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The article discusses the result of an experimental study which shows that people do not follow the optimal strategy in practice and suggests two strategies for defeating human opponents in rock-paper-scissors (RPS). The study found that the probability of repeating a game on the next trial is well above one-third, while the strategy of always playing the symbol is assessed to be an effective strategy in defeating the symbol that the other player has previously played. The study also observed that the wins of each competition have increased by 26.4%, while the losses are decreased by 9.51%.

The use of the efficient score statistic in sequential monitoring procedures is reviewed and analysed. Various models that arise in applications are considered. The efficient score vector has the same optimality property as the generalized likelihood ratio, but it has a simple-structure requiring fewer estimations, and this is especially important when the data have a complicated structure. Furthermore, with the efficient score vector it is possible to detect which component of the parameter vector is different from the hypothetical or the historical value. The problems we solve here were the subjects of separate publications, but with the new methodology they are easily calculated examples. [ABSTRACT FROM PUBLISHER]

A non-smooth biobjective optimization problem for designing the shape of a slice channel in a paper machine headbox is described. The conflicting goals defining the optimization problem are the ones determining important quality properties of produced paper: 1) basis weight should be even and 2) the wood fibers of paper should mainly be oriented to the machine direction across the width of the whole paper machine. The novelty of the considered approach is that maximum deviations are used instead of least squares when objective functions are formed. For the solution of this problem, a multiobjective genetic algorithm based on nondominated sorting is considered. The numerical results demonstrate the ability to obtain a large set of nondominated designs. [ABSTRACT FROM AUTHOR]

This article is intended to indicate and discuss some errors in N. Lavi’s paper “A Ganzstellensatz for semi-algebraic sets and a boundedness criterion for rational functions”. [ABSTRACT FROM AUTHOR]

The idea of cutting out a curve while looking at the direction of cut of the scissors is used to explore concepts related to curves, tangents and derivatives, especially tangent line, concavity and points of inflection, curvature, and a curve as envelope of tangent lines. [ABSTRACT FROM AUTHOR]

It is a privilege to have the chance of congratulating Professor Efron first on this wise paper, then on the richly merited International Prize, the award of which the paper commemorates, but above all on the whole body of his deeply impressive, wide-ranging contributions to our subject. One of the great masterpieces of our field, largely unread nowadays, is M.S. Bartlett's (1958) I Introduction to stochastic processes and their application i and Bartlett's influence on statistical development, at least in UK, was second only to Fisher's. Professor Efron in his theoretical papers manages with great skill and panache to combine careful mathematical discussion with judicious statistical emphasis. [Extracted from the article]

I present the development of a modular origami design based upon the Pajarita, a figure from the traditional Spanish paper-folding art. The work is a modular cube decorated with Pajaritas with the colour pattern produced by folding of individual units to be topologically identical but with distinct colour patterns on each. The mathematics of the cube-colouring and unit-colouring problems are analysed. Two unique solutions are found and presented for the easiest possible cube and a solution for the hardest possible cube. [ABSTRACT FROM AUTHOR]

In the article 'How long is my toilet roll-a simple exercise in mathematical modelling' several models of increasing complexity are introduced and solved to calculate indirectly the length of paper on a toilet-roll. All these results are presented without errors. The authors of this comment believe the error analysis of measurements made in a laboratory is an important part of the experiment. The calculation of the absolute errors in indirect measurements provides us with information about the confidence that we must have in our experimental results. For that reason, the error calculation for all approximations has been made. [ABSTRACT FROM AUTHOR]

Automated identification of mathematical expressions (MEs) is essential in transforming scientific and engineering documents into electronic form. Even though character and symbol recognizers have achieved commendable performance for digitizing documents, structure analysers still face a challenge in correctly interpreting the maths expressions. This review paper compares the salient aspects of past works dealing with structure analysis of printed and handwritten MEs. To the best of our knowledge, no previous work has done a systematic study of structural analysis methods in mathematical expression recognition. We present distinguishing aspects of different grammars and their production rules for semantic parsing of ME. Our study contributes by providing information on the existing datasets, their desirable properties, different evaluation measures, distinguishing aspects of techniques used and future research directions in structural analysis. [ABSTRACT FROM AUTHOR]

This text contains Mazzola's comments on Geraint A. Wiggins’ position paper Music, mind and mathematics: Theory, reality and formality. [ABSTRACT FROM PUBLISHER]

Dissemination of ideas from theory to practice is a significant challenge in statistics. Quick identification of articles useful to practitioners would greatly assist in this dissemination, thereby improving science. This article uses the citation count history of articles to identify key papers from 1985 to 2002 from 12 statistics journals for applied biostatisticians. One feature requiring attention in order to appropriately rank an article's impact is assessment of the citation accrual patterns over time. Citation counts in statistics differ dramatically from fields such as medicine. In statistics, most articles receive few citations, with 15-year-old articles from five key journals receiving a median of 13 citations compared to 66 in the Journal of Clinical Oncology. However, statistics articles in the top 2%-3% continue to gain citations at a high rate past 15 years, exceeding those in JCO, whose counts slow dramatically around 8 years past publication. Articles with the highest expected applied uses 20 years post publication were identified using joinpoint regression. In this evaluation, the fraction of citations that represent applied use was defined and estimated. The false discovery rate, quantification of heterogeneity in meta-analysis, and generalized estimating equations rank as the ideas with the greatest estimated applied impact. [ABSTRACT FROM AUTHOR]

The article focuses on the use of context in post-16 pure mathematics questions set by the Examination Boards for national assessment in Great Britain. The study uses the grounded theory approach with six items from each specification analyzing and re-analyzing for identifying categories and relationships. Base from these questions, a framework analysis with three components is proposed. The accessibility of the context to all students is the first framework component. The second component pertains to its realistic appearance in the modeling experience and in test specific mathematics. The authenticity of the context in mathematical content is the third component. Further research is conducted for the verification of the framework result.

A theorem in the article “Characterization of Monoids by Properties of Generators,” written by Kilp and Knauer, states that amalgamated coproducts of generators are generators in the categoryAct-S of right S-acts over a monoid S. In this note we give a counterexample to deny this theorem. However, we show that the results in that article based on the mentioned theorem still remain valid. Moreover, an incorrect proposition in the monographMonoids, Acts and Categoriesby Kilp et al. which states that coamalgamated product of cogenerators are cogenerators is denied by a counterexample. [ABSTRACT FROM PUBLISHER]

The charging coil plays an important role in the wireless charging system system. However, there are still some problems in the design of the wireless charging coil, such as the low coupling coefficient. In order to improve the coupling effect, this paper proposes an optimized design scheme for the metal shielding layer structure of DD coil. Firstly, the influence of the structure size of DD coil metal plate on the coupling coefficient is studied by the mathematical modeling analysis. Futhermore, the maxwell simulation is used to study the metal plate coupling coefficients with varying structure sizes, addressing receiving uniformity issues. The optimal size of the shielding layer is designed for optimal magnetic coupling in wireless charging. Finally, this paper validates the feasibility of the improved metal shielding layer through experiments. The research in this paper may have a reference role in the wireless charging system of electric vehicles. [ABSTRACT FROM AUTHOR]

A dual-sided metasurface structure, consisting of two different sets of sub-wavelength periodic metallic patterns on its two sides, can offer a promising platform for the design of multifunctional and directional insensitive devices. This paper presents an elaborative study of the structural and mathematical analyses of the frequency response of a dual-sided metasurface structure. It has been found that the ratio between resonating wavelength and the structure's thickness plays a deterministic role in achieving multi-functionality in such designs. The paper further presents an equivalent circuit model of the dual-sided metasurface structure to mathematically analyze the role of impedance in achieving directional insensitivity in such devices. The proposed structural and mathematical analysis has been validated together by designing a directional insensitive rasorber in the latter half of the paper. The analyses done in this paper can open up a broad avenue for the research and development of metasurface-based directional insensitive multifunctional optoelectronics devices. [ABSTRACT FROM AUTHOR]

WSN consists of many sensors, they need high throughput and network lifetime to get involved in communication. Duty Cycle is a key factor in sensor nodes to maintain sleep, active condition in the presence of overhearing, collisions of packets while data transmission between sensor nodes. The key challenge of sensor nodes is to attain high energy efficiency, throughput and low End-End Delay. This paper presents several of existing approaches for MAC protocol. They are (1) Synchronization between nodes (2) Mathematical Analysis (3) TDMA based MAC and (4) Cross-Layer Design. We proposed a new method for MAC protocol with variable duty cycle. Neighboring nodes follow same duty cycle and same active time. Far away nodes doesn't maintain same duty cycle, hence their active time is not same. The duty cycle is maintained in synchronous way and adaptive manner among the nodes within the network. In this paper, a conventional MAC and proposed MAC are simulated using NS-2.35. Variable duty cycle approach in the proposed MAC with sleep and idle states for the nodes yields better throughput and energy efficiency with respect to other conventional technique. These results validate that the proposed variable DC-MAC is feasible for Wireless Sensor Network applications. [ABSTRACT FROM AUTHOR]

Lutsky in 2008 and 2009, where they investigated the invertibility of parabolic pseudo-differential operators with rapidly growing symbols and obtained estimates of exponential behaviour of solutions of pseudo-differential operators with growing and discontinuous symbols. During several years which followed the defense of the PhD thesis there appeared Vladimir's publications presenting interesting results for quasi-elliptic pseudodifferential operators and on solvability of Cauchy and Goursat problems for parabolic pseudodifferential equations (1971-1979 and later on), on solvability difference-differential equations (1978-1985 and later on), on Fredholmness of elliptic pseudodifferential operators and associated boundary value problems on noncompact manifolds (papers of 1971-1979). In 1993 he defended his doctoral thesis "The method of limit operators in solvability of pseudo-differential equations and convolution equations". [Extracted from the article]

Human body has a great ability to maintain homeostasis and the respiratory system plays a pivotal role in physiological processes. In this paper, a mathematical model of oxygen and carbon dioxide transport in the human body through capillary and tissue system has been formulated. The model is given by four ordinary differential equations for the oxygen and carbon dioxide transport, two equations for the capillary and other two for the tissue. An analytic approach based on Taylor's series method has been presented in this paper to obtain a computable approximate solution of the differential equation to model the oxygen and carbon dioxide diffusion in a spherical tissue. The concentration profiles at the capillary and tissue regions has been estimated in relation with partial pressure as the main driving force. The results are in agreement with the literature data those arrived at by Whiteley et al. (2005). The results obtained may help bio-medical sciences to deal with hypoxia and other respiratory ailments faced by the people living at high altitudes. Moreover, facilitated diffusion due to haemoglobin has been presented. [ABSTRACT FROM AUTHOR]

The article discusses on an article by David R. Bellhouse published within "Historia Mathematica" in its May 2007 issue. The article by Bellhouse discusses on the work of Philip Stanhope, the second earl of Stanhope, on probability theory and his correspondence with Bishop Berkeley's criticism on Isaac Newton's calculus. Bellhouse writes that Stanhope was strongly influenced by Abraham de Moivre's work on a method of calculating the probability of events in play and by Pierre Rémond's essay. Bellhouse adds that one of Stanhope's contribution to mathematics was his work on determining the probability of a run of at least r sucesses in n trials which was posed by de Moivre. Stanhope also worked on the duration of play in the gambler's ruin problem.

Creasing is a process which indents a section of corrugated board along fold lines to facilitate a neat fold. The most common failure site in a box made out of corrugated board is at the folds, where the stiffness is reduced by the creasing operation. Crease depth is an important parameter to be controlled. If the crease is too shallow, the section will crack during folding due to excessive strain on the outer liner. On the other hand, if the crease is too deep, the board may crack during the creasing operation itself or it may fail during handling due to excessive reduction in local strength along the fold line. A review of the literature reveals that only a limited amount of research has been carried out on experimental creasing of corrugated boards and comparison with numerical analyses. However, modelling of paper for corrugated board has been successfully done using Hill's plasticity model. In this work, experimental investigations on creasing of corrugated paperboard are carried out. These are complemented by finite element simulations of the creasing process. The simulations are found to be in good agreement with the experimental results. The findings of the work done are helpful in understanding the mechanics of creasing more clearly and in arriving at an appropriate crease depth in order to reduce cracking of corrugated board during the creasing process. [ABSTRACT FROM AUTHOR]

Puzzle-based storage systems consist of densely stored unit loads on a square grid. The problem addressed in this paper is to retrieve a stored unit load from a puzzle-based storage using the minimum number of item moves. While previous research contributed optimal algorithms for only up to two empty locations (escorts), our approach solves configurations where multiple empty locations are arbitrarily positioned in the grid. The problem is formulated as a state space problem and solved to optimality using an exact search algorithm. To reduce the search space, we derive bounds on the number of eligible empty locations and develop several search-guiding estimate functions. Furthermore, we present a heuristic variant of the search algorithm to solve larger problem instances. We evaluate both solution algorithms on a large set of problem instances. Our computational results show that the algorithms clearly outperform existing approaches where they are applicate and solve more general configurations, which could not be solved to optimality before. The heuristic variant efficiently yields high-quality solutions for significantly larger instances of practically relevant size. [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]

This paper introduces a modified method for construction of a new design-control 6-point approximating refinement scheme. The construction of the new scheme is based on translation of the points of 4-point approximating refinement scheme to the new position according to the linear combination of certain displacement vectors. The initial and terminal points of these vectors are the refinement points of two 4-point approximating binary schemes. The new scheme contains three design-control parameters. These parameters increase the efficiency and flexibility of the new scheme. The mathematical and graphical analysis of the refinement scheme show that this scheme is good choice for curve modeling. [ABSTRACT FROM AUTHOR]

In this paper, we study a three-species predator-prey model with modified LG-Holling type II with Lévy jumps, and we take the competition among predators into consideration. First, We use an Ornstein-Uhlenbeck process to describe the environmental stochasticity and prove that there is a unique positive solution to the system by mathematical analysis skills such as comparison theorem. Futhermore, the extinction or persistence in the mean of each species under different conditions is obtained. Finally, some numerical simulations are carried out to support our main results. [ABSTRACT FROM AUTHOR]

Tuberculosis (TB) is a communicable, airborne infection caused by the bacillus Mycobacterium tuberculosis. Pulmonary tuberculosis (PTB) is the most common presentation, although infection can spread anywhere to cause extra-pulmonary tuberculosis (EPTB). In this paper, a novel fractional order mathematical model is designed for the transmission dynamics of tuberculosis. Uninfected vulnerable individuals are categorized into the following: susceptible with underline ailment and susceptible without underline ailment. The research seeks to qualitatively and quantitatively analyze the proposed model and suggests comprehensive intervention measures for the control of tuberculosis among individuals with underline ailment. Some of the major highlights from the numerical investigation points out that TB vaccination is key to reducing the spread of TB among individuals with underline ailment. Furthermore, efforts to step down the spread of TB through awareness campaigns could significantly reduce the burden of the disease among individuals with co-morbidity. [ABSTRACT FROM AUTHOR]

A recent paper published in this Journal purported to provide a quantitative test of the thermogenetic hypothesis of cetacean brain evolution. While using appropriate statistical analyses that account for phylogenetic inertia, errors in the raw data and in interpretation of the thermogenetic hypothesis raise concerns about the validity of the statistical results and the conclusions of the paper. In this commentary the errors in raw data, mathematical approaches, the lack of inclusion of certain data points and misinterpretation of the thermogenetic hypothesis are detailed. The conclusion being that the thermogenetic hypothesis has not been correctly tested by the study. [ABSTRACT FROM AUTHOR]

Wireless sensor network (WSN) physical layer (PHY) uses M-ary spread spectrum (MaSS). This paper explores MaSS and emphasizes that based on the implementation approach; the technology has the potential to provide security at the PHY of wireless devices. The MaSS parameters, namely, spreading sequences and symbol to sequence mapping logic, can be obfuscated for security implementation. In this paper, we have focused our analysis on obfuscating mapping logic, i.e. Mapping Obfuscation (MO). Mathematical analysis reveals that an eavesdropper with processing speed in the order of 1018 operations/sec can intercept and decode short length (maximum 8–10 bytes) packets in <100 s. Simulation exposes that the eavesdropper can achieve a success rate of 50% for short-length packets if its signal-to-noise ratio exceeds −1 dB. An attacker has only one check metric for mapping sequence detection that is correct frame check sequence (FCS) detection. However, FCS detection may be misleading; if packet-embedded FCS and eavesdropper-generated FCS are the same for the wrong mapping sequence. For MO-based MaSS, false FCS detection probability is 30 times more than valid FCS detection probability. To reduce false FCS probability attacker need to analyse multiple radio frequency (RF) packets for detecting a valid mapping key; this increases the computation time. For MO-based PHY security, correct mapping sequence identification by exhaustive search demands cluster-based parallel processing. [ABSTRACT FROM AUTHOR]

A comparison of the performance on the final exam for subpopulations of students in College Algebra was used to assess the effectiveness of online homework. Data was collected for two small groups of students, one with traditional paper homework and the other with online homework. The groups of students were further classified by incoming skill level measured by a departmental placement test. The data suggests that online homework was beneficial to the incoming higher-skilled group, whereas, the lower-skilled students did not benefit from online homework. [ABSTRACT FROM PUBLISHER]

Product line planning (PLP) aims at an optimal combination of product feature offerings, suggesting itself to be a determinant decision for a company to satisfy diverse customer needs and gain competitive advantages. Fulfilment of planned product lines must make trade-offs between product variety and production costs. To balance the costs of product lines, manufacturers often adopt a product platform configuration (PPC) approach to redesign product and process platforms by adding new modules to the legacy platforms. The PPC is an effective means of providing product variety while controlling the manufacturing costs. The PLP and PPC problems have traditionally been investigated separately in the marketing research and engineering design fields. It is important to coordinate PLP and PPC decisions within a coherent optimisation framework. This paper proposes a bilevel mixed 0–1 nonlinear programming model to formulate coordinated optimisation for platform-driven product line planning. The upper level deals with the PLP problem by maximising the profit of an entire product line, whilst the lower level copes with the multiple product platforms optimisation for the optimal PPC in accordance with the upper level decisions of product line structure. To solve this bilevel programming model, a bilevel genetic algorithm is developed to find the optimal solution. A case study of coordinated optimisation between an automobile line and its product platforms is presented to demonstrate the feasibility and effectiveness of the proposed bilevel programming in comparison with a typical ‘all-in-one’ approach and a non-joint optimisation programming. [ABSTRACT FROM AUTHOR]

This paper is concerned with the distributed fault estimation problem for a class of uncertain stochastic systems over sensor networks. The norm-bounded uncertainty enters into the system in a random way governed by a set of Bernoulli distributed white sequence. The purpose of the addressed problem is to design distributed fault estimators, via available output measurements from not only the individual sensor, but also its neighbouring sensors, such that the fault estimation error converges to zero exponentially in the mean square while the disturbance rejection attenuation is constrained to a give level by means of theperformance index. Intensive stochastic analysis is carried out to obtain sufficient conditions for ensuring the exponential stability as well as prescribedperformance for the overall estimation error dynamics. Simulation results are provided to demonstrate the effectiveness of the proposed fault estimation technique in this paper. [ABSTRACT FROM AUTHOR]

In the paper, the concept of self-healing effects, permanent or limited duration on system health, is introduced by building a class of cumulative damage shock models in terms of the integral for counting processes including Poisson process, Hawkes process and Affine process, and so on. Based on the established shock models, the property on lifetime and the bounds of system reliability are discussed, especially for the simplest case. Then the general simulation algorithm is given for the general situation under the given cumulative damage shock models, because it is impossible to present the general analytical results on the reliability of systems. Some numerical examples are given to illustrate the algorithm and bounds of reliability. Finally, the whole works in the paper are concluded. [ABSTRACT FROM AUTHOR]

The Nagata ring R(X) and the Serre’s conjecture ring R⟨X⟩ are two localizations of the polynomial ring R[X] at the polynomials of unit content and at the monic polynomials, respectively. In this paper, we contribute to the study of Prüfer conditions in R(X) and R⟨X⟩. In particular, we solve the four open questions posed by Glaz and Schwarz in Section 8 of their survey paper [38] related to the transfer of Prüfer conditions to these two constructions. [ABSTRACT FROM AUTHOR]

This paper deals with the study of the behaviour of a large class of Petri net: weighted T-systems (WTS). We recall recent results which propose to linearize WTS on a marked graph (MG), in order to obtain a model which can be analysed using tropical algebra like (max,+) or (min,+). In the last part, we present a transformation to extend the previous results. The idea is to introduce synchronization in the model; this kind of transition enriches the model and gives the opportunity to apply the different results. [ABSTRACT FROM AUTHOR]

This paper presents a dual voltage source inverter (DVSI)-based Distributed Static Compensator (DSTATCOM) to enhance the power quality in the power utility system (PUS). The proposed DSTATCOM consists of two numbers of two-level voltage source inverters (VSI) which controls the reactive power. One of them is regarded as the main voltage source inverter (MVSI) and the other is considered as auxiliary voltage source inverter (AVSI). The i cos ⁡ ϕ control algorithm is employed to generate the reference source currents as well as switching pulses. The detailed control algorithm is formulated by mathematical analysis using MATLAB/Simulink, and compared with different case studies. Among all the theoretical findings, the DVSI offers better voltage regulation, voltage balancing, source current harmonic reduction and power factor correction under various loading scenarios. Apart from these, reliability, stress balancing of the both MVSI and AVSI, cost reduction due to a decrease in the filter size and better operation of PUS is obtained. To check the effectiveness, the performance of the DVSI-based DSTATCOM is carried out as per the benchmark value of the IEEE-519-2014 and IEC-61000-1 grid code. [ABSTRACT FROM AUTHOR]

The widely known hermite-hadamard-Fejer type inequalities are so important in the field of mathematical analysis. Many researchers have studied on these inequalities. In this paper, we have obtained several inequalities related to the Hermite-Hadamard inequality for a special class of the functions called uniformly convex functions. We have also presented applications of these obtained inequalities in some error estimates for higher moments of random variables. [ABSTRACT FROM AUTHOR]

Considering the potential for new product design possibilities and the reduction of environmental impacts, Additive Manufacturing (AM) processes are considered to possess significant advantages for automotive, aerospace and medical equipment industries. One of the commercial AM techniques is Binder-jetting (BJ). This technique can be used to process a variety of materials including stainless steel, ceramic, polymer and glass. However, there is very limited research about this AM technology on energy consumption aspect. This paper presents a method to build an energy consumption model for printing stage of BJ process. Mathematical analyses are performed to find out the correlation between the energy consumption and geometry of the manufactured part. Based on the analyses, total energy consumption is calculated as a function of part geometry and printing parameters. Finally, test printing is performed to check the accuracy of the model. This process model provides a tool to optimise part geometry design with respect to energy consumption. [ABSTRACT FROM PUBLISHER]

Many problems in engineering and science involve calculation of difficult Laplace integrals of the form:In previous papers [Hanna and Davis (2011), Davis and Hanna (2013), referred to as Papers I and II, respectively], the authors introduced two new complementary analytical methods for theimprovedasymptotic (x→ ∞) approximation of these integralswhen the upper limit A equal to ∞[the general Watson lemma (WL) problem for anyAifx→ ∞]. A procedure is developed here that extends application of the previous improvement methods to thedifficult problem of Laplace integrals having a finite upper limit (FUL) = A. In addition, problems havinggrowingexponential behavior, certain infinite Fourier integrals and problems having large (tα) factors, are also considered. The main result is that, with some modifications, the exponential, expansion-point, and combination procedures developed forinfiniteintegrals (Papers I and II) can be easily applied directly to FUL Laplace integrals. This is accomplished with the aid of a simple new “generalized incomplete gamma function (IGF)” algorithm which itself utilizes an improvement procedure. The new FUL procedure requires onlyF(t),F′(t), and a few terms of the Taylor expansion. A simple EXCEL program which implements the new procedure is discussed in detail in Appendix A and is freely available to users athttp://www.d.umn.edu/~rdavis/CEC/. Many numerical comparisons presented here indicate that good engineering accuracy is achieved for these improved approximations at virtually all positiveAvalues, over a very wide range inx, for variousα, β,andF(t) functions. Where comparisons are possible (A = ∞), the new results are far superior to those of the best Watson’s lemma results. [ABSTRACT FROM AUTHOR]

Photovoltaic systems are sensitive to weather conditions in terms of fluctuation, intermittentness and randomness, which could be affected drastically by the factors such as fast variation from sunlight conditions, environment temperature, cloud shadings under outdoor environmental conditions. The performance of photovoltaic systems could pose greater impact on the security and stability to the power grid especially under extreme irradiance condition. This paper established a mathematical analysis model for photovoltaic system under over-irradiation (OI) condition (>1000 W/m2) combined with the experimental data of a 5.605 kWp monocrystal silicon modules system from 2019 to 2020 in arid climate. The result evaluated the data in aspects of amplitude, frequency, velocity and duration of the performance of the system along with the weather data. The results show that the yield of the system under OI status accounts for 15.09% of the total energy generation, the maximum operating current exceeded the short-circuit current by 26.8% with average duration reaches 272 seconds. Finally, the four typical OI days were chosen from the date and demonstrated that the fuses of the string and inverters in the system would undertake an over-rated status over 12,050 seconds, which raised a challenge to the response time of the inverter and the MPPT algorithm as well as the fuses reliability. [ABSTRACT FROM AUTHOR]

Mathematical modelling of the simplest Takagi-Sugeno fuzzy Two-Input Two-Output (TITO) Proportional-Integral/Proportional-Derivative (PI/PD) controller is presented in this paper. Mathematical model of fuzzy PI/PD controller is proposed using Algebraic Product (AP) t-norm, Bounded Sum (BS) t-co-norm and Center of Gravity (CoG) defuzzifier. The inputs are fuzzified by fuzzy sets having L and type membership functions. The rule base consists of five rules with different linear models in the consequent parts. Both static and dynamic couplings are taken into account while deriving the models. The model of the fuzzy PI/PD controller reveals that it is a variable gain/structure controller. Also, each output of the TITO fuzzy controller is the sum of two nonlinear PI or PD controllers with variable gains. The properties and the gain variations of the controllers are investigated. [ABSTRACT FROM AUTHOR]

This paper studies a model for flow in a fractured porous medium with intersecting fractures. The fractures are treated as lower-dimensional manifolds and then physical transmission conditions express the pressure jump and the continuity of the flux across the fractures. Specific attention is borne to the conditions when several fractures intersect. The resulting system is discretized with mixed finite element, and the well-posedness of both the continuous and the discrete problems are proved. Then a domain decomposition method is formulated, so that the problem is reduced to the set of fractures, and a simple preconditioner is proposed. Numerical results exemplify the performance of the method. [ABSTRACT FROM AUTHOR]

Let G = (V (G) , E (G)) be a simple molecular graph without directed and multiple edges and without loops. Graph theory has become an important component of the chemical mathematics, and it has become one of the most powerful mathematical tools in the analysis and study of the architecture of a chemical network. It studies of descriptors in quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies in the chemistry science. There are a lot of topological indices in QSPR/QSAR studies. In this paper, some eccentricity-based topological indices namely the eccentric connectivity index ξ c (G) , the modified eccentric connectivity index ξ c (G) , the total eccentricity index ξ (G) , the second Zagreb eccentricity index M 1 * * (G) and the average eccentricity index avec (G) are computed for the para-line graphs of some hexagonal cactus chains namely the para-chain L n , the ortho-chain O n and the meta-chain M n. [ABSTRACT FROM AUTHOR]

It is an open question whether the results of human evaluations of product aesthetics can be reasonably predicted from eye-tracking data. In this paper, we investigate the correlation mechanism between eye-tracking data and product aesthetic ratings so that the eye-tracking data can form a scientific reference in product aesthetic evaluation to better guide product design. It is proven that the four chosen eye-tracking indices, including total fixation duration, fixation count, visit count and total visit duration, are significantly correlated with product aesthetic ratings, and it is possible to achieve objective quantification of product aesthetics. The correlation between eye-tracking data and product aesthetic ratings is analysed, and an evaluation model of the product aesthetic correlation mechanism is proposed based on eye-tracking data. Experimental results demonstrate that product aesthetic evaluation is not mysterious or unique and can be reasonably described through data analysis and mathematical algorithms. If the correlation mechanism between eye-tracking data and product aesthetics is well established, the scientific evaluation of product aesthetics can be easily achieved. [ABSTRACT FROM AUTHOR]

In this paper, we present a mathematical analysis to a Cahn-Hilliard/Allen-Cahn system with degenerate mobility that models an isothermal process of solidification of a binary alloy. This model is able to predict an observable phenomenon called solute trapping. The existence of global weak solutions for the system is proved. We approximate the degenerate system and show the convergence of solutions to the approximated non-degenerate problem to a solution of the degenerate one. We also investigated deeply the non-degenerate system by showing the existence of global weak solutions, the existence of global strong solutions in the two-dimensional case, and local strong solutions in the three-dimensional case, as well as, providing conditions to the uniqueness be satisfied. [ABSTRACT FROM AUTHOR]

This special issue is based on a selection of the four best papers from the Third International Seminar on Railway Operations Modelling and Analysis held in Zurich from 11 to 13 February 2009. The papers have been selected and reviewed by Board and other senior members of the International Association of Railway Operations Research (IAROR) and subsequently revised by their authors. The authors and their papers come from universities in Sweden, The Netherlands, Italy, Switzerland and Portugal. They represent valuable contributions to the current state of scientific and professional knowledge in the area of railway operations that can stimulate the broader application and further development of advanced analytical, combinatorial and simulation models. [ABSTRACT FROM AUTHOR]

This paper studies John Buridan's octagons of opposition for the de re modal propositions and the propositions of unusual construction. Both Buridan himself and the secondary literature have emphasized the strong similarities between these two octagons (as well as a third one, for propositions with oblique terms). In this paper, I argue that the interconnection between both octagons is more subtle than has previously been thought: if we move beyond the Aristotelian relations, and also take Boolean considerations into account, then the strong analogy between Buridan's octagons starts to break down. These differences in Boolean structure can already be discerned within the octagons themselves; on a more abstract level, they lead to these two octagons having different degrees of Boolean complexity (i.e. Boolean closures of different sizes). These results are obtained by means of bitstring analysis, which is one of the key tools from contemporary logical geometry. Finally, I argue that this historical investigation is directly relevant for the theoretical framework of logical geometry, and discuss how it helps us to address certain open questions in this framework. [ABSTRACT FROM AUTHOR]

An important problem in network analysis is to identify significant communities. Most of the real-world data sets exhibit a certain topological structure between nodes and the attributes describing them. In this paper, we propose a new community detection criterion considering both structural similarities and attribute similarities. The clustering method integrates the cost of clustering node attributes with the cost of clustering the structural information via the normalized modularity. We show that the joint clustering problem can be formulated as a spectral relaxation problem. The proposed algorithm is capable of learning the degree of contributions of individual node attributes. A number of numerical studies involving simulated and real data sets demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the design of networked recursive filter is investigated for a kind of nonlinear stochastic systems subject to missing measurements, fixed time-delay and uniform quantisation under the Round-Robin protocol. In a digital platform, the information coming from multi-sensors could be subject to missing measurements due to the environment effect and then need to be transformed into digital signals via uniform quantizers. In addition, the Round-Robin protocol is adopted to govern the token accessing to channel media so as to both save energy and mitigate the data congestion. A novel extended Kalman-type recursive filter is constructed that firstly combines the Round-Robin protocol, namely, in the form of the augmentation of the plant system dynamics and the protocol-induced periodic measurements. In the simultaneous consideration of system delays, missing measurements, uniform quantisation, as well as the Round-Robin protocol, the purpose for the discussed filtering problem is to obtain a set of filter parameters over a finite-horizon to minimise the upper bound of filtering error covariance as far as possible. Via elaborate mathematical analysis, the desired filter parameter is obtained by virtue of solving two Riccati-type optimisation equations, which are dependent on the latest estimation states. The genetic algorithm has been introduced to optimise the dynamic parameter selections. In addition, it is revealed in theory that the trace of the upper bound of filtering error covariance is non-decreasing as the quantisation level increases. Finally, the effectiveness of the proposed design scheme is inspected by a discretised maneuvering target tracking system. [ABSTRACT FROM AUTHOR]

This paper describes a research project implemented in a course of Real Analysis II. The aim of this project is to analyse students' comprehension of the limiting behaviour of a function from R2 to R at a point focusing on the formal definitions. Alternative definitions and other statements are discussed, some of which meet both sufficient and necessary conditions, while others meet only sufficient conditions; some involve neighbourhoods and others 'paths'. Emphasis is placed on the criteria according to which students choose one of the given definitions, equivalence or not of these and their overall influence on the concept images formed by the students for the limit concept. In particular, the paper discusses how students come to a conclusion about the existence of the limit of a function in R2 through the consideration of contour curves. We also present and analyse data from a written test as well as from the conducted interviews. [ABSTRACT FROM AUTHOR]

In this paper, we study a free boundary problem for a class of nonlinear nonautonomous size-structured population model. Using the comparison principle and upper-lower solution methods, we establish the existence of the solution for such kind of a model. [ABSTRACT FROM AUTHOR]