Division Problems Research Articles

Vehicle distribution strategy in urban traffic by using coverage control

In order to optimize the distribution of the urban emergency rescue vehicles and achieve the rapid response of the traffic accident, the distribution of multi-emergency rescue vehicles for the minimum rescue time is studied. According to the coverage control and the influence of traffic congestion for rescue time, the main research contents are as follows: analysis of the overall time consumption on the target area, establishment of the optimization model which considers the responsible area and the driving constraints of each vehicle for rescue time consumption. In details, for the division problem of responsible area of emergency rescue vehicle, the responsible area of each vehicle is calculated by using Voronoi region allocation principle and taking the driving time of vehicle to any point in urban road networks as evaluation index. Then, in consideration of the driving constraints in urban road networks, the constraints in the optimization model is clarified further on the premise of analyzing the vehicle kinematic characteristics. Finally, the optimal distribution position of multi-emergency rescue vehicles in the target area and the corresponding responsible area are calculated by gradient descent. The results show that the vehicle can converge to the optimal distribution position from any position in the target city, and the traffic accidents in responsible area can be timely response.

Adaptive variability in children’s conceptual models of division

This study examined whether different types of commonly used mathematical tasks affect how children think about whole number division problems. Prior research suggested that children tend to rely on the partitive model to understand whole number division, which is likely problematic when students transition to learning about fraction division. We assessed variability in correct whole number division problem-solving strategies among 63 elementary school children (41.5% female, 58.5% male, 0% nonbinary/gender expansive; 69.2% White, 10.7% multiracial, 6.1% Black, 4.6% Latino, 3.3% other/unidentified, 6.1% preferred not to answer). Each participant was asked to demonstrate four whole number division problems in each of three contexts (within participants): objects, story problems, and number lines. Most children displayed understanding of multiple conceptual models of division, but strategies varied by context. Story problems elicited partitive models, number lines elicited quotative models, and objects elicited both. Finally, elementary school children used strategies adaptively. Number line representations may afford conceptual connections between earlier-learned whole number concepts and analogous later-learned fraction concepts, supporting the integration of children’s whole number and fraction knowledge.

Synergistic study of cellulose enzymatic factors and cellulase adsorption properties under bioinformatics

Abstract Cellulose enzymatic saccharification is a key link in converting lignocellulose to fuel ethanol via a sugar platform. In this paper, the maximum information coefficient (MIC) algorithm is proposed to detect linear correlations and nonlinear correlations between bioinformatics variables from the application of bioinformatics. Meanwhile, to address the problems of excessive grid division and low statistical efficacy of MIC algorithm, BackMIC, an optimization algorithm using quiz control number of segments, is proposed to terminate the network search using the chi-square test. Then, cellulase hydrolysis and adsorption experiments were designed and performed, and the experimental data were analyzed based on the BackMIC algorithm. The optimum activity temperature of different cellulases was around 50°C, while the hydrolysis rate of cellulases of different treated raw materials increased and then decreased with the increase of temperature, and basically, the maximum was achieved in the temperature range of 50~55°C. In the pH test, the optimum temperature of cellulase hydrolysis was concentrated at 4.4~4.5. In the cellulase adsorption experiments, the enzymatic activity of steam-popped wheatgrass was adsorbed in the following order: FPA> C1> CMCase> β-Case. The study of cellulase hydrolysis based on bioinformatics reveals the synergistic relationship between cellulase hydrolysis and adsorbed properties, which provides a theoretical basis for reducing the ineffective adsorption of cellulose and the development of enzymatic strengthening technology. The theoretical basis for reducing the ineffective adsorption of cellulose and the development of enzymatic enhancement technology can help reduce the cost of lignocellulose enzymatic digestion.

Stable sharing

We propose a simple model in which agents are matched in pairs in order to complete a task of unit size. The preferences of agents are single-peaked and continuous on the amount of time they devote to it. Our model combines features of two models: assignment games (Shapley and Shubik (1971)) and the division problem (Sprumont (1991)). We provide an algorithm (Select-Allocate-Match) that generates a stable and Pareto efficient allocation. We show that stable allocations may fail to exist if either the single-peakedness or the continuity assumption fail.

Fair Division with Prioritized Agents

We consider the fair division problem of indivisible items. It is well-known that an envy-free allocation may not exist, and a relaxed version of envy-freeness, envy-freeness up to one item (EF1), has been widely considered. In an EF1 allocation, an agent may envy others' allocated shares, but only up to one item. In many applications, we may wish to specify a subset of prioritized agents where strict envy-freeness needs to be guaranteed from these agents to the remaining agents, while ensuring the whole allocation is still EF1. Prioritized agents may be those agents who are envious in a previous EF1 allocation, those agents who belong to underrepresented groups, etc. Motivated by this, we propose a new fairness notion named envy-freeness with prioritized agents EFprior, and study the existence and the algorithmic aspects for the problem of computing an EFprior allocation. With additive valuations, the simple round-robin algorithm is able to compute an EFprior allocation. In this paper, we mainly focus on general valuations. In particular, we present a polynomial-time algorithm that outputs an EFprior allocation with most of the items allocated. When all the items need to be allocated, we also present polynomial-time algorithms for some well-motivated special cases.

Effects of intelligence and approximate number system on the non-symbolic division ability in preschoolers.

Recently, it has become evident that cognitive abilities such as the approximate number system (ANS), number knowledge, and intelligence affect individuals' fundamental mathematical ability. However, it is unclear which of these cognitive abilities have the greatest impact on the non-symbolic division ability in preschoolers. Therefore, in the present study, we included 4- to 6-year-old Korean preschoolers without prior formal education of division in order to test their ability to solve non-symbolic division problems, ANS acuity, and intelligence, and to determine the interrelationships among those functions (N = 38). We used the Panamath Dot Comparison Paradigm to measure the ANS acuity, employed non-symbolic division tasks to measure the ability to solve non-symbolic division problems, and measured the intelligence using the Korean version of the WPPSI-IV (Wechsler Preschool Primary Scale of Intelligence-IV). Our results showed that, in all conditions of the non-symbolic division tasks, the 4- to 6-years old children were able to perform better than chance level. Additionally, in a relatively easy condition, the children's performance showed a significant positive correlation with full-scale intelligence quotient (FSIQ) and ANS acuity; however, in a more complex condition, only FSIQ was significantly correlated with their performance. Overall, we found significant relationships between the children's performance in the non-symbolic division tasks and verbal comprehension, fluid reasoning, and processing speed index. Taken together, our findings demonstrate that preschoolers without formal education on the arithmetic problem solving can solve non-symbolic division problems. Moreover, we suggest that both FSIQ and ANS ability play essential roles in children's ability to solve non-symbolic division problems, highlighting the significance of intelligence on children's fundamental mathematical ability.

Assessing student teachers’ procedural fluency and strategic competence in operating and mathematizing with natural and rational numbers

AbstractProcedural fluency and strategic competence in operating and mathematizing with natural and rational numbers are based on a flexible and meaningful use of mental models, strategies, and procedures. The study to be presented in this paper pursued the question as to which subdomains or tasks relating to procedural fluency and strategic competence at upper primary school level are particularly challenging for elementary school student teachers. The newly devised assessment instrument included mathematical problems from a wide variety of content domains such as numbers and operations with natural and rational numbers, place value, computational strategies, estimation, (inverse) proportion, combinatorics, mathematization, and word problems. A preceding theoretical task analysis ensured that the solution of the problems required adaptation of strategies and flexible reasoning about a procedure or a formula. In the assessment, each of the 15 tasks were presented to 280 first-semester student teachers. As the results of the analyses indicate, combinatorial problems and division problems with rational numbers proved to be particularly challenging for a large proportion of the participants. Supplemental qualitative analyses of solution pathways confirmed that the assessment tasks allowed for multiple solution pathways. The item difficulties could be explained by a lack of ability to link mental models, strategies, and procedures. The study makes a connection between theoretical and empirical research on educational standards and teacher education. It contributes to the international state of research about student teachers’ content knowledge by providing specific insights concerning procedural fluency and strategic competence.

On 7-division fields of CM elliptic curves

Let be a CM elliptic curve defined over a number field K, with Weiestrass form y^3=x^3+bx or y^2=x^3+c. For every positive integer m, we denote by the m-torsion subgroup of and by the m-th division field, i.e. the extension of K generated by the coordinates of the points in . We classify all the fields K_7. In particular we give explicit generators for K_7/K and produce all the Galois groups textrm{Gal}(K_7/K). We also show some applications to the Local–Global Divisibility Problem and to modular curves.

Research on characteristics of splash lubrication and power losses of reducer based on MPS method

AbstractThe distribution of lubricant flow field inside the two‐stage transmission reducer is very complicated during splash lubrication, which is difficult to be visually simulated and analysed using traditional finite element methods (FEM). There are many problems in model processing, algorithm selection, mesh division, and computational workload. Through sufficient investigation and experimental validation based on literature, the moving particle semi‐implicit (MPS) method is proposed to study the splash lubrication characteristics of a rail vehicle reducer. Through this method, the visual simulation calculation of multiple working conditions of reducer with complex structure is realised, and the unreasonable structure of the gearbox body is optimised. The model of oil supply demand in the Hertz contact zone of gear transmission is established, and the time‐domain variation law of oil particles number in the contact zone and oil supply state are analysed. It is found that the optimised reducer model can meet the demand of oil supply under the four typical working conditions of the rail vehicle. The higher the initial oil volume is, the more sufficient the oil supply is. Compared with the working temperature conditions of 20 and 80 °C, the lubrication effect is better at 40 and 60 °C. By analysing the power loss proportion of each gear, it is found that the sum of power loss of gear 1 and gear 2 is dominant under different working conditions, reaching 76%–99.5% of the total churning power losses.

Study on the Management Way of “Banning Electric Bicycles from Going Upstairs” in Tianjin

In recent years, the number of electric bikes in Tianjin is close to 4.59 million. Since 2018, there have been 241 electric bicycle fires in Tianjin, with direct property losses of 1.36 million yuan. Although the newly revised “Tianjin Fire Control Regulations” was officially implemented on November 9, 2021, the problems of unclear division of management rights and responsibilities and weak law enforcement force have been unable to be solved. Through literature collection, questionnaire survey, grassroots research and other methods, the paper inspects the implementation of relevant policies in Tianjin residential communities, summarizes the outstanding problems, carries out the grass-roots law publicity, and puts forward a series of specific measures.

Computer-based feedback matters when relevant prior knowledge is not activated

BackgroundHow feedback is given may influence its utility. AimWe examined the effect of activated prior knowledge on learning from feedback by manipulating whether knowledge of a foundational concept was activated before solving fraction division problems. Sample and methodsUndergraduates (N = 171) were randomly assigned in a 3 (feedback timing: delayed, immediate, or no feedback) x 2 (knowledge activation: relevant or not) between-subjects design. ResultsIf irrelevant knowledge was activated, immediate feedback enhanced learning as compared to no feedback during the learning task, whereas if relevant knowledge was activated, then there was no impact of immediate feedback. On the posttest, any feedback (immediate or delayed) resulted in greater performance, but feedback timing did not matter. Thus, activating prior knowledge moderates the effect of feedback on learning. ConclusionWhen researchers or practitioners are investigating or giving feedback, they must also consider individual differences of the learner such as the prior knowledge they bring to the task.

And There Was Light: Abraham Lincoln and the American Struggle by Jon Meacham

Reviewed by: And There Was Light: Abraham Lincoln and the American Struggle by Jon Meacham Jon Diefenthaler And There Was Light: Abraham Lincoln and the American Struggle. By Jon Meacham. New York: Random House, 2022. 676 pp. Do we need another book on Abraham Lincoln? Among the multitude of others, what makes And There Was Light stand out is Jon Meacham's remarkable effort to let America's sixteenth President provide an illuminating perspective on a nation that is currently as deeply divided and struggling to survive as a democracy as it was before and during the Civil War. As helpful as this book may be for any American citizen to read, I am motivated to review it for this church-related journal because I believe the historical insights this noted author provides are potentially useful to Lutheran clergy and other ecclesiastical leaders seeking to navigate these same troubled waters and to address the socio-political divisions that continue to wash into their congregations and church bodies. Aptly subtitled "Abraham Lincoln and the American Struggle," Meacham's book covers most of the bases one would expect to find in a comprehensive biography, including Lincoln's family of origin, his hardscrabble upbringing, his first love Ann Rutledge, his turbulent marriage to Mary Todd and the loss of two of their progeny, his elections to office, as well as his anguished presidency and subsequent assassination. But in most every chapter on Lincoln's life, Meacham chooses to give us a measure of insight into the role religion played as the Illinois rail splitter sought to deal with the towering and divisive problem of slavery. At work in Lincoln's mind, in Meacham's estimation, were history, reason, and faith. For him, the Constitution, which viewed slaves as the property of their owners, took a back seat in America's history to the Declaration of Independence, which unequivocally stated that "all men are created equal." In contrast to historians who have stated that Lincoln's opposition to slavery evolved, Meacham provides ample evidence to substantiate the president's later [End Page 188] conscience-grounded claim that it was always in his nature to believe that "if slavery is not wrong, nothing is wrong." As Meacham sees it, what evolved was Lincoln's continuous search for a reasonable political solution to the problem. While African colonization of slaves piqued his interest, this proposal quickly proved to be less than feasible. Recognizing that various legislative compromises would only extend the Southern slave empire, he felt compelled to oppose them. The political necessity of gaining the support of Whites in order to outlaw slavery prompted his willingness to concede that Blacks were an inferior breed. The "popular sovereignty" solution advocated by Stephen Douglas in his campaigns for office only seemed to fan the flames of self-interest and secession. What Meacham in fact demonstrates is that as Lincoln's reliance on reason waned and as "war came," his faith in God took on a much greater role. According to Meacham, Lincoln's "creed was of his own making—and it was always evolving with enormous consequences for the nation he led and for the nation he left behind" (xxxv). His piety included regular reading of the King James Bible and, at his most critical hours, getting on his knees to pray to God. At the same time, his reading of Thomas Paine's Age of Reason ("my own mind is my own church") made him a "doubting Thomas" among believers, and for this reason, he never became the member of a Christian congregation. Lincoln found some of the Evangelical Protestant beliefs featured by the Second Great Awakening, such as the divinity of Jesus, too difficult to embrace. Instead, he favored the brand of theology set forth by the New England Transcendentalists. Theodore Parker in particular helped him focus on Nature's God and to believe that the universe was inherently moral, and that its history arced in the direction of justice. Nevertheless, Meacham reveals elements of Lincoln's religion that coincide with those of the Christian faith. For one thing, he recognized the pervasiveness of human depravity. Persistent awareness of his own shortcomings prevented any consideration...

Religion and identity polarisation: A slight note from the frontier region

This article examined the recent emergence of the national and international issue of religious polarisation and identity, which affects some groups’ populism and fanaticism. Regarding social phenomena, religion and identity are intertwined like the two sides of a coin. This discourse has an impact how to interpret diversity on religious issues that are caused by political influences. Given the polarisation of identity politics and religion, the national and state campaign slogan ‘unity in diversity’ is merely wishful thinking. The polarisation of identity and religion is heavily implicated in the Indonesia–Philippines border case; consequently, in some instances, the ‘seeds’ of these cases are discovered, eventually resulting in group fanaticism. This article employed the historical way of writing while also taking a social science angle that interacts with the research being done. For some communities, religion and identity may take on symbolic meaning, affecting how well they adapt and are accepted. However, the qualities of a community group or region are also shaped by historical events. According to the study’s findings, religion and ethnic identity have played important roles in long-standing historical processes and impacted them. This study is anticipated to ‘suppress’ the problem of political division involving religion and identity because the identification of ‘border’ communities depends not only on entity and identity issues but also on the community’s culture.Contribution: The contribution in this study is that it has an impact on religious issues and cultural identity relations perspectives.

학교 내 직종 간 업무분장 표준화와 협의기구 제도화를 위한 제언

Objectives This study aims to propose policy measures for standardizing the division of work and establishing institutional mechanisms in order to suggest alternatives regarding the division of work among teachers, administrative staffs, and non-fixed term workers (teaching support workers, administrative support workers, etc.) in schools.
 Methods To the purpose, we used prior literature researches, office of education’s data, Korean education statistics service data, online 263 questionnaires on the division of duties of three occupations in schools, and FGI for the relevant expert groups (16 people).
 Results As a result, specific tasks with insufficient the division of works turned out to be low-income families support work, CCTV related work, safety work, recruitment work for fixed-term workers etc. If these works are listed, they are not consistently in charge of a specific occupation in the school's work list, and even they are not listed in many cases. Therefore there is a great need to standardize the division of works.
 Conclusions We have proposed several points of policy measures as follows. First, the problem of division of works needs to be dealt with in conjunction with the reduction of the total amount of work of school workers. Secondly, standardization of the division of works among three occupational types should be achieved above a certain level. Thirdly, a certain degree of autonomy should be required at the school level. Lastly, existing trade unions in each occupational types should participate in consultative bodies. At this time, in order to reduce the total amount of work, it is necessary to conduct a fact-finding survey on work in schools and eliminate unnecessary work that has no need to be carried out.

The Matter With Things: Our Brains, Our Delusions, and the Unmaking of the World

The Matter With Things: Our Brains, Our Delusions, and the Unmaking of the World

Does more schooling imply improved learning? Evidence from the Kanyashree Prakalpa in India

Studies on Conditional Cash Transfer (CCT) programs have documented positive effects on school enrollment though evidence on learning outcomes is mixed. Using representative data, we evaluate one of the largest CCT programs, Kanyashree Prakalpa (KP), which was implemented in the state of West Bengal, India, in 2013. In particular, we examine the effect on female school enrollment and learning outcomes. Exploiting the timing of the program implementation for identification and applying difference-in-difference regressions, we document a positive effect on enrollment with no discernible impact on secondary and higher secondary school completion. We also observe significant improvements in lower-level learning outcomes but a marked deterioration in higher-level skills like solving simple division problems. Complementary investments like classroom availability and teacher attendance appear to have fallen after the implementation of KP, which explains the decline in learning skills despite higher schooling exposure, thereby underscoring the need for supply-side interventions in school amenities.

Extracting transition features among brain states based on coarse-grained similarity measurement for autism spectrum disorder analysis.

The abnormal brain functional connectivity (FC) of patients with mental diseases is closely linked to the transition features among brain states. However, the current research on state transition will produce certain division deviations in the measurement method of state division, and also ignore the transition features among multiple states that contain more abundant information for analyzing brain diseases. To investigate the potential of the proposed method based on coarse-grained similarity measurement to solve the problem of state division, and consider the transition features among multiple states to analyze the FC abnormalities of autism spectrum disorder (ASD) patients. We used resting-state functional magnetic resonance imaging to examine 45 ASD and 47 healthy controls (HC). The FC between brain regions was calculated by the sliding window and correlation algorithm, and a novel coarse-grained similarity measure method was used to cluster the FC networks into five states, and then extract the features both of the state itself and the transition features among multiple states for analysis and diagnosis. (1) The state as divided by the coarse-grained measurement method improves the diagnostic performance of individuals with ASD compared with previous methods. (2) The transition features among multiple states can provide complementary information to the features of the state itself in the ASD analysis and diagnosis. (3) ASD individuals have different brain state transitions than HC. Specifically, the abnormalities in intra- and inter-network connectivity of ASD patients mainly occur in the default mode network, the visual network, and the cerebellum. Such results demonstrate that our approach with new measurements and new features is effective and promising in brain state analysis and ASD diagnosis.

Consensus-Halving: Does It Ever Get Easier?

In the $\varepsilon$-Consensus-Halving problem, a fundamental problem in fair division, there are $n$ agents with valuations over the interval $[0,1]$, and the goal is to divide the interval into pieces and assign a label "$+$" or "$-$" to each piece, such that every agent values the total amount of "$+$" and the total amount of "$-$" almost equally. The problem was recently proven by Filos-Ratsikas and Goldberg [2019] to be the first "natural" complete problem for the computational class PPA, answering a decade-old open question. In this paper, we examine the extent to which the problem becomes easy to solve, if one restricts the class of valuation functions. To this end, we provide the following contributions. First, we obtain a strengthening of the PPA-hardness result of [Filos-Ratsikas and Goldberg, 2019], to the case when agents have piecewise uniform valuations with only two blocks. We obtain this result via a new reduction, which is in fact conceptually much simpler than the corresponding one in [Filos-Ratsikas and Goldberg, 2019]. Then, we consider the case of single-block (uniform) valuations and provide a parameterized polynomial time algorithm for solving $\varepsilon$-Consensus-Halving for any $\varepsilon$, as well as a polynomial-time algorithm for $\varepsilon=1/2$. Finally, an important application of our new techniques is the first hardness result for a generalization of Consensus-Halving, the Consensus-$1/k$-Division problem [Simmons and Su, 2003]. In particular, we prove that $\varepsilon$-Consensus-$1/3$-Division is PPAD-hard.

High Resolution ID‐TIMS Redefines the Distribution and Age of the Main Mesozoic Lacustrine Hydrocarbon Source Rocks in the Ordos Basin, China

AbstractUsing high‐precision zircon U‐Pb ID‐TIMS geochronology, tuffs from the Chang 9 shale and the Chang 7 shale were dated. The tuff in the Chang 9 shale is 241.47 ± 0.17 Ma, which falls between the top tuff age of 241.06 ± 0.12 Ma and the bottom tuff age of 241.558 ± 0.093 Ma in the Chang 7 shale. These reveal that the Chang 9 and Chang 7 shales are contemporaneous, belonging to the Ladinian stage of the Middle Triassic. This insight expands the region of the main source rock of Chang 7 to the northeast and will inform the search for the deep Chang 9 shale petroleum system, increasing the scope for exploring the Chang 7 shale system in northern Shaanxi. The research results clarify the relationship between the two sets of shale in the Yanchang Formation and redefine the distribution range of the Chang 7 shale in the Ordos Basin. At the same time, it shows that there is a cross‐layer problem in the stratigraphic division of the Yanchang Formation in different regions, the high‐precision U‐Pb dating technology providing a reference for the fine stratigraphic correlation of other continental basins in the world.

The Old Believers of Simbirsk and Samara in the Second Half of the 19th – Beginning of the 20th Century (according to the Materials of the Samara and Simbirian Diarish Departments)

Abstract Introduction. The presented article describes the Old Believer movement in the Simbirsk-Samara Volga region through the periodical press of this region. The chronological framework of the work covers the middle of the 19th – the beginning of the 20th century. The presented material touches on one of the dramatic problems of Russian history, the church schism and the emergence of the Old Believers movement. The relevance of the presented material lies in the growing interest of the Russian society in this topic, and especially among Orthodox youth. The problem of splits and divisions in Russian society is not a new phenomenon in our country. The reform, which began as a political adventure of Patriarch Nikon, led to a split of Orthodox Christians into Old Believers and Nikonians. The Old Believers have experienced a lot and in spite of everything they have preserved that ancient spiritual heritage, in which the spirit of Holy Russia has been preserved. The purpose of the article is to define, on the basis of newspaper materials, the role of the Old Believers in Russia, its uniqueness for the further history of the country. Materials and Methods. The main sources are periodicals. The work is based on the principles of historicism to the study of the past. The research methodology is based on special-historical general historical methods – scientific description. Research Results. As a result of the study, the author introduces into scientific circulation historical facts from diocesan records that have not previously been presented in modern historical science. Having a monopoly position in the state and society, the official church in its diocesan publications openly criticized all Old Believer trends (except for co-religionists). The anti-schismatic tone in publications has not changed throughout the existence of diocesan journals. At the beginning of the 20th century, the authorities and the church made significant compromises with regard to the Old Believers, but in the press, they remained the same sectarians who must be joined to the “true faith”. Discussion and Conclusion. The fight against the “schism” in Russia has always occupied a huge place in the life of the Russian Orthodox Church. The official church tried by all means to join the schismatics. The Old Believers, in conditions of severe persecution, actively continued to defend the principles of their faith, traditions and way of life. After the First Russian Revolution, there were hopes for the legal existence of the Old Believer Church. The February revolution completely gave the Old Believers freedom, but new persecutions began under the Bolsheviks. Relations between the New Believers and supporters of the “old times” change in the Soviet era, when both denominations existed under the yoke of the Soviets. Formal reconciliation did not lead to the restoration of both churches, the “historical schism” turned out to be deeper and harder. It can be concluded that this topic is still relevant today. The proposed provisions and conclusions create prerequisites for further study of this problem.