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A new model for the asymmetrical rolling is proposed to calculate the minimum rollable thickness simply and fast by the slab method. The calculation formulas of the rolling pressure, the rolling force, the critical roll speed ratio and the critical front tension under different deformation zone configurations are proposed, and the deformation zone configuration - rolling parameters relationship diagram is given and analyzed. The results show that the minimum rollable thickness can be reached when the rolling parameters keep the deformation zone configuration as cross-shear zone + backward-slip zone (C+B) or all cross-shear zone (AC). The calculation formulas of the minimum rollable thickness and the required rolling parameters for different deformation zone configurations are proposed respectively. The calculated value is in good agreement with the experimental results.

In this paper, a multi-value cellular automata model under Lagrange coordinates is proposed based on reality, the traffic flow in the Lagrange coordinate is simulated on the basis of the evolution equation of the model. From the fundamental diagram of the results under various conditions, it found that the three commonly used parameters of traffic flow in simulation is consistent with the empirical data. Specifically, traffic density and the number of lanes have a significant impact on traffic flow. The lower the density is, the more lanes there are, and the greater the flow. The research of this paper can help to develop more advanced traffic research technology, and improve the efficiency of traffic work subsequently. Simultaneously, it will bring convenience to people and promote the development of green traffic.

We answer the question by Matt Brin on the structure of diagram groups over semigroup presentation ${\mathcal P}=\langle a,b,c\mid a=bc,b=ca,c=ab\rangle$. In the talk on Oberwolfach workshop, Brin conjectured that the diagram group over $\mathcal P$ with base $a$ is isomorphic to the generalized Thompson's group $F_9$. We confirm this conjecture and consider some generalizations of this fact., Comment: arXiv admin note: text overlap with arXiv:math/0211396

We study the Reconstruction-of-the-Measure Problem (ROMP) for commuting 2-variable weighted shifts $$W_{(\alpha ,\beta )}$$ , when the initial data are given as the Berger measure of the restriction of $$W_{(\alpha ,\beta )}$$ to a canonical invariant subspace, together with the marginal measures for the 0–th row and 0–th column in the weight diagram for $$W_{(\alpha ,\beta )}$$ . We prove that the natural necessary conditions are indeed sufficient. When the initial data correspond to a soluble problem, we give a concrete formula for the Berger measure of $$W_{(\alpha ,\beta )}$$ . Our strategy is to build on previous results for back-step extensions and one-step extensions. A key new theorem allows us to solve ROMP for two-step extensions. This, in turn, leads to a solution of ROMP for arbitrary canonical invariant subspaces of $$\ell ^2({\mathbb {Z}}_+^2)$$ .

Advanced high-strength steels (AHSSs) are often illustrated in the steel strength–ductility diagram, which is also known as the “banana chart” due to the distribution trend of the tensile properties of the steel family. Both academia and industry frequently refer to such a diagram not only to categorize the evolving AHSS generations but also to direct future development objectives. Nevertheless, with various new AHSSs developed in recent years, the “banana chart” is considered too simplified to represent the sophisticated tensile properties of these AHSSs, especially when some practical conditions are taken into account. Therefore, this work focuses on investigating how the temperature and strain rate affect the tensile properties of selected AHSSs and correspondingly shift their distributions in the “banana chart.” Explanations and discussions on the possible mechanisms behind these effects are also presented.

Visual representations, such as diagrams, are known to be valuable tools in problem solving and proof construction. However, previous studies have shown that simply having access to a diagram is not sufficient to improve students’ performance on mathematical tasks. Rather, students must actively extract information about the problem scenario from their diagrams for them to be useful. Furthermore, several studies have described the behaviors of mathematicians and students when solving problems and writing proofs, but few have discussed students’ behaviors in the context of proof writing in introductory point-set topology. We present a case study of an undergraduate, Stacey, enrolled in a general topology course. Throughout a semester, we presented Stacey with several proof-related tasks and examined how and why Stacey used diagrams when working on these tasks. Based on our analysis, we concluded that Stacey’s diagram creation and subsequent use during the construction of a given proof was an effort to identify the key idea of the proof. We describe Stacey’s overall proving behaviors through the lens of a problem-solving framework and present Stacey’s use of diagrams as an aid to discovering the key ideas of proofs in topology.

A complex non series–parallel system of (m, $${n}_{c}$$ , l) order is developed by introducing ‘l’ additional components linked to arbitrary non-adjacent ith and jth components of ‘m’ parallel subsystems each containing $$\left\{{n}_{c};1\le c\le m\right\}$$ components connected in series. The efforts have been made to determine the best possible structure of the components in order to develop highly reliable system. The logic diagram technique is used to form maximal number of effective duplication paths between IN and OUT terminals according to the flow of information. Each path contains components whose successful operation can lead to successful operation of the system. The path which dominates over any other path is discarded keeping in view of the fact that this path has no effect on reliability of the system. The expressions for reliability and mean time to system failure are derived for the system by considering Rayleigh failure laws using path tracing method. An illustration is given to justify the application of the present work.

Chord diagrams and 4-term relations were introduced by Vassiliev in the late 1980. Various constructions of weight systems are known, and each of such constructions gives rise to a knot invariant. In particular, weight systems may be constructed from Lie algebras as well as from the so-called 4-invariants of graphs. A Chmutov–Lando theorem states that the value of the weight system constructed from the Lie algebra $$\mathfrak {sl}_2$$ on a chord diagram depends on the intersection graph of the diagram, rather than the diagram itself. This inspired a question due to Lando about whether it is possible to extend the weight system $$\mathfrak {sl}_2$$ to a graph invariant satisfying the four term relations for graphs. We show that for all graphs with up to 8 vertices such an extension exists and is unique, thus answering in affirmative to Lando’s question for small graphs.

To improve the efficiency of complex assemblies in large-scale assembly sequence planning, an intelligent sequence planning method for constructing an assembly hybrid G-diagram model to realize the hierarchy of assembly structures is proposed. The assembly hybrid G-diagram model is constructed according to the assembly relationship semantics, and the assembly relationship semantics can be transformed into the corresponding assembly connection matrix and assembly priority matrix. Subassembly discriminant conditions are given to realize subassembly and isolated parts extraction, and the assembly structure is divided into part-level and subassembly-level. According to the assembly hybrid G-diagram, all feasible assembly sequences of part-level (within subassembly) and subassembly-level (subassembly as a whole) are solved, respectively. The particle swarm algorithm is used to optimize the assembly sequence with the goal of aggregation and redirection. The optimal sequence of part-level and subassembly-level is obtained, respectively. The sequence information is integrated to obtain the complete assembly sequence with the highest assembly efficiency under parallel planning. The feasibility and effectiveness of the assembly sequence optimization method are verified using a V-type dual-cylinder engine as an example. This planning method can greatly reduce the search space and avoid infeasible sequences when solving assembly sequences. In parallel planning, the sequence optimization process can be greatly shortened to ensure the assembly efficiency.

The purpose of the paper is to build up the related theory of weakly quasitriangular dual pairs suitably for non-standard R-matrices (irregular), and establish the generalized double-bosonization construction for irregular R, which generalizes Majid’s results for regular R’s in [M1]. As an application, the type-crossing construction for the exceptional quantum group of type G2 is given explicitly. This affirms Majid’s expectation that the tree structure of nodes diagram associated with quantum groups can be grown out of the node corresponding to $${U_q}({\mathfrak{sl}_2})$$ by the (generalized) double-bosonization procedures.

We examine the ideals of nowhere dense sets in three topologies on the set of positive integers, namely Furstenberg’s, Rizza’s and the common division topology. We mainly concentrate on inclusions between these ideals, we present a diagram showing these and we explore all possible inclusions between them. We present a formula for the closure of a set in the common division topology. We answer a question posed by Kwela and Nowik (Topol Appl. 248:149–163, 2018) by constructing a set in $${{\mathcal {I}}}_G {\setminus } ({{\mathcal {I}}}_K \cup {{\mathcal {I}}}_F)$$ I G \ ( I K ∪ I F ) . Therefore, the main diagram of comparison between the ideals of nowhere dense sets in various topologies from the article by M. Kwela and A. Nowik is completed.

In this paper, novel modular representations and diagrams for service robots are introduced based on the work of ISO TC299-Working Group 6, aiming to provide a standard guideline for the users to present the modular service robots with a unified form, taking hardware connectivity and software aspect into account. The suggested modularity representation mainly consists of a line diagram, a circle diagram, a task-based diagram and a block diagram. At first, their concrete forms and introduction are illustrated in detail. Afterwards, some user case examples are provided, using the suggested diagrams, to present the real commercial modular designed service robots.

In this study, the isothermal saturation method was applied to obtain the data for solid–liquid equilibria in a system consisting of four solids (LiCl + NaCl + Li2SO4 + Na2SO4) and water at 288.15 K. The chemical composition of the liquid phase was experimentally determined, and the corresponding phase diagrams were constructed. The obtained diagram exhibited 6 crystallization areas, 10 univariant curves, and 5 invariant points. The 6 crystallization regions consisted of LiCl·2H2O, Li2SO4·H2O, NaCl, Na2SO4·10H2O, Li2SO4·3Na2SO4·12H2O and Li2SO4·Na2SO4. The solid-phase solubilities and phase equilibria were derived from the experimental data at 288.15 K using Pitzer’s equations. The calculated data were compared with the experiment, and the corresponding phase diagrams for both datasets were calculated. Experimental and theoretical diagrams were in good agreement.

This study aims to evaluate the performance of an extended floating car data (xFCD)-based traffic state estimation method proposed by Seo et al. (2015), which does not rely on any strong assumptions such as Fundamental Diagram, using high-resolution complete trajectory data, viz. Zen Traffic Data (ZTD). Traffic state estimated by this method, considering randomly sampled trajectories of ZTD as those of probe vehicles with known penetration rates, are compared with ones obtained by complete ZTD by applying Edie’s generalized definitions. The variation in estimation errors and covering percentages are analyzed for varying settings: spatiotemporal resolution and probe penetration rates.

We calculate the spectrum of the diagram for each finite 3-transposition group. Such graphs with a given minimum eigenvalue have occurred in the context of compact Griess subalgebras of vertex operator algebras.

In this paper, a new 2-dimensional chaotic map with a simple algebraic form is proposed. And the numerical solution of the corresponding fractional-order map is derived. It is novel that the new map still exhibits chaotic behaviors when the new map is expanded to fractional-order and improper fractional-order. The dynamical characteristics of these three forms are detected through the bifurcation diagram, the maximum Lyapunov exponent spectrum, Kolmogorov entropy and attractor portraits. More interestingly, the new map has multiple coexisting attractors, but the multistability of the fractional-order and improper fractional-order is more complicated than the integer-order form. In addition, the Permutation entropy (PE) complexity algorithm and 2-dimensional maximum Lyapunov exponent diagram are used to explore the dynamic changes of three forms when the amplitude changes simultaneously. The analysis shows that under the appropriate order, the chaotic range of the fractional-order and improper fractional-order is larger than that of the integer order. This research provides guidance on the application and teaching of discrete fractional-order systems.

Based on four reanalyses or gridded data sets (ERA5, 20CR, APHRODITE and REGEN), we provide an overview of 23 Historical and 7 HighResMIP experiments’ performance from the Coupled Model Intercomparison Project Phase 6 (CMIP6) (for short, 6-Hist, HighRes) in simulating seven extreme precipitation indices over Asia defined by the Expert Team on Climate Change Detection and Indices (ETCCDI). We compare them with 28 Historical experiments in CMIP5 (5-Hist). CMIP5 and CMIP6 models are generally able to reproduce extreme precipitation’s spatial distribution and their trend patterns in comparison to the benchmark data set (APHRODITE). The overall performance of individual model is summarized by a “portrait” diagram based on four statistics for each index. We divide all 58 models into three groups (A, the top 20%; B, the median 60% and C group, the last 20%) according to MR rankings (the comprehensive ranking measure). Based on the “portrait” diagram and MR rankings, models that perform relatively well for all seven extreme precipitation indices include HadCM3, HadGEM2-AO, HadGEM2-CC and HadGEM2-ES from 5-Hist, EC-Earth3, EC-Earth3-Veg from 6-Hist and ECMWF-IFS-HR, ECMWF-IFS-LR, ECMWF-IFS-MR from HighRes. The simulated performance of CMIP6 is polarized, for the top four and the last five ranking models are both from CMIP6. Compared with the counterpart models in CMIP6 and CMIP5, the improvement of PCC (pattern correlation coefficient) is more obvious. Furthermore, the dry biases of CMIP6 (both 6-Hist and HighRes) in Southern China and India and the wet biases of CMIP6 in Tibet are reduced compared to CMIP5. This may benefit from the improvement that CMIP6 models can capture the characteristics of meridional moisture flux convergence, and improve the overestimation or underestimation of meridional and zonal specific humidity eddies compared to CMIP5.

Using published and presently calculated diffusivities, a reliable and self-consistent atomic mobility description of the liquid and fcc phases in a Nd-Fe-B system is established by DIffusion-Controlled TRAnsformation software. Based on the obtained atomic mobility-coupled thermodynamic descriptions of the Nd-Fe-B system, a wheel speed-dependent solidification diagram for a model Nd2Fe14B alloy is constructed, which allows us to examine the influence of wheel speed on the solidification behavior of the quenching Nd2Fe14B alloy. According to the theoretically obtained solidified microstructures and their relationship with the magnetic properties, the optimal wheel speed when melt-spinning the quenching Nd2Fe14B ribbons is determined to be 35 m/s. The experimental microstructural characterizations and magnetic hysteresis loop measurements confirm that the ribbon prepared at a wheel speed of 35 m/s exhibits the best comprehensive magnetic properties because the remaining bcc-Fe phase is significantly suppressed and the main Nd2Fe14B phase was well refined to an ultrafine-grained microstructure. The grain refinement mechanism of the main phase in the ribbons is also described.

Separation of geochemical anomalies from the background using various methods for identifying areas of higher mineral potential is a critical first step in Greenfield and Brownfield programs. There are several methods for differentiating anomalous regions from the background. The U-spatial statistics is an effective technique that provides the opportunity of reaching this goal by considering the geochemical sample locations in the separation of geochemical anomalies. In this study, a developed form of the U-spatial statistics method is introduced, which not only considers the existence of anisotropic spatial variations in input data but also reduces the computational (CPU) time. While the previous method is based on the isotropic assumption in the study area and a set of search windows at different times, here, the geochemical anomaly is determined by pasting only one ellipsoid window, effectively combining the flexibility of the U-spatial statistics method with the advantages of geostatistical approaches. This paper compares various approaches (the previous and developed version of the U-spatial statistics method, concentration-area (C–A) fractal model, and probability diagram modeling) for the separation of anomalous areas in the presence of heterogeneous spatial variations. This is done with an application to a Baghqloom porphyry copper deposit located in southeastern Iran. The high potential areas identified via different approaches show an anomalous region in central parts of the Baghqloom area, which partially coincides with an intense potassic alteration area. Compared to other methods, our algorithm separated the high potential areas at a greater spatial resolution.

The method of tomographic reconstruction of inhomogeneities in case of an arbitrary directional diagram and scanning along one coordinate is described. It is shown that in this case registered data (projections) are represented as the sum of the line-by-line convolutions of the lines of the directional diagram and the corresponding line of the reconstructed distribution. The features of projection data, backprojections are analyzed. It is proposed to construct a cumulative image as an additive or conjunctive combination of the backprojection results for different orientation diagrams. An iterative procedure for constructing sequential approximations to the desired solution is proposed.

While there has been much interest in the power of student-generated multiple representations to promote student reasoning and conceptual understanding, most studies of student explanations have been of written artefacts or only included diagrams as an adjunct to written explanations. This approach may be because teachers do not have an accessible framework with which to evaluate students’ diagrams as being explanations. Adapting de Andrade et al.’s Research in Science Education, 49, 787-807 (2019) evaluation framework for written explanations, this study explored the benefits and limitations of a framework to evaluate students’ explanatory diagrams. Seventeen grade 5 and 6 students produced a series of explanatory diagrams over six chemistry lessons on particle theory. Their diagrams were coded and evaluated using the proposed diagram analysis framework. Some sample diagrams are included to illustrate how the framework assisted the evaluation of students’ diagrams. The framework helped identify key features of students’ diagrams and evaluate their explanatory powers consistently and effectively. This research also indicates that a series of stand-alone diagrams can effectively be used by teachers to assess how students communicate their understanding of causal explanations in terms of sub-microscopic entities of the underlying phenomena.

As direct prospecting data, geochemical data play an important role in modelling prospect potential. Geochemical element assemblage anomalies are usually reflected by the correlation between elements. Correlation coefficients are computed from the values of two elements, which reflect only the correlation at a global level. Thus, the spatial details of the correlation structure are ignored. In fact, an element combination anomaly often exists in geological backgrounds, such as on a fault zone or within a lithological unit. This anomaly may cause some combination of anomalies that are submerged inside the overall area and thus cannot be effectively extracted. To address this problem, we propose a local correlation coefficient based on spatial neighbourhoods to reflect the global distribution of elements. In this method, the sampling area is first divided into a set of uniform grid cells. A moving window with a size of 3×3 is defined with an integer of 3 to represent the sampling unit. The local correlation in each unit is expressed by the Pearson correlation coefficient. The whole area is scanned by the moving window, which produces a correlation coefficient matrix, and the result is portrayed with a thermal diagram. The local correlation approach was tested on two selected geochemical soil survey sites in Xiao Mountain, Henan Province. The results show that the areas of high correlation are mainly distributed in the fault zone or the known mineral spots. Therefore, the local correlation method is effective in extracting geochemical element combination anomalies.

Traditional observation methods of the boundary layer are susceptible to external factors. In particular, detection data are relatively scarce in special areas such as plateaus and oceans. However, occultation observation data have the unique advantage of global coverage, and the boundary layer information of the occultation profile is rich. Based on the machine learning algorithm, this paper combines GPS occultation technology to improve the algorithm and constructs the boundary layer height simulation model based on the actual situation and analyzes its functional structure one by one. Moreover, in order to verify the validity of the simulation model, a simulation analysis is performed in combination with actual data. In addition, the performance of the model is verified from multiple aspects, and the results of the research are calculated by mathematical statistics, and the corresponding statistical diagram is drawn. Through experimental analysis, it can be known that the model constructed in this paper can effectively simulate the boundary height and has certain practical effects.

The MnS–Tb2S3 phase diagram has been plotted by using physico-chemical methods of analysis. This diagram refers to the transition type from the eutectic system MnS–Gd2S3 to the systems with the formation of intermediate compounds. Two MnTb4S7 and MnTb2S4 complex sulfides are formed in the MnS–Tb2S3 system. The thermal effects of solid-phase decomposition of complex sulfides are as follows: ΔH = 27.4 kJ/mol at 1643 K for MnTb4S7 and ΔH = 16 kJ/mol at 1574 K for MnTb2S4. The solubility of MnS in γ-Tb2S3 at 1650 K is 16 mol.%, and 5 mol.% of MnS is dissolved in α-Tb2S3 at 1170 K. The solubility of Tb2S3 in α-MnS-based solid solution (SS) is 6 mol.% at 1650 K and 3 mol.% of Tb2S3 at 1170 K. The temperature of the γ-Tb2S3 solid solution eutectoid decomposition is equal to 1350 K, and the composition of the eutectoid is 87 mol.% of Tb2S3. The coordinates of the eutectic between MnS-based solid solution and γ-Tb2S3-based solid solution is assumed to be equal to 27 mol.% of Tb2S3 and 1666 K. Calculations of the liquidus line, carried out using the Van Laar's equation, are in agreement with the experimental data. The Gibbs excess partial energies are calculated for the MnS–Tb2S3 system, and their negative values are correlated with the formation of two complex sulfides MnTb2S4 and MnTb4S7 in the system.

We address the problem of offline handwritten diagram recognition. Recently, it has been shown that diagram symbols can be directly recognized with deep learning object detectors. However, object detectors are not able to recognize the diagram structure. We propose Arrow R-CNN, the first deep learning system for joint symbol and structure recognition in handwritten diagrams. Arrow R-CNN extends the Faster R-CNN object detector with an arrow head and tail keypoint predictor and a diagram-aware postprocessing method. We propose a network architecture and data augmentation methods targeted at small diagram datasets. Our diagram-aware postprocessing method addresses the insufficiencies of standard Faster R-CNN postprocessing. It reconstructs a diagram from a set of symbol detections and arrow keypoints. Arrow R-CNN improves state-of-the-art substantially: on a scanned flowchart dataset, we increase the rate of recognized diagrams from 37.7 to 78.6%.

Software testing is leading toward automation that reduces the effort to find errors or bugs. The identification of test cases and its critical domain requirements is done with generation of test cases. The brooding characteristic of the cuckoo bird is explained through the adaptive cuckoo search meta-heuristic algorithm (ACSA) that further narrates that host nest is used by the cuckoo bird for laying their eggs and the next generation also sees the best quality eggs from the host bird’s nest. This paper focuses on the adoption of ACSA for analysis, generation, and optimization of random test cases. In addition to that, the present work also explains the model driven approach to automatically generate and optimize the test cases with the help of unified modeling language diagram like sequence diagram. Then, the respective sequence diagram is converted into a sequence diagram graph that shows the flow of sequences being produced. Thereafter, it is optimized using ACSA by taking a case study of withdrawal operation of ATM transaction. The said approach is also evaluated in terms of efficiency and usefulness for generating the test cases through simulated experiments. In addition to that, the projected approach also identifies the operational faults as well as message faults.

Punch–die misalignment is one of the factors that can contribute to drawn cup defects such as thinning and tearing. Deep drawing is a closed-die process, and defects can be identified only after the drawing is finished. In this work, the effect of punch–die misalignment severity on the drawing force and wall thickness distribution of electrolytic zinc-coated steel blank (SECC) was investigated. The stress–strain diagram and forming limit diagram of SECC material was determined and simulated using the Hill’48 model. Two conditions of punch–die misalignment were studied: single-axis and multi-axis misalignment. A high punch–die misalignment severity contributes to the increment in the drawing force. Furthermore, wall thickness distribution becomes non-uniform, and the thinning pattern increases due to the greater misalignment severity. For validation, an experiment was conducted on a universal tensile machine.

The $\mathfrak {s}\mathfrak {l}_{3}$ colored Jones polynomial $J_{\lambda }^{\mathfrak {s}\mathfrak {l}_{3}}(L)$ is obtained by coloring the link components with two-row Young diagram λ. Although it is difficult to compute $J_{\lambda }^{\mathfrak {s}\mathfrak {l}_{3}}(L)$ in general, we can calculate it by using Kuperberg’s A2 skein relation. In this paper, we show some formulas for twisted two strands colored by one-row Young diagram in A2 web space and compute $J_{(n,0)}^{\mathfrak {s}\mathfrak {l}_{3}}(T(2,2m))$ for an oriented (2,2m)-torus link. These explicit formulas derives the $\mathfrak {s}\mathfrak {l}_{3}$ tail of T(2,2m). They also give explicit descriptions of the $\mathfrak {s}\mathfrak {l}_{3}$ false theta series with one-row coloring because the $\mathfrak {s}\mathfrak {l}_{2}$ tail of T(2,2m) is known as the false theta series.

In this work, austenite–martensite transformation in a low alloy steel is modeled using Voronoi algorithm. The evolved fraction of martensite is predicted from the geometry of the Voronoi diagram constructed, incorporating nucleation kinetics of martensite and Voronoi algorithm. The obtained results are validated against the Koistinen–Marburger equation. The geometrical properties of evolved martensite phase are identified using the characteristics of Poisson–Voronoi diagram. Finally, the microstructure developed is used to analyze local stress–strain behavior of different phases in the microscale. Results show that higher stress values are distributed in martensite phase and higher strain values are distributed in austenite phase.

A plane-displacement diagram showing the four twinning elements, planes and directions, is fundamental to the classical theory of twinning. One aspect of the classical theory of type I and II twinning is shown to be inapplicable when the twin rotation is large. We employ the topological model with certain nonlinear characteristics to deduce a modified set of twinning elements. For twinning associated with a small rotation, both the classical theory and the topological model for type I and II twinning are shown, which give the same set of twinning elements. However, only the topological model is applicable for the large rotation case. As for the classical model, the twin plane in the type II twinning case is irrational unless it, and the type I twin is compound. Often, this irrational plane is close to a low-index orientation for a given orientation relationship. Then it can be favorable for the interface to break up into low-index, rational facets, separated by disconnections. This occurs without changing the orientation relationship. We apply the topological model to describe both the irrational type II twins and faceting in NiTi. The results agree with TEM observations.

This paper explores different goodness-of-fit (GOF) criteria’s used in the various fields of science to compare candidate probability density functions (pdfs) to annual maximum temperature records and discusses their usefulness and drawbacks. The L-moment ratio diagram method is also proposed as alternative approach for the GOF of the pdfs. The advantage this method allows for an easy comparison of the fit of many pdfs for several stations on a single diagram. To gain knowledge about higher order moments (i.e. shape, skewness and kurtosis) of the station data set, plotting the position of a given temperature data set in L-moment ratio diagram space is prompt and effective and can provide a useful addition to the GOF criterion. Both the L-moment ratio diagrams and many GOF criteria are used on real data to assess the fit of the pdfs for temperature data in the state of New South Wales, Australia. The analysis of the L-moment ratio diagrams reveals that the generalized extreme value and normal distributions generally fit best the annual maximum temperature series. The other two- and three-parameter distributions also showed viable fits in some instances. Results obtained from L-moment diagrams, temperature frequency histograms, cumulative density plots and the simulation study are compared with those obtained from GOF statistics, and a good agreement is generally observed between all these approaches. In conclusion the L-moment ratio diagram can represent a simple, effective and efficient approach to be used as a complementary method along with the traditional GOF criteria.

Parameters like aquifer depth, aquifer replenishment rate, aquifer medium, soil medium, percolation medium, and the coefficient of permeability are considered during the preparation of a groundwater vulnerability diagram. The analytic hierarchy process is used for evaluation, and expert scoring is used to analyze and establish the judgment matrix, and then new weights have been computed for each DRASTIC parameter, such that some subjectivity can be reduced to some extent and the weight value tends to be reasonable. Various spatially referenced digital data layers are overlaid to analyse with the partition diagram in GIS spatial analysis and a comprehensive simple and straight diagram is drawn. The study area is a plain of Naiman Banner, Inner Mongolia China, and covers an area of approximately 10,700km2. The areas of lower vulnerability are mainly located in the south. Slightly higher vulnerability areas are mainly located in the north, and the others have medium vulnerability.

Recently, researchers have conducted long-term statistical studies to prove the correspondence between earthquakes and thermal infrared (TIR) anomalies. Upon obtaining relatively high true positive rates (TPR), it was concluded that TIR anomalies are closely related to earthquakes. However, the temporal-spatial clustering of earthquakes and overly large temporal-spatial windows will also contribute to high TPRs, and it is improper to correlate TIR anomalies with earthquakes without excluding these influences. In this paper, relevant studies will be tested according to the prior probability, random earthquake catalogs and Molchan diagram weighted by the Relative Intensity (RI) index. Our results show that the high TPR in the previous studies were caused by overly large determining windows, and the result was close to random guessing, which means that the extracted TIR anomalies make no contributions to predicting the timing, epicenter and magnitude of earthquakes. By comparing the original Molchan diagram and the Molchan diagram weighted by the RI index, we found that simply taking the fraction of space-time occupied by alarm may give a wrong evaluation for alarm. Moreover, long-term statistical evidence proving the correspondence between earthquakes and TIR anomalies in Greece and Taiwan are still absent.

Micro-scale thin-walled parts have the characteristics of small size and low rigidity, so chatter is very easy to occur in high speed micro-milling, which influences machining precision and surface quality of the parts. To solve this problem, the authors first establish micro-milling force models in micro-milling thin-walled parts that consider the elastic deflection of both thin-walled part and micro-milling tool. According to the Lagrange’s equation, the dynamic characteristics of thin-walled part that vary with the cutting position of the tool are obtained combined with the Rayleigh-Ritz method. The relative transfer function between the micro-milling tool and the thin-walled part is achieved through the relationship between cutting force and vibration vector and then the dynamic characteristics of the system are obtained. Finally, the stability lobe diagram is drawn through time-domain simulation and verified by micro-milling experiments. The comparison results show that the prediction results of the stability lobe diagram are consistent with the experimental results. The research is a meaningful exploration of the mechanism of micro-milling thin-walled parts and provides a basis for the selection of cutting parameters for stable cutting.

The article published on January 3 in 2017 is well-written and of interest, but remains several questions that are required for clarifications, such as the production of ten clusters of 11,359 journals based on 2015 data using VOSviewer for classification and visualization. After viewing the detailed information about the data in Fig. 1, we are interested in producing the similar Figure on a dashboard with a video MP4 provided to readers who can click on the link to manipulate the scenarios on their own. We found that the process of making diagram of social network analysis on Google Maps using the MS Excel VBA codes. The individual-/cluster-type relations of journals are easily examined on Google Maps.

In this study, we report on the design and use of an apparently unbounded spatial diagram to explore shearing, an area-preserving transformation. Apparently unbounded spatial diagrams are realizations of geometric objects, such as lines, that appear to extend indefinitely. They can be rendered in virtual reality displays where users who are visually immersed in a virtual world can interact with them through natural body movements (e.g. walking, grasping, head-turning). We developed an immersive environment that contained a dynamic spatial diagram of a triangle whose vertices were points on two apparently unbounded parallel lines. The diagram offered orthogonal and non-orthogonal perspectives on the parallel lines, mediated by walking and head-turning. Pairs of learners engaged in open-ended inquiry with the diagram. We analyzed their interactions with it and each other to distill mathematical arguments. The participants relied upon spatiographic observations of the diagram, as they might rely upon such observations of large-scale objects (e.g. buildings), in order to make arguments about how shearing affected the triangle. We discuss how natural bodily interactions with large-scale spatial diagrams can create new opportunities for learning and teaching.

The first part of this study presented low-cycle fatigue and cyclic fracture toughness test methods for 10GN2MFA steel at 20 and 270°C, experimental results to construct kinetic fatigue fracture diagrams and to determine low-cycle plastic strain and fracture characteristics. Here, those results are estimated as to the application of cyclic plasticity to describe the fatigue crack growth rate. The cyclic strain-hardening coefficient and the Paris–Erdogan equation exponent for ferrite-pearlite steels are shown, to be closely related as well as the intersection point of the diagram in the range of high crack growth rates was defined. The parameters of the above relation and coordinates of the intersection point were determined for the steels of this class. In the latter case, the optimization methods were used to find the minimum sum of squares of residual functions. Based on the correlation between the cyclic strain-hardening coefficient and Paris–Erdogan equation exponent, the conclusion was drawn of the lower boundary value of this characteristic predicted for an ideal elastoplastic material (zero cyclic strain-hardening coefficient), to be equal to 1.0. As also follows, other classes of the materials (and other cycle asymmetries) can exhibit similar relations in the form of rays coming from the point (0; 1.0) at a corresponding experimental slope to the coordinate axes. From the common intersection point of the diagram (Gurney point) and their slopes to the axes for ferrite-pearlite steels, the procedure was advanced to construct the linear section of the diagram based on the results of low-cycle fatigue tests with plotting the stress amplitude vs. plastic strain amplitude curve. The procedure was approved on 10GN2MFA steel at 20 and 270°C and SAE-1020 and API5L X60 steels taken from the literature. In view of data scattering for cyclic fracture toughness test results, the estimation of the linear diagram sections is quite adequate, and the procedure of their construction is appropriate and can be extended to other classes of the materials and stress ratios.

We propose a computational model for the evaluation of the service life of fiber-reinforced concrete structural elements subjected to long-term tension. The model is based on the first law of thermodynamics and a proposed idealized tensile stress-strain diagram of fibrous concrete. This model is used for the evaluation of the service life of a fiber-reinforced concrete plate containing a circular hole under the conditions of long-term bilateral tension.

The specific features of quaternary system phase diagram transformations induced by formation ofboundary tangential azeotrope were investigated. The characteristics of bifurcation states corresponding to the transition from one structure of the diagram to another were determined. The principal possible transformations of diagrams with varying pressure were illustrated by the systems acetone-chloroform-ethanol-water and chloroform-ethanol-cyclohexane-water. The obtained results expand the understanding of thermodynamics of heterogeneous equilibria of multicomponent systems and make it possible to solve the practical problem of maintaining favorable phase equilibrium conditions for rectification in certain pressure ranges.

There exists a well-known hook-length formula for calculating the dimensions of two-dimensional Young diagrams. Unfortunately, an analogous formula for the three-dimensional case is unknown. We introduce an approach to calculating estimated dimensions of three-dimensional Young diagrams, also known as plane partitions. The most difficult part of this task is the calculation of the cotransition probabilities for a central Markov process. We suggest an algorithm for an approximate calculation of these probabilities. It generates numerous random paths to a given diagram. In the case where the generated paths are uniformly distributed, the proportion of paths passing through a certain edge gives us an approximate value of the cotransition probability. As our numerical experiments show, a random generator based on the randomized version of the Schutzenberger transformation allows one to obtain accurate values of cotransition probabilities. Also, a method for constructing three-dimensional Young diagrams with large dimensions is suggested. Bibliography: 13 titles.

We consider the problem of finding a Young diagram minimizing the sum of evaluations of a given pair of functions on the parts of the associated pair of conjugate partitions. While there are exponentially many diagrams, we show it is polynomial time solvable.

Model efficiency performance provides reliable and acceptable criteria by comparing the factual data with the model results based on a set of significant parameters' comparisons. In this paper, a standard triangular diagram (STD) is proposed for such a goal through the comparisons of arithmetic averages, standard deviations, and serial correlation coefficients ratios. It provides also the comparison among different dimensional units. The application of the STD concept is presented for a set of annual rainfall records at different locations based on monthly hydro-meteorological data (rainfall, potential evaporation, soil moisture, and surface runoff) from Salt Lake (in Turkey) region, monthly flow series from trans-boundary Tigris River and autoregressive moving average, ARIMA, and stochastic model ensemble of simulations.

Despite the last 40 years of research showing that computer-aided diagramming tools improve student learning, very little research reveals the cognitive processes that explain why and how diagramming tools and specific features of the tools affect learning. This study developed a tool that graduate students used to diagram and analyze arguments as the tool mined each students’ actions. The mined data was used to develop algorithms to operationalize and measure the use of backward, forward, breadth, depth-first reasoning. Regression models were then compared to identify which algorithm produced measures that best predicted diagram scores, and to determine the combined and relative impact of each reasoning process on diagram scores. The findings show that observing the placement and location of the first five nodes moved and positioned on screen in relation to the location of the previously moved node provides sufficient data to generate backward/forward and breadth/depth-first ratio scores that predict diagram scores, while individual frequency counts of each of the four processes do not predict scores. The best-fit regression model using the ratio scores show that students using more backward and depth-first processing construct diagrams with higher scores – scores based on criteria that gauge the depth of analysis and not just the number of correct diagram links. This study presents new tools, methods, and new lines of inquiry to advance research on ways to integrate learning analytics into computer-aided diagramming tools.

Rub-impact of rotor–stator is one of the major problems for stability and safety of a rotating machine. As a result, the characterization of rub-impact force gradually becomes a crucial factor in the dynamic responses prediction of the rotor system. First, the applicable scope of classical rotor–stator rub-impact force models is discussed in this paper. Then, taking a Jeffcott rotor as the research object, rub-impact force models under hard coating, soft coating and general condition are established respectively based on the equivalent linearized method. Finally, dynamic responses of the rotor system are numerically calculated by the linear interpolation method, and the change laws of impact stiffness are further analyzed under different conditions. Then, the effects of the engine coatings on the dynamic characteristics of the rotor system are studied in detail. By means of bifurcation diagram, time histories, whirling orbits, spectrum and impact force diagram, the dynamic variations are revealed. The results suggest that the dynamic responses of system are closely related to the coating hardness. Meanwhile, the full annular rub and partial rub are affected by the coating hardness to a great extent.

Numerous theoretical designs based on the geometrical shape of ad quadratum, sequences of squares or/and octagons have been used to speculate for the existence of archetype patterns in architecture. However, up to now no archaeological evidence of the existence of any such pattern has been documented. The present work examines whether a diagram incised on stone found in the Octagon in Thessaloniki could be a first evidence of a conceptual design in architecture. Two statistically validated models are presented, one to explain the geometrical patterns on the Octagon diagram and another to describe the Octagon’s ground plan. The results are anticipated to contribute not only to the discussion concerning the function of the Octagon monument, but also to the debate concerning the role of type in architecture and the origin of form in central-plan and octagonal buildings.

In this research, three aspects of modeling, analyzing, and optimizing spiral plate heat exchangers (SPHEs) are studied. The main objective of this work is to pave the way for comparing manufacturers’ designed SPHEs with theoretical designed SPHEs without involving designers in using computational methods. To begin, with assumption of constant overall heat transfer coefficient and specific heat capacities, a mathematical modeling of SPHE based on energy balance equations is developed to model the SPHE as a network of series-connected equivalent internal heat exchangers to determine the temperature distribution in spiral turns. This modeling can facilitate the usage of temperature-enthalpy diagram in SPHEs’ analysis and design. Furthermore, a new algorithm for thermal design optimization of SPHEs has been proposed. The proposed algorithm is based on maximizing pressure drops at channels, considering geometric proportion of SPHE and minimizing the total cost simultaneously. To show the proposed method applicability in analyzing thermal and hydraulic design parameters, a single-phase counter-current SPHE is assessed and optimized for different design cases with temperature approach variations. Results of comparing manufacturers’/standard designed SPHEs and research/theoretical designed SPHEs by defining appropriate geometric proportion ranges confirmed that temperature approach variations can improve SPHE performance to a higher extent, such as finding temperature approach ranges for optimized SPHEs with higher compactness to reduce the manufacturing cost. This fact is revealed by introducing compactness-temperature approach diagram which depicts the geometric optimization of SPHEs and the effects of temperature differences in SPHE’s optimization.

A novel automatic operational modal analysis method is proposed based on the image recognition of stabilization diagrams with uncertainty quantification. The method not only enriches the contents of the stabilization diagrams to make them much clearer—it can also avoid heavy manual analysis of the stabilization diagrams by automatically obtaining operational modal parameters. In order to increase the efficiency in identifying modal parameters of structures, a traditional stabilization diagram is re-constructed to convey the uncertainty estimates. These stabilization diagrams are then resolved into single mode stabilization diagrams (SMSDs) with a specified frequency interval, for image recognition. Subsequently, a convolutional neural network (CNN) is adopted to automatically analyze the SMSDs. In this study, the CNN is trained by the SMSDs derived from the stabilization diagrams of two numerical examples and three engineering structures. The trained CNN is then validated with a 6 degree-of-freedom model, the Heritage Court Tower building, and the Ting Kau Bridge. The robust learning and prediction results establish that the constructed CNN is effective for analyzing the stabilization diagrams of different structures. It can automatically and accurately identify the physical modes on the stabilization diagrams, without extracting any characteristic parameters.

The phase equilibria in the quinary Na, K, Mg//Cl, SO4–H2O sea-water system at 0 °C were determined and a total phase equilibria diagram for the system was constructed by means of the translation method consistent with available literature data. There are seven points, 21 curves and 22 fields saturated, respectively, with 4, 3 and 2 equilibrium solid phases, for the quinary composition of the system. The constructed total phase equilibria diagram of the system was fragmented into divariant co-crystallization fields of two different solid phases and trivariant crystallization volumes of each of the solid phases at equilibrium. The structures of nine Janecke dry-salt phase diagrams were obtained by fragmentation of the total phase equilibria diagram into crystallization volumes. The comparison with the available literature data shows that, the obtained crystallization volume for halite agrees well with the available experimental data.

A new constant life diagram (CLD) model featuring asymmetric bilinear constant-life curves was proposed to better describe the longitudinal fatigue behavior of unidirectional laminae (UD) under a wide range of stress ratios. This model is able to predict S-N curves with satisfactory accuracy not only in tension-tension (T-T) fatigue mode but also in tensioncompression (T-C) and compression-compression (C-C) modes, whereas the conventional Goodman CLD model shows inferior performance especially in T-C and C-C modes. Apart from static tension and compression tests, high- and low-cycle fatigue tests at two stress ratios corresponding to T-T and C-C modes should be performed to determine the parameters in the proposed model. Fatigue test data of several different GFRP UDs at various stress ratios were utilized to validate the proposed model, and the S-N curves predicted by the proposed model agreed well with the experimental results. Compared with the Goodman CLD model, the proposed CLD model demonstrates an enhanced predictive capability without losing its simplicity.

With the reduction in fossil fuels and their environmental impacts, the use of solar cells as green energies in various countries is expanding. It is certainly neither effective nor necessarily possible to generalize a single specific model for different countries considering their different conditions. Therefore, this study, with the aim of providing a business environment analysis model for the third-generation solar energy market in Iran, first, used a systematic search by using the meta-synthesis method to extract important factors. Thirty-four variables in eight dimensions were found to be effective in the solar energy business in Iran. Then, an interpretive structural modeling was provided to derive a priority diagram. Finally, the causal graph and the stock and flow diagram were drawn and the behavior of the variables was examined under three scenarios. The results indicated that using solar cells to generate electricity is economically efficient in the long run and can help to protect the environment.