Easy Problem Research Articles

The Effect of a Training Program Based on Mathematical Problem-Solving Strategies on Critical Thinking Among Seventh-Grade Students

The present study aimed at investigating the effect of a training program based on mathematical problem-solving strategies on critical thinking skills among seventh-grade students in King Abdullah II schools of Excellence. The study adopted the quasi-experimental research approach. The participants of the study comprised of 29 male seventh graders. The participants were randomly distributed into a control group (n = 14) and an interventional group (n = 15). The study adopted the critical thinking skills test (75 items). The tests consisted of five subtests (identifying assumptions, deduction, conclusion, interpretation, and discussion). The interventional training program was a group of training situations complementary to the official curriculum. These situations were based on the strategy of building an organized list or a table, the strategy of finding a pattern, trial and error strategy, the strategy of using an equation or a law, the strategy of building a model or a diagram, the strategy of solving an easier problem, deletion strategy, go backward strategy, and logical justification strategy. The results showed that there were significant statistical differences in the critical thinking post-test scores between the control group (M = 26.5714, SD = 3.95580) and the interventional group (M = 43.6667, SD = 4.68534, t = 10.640, p = 0.000). The study concluded that the training program based on solving mathematical problems is an effective interventional tool to improve the seventh graders’ critical thinking skills. The study recommends reviewing the content of the curricula designed for the elementary stage in Jordan and including drills related to solving mathematical problems that aim to improve critical thinking skills of the elementary stage students.

Scheduling with complete multipartite incompatibility graph on parallel machines: Complexity and algorithms

In this paper, the problem of scheduling on parallel machines with a presence of incompatibilities between jobs is considered. The incompatibility relation can be modeled as a complete multipartite graph in which each edge denotes a pair of jobs that cannot be scheduled on the same machine.The paper provides several results concerning schedules, optimal or approximate with respect to the two most popular criteria of optimality: Cmax (makespan) and ∑Cj (total completion time). The problems are considered for a variety of machine types: identical, uniform and unrelated. The results consist of delimitation of the easy (polynomial) and NP-hard problems within these constraints. Also, polynomial-time exact algorithms are provided for easier problems and algorithms with a guaranteed constant worst-case approximation ratio for harder ones.In particular, there is provided a polynomial-time approximation scheme (PTAS) for scheduling with respect to ∑Cj on uniform machines, when the number of parts (i.e. sets of vertices constituting the mentioned graph) is bounded. The problem is addressed by developing a linear programming relaxation technique with appropriate rounding. This technique together with an exhaustive search (albeit in a manner controlled by the precision parameter) allows to provide the desired algorithm. For Cmax a PTAS is provided for the case of unit time jobs, but when the number of parts is part of the input. Interestingly, the latter result shows a connection between the considered problem of scheduling and covering problems.

Multistage stochastic decision problems: Approximation by recursive structures and ambiguity modeling

Stochastic multistage decision problems appear in many - if not all - application areas of Operations Research. While to define such problems is easy, to solve them is quite difficult, since they are of infinite dimension. Numerical solution can only be found by solving an approximate, easier problem. In this paper, we show good approximations can be found, where we emphasize the recursive structure of the involved algorithms and data structures.In a second part, the problem of coping with the model error of approximations is discussed. We present algorithms for finding distributionally robust solutions for the model error problem. We also review some application cases of such situations from the literature.

QPALM: a proximal augmented lagrangian method for nonconvex quadratic programs

We propose QPALM, a nonconvex quadratic programming (QP) solver based on the proximal augmented Lagrangian method. This method solves a sequence of inner subproblems which can be enforced to be strongly convex and which therefore admit a unique solution. The resulting steps are shown to be equivalent to inexact proximal point iterations on the extended-real-valued cost function, which allows for a fairly simple analysis where convergence to a stationary point at an \(R\)-linear rate is shown. The QPALM algorithm solves the subproblems iteratively using semismooth Newton directions and an exact linesearch. The former can be computed efficiently in most iterations by making use of suitable factorization update routines, while the latter requires the zero of a monotone, one-dimensional, piecewise affine function. QPALM is implemented in open-source C code, with tailored linear algebra routines for the factorization in a self-written package LADEL. The resulting implementation is shown to be extremely robust in numerical simulations, solving all of the Maros-Meszaros problems and finding a stationary point for most of the nonconvex QPs in the Cutest test set. Furthermore, it is shown to be competitive against state-of-the-art convex QP solvers in typical QPs arising from application domains such as portfolio optimization and model predictive control. As such, QPALM strikes a unique balance between solving both easy and hard problems efficiently.

Differenciating Oil, Gas And Water In Seismic Section Using Spectral Decomposition

Oil, Gas And Water Contained In The Pore Spaces Should Give Different Response In The Seismic Trace, But This Is Not An Easy Problem. However, From The Physical Point Of View Oil Is Quite Compressible, Gas Is Very Compressible And Water Is Incompressible, So In Principle They Should Give Different Response In Seismic Record. Since The Response In The Time Domain Is Sometimes Complicated In Nature, An Effort Has Been Carried Out To Remedy The Problem In The Frequency Domain. A Recent Advance In Signal Analysis Which Is Referred To As The Spectral Decomposition Has Been Used To Differentiate Oil, Gas And Water In Seismic Section. In This Case A Specifi C Method In Spectral Decomposition Called As The Continuous Wavelet Transform (CWT) Was Utilized For This Purpose. The Result Demonstrates That Oil, Gas And Water Can Be Differentiated Clearly In The CWT Spectrum Using The Data From The Deep Water Part In The Makassar Strait. The Results Are Encouraging.

Spatial abilities associated with open math problem solving

AbstractOpen math problem solving is critical to help students deepen the understanding and promote transfer of mathematics knowledge. However, the cognitive mechanism for open math problem solving, particularly the role of spatial abilities, has not been paid enough attention. This study recruited 192 junior middle school students (14.30 ± 0.48 years old). Results showed that both spatial visualisation (measured by paper folding) and spatial working memory (measured by spatial 2‐back) significantly associated with open math problem solving with controlled variables including age, sex, nonverbal matrix reasoning, and arithmetic principles. Moreover, spatial working memory was more associated with easy open math problem solving, while spatial visualisation more associated with difficult open math problem solving. These findings suggested that as the difficulty of open math problems increased, the construction of problem space mattered more than retaining and updating problem space in open math problem solving.

Предельное распределение периметра выпуклой оболочки, порожденной пуассоновским точечным процессом в выпуклом многоугольнике

In this paper, we study various functionals of convex hulls generated by the realization of a homogeneous Poisson point process in a polygon on a plane. The convex hull is a generalization of the extreme elements of the sample when estimating the carrier of the distribution; and in the multidimensional case, as an estimate of the carrier of the distribution, it retains many properties of one-dimensional estimates, such as consistency, asymptotic unbiasedness, and sufficiency. Works on the study of random convex hulls in polygons and various functionals of them are usually referred to the field of probabilistic geometry. It should be noted that studying the properties of even the simplest functionals of convex hulls, such as the number of vertices or the area, is not an easy problem (see, for example, [1-4]). This also explains the fact that before the appearance of the work of P. Groeneboom [6], the main progress in this field was achieved only in the study of the properties of the mean values of such functionals. In [6], he succeeded in proving the central limit theorem for the number of vertices of a convex hull in the case when the support of the original uniform distribution is either a convex polygon or an ellipse. The main result of this paper consists in proving that the difference between the perimeters of the distribution carrier and the convex hull converges in probability to a random variable that has a distribution different from normal, and it is asymptotically independent of the number of vertices and the area of the convex hull.

Solving binary semidefinite programming problems and binary linear programming problems via multi-objective programming

‎In recent years the binary quadratic program has grown in‎ ‎combinatorial optimization‎. ‎Quadratic programming can‎ ‎be formulated as a semidefinite programming problem‎. ‎In this paper‎, ‎we consider the general form of‎ ‎binary semidefinite programming problems (BSDP)‎.‎ ‎We show the optimal solutions of the BSDP belong to the efficient set of a semidefinite multiobjective programming problem (SDMOP)‎. ‎Although‎ ‎finding all efficient points for multiobjective is not an easy problem‎, ‎but‎ ‎solving a continuous problem would be easier than a discrete variable problem‎. ‎In this paper‎, ‎we solve an SDMOP‎, ‎as an auxiliary‎, ‎instead of BSDP‎. We show the performance of our method by generating and solving random problems.

Semi-Global Leaderless Output Consensus of Heterogeneous Multi-Agent Systems With Input Saturations

This paper studies the semi-global leaderless output consensus problem for heterogeneous multi-agent systems with input saturations. To solve the consensus problem under the input saturations, the consensus trajectory should be bounded such that the control inputs of all agents are not saturated. However, generating a bounded trajectory satisfying this condition is not an easy problem. Accordingly, we construct the modified reference generator to generate the bounded trajectory for any bounded initial states, and two types of distributed controllers depending on the available information are proposed to track the generated trajectory. Specifically, we construct the distributed controllers using the state feedback and the output feedback based on the output regulation approach, respectively. Then, utilizing the low gain method, we show the existence of the solution for the semi-global output consensus problem. Finally, we provide numerical examples to demonstrate the theoretical results.

ПЕР. СТ.: РИФФЕР Ф. СОЗНАНИЕ: ТОЧКА ЗРЕНИЯ ФИЛОСОФИИ ПРОЦЕССА И ГЕНЕТИЧЕСКОГО СТРУКТУРАЛИЗМА - КРИТИЧЕСКОЕ СРАВНЕНИЕ И НЕКОТОРЫЕ ПОСЛЕДСТВИЯ

A selective translation of the article by the Austrian philosopher, theologian, psychologist and teacher from the Department of Pedagogical Sciences of the University of Salzburg F. Riffer seems appropriate, since it highlights the modern philosophical debates about the phenomenon of consciousness based on D. Chalmers' distinction between its easy and difficult problems. A.N. Whitehead's philosophy of the process provides a promising basis for solving a difficult problem in connection with the rootedness of the concept of consciousness in metaphysical theory. Whitehead's reflection is compared with the results of empirical studies of the phenomena of consciousness of J. Piaget. If they partially coincide, the position of the former seems to be more reasonable. This corresponds to W.E. Seeger's suggestion to pay more attention to processalism or the concept of a philosophical process. Whitehead's point of view on learning, consciousness and artificial intelligence is considered.

Four Tier Diagnostic Tes Instrument To Identify Misconceptions For Grade Ix Junior High School Students In Jember Regency

Misconception is an event where there is a fallacy of the concept received by students after following a learning process, this accepted concept is not in accordance with existing scientific studies. One of the most common materials is material related to human heredity material class IX junior high school. The development of a Four-Tier Diagnostic Test instrument is one of the efforts in identifying the misconception of the material. This study aims to find out the validity level of the Four-Tier Diagnostic Test instrument as a good measuring tool in identifying the misconception of class IX junior high school human heredity material located in Jember Regency. This study involved 29 learners from Muhammadiyah Junior High School 4 Tanggul for instrument validity test. This type of research is descriptively quantitative using purposive sampling methods. Based on the analysis of expert validity tests obtained validity rate of 84.16% (very valid), instrument validity test value of 92.30% valid questions and 7.69% of invalid questions, reliability test value obtained 12 questions have reliability value of 0.785, difficulty tests obtained results of 75% of moderate problems, 8.30% of easy problems, and 16.60% of difficult problems, and different power tests obtained results of 33.33% of sufficient questions, 41.66% about good, 16.66% about good, and 8.33% bad.

Intelligent Automatic Segmentation of Wrist Ganglion Cysts Using DBSCAN and Fuzzy C-Means.

Ganglion cysts are common soft tissue masses of the hand and wrist, and small size cysts are often hypoechoic. Thus, identifying them from ultrasonography is not an easy problem. In this paper, we propose an automatic segmentation method using two artificial intelligence algorithms in sequence. A density based unsupervised learning algorithm called DBSCAN is performed as a front-end and its result determines the number of clusters used in the Fuzzy C-Means (FCM) clustering algorithm for quantification of ganglion cyst object. In an experiment using 120 images, the proposed method shows a higher extraction rate (89.2%) and lower false positive rate compared with FCM when the ground truth is set as the human expert’s decision. Such human-like behavior is more apparent when the size of the ganglion cyst is small that the quality of ultrasonography is often not very high. With this fully automatic segmentation method, the operator subjectivity that is highly dependent on the experience of the ultrasound examiner can be mitigated with high reliability.

Christianity for Weak People: How The Holy Spirit Prays for Believers according to Romans 8:26-27

For many Christian believers, especially whose family members suffer a prolonged sickness or multiple disease complications, it is often perplexing for them that God seems delaying to answer their prayers. And in many cases, God seems to let those family members to die. How could it be understood? That is not an easy problem to digest for many believers, especially if they think they already serve God in ministry, or churches, or other occasions. Fortunately, there are also comforting words to encourage us in such a perplexing situation, such as Romans 8:26-27, which suggests that the Holy Spirit also do intercession prayers for believers. And these two verses were followed by verse 8:28, where St. Paul concluded that from the previous two verses, we know that God works through everything for good to them that love God. Probably, that is the origin of a famous phrase: “God works often in mysterious ways.” This reflective article is intended to shed light on this old question

Decentralised PI controller design based on dynamic interaction decoupling in the closed-loop behaviour of a flotation process

An enhanced method for design of decenralised proportional integral (PI) controllers to control various variables of flotation columns is proposed. These columns are multivariable processes characterised by multiple interacting manipulated and controlled variables. The control of more than one variable is not an easy problem to solve as a change in a specific manipulated variable affects more than one controlled variable. Paper proposes an improved method for design of decentralized PI controllers through the introduction of decoupling of the interconnected model of the process. Decoupling the system model has proven to be an effective strategy to reduce the influence of the interactions in the closed-loop control and consistently to keep the system stable. The mathematical derivations and the algorithm of the design procedure are described in detail. The behaviour and performance of the closed-loop systems without and with the application of the decoupling method was investigated and compared through simulations in MATLAB/Simulink. The results show that the decouplers - based closed-loop system has better performance than the closed-loop system without decouplers. The highest improvement (2 to 50 times) is in the steady-state error and 1.2 to 7 times in the settling and rising time. Controllers can easily be implemented.

More Effort, Less Fatigue: The Role of Interest in Increasing Effort and Reducing Mental Fatigue.

People generally prefer easier over more difficult mental tasks. Using two different adaptations of a demand selection task, we show that interest can influence this effect, such that participants choose options with a higher cognitive workload. Interest was also associated with lower feelings of fatigue. In two studies, participants (N = 63 and N = 158) repeatedly made a choice between completing a difficult or easy math problem. Results show that liking math predicts choosing more difficult (vs. easy) math problems (even after controlling for perceived math skill). Two additional studies used the Academic Diligence Task (Galla et al., 2014), where high school students (N = 447 and N = 884) could toggle between a math task and playing a video game/watching videos. In these studies, we again find that math interest relates to greater proportion of time spent on the math problems. Three of these four studies also examined perceived fatigue, finding that interest relates to lower fatigue. An internal meta-analysis of the four studies finds a small but robust effect of interest on both the willingness to exert greater effort and the experience of less fatigue (despite engaging in more effort).

Assessing the implementation of machine learning models for thermal treatments design

ABSTRACT The latest progress in machine learning (ML) algorithms enabled to predict some steel physical properties previously modelled by linear regression (LR), such as the Ms temperature. Authors claimed that the performance given by ML models could improve the one of previous LR models, although they did not include fair comparisons. In this work, a large database was used to train different ML algorithms, whose Ms temperature predictions were compared to the ones of previous literature empirical models. ML methods were proved to require longer computational times and wider knowledge, while leading to similar results. Therefore, we recommend that ML methods are not always considered as the first option when trying to solve easy problems that can be modelled by LR techniques.

Position Paper: Incremental Search Algorithms Considered Poorly Understood

Incremental search algorithms, such as D* Lite, reuse information from previous searches to speed up the current search and can thus solve sequences of similar search problems faster than Repeated A*, which performs repeated A* searches. In this position paper, we study goal-directed navigation in initially unknown terrain and point out that it is currently not well understood when D* Lite runs faster than Repeated A*. In general, it appears that Repeated A* runs faster than D* Lite for easy navigation problems (where the agent reaches the goal with only a small number of searches), which means that it runs faster than D* Lite quite often in practice. We draw two conclusions, namely that incremental search algorithms need to be evaluated in more diverse testbeds to improve our understanding of their properties and that they can be improved to be more competitive for easy navigation problems.

Mechanical Properties of Laser Treated Thin Sample of an Amorphous-Nanocrystalline Metallic Alloy Depending on the Initial Annealing Temperature

The ability to control the mechanical properties of metal alloys is an urgent task in materials science. For formation of certain operational properties, in most cases, it is enough to treat the working surface of the product by laser radiation. Classical processing methods are ineffective in relation to multicomponent amorphous-nanocrystalline metallic alloys. This is due to their limited use. Usually, this treatment leads to the loss of unique properties the amorphous-nanocrystalline material. Increasing crack resistance and microhardness is not an easy problem. The structure of an amorphous nanocrystalline material can be destroyed under the action of laser processing. Laser nanosecond treatment, as result of a complex effect on the surface, slightly affects the structure of material. The treated material is characterized by increased microhardness and crack resistance, while at the same time such changes may be controlled.

A hack for learning math: starting and ending on high notes to create a more pleasurable learning experience

The present study focuses on creating a more pleasurable learning experience for students learning maths. Participants completed two lists of maths problems, a short list of only difficult maths problems and an extended list with both difficult maths problems and moderately difficult maths problems, placed in the beginning, end, or both beginning and end of the list. When asked to choose a third list to complete, participants preferred one of the extended list over the short list and found the extended lists to be less discomforting. Of the three types of extended lists, participants reported the one in which the moderately difficult maths problems were situated at both the beginning and end of the list to be the least discomforting. Participants self-reported maths anxiety did not moderate these effects. However, participants’ maths anxiety was negatively correlated with predicted and actual maths performance and positively correlated with discomfort ratings. These results suggest that by creating lists of maths problems in which the relatively easier problems are given before or after the more difficult maths problems, educators can create a more favourable learning experience that could help both maths-anxious and nonmath-anxious students practice more maths problems.

Accelerated impurity solver for DMFT and its diagrammatic extensions

We present ComCTQMC, a GPU accelerated quantum impurity solver. It uses the continuous-time quantum Monte Carlo (CTQMC) algorithm wherein the partition function is expanded in terms of the hybridisation function (CT-HYB). ComCTQMC supports both partition and worm-space measurements, and it uses improved estimators and the reduced density matrix to improve observable measurements whenever possible. ComCTQMC efficiently measures all one and two-particle Green's functions, all static observables which commute with the local Hamiltonian, and the occupation of each impurity orbital. ComCTQMC can solve complex-valued impurities with crystal fields that are hybridized to both fermionic and bosonic baths. Most importantly, ComCTQMC utilizes graphical processing units (GPUs), if available, to dramatically accelerate the CTQMC algorithm when the Hilbert space is sufficiently large. We demonstrate acceleration by a factor of over 600 (100) in a simulation of δ-Pu at 600 K with (without) crystal fields. In easier problems, the GPU offers less impressive acceleration or even decelerates the CTQMC. Here we describe the theory, algorithms, and structure used by ComCTQMC in order to achieve this set of features and level of acceleration. Program summaryProgram Title: ComCTQMCCPC Library link to program files:https://doi.org/10.17632/x2gzgm8njh.1Licensing provisions: GPLv3Programming language: C++/CUDANature of problem: In dynamical mean-field theory (DMFT), the computational bottleneck is the repeated solution of a quantum impurity problem [1]. The continuous-time quantum Monte-Carlo (CTQMC) algorithm has emerged as one of the most efficient methods for solving multiorbital impurity problems at moderate-to-high temperatures [2]. However, the low-temperature regime remains inaccessible, particularly for f-shell systems, and the measurement of two-particle correlation functions on an impurity adds a substantial computational burden. The bottleneck of the CTQMC solver is itself the computation of the local trace which includes the multiplication of many moderate-to-large sized matrices. The efficient solution of the impurity, measurement of the two-particle correlation functions, and acceleration of the trace computation are therefore critical.Solution method: ComCTQMC uses the hybridisation expansion of the impurity action to explore partition space [3]. It uses the worm algorithm [4] to explore the union of the partition space with observables spaces, e.g., the two-particle correlation functions. It uses improved estimators to more accurately measure the one- and two-particle Green's functions [5]. Identical impurities are solved across all MPI ranks (for ideal weak scaling) and the trace computations of these impurities are distributed to and accelerated by GPUs (when available). The lazy-trace algorithm [6] is used to further reduce the burden of the local trace calculation.Additional comments including restrictions and unusual features: ComCTQMC solves nearly arbitrary impurities, including those with complex valued and time-dependent interactions. However, there are two restrictions: (1) The retarded part of the interaction is described by a set of bilinears (a paired creation and annihilation operator), and these bilinears must commute with the local Hamiltonian and have real quantum numbers; (2) If a local Green's function vanishes, then the corresponding hybridisation function also vanishes.