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We demonstrate experimentally and numerically the control of magnetization circulation of the closure domain state in thin permalloy squares divided diagonally into four dipolar-coupled isosceles triangles. The control over the magnetization circulation was achieved by the mutual application of a suitable external in-plane magnetic field and interaction with a magnetic force microscopy (MFM) tip. Numerical simulations confirm that the proposed switching protocol is valid for the broad range of MFM tips. Experiments performed on four diagonally cut squares show that this method is robust against slight imperfections in the fabrication process. Moreover, by varying the polarity of the applied field and the direction of the MFM scanning, proper symmetry response of the switching method is observed. [ABSTRACT FROM AUTHOR]

Inkjet-printed micro-patterns on hydrophobic surfaces have promising applications in the fabrication of microscale devices such as organic thin-film transistors. The low wettability of the surface prevents the inkjet-printed droplets from spreading, connecting to each other, and forming a pattern. Consequently, it is challenging to form micro-patterns on surfaces with low wettability. Here, we propose a sequential printing and drying method to form micro-patterns and control their shape. The first set of droplets is inkjet-printed at a certain spacing and dried. The second set of droplets is printed between these dry anchors on the surface with low wettability. As a result, a stable bridge on the surface with low wettability forms. This printing method is extended to more complicated shapes such as triangles. By implementing an energy minimization technique, a simple model was devised to predict the shape of the inkjet-printed micro-patterns while confirming that their equilibrium shape is mainly governed by surface tension forces. The gradient descent method was utilized with parametric boundaries to emulate droplet pinning and wettability of the anchors and to prevent convergence issues from occurring in the simulations. Finally, the energy minimization based simulations were used to predict the required ink to produce dry lines and triangles with smooth edges. [ABSTRACT FROM AUTHOR]

In this article, we present a new high‐order discontinuous Galerkin (DG) method, in which neither a penalty parameter nor a stabilization parameter is needed. We refer to this method as penalty‐free DG. In this method, the trial and test functions belong to the broken Sobolev space, in which the functions are in general discontinuous on the mesh skeleton and do not meet the Dirichlet boundary conditions. However, a subset can be distinguished in this space, where the functions are continuous and satisfy the Dirichlet boundary conditions, and this subset is called admissible. The trial solution is chosen to lie in an augmented admissible subset, in which a small violation of the continuity condition is permitted. This subset is constructed by applying special augmented constraints to the linear combination of finite element basis functions. In this approach, all the advantages of the DG method are retained without the necessity of using stability parameters or numerical fluxes. Several benchmark problems in two dimensions (Poisson equation, linear elasticity, hyperelasticity, and biharmonic equation) on polygonal (triangles, quadrilateral, and weakly convex polygons) meshes as well as a three‐dimensional Poisson problem on hexahedral meshes are considered. Numerical results are presented that affirm the sound accuracy and optimal convergence of the method in the L2$$ {L}^2 $$ norm and the energy seminorm. [ABSTRACT FROM AUTHOR]

Paul Yiu proved that all Heron triangles are realizable on the integer lattice. We give an analogous result for triangles with vertices on the Eisenstein lattice. [ABSTRACT FROM AUTHOR]

This paper examines the effect of temperature variation on the surface triangular grating of the surface plasmon polariton (SPP) on the effectiveness of the entire array of silicon thin-film solar cells. Thin-film solar cells' optical and electrical characteristics are examined using the electromagnetic and semiconductor models. The 3D Multiphysics simulator is used to present this study. The MATLAB/SIMULINK model based on mathematical formulas is developed to simulate the entire array of solar cells with thin films. This approach is suggested for quickly simulating the thin-film array. The presented model was applied on thin-film solar cells with and without SPP depending on the complete cell parameters from the COMSOL Multiphysics model. The triangle's SPPs accomplish a 14.76% efficiency increase of 1.07% over a solar cell without SPPs. [ABSTRACT FROM AUTHOR]

Opportune detection of Anthonomus eugenii is a fundamental aspect of any management program to this pest. Yellow traps are the most common monitoring strategy, and its efficacy is related with the trap design and placement within crops. However, there's limited information on this. Two outdoor experiments were performed to determine the efficiency of traps with six different shapes (circle, square, diamond, ellipse, rectangle, and triangle) and seven frame colors (yellow, dark green, black, red, white, purple, and blue); seven to the traps placement at four orientations (North, South, East and West), five aside distances from the bed center (0, 20, 40, 60 and 80 cm aside to the inter-bed space) and six heights (0, 20, 40, 60, 80 and100 cm) on A. eugenii adults. There wasn't significant difference among shapes and orientations. Traps with yellow, dark green and black frames had the highest number of insects. For the aside distance, the plots were categorized according to their width as narrow (54–65 cm) and wide (71–81 cm), the highest insects caught was exhibited on traps at 0–20 and 0–40 cm, respectively. Regarding the traps height, they were classified according to their height as short (62–64 cm), medium (78–82 cm) and tall (90–92 cm), the highest insects caught was exhibited on traps at 20–40, 40–60, and 40–80 cm, respectively. Regression analyzes indicate that catches decrease as the traps are installed into the inter-bed space and above the canopy. This study provides novel information to improve outdoor programs to monitor A. eugenii. [ABSTRACT FROM AUTHOR]

This paper overviews Bowen family systems theory and its approach to family therapy. It aims to introduce this influential approach and a sample of developments in theory and practice since Bowen's first publications of his research and theory. This paper is the second edition of a 1999 article with the same title (Brown, Australian and New Zealand Journal of Family Therapy, 20, 94 and 1999) and, 25 years later, offers new insights from the original author's ongoing research into the theory. This new edition is in collaboration with a second author and Bowen theory scholar, bringing fresh perspectives on the theory's applicability to family therapy practice. The core concepts are presented briefly, and a case example with a parent and symptomatic adolescent demonstrates how theory informs the role of the therapist and the therapeutic work. Examples of criticisms of Bowen theory are also discussed, including the misinterpretation around the idea of emotion in Bowen theory that is communicated in Gottman's training. Differentiation of self is clarified as the integration of emotion and intellect rather than privileging one over another, which affords the opportunity for individuals to avoid being governed by the invisible strings of sensitivities in relationships and instead be themselves in good emotional contact with the other person. [ABSTRACT FROM AUTHOR]

The concept of differentiation of self and its relationship to the natural capacity of humans and other social animals to adapt underpins clinician and researcher Victoria Harrison's long‐term investigation of the biology of reactivity in relationships. Victoria's early research related to infertility and reproduction demonstrated how reactivity in at least three prior generations can contribute to chronic conditions, such as endometriosis, that are less amenable to intervention. Her most recent project, the ‘Observations of Change in Physiology and Family’ research, highlights how work on differentiation of self improves functional outcomes in physical and mental health for the family. While an individual may not experience the ‘calm mind’ that is often the goal of conventional therapeutic intervention, a significant reduction in symptoms and an improvement in overall functioning and relatedness are outcomes. This occurred when participants focused on increasing person‐to‐person contact with extended family members, reducing their emotional reactivity to significant others in the important triangles of their life and family and maintaining intellectual activity, often described as curiosity, even while reacting. [ABSTRACT FROM AUTHOR]

This study used a double machine learning model (based on the random forest algorithm) and spatial Durbin DIDs model to conduct quasi-natural experiments. The results are as follows: (1) innovation and reform policy regarding regional industrial chains as well as their resilience can significantly and positively address the development of China's impossible triangle coupling of energy; (2) implementing the innovation and reform policy for regional industrial chains in other regions can have a significant positive spatial transmission effect on the impossible triangle coupling coordinated development of energy in the region; (3) regional industrial chain resilience can produce a significant positive mediating effect between the innovation and reform policy of regional industrial chains and the safety, reliability, and economic feasibility of green and clean energy systems; (4) under the counterfactual framework, the mechanism path "innovation and reform policy of the regional industry chain→regional industry chain resilience→coordination degree of impossible triangle coupling of energy" has significantly positive direct and indirect effects in both the treatment group and the control group. However, "innovation and reform policy of the regional industrial chain→regional industrial chain resilience→the energy sector's impossible triangle coupling coordination degree" and "innovation and reform policy of the regional industrial chain→leading power of the regional industrial chain→the energy sector's impossible triangle coupling coordination degree" have significantly positive direct and indirect effects in the treatment group, but only the direct effect is significant in the control group. [ABSTRACT FROM AUTHOR]

Carbon fiber laminates have become popular in the manufacturing industry for their many desirable properties, like good vibration damping, high strength-to-weight ratio, toughness, high dimensional stability, and low coefficient of thermal expansion. During the manufacturing process, undesirable foreign objects, such as peel-ply strips, gloving material, and Kapton film, can be introduced into the part which can lead to a localized weakness. These manufacturing defects can function as stress concentration points and oftentimes cause a premature catastrophic failure. In this study, a method using high-resolution pulse-echo ultrasound testing is employed for the detection and quantification of the dimensions of foreign object debris (FOD) embedded within carbon fiber laminates. This research presents a method to create high-resolution C-scans using an out of immersion tank portable housing ultrasound scanning system, with similar capabilities to that of a full immersion system. From the full-waveform dataset, we extract the FOD depth and planar dimensions with an automatic edge detection technique. Results from several carbon fiber laminates are investigated with embedded foreign objects that are often considered undetectable. Results are presented for FOD identification for two different shapes: circles with diameters ranging from 7.62 mm to 12.7 mm, and 3-4-5 triangles with hypotenuses ranging from 7.6 mm to 12.7 mm. CT imaging is used to confirm proper FOD placement and that the FOD was not damaged or altered during manufacturing. Of importance for the ultrasound inspection results, in every single case studied, the FOD is detected, the layer depth is properly identified, and the typical error is less than 1.5 mm for the primary dimension. [ABSTRACT FROM AUTHOR]

Let ρ (G) be the spectral radius of a graph G with m edges. Let S m − k + 1 k be the graph obtained from K 1 , m − k by adding k disjoint edges within its independent set. Nosal's theorem states that if ρ (G) > m , then G contains a triangle. Zhai and Shu showed that any non-bipartite graph G with m ≥ 26 and ρ (G) ≥ ρ (S m 1) > m − 1 contains a quadrilateral unless G ≅ S m 1 M.Q. Zhai and J.L. Shu (2022) [25]. Wang proved that if ρ (G) ≥ m − 1 for a graph G with size m ≥ 27 , then G contains a quadrilateral unless G is one out of four exceptional graphs Z.W. Wang (2022) [22]. In this paper, we show that any non-bipartite graph G with size m ≥ 51 and ρ (G) ≥ ρ (S m − 1 2) > m − 2 contains a quadrilateral unless G ≅ S m 1 or G ≅ S m − 1 2. Moreover, we show that if ρ (G) ≥ ρ (S m + 4 2 , 2 −) for a graph G with even size m ≥ 74 , then G contains a C 5 + unless G ≅ S m + 4 2 , 2 − , where C t + denotes the graph obtained from C t and C 3 by identifying an edge, S n , k denotes the graph obtained by joining every vertex of K k to n − k isolated vertices and S n , k − denotes the graph obtained from S n , k by deleting an edge incident to a vertex of degree k , respectively. [ABSTRACT FROM AUTHOR]

We study the geometry of smooth projective surfaces defined by Frobenius forms, a class of homogenous polynomials in prime characteristic recently shown to have minimal possible F-pure threshold among forms of the same degree. We call these surfaces extremal surfaces , and show that their geometry is reminiscent of the geometry of smooth cubic surfaces, especially non-Frobenius split cubic surfaces. For instance, extremal surfaces have many lines but no triangles, hence many "star points" analogous to Eckardt points on a cubic surface. We generalize the classical notion of a double six for cubic surfaces to a double 2 d on an extremal surface of degree d. We show that, asymptotically in d , smooth extremal surfaces have at least 1 16 d 14 double 2 d 's. A key element of the proofs is the large automorphism group of an extremal surface, which we show to act transitively on many associated sets, such as the set of triples of skew lines on the extremal surface. [ABSTRACT FROM AUTHOR]

The abundance of data about social relationships allows the human behavior to be analyzed as any other natural phenomenon. Here we focus on balance theory, stating that social actors tend to avoid establishing cycles with an odd number of negative links. This statement, however, can be supported only after a comparison with a benchmark. Since the existing ones disregard actors' heterogeneity, we extend Exponential Random Graphs to signed networks with both global and local constraints and employ them to assess the significance of empirical unbalanced patterns. We find that the nature of balance crucially depends on the null model: while homogeneous benchmarks favor the weak balance theory, according to which only triangles with one negative link should be under-represented, heterogeneous benchmarks favor the strong balance theory, according to which also triangles with all negative links should be under-represented. Biological networks, instead, display strong frustration under any benchmark, confirming that structural balance inherently characterizes social networks. According to balance theory, social actors avoid establishing cycles with an odd number of negative links. This statement can be supported only after a comparison with a benchmark. The authors find that the level of balance depends on the null-model employed: homogeneous ones favor the weak balance theory; heterogeneous ones favor the strong balance theory. [ABSTRACT FROM AUTHOR]

This study aimed to assess the knowledge regarding impacts, causes and management of black triangles (BT) among participants from different educational backgrounds including dental students, dentists and laypeople. This descriptive cross-sectional observational research included 435 participants who comprised 4 groups: pre-clinical (3rd year) dental students, clinical (4th and 5th year) dental students, dentists, and laypeople. A constructed self-reported questionnaire was utilized to assess participants' demographic data and their knowledge of the impacts, causes and management of BT. The VAS scale was used to assess participants' ratings for the impacts of BT on esthetics, with 0 meaning no impact and 10 meaning very severe negative impacts. The most reported treatments for BT were "cannot be treated" 99.3% and "non-surgical periodontal treatment" 67.1%. Meanwhile, the least reported was "modify the porcelain" 41.8%. The most reported cause of BT was "periodontal disease" 85.1%. However, the least reported were "parafunction" and "deep implants" 33.1% each. Dental professionals had better knowledge of the causes (t = 8.189, P < 0.001) and management (t = 8.289, P < 0.001) of BT than the non-dental participants. The dentists had the best knowledge, while the laypeople had the least knowledge of the causes (F = 62.056, P < 0.001) and treatment (F = 46.120, P < 0.001) of BT. The knowledge of the causes (t = 0.616, P = 0.538) and treatment (t = 1.113, P = 0.266) for BT was not significantly different between males and females. Age was not significantly related to the total knowledge about the causes (r = −0.034, P = 0.475) or treatment (r = −0.034, P = 0.482) for BT. Dental professionals had better knowledge of the impacts, causes and management of BT than the non-dental participants. The dentists were the best, while the laypeople were the worst in this regard. Age and gender had no relationships with the knowledge of causes or management of BT. [ABSTRACT FROM AUTHOR]

Discrete Laplacians are the basis for various tasks in geometry processing. While the most desirable properties of the discretization invariably lead to the so‐called cotangent Laplacian for triangle meshes, applying the same principles to polygon Laplacians leaves degrees of freedom in their construction. From linear finite elements it is well‐known how the shape of triangles affects both the error and the operator's condition. We notice that shape quality can be encapsulated as the trace of the Laplacian and suggest that trace minimization is a helpful tool to improve numerical behavior. We apply this observation to the polygon Laplacian constructed from a virtual triangulation [BHKB20] to derive optimal parameters per polygon. Moreover, we devise a smoothing approach for the vertices of a polygon mesh to minimize the trace. We analyze the properties of the optimized discrete operators and show their superiority over generic parameter selection in theory and through various experiments. [ABSTRACT FROM AUTHOR]

In this study, the influence of zinc oxide (ZnO) nanostructures with various morphologies on the performance of dye-sensitized solar cells (DSSCs) was investigated. Photo-electrodes were fabricated incorporating ZnO transport layers of distinct nanoscale morphologies—namely nanoparticles, microballs, spiky microballs, belts, and triangles—and their respective current–voltage characteristics were evaluated. It was observed that the DSSCs employing the triangular ZnO nanostructures, with a side length of approximately 30 nm, achieved the highest power conversion efficiency of 2.62%. This was closely followed by the DSSCs using spherical nanoparticles with an average diameter of approximately 20 nm, yielding an efficiency of 2.54%. In contrast, the efficiencies of DSSCs with microball and spiky microball ZnO nanostructures were significantly lower, measuring 0.31 and 1.79%, respectively. The reduction in efficiency for the microball-based DSSCs is attributed to the formation of micro-cracks within the thin film during the fabrication process. All DSSC configurations maintained a uniform active area of 4 mm². Remarkably, the highest fill factor of 59.88% was recorded for DSSCs utilizing the triangular ZnO morphology, with the spherical nanoparticles attaining a marginally lower fill factor of 59.38%. This investigation corroborates the hypothesis that reduced particle size in the transport layer correlates with enhanced DSSC performance, which is further amplified when the nanoparticles possess pointed geometries that induce strong electric fields due to elevated charge concentrations. [ABSTRACT FROM AUTHOR]

Following a theorem of Hayes, we give a geometric interpretation of the special value at s = 0 of certain 1 -cocycle on PGL 2 (ℚ) previously introduced by the author. This work yields three main results: an explicit formula for our cocycle at s = 0 , a generalization and a new proof of Hayes' theorem, and an elegant summation formula for the zeroth coefficient of the Ehrhart quasi-polynomial of certain triangles in ℝ 2 . [ABSTRACT FROM AUTHOR]

In his Exegesis, Hipparchus explicitly states that he developed a method to calculate simultaneous risings and settings, It is generally assumed that Hipparchus used either Menelaus' Theorem, or stereographic projections, even if both methods are only attested for later periods and their availability to Hipparchus is debated. In this article we argue that simultaneous risings and settings could be calculated using less advanced mathematical tools unquestionably available to Hipparchus: Elements I.47 (commonly known as the theorem of Pythagoras), the Rule of Three (applied to simple proportions between right triangles), and the Table of Chords. Without claiming that this was indeed the method that Hipparchus used, we argue that there is no need to postulate the availability of more sophisticated tools to carry out the calculations which Hipparchus mentions in the Exegesis. [ABSTRACT FROM AUTHOR]

Opening the oculomotor triangle (OT) and removing the posterior fossa lesion by endoscopic endonasal approach (EEA) is challenging for even an experienced endoscopic neurosurgeon. We summarize the treatment experience and technical nuances with EEA for resection of pituitary neuroendocrine tumors and cavernous sinus (CS) meningiomas invading through the OT. Between 2018 and 2022, 8 patients, comprising 5 with pituitary neuroendocrine tumors (3 with nonfunctioning and 2 with somatotroph tumors with increased levels of growth hormone) and 3 CS meningiomas, were treated using an endoscopic endonasal transoculomotor triangle approach. The critical surgical technique is continuously opening the diaphragma sellae from medial to lateral toward the interclinoidal ligament and transecting it to enlarge the OT. We evaluated preoperative tumor size, previous surgical history, preoperative symptoms, extent of tumor resection, histopathology, and postoperative complications for all patients. The gross total resection (defined as complete removal) in 3 patients (38%), near-total resection (defined as >95% removal) in 4 patients (50%), and subtotal resection (defined as ≤90% removal) in 1 patient (12%) and gross total resection of tumor invading through the OT was achieved in all patients through pure EEA. Two of 3 patients with visual deficits in nonfunctioning pituitary neuroendocrine tumors improved, and the other remained stable postoperatively. One patient showed transient oculomotor nerve palsy. The growth hormone level of the 2 patients with somatotroph tumors declined to normal. For 3 patients with CS meningiomas, cranial nerve palsy improved in 2 patients, whereas the other patient developed increased facial numbness after surgery. The endoscopic endonasal transoculomotor triangle approach is an efficient surgical option for tumors with CS invasion and OT penetration. [ABSTRACT FROM AUTHOR]

A convex geometry is a closure system satisfying the anti-exchange property. This paper, following the work of Adaricheva and Bolat (Discrete Math 342(N3):726–746, 2019) and the Polymath REU 2020 team (Convex geometries representable by at most 5 circles on the plane. arXiv:2008.13077), continues to investigate representations of convex geometries on a 5-element base set. It introduces several properties: the opposite property, nested triangle property, area Q property, and separation property, of convex geometries of circles on a plane, preventing this representation for numerous convex geometries on a 5-element base set. It also demonstrates that all 672 convex geometries on a 5-element base set have a representation by ellipses, as given in the appendix for those without a known representation by circles, and introduces a method of expanding representation with circles by defining unary predicates, shown as colors. [ABSTRACT FROM AUTHOR]

We develop a new simple approach to prove upper bounds for generalizations of the Heilbronn's triangle problem in higher dimensions. Among other things, we show the following: for fixed d⩾1$d \geqslant 1$, any subset of [0,1]d$[0, 1]^d$ of size n$n$ contains d+1$d+1$ points that span a simplex of volume at most Cdn−logd+6$C_d n^{-\log d+ 6}$,1.1d$1.1 d$ points whose convex hull has volume at most Cdn−1.1$C_d n^{-1.1}$,k⩾3d$k\geqslant 3\sqrt {d}$ points that span a (k−1)$(k-1)$‐dimensional simplex of volume at most Cdn−k−1d−k28d2$C_d n^{-\frac{k-1}{d} - \frac{k^2}{8d^2}}$. [ABSTRACT FROM AUTHOR]

Lesion segmentation is a fundamental task that has been widely studied in biomedicine. State‐of‐the‐art methods still struggle with the inherent challenges of dermoscopic images such as uncertain boundaries or severe occlusion. In this study, we argue that this task can be better resolved by introducing user interaction and proposing a deep interactive framework for lesion segmentation. Our method is designed to best reflect user expertise to iteratively refine the segmentation results. In each iteration, professional users are expected to click three points on the boundary of the lesion to encourage the network to update the previous round of the segmentation result. To best exploit the clues from the interaction, we explore a novel encoding strategy by producing a triangle map whose vertices are the three clicked points. Owing to the strong guidance within such triangle maps, our method can outperform state‐of‐the‐art methods with baseline segmentation backbones. Extensive experimental results and ablation studies on three commonly used lesion segmentation data sets demonstrated the effectiveness of our method in terms of segmentation accuracy and encoding effectiveness. © 2024 The Authors. IEEJ Transactions on Electrical and Electronic Engineering published by Institute of Electrical Engineer of Japan and Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

In this paper, we prove a new extremal property of the Reuleaux triangle: it maximizes the Cheeger constant among all bodies of (same) constant width. The proof relies on a fine analysis of the optimality conditions satisfied by an optimal Reuleaux polygon together with an explicit upper bound for the inradius of the optimal domain. As a possible perspective, we conjecture that this maximal property of the Reuleaux triangle holds for the first eigenvalue of the p -Laplacian for any p ∈ (1 , + ∞) (this paper covers the case p = 1 whereas the case p = + ∞ was already known). [ABSTRACT FROM AUTHOR]

The circular intuitionistic fuzzy set (CIFS) extends the concept of IFS, representing each set element with a circular area on the IFS interpretation triangle (IFIT). Each element in CIFS is characterized not only by membership and non-membership degrees but also by a radius, indicating the imprecise areas of these degrees. While some basic operations have been defined for CIFS, not all have been thoroughly explored and generalized. The radius domain has been extended from [0, 1] to [0, √2]. However, the operations on the radius domain are limited to min and max. We aimed to address these limitations and further explore the theory of CIFS, focusing on operations for membership and nonmembership degrees as well as radius domains. First, we proposed new radius operations on CIFS with a domain [0, ψ], where ψ ∈ [1, √2], called a radius algebraic product (RAP) and radius algebraic sum (RAS). Second, we developed basic operators for generalized union and intersection operations on CIFS based on triangular norms and conorms, investigating their algebraic properties. Finally, we explored negation and modal operators based on proposed radius conditions and examined their characteristics. This research contributes to a more explicit understanding of the properties and capabilities of CIFS, providing valuable insights into its potential applications, particularly in decision-making theory. [ABSTRACT FROM AUTHOR]

Wall periodic response factors are a very usual calculation method of transient heat transfer through building envelope elements (walls, roofs ...) in steady periodic conditions, used in popular heat load calculation procedures as ASHRAE's RTS method [Spitler, Jeffrey D., Daniel E. Fisher, and Curtis O. Pedersen. 1997. "The Radiant Time Series Cooling Load Calculation Procedure." ASHRAE Transactions 103 (2): 503–515]. This response factors, time sampled heat flux responses of a multi-layer wall to a 24h-periodic unit triangle function, can be obtained by means of multiple methods: Laplace's method, state space method, frequency domain methods, etc. These methods are numerical since there is no analytical way of obtaining these response factors. The aim of this work is, taking advantage of the periodic nature of excitations, use Fourier series to represent boundary conditions, and this way find an easier and less computationally demanding procedure to calculate these response factors. Additionally, the convergence of these Fourier series will be analysed to determine the minimum set of frequencies needed to ensure a fixed admissible error for wall periodic response factors. [ABSTRACT FROM AUTHOR]

INTRODCTION: The study of automatic marking methods in the Department of Language Translation is conducive to the fairness and rationality of marking by examining the comprehensive level of the students' language, as well as sharing the objectivity and pressure of the marking teachers in marking the scripts. OBJECTIVES: Aiming at the current automatic scoring methods of translation systems, which have the problems of not considering the global nature of influence features and low precision. METHODS: This paper proposes an automatic scoring method for translation system based on intelligent optimization algorithm to improve the deep network. First, by analyzing the language translation scoring problem, selecting the key scoring influencing factors and analyzing the correlation and principal components; then, improving the long and shortterm memory network through the triangle search optimization algorithm and constructing the automatic scoring model of the translation system; finally, the high efficiency of the proposed method is verified through the analysis of simulation experiments. RESULTS: The proposed method is effective and improves the accuracy of the scoring model. CONCLUSION: solves the problem of inefficient scoring in the automatic scoring method of the translation system. [ABSTRACT FROM AUTHOR]

Flip processes, introduced in [Garbe, Hladký, Šileikis, Skerman: From flip processes to dynamical systems on graphons], are a class of random graph processes defined using a rule which is just a function ℛ:ℋk→ℋk$$ \mathcal{R}:{\mathscr{H}}_k\to {\mathscr{H}}_k $$ from all labelled graphs of a fixed order k$$ k $$ into itself. The process starts with an arbitrary given n$$ n $$‐vertex graph G0$$ {G}_0 $$. In each step, the graph Gi$$ {G}_i $$ is obtained by sampling k$$ k $$ random vertices v1,...,vk$$ {v}_1,\dots, {v}_k $$ of Gi−1$$ {G}_{i-1} $$ and replacing the induced graph Gi−1[v1,...,vk]$$ {G}_{i-1}\left[{v}_1,\dots, {v}_k\right] $$ by ℛ(Gi−1[v1,...,vk])$$ \mathcal{R}\left({G}_{i-1}\left[{v}_1,\dots, {v}_k\right]\right) $$. Using the formalism of dynamical systems on graphons associated to each such flip process from ibid. we study several specific flip processes, including the triangle removal flip process and its generalizations, 'extremist flip processes' (in which ℛ(H)$$ \mathcal{R}(H) $$ is either a clique or an independent set, depending on whether e(H)$$ e(H) $$ has less or more than half of all potential edges), and 'ignorant flip processes' in which the output ℛ(H)$$ \mathcal{R}(H) $$ does not depend on H$$ H $$. [ABSTRACT FROM AUTHOR]

Dealing with complex shell surfaces using the finite element method, we are often limited to simple geometric meshes such as triangles and quadrangles and have to refine the meshes to meet the calculation accuracy requirements, significantly increasing the calculation cost. The virtual element method (VEM), a new numerical method with high mesh flexibility, has been widely applied to many physical and mechanical problems. To the best of our knowledge, this method has yet to be studied for membrane shell models so far. In this paper, for the first time, we provide an enriched conforming VEM discrete scheme for the two‐dimensional three‐component (2D‐3C) generalized membrane shell (GMS) model proposed by Ciarlet et al. Furthermore, we prove the VEM discrete solution's existence and uniqueness for the GMS. Numerical experiments demonstrate that this discrete scheme is convergent and stable and can accurately represent the membrane stress state of conical, cylindrical, hyperbolical, and spherical shells clamped along a portion of their lateral faces. At the same time, we show the diversity of the grid subdivision. Thus, we develop the VEM for the GMS model successfully. In the future, we will continue to study the VEM for other shell models. [ABSTRACT FROM AUTHOR]

Maritime transportation plays a vital role in global trade, and studying the resilience of the global maritime network is crucial for ensuring its sustainable development. Currently, the ongoing conflict between Russia and Ukraine has garnered significant global attention. However, there is a lack of specific research on the impact of the conflict on maritime shipping, particularly the resilience of the global maritime network. This paper proposes a resilience assessment framework under the influence of significant events by combining complex network metrics and network performance indicators from the resilience triangle model. It quantitatively evaluates the resilience changes in the global maritime network before and after the outbreak of the Russia–Ukraine conflict. The experiment utilizes real automatic identification system (AIS) maritime trajectory data to quantify and visualize the changes in global maritime traffic during a 20-day period before and after the conflict, constructing the global maritime network for resilience calculations. The research findings indicate the following changes occurred after the Russia–Ukraine conflict. Firstly, the global maritime industry experienced overall growth, with increased ship transportation between ports. Transportation in certain regions was negatively affected, with a significant decrease in ship activities in the Black Sea and Adriatic Sea areas. The positions of Russia and Ukraine in the world maritime industry noticeably declined. Secondly, the network connectivity, network size, and network density of the global maritime network significantly increased, indicating an enhanced network resilience. According to our quantitative results, from a topological perspective, we observed the following changes: network connectivity increased by 27.2%, network scale increased by 36.6%, network density increased by 32.4%, and network resilience increased by 18.6%. Thirdly, the global maritime network is characterized by a high degree of heterogeneity, and the impact of conflicts on the heterogeneity of the shipping network is not significant. Finally, the network exhibited a slower performance decline under random attacks, while deliberate attacks led to a sharp decline. Due to the adaptive nature of the maritime network, the resilience of the network improves in terms of its topology following the outbreak of conflicts. After conflict incidents, the rate of performance decline during simulated attacks is lower compared to the pre-conflict period. [ABSTRACT FROM AUTHOR]

To investigate the suppression effect of fluorine-containing explosion suppressants (FESs) on methane (CH4) explosions and the corresponding suppression mechanism, a 20-L spherical explosion testing device was used to analyze and compare the effects of perfluorohexanone (C6F12O) and heptafluoropropane (C3F7H) on CH4 explosion parameters. The explosion limit and pressure were obtained before and after adding these FESs. CH4 explosion triangles under the action of the FESs were drawn, and the explosion hazard degree (F) was determined. The results reveal that the addition of C6F12O and C3F7H reduces the upper explosion limit (UEL) and lower explosion limit (LEL) of CH4, with increased concentrations of C6F12O and C3F7H causing faster decreases in the UEL than in the LEL. The explosion limit range of CH4 with C6F12O is smaller than that with C3F7H. When the concentration of CH4 is low, increases in the C6F12O and C3F7H concentrations first cause an increase and then a decrease in the explosion pressure, and the rise rate of explosion pressure increases. After adding the aforementioned FESs, F first increases and then decreases. When the concentration of CH4 is high, the two FESs only inhibit the explosion pressure. Compared with C3F7H, C6F12O has a stronger inhibitory effect; C6F12O has a smaller CH4 explosion triangle area, higher critical oxygen concentration (18.27% vs. 17.70%), and lower F value. Both FESs have promotion and inhibition effects on CH4 explosion because of the comprehensive physical and chemical effects on CH4 explosions; however, the performance of C6F12O is superior to C3F7H. [ABSTRACT FROM AUTHOR]

We introduce the notion of ideal mutations in a triangulated category, which generalizes the version of Iyama and Yoshino [15] by replacing approximations by objects of a subcategory with approximations by morphisms of an ideal. As applications, for a Hom -finite Krull-Schmidt triangulated category T over an algebraically closed field K. (1) We generalize a theorem of Jorgensen [17, Theorem 3.3] to a more general setting; (2) We provide a method to detect whether T has Auslander-Reiten triangles or not by checking the necessary and sufficient conditions on its Jacobson radical J : (i) J is functorially finite, (ii) Gh J = CoGh J , and (iii) Gh J -source maps coincide with Gh J -sink maps; (3) We generalize the classical Auslander-Reiten theory by using ideal mutations. [ABSTRACT FROM AUTHOR]

A data-driven channel prediction method for distribution automation master is proposed to address the poor quality of communication network and communication system transmission problems in distribution network communication. In this paper, an adaptive broad learning network (ABLN) consisting of a standard broad learning network and a hybrid learning network is introduced to predict the channel state information of the communication system. Among them, the hybrid learning network is used to solve the ill-conditioned solution problem when estimating the output weight matrix of the standard broad learning network. Therefore, the ABLN produces sparse output weight matrices and provides excellent prediction performance. In the simulation analysis, the outdoor and indoor scenes are considered based on OFDM system. The prediction performance of ABLN is subsequently evaluated in one step prediction and multistep prediction. The results show that for the prediction performance is concerned, the maximum improvement of ABLN is about 96.49% as compared to other evaluation models, indicating that the CSI is effectively predicted by the ABLN to support the adaptive transmission of the main station of the distribution automation and to satisfy the quality of the communication network of the distribution network. [ABSTRACT FROM AUTHOR]

We study the possible positions of an inscribed equilateral triangle with vertices on the sides of a generic triangle. We show that infinitely many such configurations exist and examine some extremal properties. [ABSTRACT FROM AUTHOR]

The purpose of this article is to find the best homoge-nous functions f(R, r), g(R, r) which minimize and maximize the sums... in a triangle. [ABSTRACT FROM AUTHOR]

A 2006 conjecture of Antunes and Freitas is addressed connecting the scaling-invariant polygonal isoperimetric and principal frequency deficits for triangles. This yields a quantitative polygonal Faber–Krahn inequality for triangles with an explicit constant. Furthermore, a problem mentioned in the 1951 book "Isoperimetric Inequalities In Mathematical Physics" by Pólya and Szegö is addressed: a formula is given for the principal frequency of a triangle. Moreover, a space of polygons is constructed for the classical Pólya and Szegö problem: in 1947, Pólya proved that if n = 3, 4 the regular polygon Pn minimizes the principal frequency of an n-gon with given area α > 0 and suggested that the same holds when n ≥ 5. In 1951, Pólya and Szegö discussed the possibility of counterexamples. This paper constructs explicit (2n − 4)–dimensional polygonal manifolds M (n , α) and proves the existence of a computable N ≥ 5 such that for all n ≥ N, the admissible n-gons are given via M (n , α) and there exists an explicit set A n (α) ⊂ M (n , α) such that Pn has the smallest principal frequency among n-gons in A n (α). Inter-alia when n ≥ 3, a formula is proved for the principal frequency of a convex P ∈ M (n , α) in terms of an equilateral n-gon with the same area; and, the set of equilateral polygons is proved to be an (n − 3)–dimensional submanifold of the (2n − 4)–dimensional manifold M (n , α) near Pn. The techniques involve a partial symmetrization, tensor calculus, the spectral theory of circulant matrices, and W2,p/BMO estimates. Last, an application is given in the context of electron bubbles. [ABSTRACT FROM AUTHOR]

Good understanding of the in-situ stress and rock mass strength or their relative magnitudes is essential to underground geomechanical practices. A prevailing technique for estimating the maximum horizontal stress is the integrated method combining stress polygon, borehole breakout, and drilling-induced tensile fracture. This research embraced all these elements into a nondimensionalized chart to interpret the triangle relation among the in-situ stress, rock mass strength, and failure observation for an underground cylindrical opening at any depth. One of the potential applications of the nondimensionalized chart was shown via the filed observations from a testing tunnel in the Canadian underground research laboratory. An approaching method of untangling two correlated stress components was also proposed to constrain the in-situ stress ratio under the framework of Coulomb frictional failure theory. It is proved to be highly efficient and considerably accurate by implementing the approaching method using the failure observations from the KTB borehole in German. [ABSTRACT FROM AUTHOR]

Querying the geodesic distance field on a given smooth surface is a fundamental research pursuit in computer graphics. Both accuracy and smoothness serve as common indicators for evaluating geodesic algorithms. In this study, we argue that ensuring that the norm of the triangle-wise estimated gradients is not larger than 1 is preferable compared to the widely used eikonal condition. Inspired by this, we formulate the geodesic distance field problem as a Quadratically Constrained Linear Programming (QCLP) problem. This formulation can be further adapted into a Quadratically Constrained Quadratic Programming (QCQP) problem by incorporating considerations for smoothness requirements. Specifically, when enforcing a Hessian-energy-based smoothing term, our formulation, named QCQP-Hessian, effectively mitigates the cusps in the geodesic isolines within the near-ridge area while maintaining accuracy in the off-ridge area. We conducted extensive experiments to demonstrate the accuracy and smoothness advantages of QCQP-Hessian. [ABSTRACT FROM AUTHOR]

In this paper we prove that among all convex domains of the plane with two axes of symmetry, the maximizer of the first non-trivial Neumann eigenvalue \mu _1 with perimeter constraint is achieved by the square and the equilateral triangle. Part of the result follows from a new general bound on \mu _1 involving the minimal width over the area. Our main result partially answers to a question addressed in 2009 by R. S. Laugesen, I. Polterovich, and B. A. Siudeja. [ABSTRACT FROM AUTHOR]

This article explores the Bystander role in greater depth and redefines its position from one of being an onlooker to one having an integral element in the drama triangle, which makes the triangle a three-dimensional drama pyramid. This new visualization highlights the role of the Cultural Parent lodged within one's psyche, which impacts all the drama roles. Recognizing invisible oppression allows us to see the game roles that we may be taking on without awareness. Including the Cultural Parent in the drama pyramid invites contextual awareness and challenges theory that primarily focuses on intrapsychic processes, thereby inviting contextual awareness. The authors propose functional fluency as a useful model that can enables us to step out of game roles. Case examples from a training session are presented where trainees recognized invisible oppression in everyday situations and found options to intervene using the functional fluency model. [ABSTRACT FROM AUTHOR]

The main result in this article is the following: Let K ⊂ R 2 be a regular convex body and let α , β , θ , be three angles such that K has α -chords, β -chords, and θ -chords of constant length and α + β + θ = π , then K is a disc. We also prove another characterization of the disc with respect to properties of its (α , β , θ) -circumscribed triangles. [ABSTRACT FROM AUTHOR]

In this paper we study the computational complexity issues of the problem of secondary domination (known also as (1, 2)-domination) in several graph classes. We also study the computational complexity of the problem of determining whether the domination and secondary domination numbers are equal. In particular, we study the influence of triangles and vertices of degree 1 on these numbers. Also, an optimal algorithm for finding a minimum secondary dominating set in trees is presented. [ABSTRACT FROM AUTHOR]

The problem of finding a maximum size matching in a graph (known as the maximum matching problem) is one of the most classical problems in computer science. Despite a significant body of work dedicated to the study of this problem in the data stream model, the state-of-the-art single-pass semi-streaming algorithm for it is still a simple greedy algorithm that computes a maximal matching, and this way obtains 1 / 2 -approximation. Some previous works described two/three-pass algorithms that improve over this approximation ratio by using their second and third passes to improve the above mentioned maximal matching. One contribution of this paper continues this line of work by presenting new three-pass semi-streaming algorithms that work along these lines and obtain improved approximation ratios of 0.6111 and 0.5694 for triangle-free and general graphs, respectively. Unfortunately, a recent work Konrad and Naidu (Approximation, randomization, and combinatorial optimization. Algorithms and techniques, APPROX/RANDOM 2021, August 16–18, 2021. LIPIcs, vol 207, pp 19:1–19:18, 2021. https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2021.19) shows that the strategy of constructing a maximal matching in the first pass and then improving it in further passes has limitations. Additionally, this technique is unlikely to get us closer to single-pass semi-streaming algorithms obtaining a better than 1 / 2 -approximation. Therefore, it is interesting to come up with algorithms that do something else with their first pass (we term such algorithms non-maximal-matching-first algorithms). No such algorithms were previously known, and the main contribution of this paper is describing such algorithms that obtain approximation ratios of 0.5384 and 0.5555 in two and three passes, respectively, for general graphs. The main significance of our results is not in the numerical improvements, but in demonstrating the potential of non-maximal-matching-first algorithms. [ABSTRACT FROM AUTHOR]

This article discusses the use of ternary energy diagrams in computational physics to model systems with energy distributed among three or more forms. The diagrams can show a system's changing energy distribution at fine intervals of time or position. The article provides examples of using ternary energy diagrams in simulations of a mass on a vertical spring, a batted baseball subject to air resistance, and an RLC circuit. The authors also provide resources and tools for introducing ternary energy diagrams to students. [Extracted from the article]

The document titled "Problems and Solutions" is an article from the American Mathematical Monthly. It contains a list of proposed mathematical problems along with their solutions. The problems cover various topics such as permutations, triangles, sets of positive integers, Fibonacci numbers, and integer matrices. The article provides detailed instructions on how to submit proposed problems and solutions. [Extracted from the article]

Consider the graph with the residue classes modulo n as vertices, and the following edges: "additive" edges from a to a + 1; "multiplicative" edges from a to ab for some fixed b. This graph illustrates a criterion for divisibility by n for numbers written in base b. By varying n and b, we see a great variety of structures: this topic connects arithmetic to graph theory and has the beauty of string art. For divisibility graphs we investigate the existence of triangles and other cycles, the girth, the minimum/maximum of the vertex degree, the chromatic number, and the planarity. [ABSTRACT FROM AUTHOR]

The notion of discrete conformality proposed by Luo (2004) and Bobenko et al. (2015) on triangle meshes has rich mathematical theories and wide applications. Gu et al. (2019) and Wu and Zhu (2020) proved that the discrete uniformizations approximate the continuous uniformization for closed surfaces of genus ≥ 1 , given that the approximating triangle meshes are reasonably good. In this paper, we generalize this result to the remaining case of genus zero surfaces, by reducing it to planar cases via stereographic projections. [ABSTRACT FROM AUTHOR]

Triangulated surfaces are compact Riemann surfaces equipped with a conformal triangulation by equilateral triangles. In 2004, Brooks and Makover asked how triangulated surfaces are distributed in the moduli space of Riemann surfaces as the genus tends to infinity. Mirzakhani raised this question in her 2010 ICM address. We show that in the large genus case, triangulated surfaces are well distributed in moduli space in a fairly strong sense. We do this by proving upper and lower bounds for the number of triangulated surfaces lying in a Teichmüller ball in moduli space. In particular, we show that the number of triangulated surfaces lying in a Teichmüller unit ball is at most exponential in the number of triangles, independent of the genus. [ABSTRACT FROM AUTHOR]

Let I = I (D) be the edge ideal of a weighted oriented graph D, let G be the underlying graph of D, and let I (n) be the n-th symbolic power of I defined using the minimal primes of I. We prove that I 2 = I (2) if and only if the following conditions hold: (i) every vertex of D with weight greater than 1 is a sink and (ii) G has no triangles. Using a result of Mandal and Pradhan and the classification of normally torsion-free edge ideals of graphs, we prove that I n = I (n) for all n ≥ 1 if and only if the following conditions hold: (a) every vertex of D with weight greater than 1 is a sink and (b) G is bipartite. If I has no embedded primes, conditions (a) and (b) classify when I is normally torsion-free. Using polyhedral geometry and integral closure, we give necessary conditions for the equality of ordinary and symbolic powers of monomial ideals with a minimal irreducible decomposition. Then, we classify when the dual of the edge ideal of a weighted oriented graph is normally torsion-free. [ABSTRACT FROM AUTHOR]

We develop a set of tools for doing computations in and of (partially) wrapped Fukaya categories. In particular, we prove (1) a descent (cosheaf) property for the wrapped Fukaya category with respect to so-called Weinstein sectorial coverings and (2) that the partially wrapped Fukaya category of a Weinstein manifold with respect to a mostly Legendrian stop is generated by the cocores of the critical handles and the linking disks to the stop. We also prove (3) a 'stop removal equals localization' result, and (4) that the Fukaya–Seidel category of a Lefschetz fibration with Liouville fiber is generated by the Lefschetz thimbles. These results are derived from three main ingredients, also of independent use: (5) a Künneth formula (6) an exact triangle in the Fukaya category associated to wrapping a Lagrangian through a Legendrian stop at infinity and (7) a geometric criterion for when a pushforward functor between wrapped Fukaya categories of Liouville sectors is fully faithful. [ABSTRACT FROM AUTHOR]