematical achievement in school. It shows that an outstanding student in school did not necessarily acquire conceptual understanding of commutative principle and the property of zero. [ABSTRACT FROM AUTHOR]

• We develop a geometric counting method adaptive to the author number (N). • The credit given to the first author is N times larger than to the last author. • Among fixed-type schemes, this method fits best with existing empirical datasets. • The method balances equal scaling and equal spacing of credit among authors. With increasing research collaboration and the increasing average author number of academic papers, a reasonable counting method is needed to allocate paper credit to authors. This work analyses the features of existing counting methods, focusing on the differences between the credit assigned to each author. Considering that the ratio of credit between neighbouring authors allocated by a rational geometric counting method should change with the author number, we propose an adaptive geometric counting method in which the ratio of the credit of the first author to that of the last author equals the author number, as with fixed-type arithmetic counting and harmonic counting. The results show that the adaptive geometric counting method fits best with the existing empirical dataset among the fixed-type counting methods. In addition to keeping the same ratio of credit between neighbouring authors, the credit allocated to the authors changes with the author rank more evenly with this method than with other counting methods, except arithmetic counting, whose result is inherently linear but does not maintain the same ratio of credit between neighbouring authors. [ABSTRACT FROM AUTHOR]

The polygonal fuzzy set is an effective tool to approximate the general fuzzy set by means of a finite number of ordered real numbers. It not only overcomes the shortcomings (which does not satisfy the closeness) of arithmetic operations of fuzzy sets based on Zadeh extension principle, but also realizes the non-linear operation of general fuzzy sets by an ordered representation of the polygonal fuzzy set. In this paper, the definition, geometric interpretation, ordered representation and arithmetic operations of the polygonal fuzzy sets are introduced for the first time, and the method of solving polygonal fuzzy sets and their ordered representation based on convex fuzzy sets are given by an example. Second, a new Euclidean metric of polygonal fuzzy sets is proposed, and the approximation accuracy of polygonal fuzzy sets to convex fuzzy sets is discussed. In addition, the linear function describing transportation cost index information of logistics companies is obtained through the ordered representation of Gauss membership function, and according to the ordered representation a new normalization method for the polygonal decision matrix is given. Finally, the method of solving the positive (negative) ideal solution and degree of relative closeness of the polygonal decision matrix is suggested by the weighted Euclidean distance. Then a new TOPSIS evaluation system is established, and the effectiveness of the proposed method is illustrated by an example of logistics transportation. [ABSTRACT FROM AUTHOR]

Power systems' efficient management and planning are crucial in renewable energy-based systems. As the global electricity demand continues to rise, there is a growing need for alternative energy sources such as solar, wind, and hydropower. Consequently, numerous research studies have focused on maintaining load balancing within the renewable energy system and improving the forecasting of renewable energy resources. This paper presents the Eagle Arithmetic Optimization Algorithm (EAOA) as a novel approach to address these challenges. By utilizing a fuzzy-based dragonfly optimization algorithm (fuzzy-DFOA), the proposed method enhances the accuracy of load-balancing analysis in renewable energy resources. Through its innovative techniques, the EAOA demonstrates its potential to significantly improve the efficiency and effectiveness of managing renewable energy systems, paving the way for a more sustainable and reliable power grid. The accuracy rate of both wind and solar datasets is given. For the wind dataset, our proposed work got 92.63%, SVR got 75.89%, CNN got 87.54%, and QODA got 83.16%. For the solar dataset presented work of fuzzy-based DFOA got 92.59%, SVR got 69.16%, CNN got 86.25%, and QODA got 82.37%. • The proposed method is more efficient in balancing the energy resources and prediction forecasting renewable energy resources. • We proposed a fuzzy-based dragonfly optimization algorithm (fuzzy-DFOA) to overcome these issues. • We improved the accuracy of the analysis of load balancing the renewable energy resource. [ABSTRACT FROM AUTHOR]

Integrating solar energy into the combined energy supply of surface water source heat pump systems is expected to reduce the electricity consumption and carbon emissions. In this paper, a solar-surface water source heat pump system model is established to maximize system performance and save economic cost. In order to find the optimal operation scheme, an improved arithmetic optimization algorithm (iAOA) is proposed. This algorithm integrates elite opposition-based and nonlinear acceleration functions to solve the model. The effectiveness of the proposed model and algorithm is verified by applying it to a SWSHP district energy system in the central area of Xiangtan city. Experimental results demonstrate that incorporating solar energy into the SWSHP district energy system can improve system performance and reduce operational costs. In comparison with several other optimization algorithms, this algorithm has a faster convergence speed and a higher convergence accuracy. Therefore, it is considered an effective method for solving solar-surface water source heat pump district energy systems. [ABSTRACT FROM AUTHOR]

The object of this paper is to examine half and full connexive extensions of the basic regular conditional logic CR. Extensions of this system are of interest because it is among the strongest well-known systems of conditional logic that can be augmented with connexive theses without inconsistency resulting. These connexive extensions are characterized axiomatically and their relations to one another are examined proof-theoretically. Subsequently, algebraic semantics are given and soundness, completeness, and decidability are proved for each system. The semantics is also used to establish independence results. Finally, a deontic interpretation of one of the systems is examined and defended. [ABSTRACT FROM AUTHOR]

Purpose - This paper aimed to present the design of a teaching module on mathematical problem solving for the upper primary mathematics. Method - The module used Polya's and Schoenfeld's problem solving models as the theoretical framework. The researchers introduced problem-solving processes through specialized mathematics "practical" lessons together with carefully selected problems from the Arithmetic strand of the Singapore primary school mathematics curriculum. In the selection of appropriate mathematical problems, the following criteria were used: the selected problem (1) could potentially capture students' interest and curiosity; (2) is accessible to students in terms of cognitive resources at the upper primary level (students aged 10 to 12); (3) can be approached in multiple ways; and (4) could potentially promote higher-order thinking and conceptual understanding. The problem-solving lessons comprised four key features, namely teacher modelling, teacher scaffolding, small-group work and independent work. The scaffolding from Toh, Quek, Leong, Dindyal and Tay (2011) was used to guide students through the entire process of problem solving. Findings - The module provided teachers a unique glimpse into students' mathematical understanding. The writing activities helped students them to think about and articulate what they know on the content topic at hand. Significance - The teaching module will provide ample support and useful guidance for primary school mathematics teachers who wish to introduce students to the problem solving as a creative process and enhance their problem solving skills. [ABSTRACT FROM AUTHOR]

The topic of this paper is our knowledge of the natural numbers, and in particular, our knowledge of the basic axioms for the natural numbers, namely the Peano axioms. The thesis defended in this paper is that knowledge of these axioms may be gained by recourse to judgments of probability. While considerations of probability have come to the forefront in recent epistemology, it seems safe to say that the thesis defended here is heterodox from the vantage point of traditional philosophy of mathematics. So this paper focuses on providing a preliminary defense of this thesis, in that it focuses on responding to several objections. Some of these objections are from the classical literature, such as Frege's concern about indiscernibility and circularity (Section 2.1), while other are more recent, such as Baker's concern about the unreliability of small samplings in the setting of arithmetic (Section 2.2). Another family of objections suggests that we simply do not have access to probability assignments in the setting of arithmetic, either due to issues related to the ω-rule (Section 3.1) or to the non-computability and non-continuity of probability assignments (Section 3.2). Articulating these objections and the responses to them involves developing some non-trivial results on probability assignments Appendix A- Appendix C), such as a forcing argument to establish the existence of continuous probability assignments that may be computably approximated Theorem 4 Appendix B). In the concluding section, two problems for future work are discussed: developing the source of arithmetical confirmation and responding to the probabilistic liar. [ABSTRACT FROM AUTHOR]

OSPF is a commonly used link state routing protocol in order to interconnect network devices inside an Autonomous System. This paper focuses on achieving a detailed modelling for OSPF by performing manual algebraic derivations according to Algebra of Communicating Processes (ACP) axioms. The aim of this detailed model is to get a realistic approach of OSPF dynamics by applying the timers involved and by describing the full Link State Advertisement (LSA) exchange process. [ABSTRACT FROM AUTHOR]

This paper focuses on Fully Fuzzy Multi-Objective Linear Programming (FFMOLP) problem in which all the coefficients and decision variables are LR flat fuzzy numbers, the more generalized version of fuzzy numbers and all the constraints are fuzzy inequalities. A new algorithm is proposed for solving FFMOLP problem which first converts it into the Multi-Objective Interval Linear Programming (MOILP) problem. Further, taking the help of fuzzy slack variable, fuzzy surplus variables, nearest interval approximation of fuzzy numbers and scalarization technique, MOILP is then converted into the Crisp Linear Programming (CLP) problem. It is shown that the optimal solution of CLP problem is the fuzzy Pareto optimal solution of FFMOLP problem. The main advantage of the proposed algorithm is that it transforms FFMOLP problem into Crisp Linear Programming problem. Moreover, to apply algorithm, only the knowledge of arithmetic operations of LR flat fuzzy numbers, centre and width of the closed intervals are required. At the end, to illustrate the proposed method and its effectiveness over the existing method, numerical examples are solved and compared. [ABSTRACT FROM AUTHOR]

Computability logic (CL) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally been. Formulas in it represent computational problems, "truth" means existence of an algorithmic solution, and proofs encode such solutions. Within the line of research devoted to finding axiomatizations for ever more expressive fragments of CL, the present paper introduces a new deductive system CL12 and proves its soundness and completeness with respect to the semantics of CL. Conservatively extending classical predicate calculus and offering considerable additional expressive and deductive power, CL12 presents a reasonable, computationally meaningful, constructive alternative to classical logic as a basis for applied theories. To obtain a model example of such theories, this paper rebuilds the traditional, classical-logic-based Peano arithmetic into a computability-logic-based counterpart. Among the purposes of the present contribution is to provide a starting point for what, as the author wishes to hope, might become a new line of research with a potential of interesting finding--an exploration of the presumably quite unusual metatheory of CL-based arithmetic and other CL-based applied systems. [ABSTRACT FROM AUTHOR]

The hybrid averaging (HA) is an aggregation operator that uses the weighted average (WA) and the ordered weighted averaging (OWA) operator in the same formulation. In this paper, we introduce several generalizations of the HA operator by using generalized and quasi-arithmetic means, fuzzy numbers and order inducing variables in the reordering step of the aggregation process. We present the fuzzy generalized hybrid averaging (FGHA) operator, the fuzzy induced generalized hybrid averaging (FIGHA) operator, the Quasi-FHA operator and the Quasi-FIHA operator. The main advantage of these operators is that they generalize a wide range of fuzzy aggregation operators that can be used in a wide range of applications such as decision making problems. For example, we could mention the fuzzy induced hybrid averaging (FIHA), the fuzzy weighted generalized mean (FWGM) and the fuzzy induced generalized OWA (FIGOWA). We end the paper with an application of the new approach in a decision making problem. [ABSTRACT FROM AUTHOR]

Abstract: Owing to more vague concepts frequently represented in decision data, mathematical objects introduced by K.T. Atanassov and studied under the name “intuitionistic fuzzy set” (IFS) are more flexibly used to model real-life decision situations. The aim of this paper is to develop a new methodology for solving multi-attribute group decision-making problems using IFS, in which multiple attributes are explicitly considered. In this methodology, for each decision maker in the group two auxiliary fractional programming models are derived from the TOPSIS to determine the relative closeness coefficient intervals of alternatives, which are aggregated for the group to generate the ranking order of all alternatives by computing their optimal degrees of membership based on the ranking method of interval numbers. The implementation process of the method proposed in this paper is illustrated with a numerical example. [Copyright &y& Elsevier]

Abstract: When a digital filter is realized with floating-point or fixed-point arithmetics, errors and constraints due to finite word length are unavoidable. In this paper, we show how these errors can be mechanically analysed using the HOL theorem prover. We first model the ideal real filter specification and the corresponding floating-point and fixed-point implementations as predicates in higher-order logic. We use valuation functions to find the real values of the floating-point and fixed-point filter outputs and define the error as the difference between these values and the corresponding output of the ideal real specification. Fundamental analysis lemmas have been established to derive expressions for the accumulation of roundoff error in parametric Lth-order digital filters, for each of the three canonical forms of realization: direct, parallel, and cascade. The HOL formalization and proofs are found to be in a good agreement with existing theoretical paper-and-pencil counterparts. [Copyright &y& Elsevier]

Counting the number of paths in a graph is easily accomplished using powers of the adjacency matrix for the graph, while enumerating these paths is difficult. There appears to be only one technique, Floyd's algorithm [1], whose end result can be used, with a considerable amount of paper and pencil manipulation, to actually list in order the vertices that make up each path. Even so, Floyd's algorithm is used only to find shortest paths. This paper describes a technique in Maple that automatically prints out all paths of any desired length, along with the name of each vertex, proceeding in order from start (beginning vertex) to finish (ending vertex). This is accomplished by defining a new matrix multiplication that produces all paths, with the option of listing only the simple ones; can handle alphanumeric entries; and eliminates the clustering of parentheses and messy output obtained when using ordinary matrix multiplication with alphabetic entries. [ABSTRACT FROM AUTHOR]

As a theoretical basis of computation with imprecise and partially reliable information, arithmetic of Z-numbers should be developed with an emphasis of informativeness. In this paper we propose an approach to develop arithmetic of Z-numbers where a result of computation can be obtained with a predefined informativeness level. The proposed approach is based on the use of horizontal membership functions and a measure of specificity concept. An example is used to show validity of the approach. [ABSTRACT FROM AUTHOR]

The recent evolution in Natural Language Processing (NLP) and machine learning have played a crucial role in the development of solving word problems written in human language. This paper, to the best of our knowledge, presents the first attempt of automatically solving Arabic arithmetic word problems. In addition, as part of this work, we prepared an Arabic annotated dataset by translating a standard arithmetic word problems English dataset (AddSub Dataset). The AddSub dataset has been used by several researchers to evaluate their models for English arithmetic word problems. The proposed algorithm relies on our automatic verbs learning approach based on the training dataset. Moreover, the algorithm utilizes various NLP tools to assign objects to problem states until reaching to the goal state such as Stanford Parser, Named Entity Recognition (NER), and Cosine Metric Distance. Our approach overcomes various issues such as tracking both entities and their related results during the transfer process as well as dealing with different forms of the same verb. The performance evaluation process showed promising results resolving 80.78% of the problems. On the other hand, there are still several areas that can be extended and improved. For instance, the lack of common knowledge, presence of irrelevant information, and quantity conversions. [ABSTRACT FROM AUTHOR]

Ancient mathematical formulae can be directly applied to the optimization of the algebraic computation. A new algorithm used to compute decimals of the inverse based on such ancient mathematics is reported in this paper. Sahayaks (auxiliary fraction) sutra has been used for the hardware implementation of the decimals of the inverse. On account of the ancient formulae, reciprocal approximation of numbers can generate "on the fly" either the first exact n decimal of inverse, n being either arbitrary large or at least > 6 in almost all cases. The reported algorithm has been implemented, and functionality has been checked in T-Spice. Performance parameters, like propagation delay and dynamic switching power consumptions, are calculated through spice-spectre of 90 nm CMOS technology. The propagation delay of the resulting 4-digit reciprocal approximation algorithm was only ~ 1.8 uS and consumed ~ 24.7 mW power. The implementation methodology offered substantial reduction of propagation delay and dynamic switching power consumption from its counterpart (NR) based implementation. [ABSTRACT FROM AUTHOR]