Set Of Branches Research Articles

МАТЕМАТИЧНА КОМПЕТЕНТНІСТЬ МАЙБУТНЬОГО ВЧИТЕЛЯ МАТЕМАТИКИ: ТЕОРЕТИЧНИЙ АНАЛІЗ

In the context of modernization of contemporary education on the basis of a competence approach, the problem of professional training of future mathematics teachers, who are able to be actively implemented in the information society, have professional competences that would meet the needs of today, becomes especially relevant. It is emphasized that an important task of training future mathematics teachers is the formation of their mathematical competence. The hierarchy of competences is characterized (according to N. Bibik): key super subjective (basic) competences, which are based on cognitive processes and displayed in different contexts; general subject competences, which belong to a certain set of subjects or branches of knowledge; subject competences - partial to the above, which are acquired in the process of studying a particular subject. The article describes the various definitions of mathematical competence proposed in the State Standard of Basic and Complete General Education (2011), the Concept of the New Ukrainian School (2018), the European Reference Framework of Key Competences for Lifelong Learning (2018), and the PISA International Education Quality Assessment (2022). Based on the analysis, it is determined that mathematical competence is defined by modern scientists as an integrated characteristic of the qualities of a mathematics teacher’s personality, which is expressed in the ability and willingness to apply mathematical knowledge and skills in order to solve professional problems using mathematical methods, applying modern methods of design, mathematical and computer modelling if necessary. Mathematical competence as a result of mathematical training of a graduate of a pedagogical education institution implies a high level of knowledge and experience of independent activity based on this knowledge for the effective professional activity of a future mathematics teacher. The structural components of mathematical competence are allocated: motivational, cognitive, value, activity, and reflexive.

VRTree: Example‐Based 3D Interactive Tree Modeling in Virtual Reality

AbstractWe present VRTree, an example‐based interactive virtual reality (VR) system designed to efficiently create diverse 3D tree models while faithfully preserving botanical characteristics of real‐world references. Our method employs a novel representation called Hierarchical Branch Lobe (HBL), which captures the hierarchical features of trees and serves as a versatile intermediary for intuitive VR interaction. The HBL representation decomposes a 3D tree into a series of concise examples, each consisting of a small set of main branches, secondary branches, and lobe‐bounded twigs. The core of our system involves two key components: (1) We design an automatic algorithm to extract an initial library of HBL examples from real tree point clouds. These HBL examples can be optionally refined according to user intentions through an interactive editing process. (2) Users can interact with the extracted HBL examples to assemble new tree structures, ensuring the local features align with the target tree species. A shape‐guided procedural growth algorithm then transforms these assembled HBL structures into highly realistic, finegrained 3D tree models. Extensive experiments and user studies demonstrate that VRTree outperforms current state‐of‐the‐art approaches, offering a highly effective and easy‐to‐use VR tool for tree modeling.

À la recherche du neutre protoroman. Réflexions à partir de l’expérience de rédaction et de révision de l’article */'ram‑u/ s.n. ‘branche ; branchage’ du DÉRom

Abstract This study describes the development of our thinking and of the analyses that we carried out while preparing the article */'ram‑u/ n.n. ‘branch; set of branches of a tree’ as part of the Dictionnaire Étymologique Roman (DÉRom) project. Throughout our contribution, we will focus our attention on the Romanian and Italian lexical items used to reconstruct the Proto-Romance etymon */'ram‑u/ n.n. and the other three morphologically evolved protoforms */'ram‑a/ f.n., */'ram‑ora/ n.pl.n. and */'ram‑u/ m.n. Indeed, the Romanian and Italian cognates have an increased importance in this case since their particularities allow (or even oblige) us to assign the neuter gender to the Proto-Romance etymon. It is not by chance that the same Romanian and Italian cognates posed the greatest difficulties during the elaboration of this article, given that the debates and commentaries carried out by Romanists concerning the neuter gender continue to be rather stormy without yet reaching a consensus.

Unraveling the Photodissociation Branching and Pathways of Methane at 118 nm by Imaging the CH3, CH2, and CH Fragments.

Under irradiation of a vacuum ultraviolet (VUV) photon, methane dissociates and yields multiple fragments. This photochemical behavior is not only of fundamental importance but also with wide-ranging implications in several branches of science. Despite that and numerous previous investigations, the product channel branching is still under debate, and the underlying dissociation mechanisms remain elusive. In this study, the photofragment imaging technique was exploited for the first time to map out the momentum and anisotropy parameter distributions of the CH3, CH2, and CH fragments at the 118 nm photolysis wavelength (10.48 eV photon energy). In conjunction with previously reported results of the H atom fragment at 121.6 nm (10.2 eV), a complete set of product channel branching in both two-body and three-body fragmentations is accurately determined. We concluded that extensive nonadiabatic transitions partake in the processes with two-body fragmentations accounting for more than 90% of overall photodissociation, for which the channel branching values for CH2 + H2 and CH3 + H are about 0.66 and 0.25, respectively. Careful kinematic analysis enables us to untangle the intertwined triple fragmentations into the CH2(X̃ 3B1 and ã 1A1) + H + H and CH(X2Π) + H + H2 channels and to evidence their underlying sequential (or stepwise) mechanisms. With the aid of electronic correlation and prior theoretical calculations of the potential energy surfaces, the most probable or dominant dissociation pathways are elucidated. Comparisons with fragmentary reports in the literature on various photochemical aspects are also documented, and discrepancies are clarified. This comprehensive study benchmarks the VUV photochemistry of methane and advances our understanding of this important process.

Method of Redevelopment of Underground Mining Facilities

Mining is a set of industrial branches engaged in exploration, extraction, primary processing and obtaining the initial semi-finished product of elements related to minerals. Deposits are ore, non-metallic and alluvial. These deposits are mined by open pit and closed pit methods. After the end of underground operations, empty mine fields remain, which on the surface are labeled as exclusion zones. The problem of cave-in zones, under which the waste mine fields of the mining industry are located, has been particularly acute for decades. These mines are located not only under the industrial zones of populated areas, but also under residential and public areas and cause irreversible transformation of the natural environment, which leads to catastrophic consequences. Transformation of underground space is the main task of redevelopment of industrial areas of this kind. It is possible to build underground structures for other purposes in worked-out mines. Due to the fact that these structures will be maintained and operated, the change in the secondary stress fields in the mountain massif will not have such catastrophic consequences as in the case of alienation-collapse zones. Besides, the reuse of worked-out workings is economically more favorable due to the fact that sinking will be minimal. In this paper only underground mining complexes and the possibility of their reuse will be considered.

Pengorganisasian dalam Lembaga Pendidikan Tinggi

Higher education is the level of education after secondary education which includes diploma, undergraduate, masters, specialist and doctoral education programs organized by universities. In the government regulation of the Republic of Indonesia Number 30 of 1990 concerning tertiary institutions that higher education is education at a higher level than secondary education in the school education pathway. Higher education is an education that becomes the final terminal for someone who has the opportunity to study at the highest level through school education. Education has an important role in producing reliable human resources. Education service providers have an obligation to create quality human beings through an effective educational process. In general, education service providers in Indonesia consist of two types of services, namely education provided by the government and the community. Higher education can be organized by educational units organized by the Government, in this case other departments or departments or other Government agencies, or by educational units organized by the community. Academic implementers in the field of education can take the form of faculties, departments, or laboratories. The faculty coordinates and/or implements academic and/or professional education in one or a set of certain branches of science, technology and/or arts. The department carries out academic and/or professional education in one or a set of certain branches of science, technology and/or art. The department carries out academic and/or professional education in one or a set of certain branches of science, technology and/or art. Laboratories/studios support the implementation of education in majors in academic and/or professional education.

AN EXACT SOLUTION FOR REAL-LIFE TRANSSHIPMENT PATH PROBLEM

In industrial engineering, transportation planning, vehicle routing problem, warehousing, inventory management, and customer service are logistics problems. Graph theory algorithms provide solutions to logistics problems such as the shortest path, minimum spanning tree, and vehicle routing problems. In a logistics company system with branches and transfer centers to which the branches are affiliated, if the sorting process is carried out in the transfer centers, the deliveries collected from the branches must be transported to a transfer center. Thus, there are situations where delivery is transferred in the sending branch, the sending transfer center, the receiving transfer center, and the receiving branch, respectively. In this flow, transferring with a single transfer center without visiting two transfer centers reduces the total cost. While moving from the sender transfer center to the receiver transfer center, stopping by some branches on the way allows us to complete the transfer process with a single transfer center and eliminates the necessity of leaving the vehicle from the receiver transfer center to these branches again. Thus, the number of vehicles that need to go from the receiver transfer center to the branches is reduced. The mentioned logistics structure is defined as a graph that is considered a network design problem. Given the sender transfer center S, the receiver transfer center T, the set of branches A connected to S, and the set of branches C that are not connected to S or T, a counting algorithm that gives the minimum value route among all combinations are designed in order to find the optimal route from the source node s ∈ A∪{S}, to the target node t=T. The algorithm has been implemented in Python and Gams and tested by the different number of elements of the set A and the set C.

Optimal warehouse location and size under risk of failure

We present an optimisation model for supply chain network design under risk of failure. The design parameters include a finite set of potential warehouse locations, a finite set of potential warehouse capacities, a set of branches with known demand for multiple products, a list of products available from each warehouse, and costs of land, building, processing and transportation. Each branch-product pair is assigned a primary and a secondary warehouse. If the primary warehouse fails, some portion of the demand will be supplied by a secondary warehouse. The major contribution of this paper is a novel method of scenarios and an algorithm to determine those scenarios, for the solution of instances of the optimisation model. The scenarios are novel in that they do not specify a subset of warehouses to be built, but rather they specify the number of warehouses of each capacity that are to be built. We give an upper bound on the number of scenarios, and the bound is linear in the difference between the largest and smallest failure probabilities. The effectiveness of the method of scenarios is demonstrated with its application to a case study of a Canadian company and to a fabricated example based in Europe.

Note on the Generalized Branching Random Walk on the Galton–Watson Tree

Let ∂T be a super-critical Galton–Watson tree. Recently, the first author computed almost surely and simultaneously the Hausdorff dimensions of the sets of infinite branches of the boundary of ∂T along which the sequence SnX(t)/SnX˜(t) has a given set of limit points, where SnX(t) and SnX˜(t) are two branching random walks defined on ∂T. In this study, we are interested in the study of the speed of convergence of this sequence. More precisely, for a given sequence s=(sn), we consider Eα,s=t∈∂T:SnX(t)−αSnX˜(t)∼snasn→+∞. We will give a sufficient condition on (sn) so that Eα,s has a maximal Hausdorff and packing dimension.

Magnitude and Slip Scaling Relations for Fault-Based Seismic Hazard

ABSTRACTScaling relations play an important role in fault-based seismic hazard estimates. Scaling relations impact estimates of the sizes and rate for a given fault area. Here, we examine which relations are the most useful for these estimates and issues that arise. These include the depth of large event ruptures, transient deepening of seismicity following large events, difficulties in using classical continuum exponent fits, and the importance of large event asymptotics. A new analysis of land-based data calls into question nonspecific exponent fitting, which is a standard practice. We show a dependence on the lower and upper cut-off magnitudes in the data in the best-fitting slope parameter relating magnitude to log area with this approach. We show as well a dependence on assumed data uncertainties. These sensitivities make using this quite standard approach very problematic. Based on this evidence and other factors, we propose recommendations for the minimal branch sets, which preserve epistemic uncertainty for use in fault-based seismic hazard estimates.

On the Frøyshov invariant and monopole Lefschetz number

Given an involution on a rational homology $3$-sphere $Y$ with quotient the $3$-sphere, we prove a formula for the Lefschetz number of the map induced by this involution in the reduced monopole Floer homology. This formula is motivated by a variant of Witten’s conjecture relating the Donaldson and Seiberg–Witten invariants of $4$-manifolds. A key ingredient is a skein-theoretic argument, making use of an exact triangle in monopole Floer homology, that computes the Lefschetz number in terms of the Murasugi signature of the branch set and the sum of Frøyshov invariants associated to spin structures on $Y$. We discuss various applications of our formula in gauge theory, knot theory, contact geometry, and $4$-dimensional topology.

On the monotonicity of functions constructed via z-ordinal sum construction

This is the second part of a two-part paper which discusses monotonicity of functions defined on the unit interval, constructed via (z)-ordinal. In Part I we characterized all non-decreasing functions defined on the unit interval which are constructed by a non-trivial ordinal sum of semigroups and gave necessary and sufficient conditions for a function constructed via ordinal sum to be monotone. In the present Part II we describe the structure of a monotone function defined on the unit interval which is constructed via z-ordinal sum construction with respect to a finite branching set and we give necessary and sufficient conditions for a function constructed via z-ordinal sum to be monotone in the case when the intermediate condition is fulfilled. The case when the intermediate condition is not fulfilled is discussed as well.

On the monotonicity of functions constructed via ordinal sum construction

The monotonicity of functions defined on the unit interval, constructed via (z)-ordinal sum is discussed. In Part I of this two-part paper we characterize all non-decreasing functions defined on the unit interval which are constructed by a non-trivial ordinal sum of semigroups. We also give necessary and sufficient conditions for a function constructed via ordinal sum to be monotone. In Part II we describe the structure of a monotone function defined on the unit interval which is constructed via z-ordinal sum construction with respect to a finite branching set and we give necessary and sufficient conditions for a function constructed via z-ordinal sum to be monotone in the case when intermediate condition is fulfilled. The case when intermediate condition is not fulfilled is discussed as well.

АНАЛІТИЧНИЙ ПІДХІД ДО ОСОБЛИВОСТЕЙ ФОРМУВАННЯ ГАЛУЗЕВОЇ СТРУКТУРИ ЕКОНОМІКИ

The sectoral structure of the national economy is the ratio of various sectors and sub-sectors (that is, qualitatively homogeneous economic units with special working conditions) in the national economy system. The purpose of the article is coverage of problematic aspects of the use of an analytical approach to the peculiarities of the formation of the sectoral structure of the economy. Methods used in the research: comparison, comparative analysis, systematization and logic, etc. The hypothesis of the study. The system of all industries that are closely interconnected is a single national economic complex. Complexity and dynamism are characteristic features of the structure of the industry). Presenting main material. Under the influence of scientific and technological progress, cyclical economic development (the process of production and distribution of goods and services in a broad sense) and a number of other factors, the sectoral structure is subject to quantitative and qualitative changes. The sectoral structure itself is a set of branches of the national economic complex, characterized by certain proportions and relationships. Originality and practical significance of the research. The sectoral structure is formed under the influence of the law of the social division of labor, the forms of manifestation of which differ significantly at the level of branches. Conclusions. In a transport way, it can be argued that the service history of goods development of economic high thought is an increase in the history of improving the model of methods of reciprocating the understanding of economic time structures based on varying levels of petroleum complexity with the goal of developing certain mechanisms which manage structural financial changes.

DSNUNet: An Improved Forest Change Detection Network by Combining Sentinel-1 and Sentinel-2 Images

The use of remote sensing images to detect forest changes is of great significance for forest resource management. With the development and implementation of deep learning algorithms in change detection, a large number of models have been designed to detect changes in multi-phase remote sensing images. Although synthetic aperture radar (SAR) data have strong potential for application in forest change detection tasks, most existing deep learning-based models have been designed for optical imagery. Therefore, to effectively combine optical and SAR data in forest change detection, this paper proposes a double Siamese branch-based change detection network called DSNUNet. DSNUNet uses two sets of feature branches to extract features from dual-phase optical and SAR images and employs shared weights to combine features into groups. In the proposed DSNUNet, different feature extraction branch widths were used to compensate for a difference in the amount of information between optical and SAR images. The proposed DSNUNet was validated by experiments on the manually annotated forest change detection dataset. According to the obtained results, the proposed method outperformed other change detection methods, achieving an F1-score of 76.40%. In addition, different combinations of width between feature extraction branches were analyzed in this study. The results revealed an optimal performance of the model at initial channel numbers of the optical imaging branch and SAR image branch of 32 and 8, respectively. The prediction results demonstrated the effectiveness of the proposed method in accurately predicting forest changes and suppressing cloud interferences to some extent.

Three-dimensional unsteady axisymmetric vortex solutions to the Bellamy-Knights equation and the distribution of boundary conditions

The Bellamy-Knights equation gives three-dimensional unsteady axisymmetric incompressible vortex solutions that are disconnected from the known exact steady solutions. In this paper, by introducing a new parameter that allows a change of the time scale, the Bellamy-Knights equation is transformed into an integro-differential equation that continuously connects with the equation for steady vortices. The new equation is viewed as describing the one-dimensional motion of a particle under conserved and nonconserved forces and leads to new regular solutions, in which the particle initially undergoes almost sinusoidal oscillations around the minimum of potential followed by a very rapid approach to the extrema of the potential. The regular solutions distribute discretely in the space of boundary conditions and are classified into types that are specified by the pattern of sequence of small and large oscillations of the axial component of velocity. Extending the solutions to singular ones, the boundary conditions for solutions of the same type are shown to form a continuous one-dimensional set, which we call a branch. The set of branches forms dense self-similar patterns with accumulation points, some of which coalesce to a single point. In an arbitrary neighborhood of the accumulation or coalescent point, any two distinct boundary conditions whose distance in the space of boundary conditions is arbitrarily small give mutually distinctive solutions with a finite difference at some region of the spatial distance. This feature of the equations signifies the extreme sensitivity of inflowing vortex solutions to boundary conditions.

Driver Distraction Detection Using Octave-Like Convolutional Neural Network

This study proposes a lightweight convolutional neural network with an octave-like convolution mixed block, called OLCMNet, for detecting driver distraction under a limited computational budget. The OLCM block uses point-wise convolution (PC) to expand feature maps into two sets of branches. In the low-frequency branches, we perform average pooling, depth-wise convolution (DC), and upsampling to obtain a low-resolution low-frequency feature map, reducing spatial redundancy and connection density. In the high-frequency branches, the expanded feature map with the original resolution is fed to the DC operator, gaining an apposite receptive field to capture fine details. The feature concatenation of the low-frequency and high-frequency branches is encoded sequentially by a squeeze-and-excitation (SE) module and PC operator, realizing feature global information fusion. Introducing another SE module at the last stage, the OLCMNet facilitates further sensitive information exchange between layers. In addition, with an augmented reality head-up display (ARHUD) platform, we create a Lilong Distracted Driving Behavior (LDDB) Dataset through a series of on-road experiments. Such a dataset contains 14808 videos collected from an infrared camera, covering six driving behaviors of 2468 participants. We manually annotate these videos at five frames per second, obtaining a total of 267378 images. Compared with the existing methods, the embedded hardware platform experiments indicate that OLCMNet hits acceptable trade-offs, namely, 89.53% accuracy for StateFarm Dataset and 95.98% accuracy LDDB Dataset when the latency is 32.8 ± 4.6ms.

Structured Binary Neural Networks for Image Recognition

In this paper, we propose to train binarized convolutional neural networks (CNNs) that are of significant importance for deploying deep learning to mobile devices with limited power capacity and computing resources. Previous works on quantizing CNNs often seek to approximate the floating-point information of weights and/or activations using a set of discrete values. Such methods, termed value approximation here, typically are built on the same network architecture of the full-precision counterpart. Instead, we take a new “structured approximation” view for network quantization — it is possible and valuable to exploit flexible architecture transformation when learning low-bit networks, which can achieve even better performance than the original networks in some cases. In particular, we propose a “group decomposition” strategy, termed GroupNet, which divides a network into desired groups. Interestingly, with our GroupNet strategy, each full-precision group can be effectively reconstructed by aggregating a set of homogeneous binary branches. We also propose to learn effective connections among groups to improve the representation capability. To improve the model capacity, we propose to dynamically execute sparse binary branches conditioned on input features while preserving the computational cost. More importantly, the proposed GroupNet shows strong flexibility for a few vision tasks. For instance, we extend the GroupNet for accurate semantic segmentation by embedding the rich context into the binary structure. The proposed GroupNet also shows strong performance on object detection. Experiments on image classification, semantic segmentation, and object detection tasks demonstrate the superior performance of the proposed methods over various quantized networks in the literature. Moreover, the speedup and runtime memory cost evaluation comparing with related quantization strategies is analyzed on GPU platforms, which serves as a strong benchmark for further research.

LIFTING HOMEOMORPHISMS AND FINITE ABELIAN BRANCHED COVERS OF THE 2-SPHERE

AbstractWe completely determine finite abelian regular branched covers of the 2-sphere $S^{2}$ with the property that each homeomorphism of $S^{2}$ preserving the branching set can be lifted.

A note on simplification of z-ordinal sum construction

We study the properties of z-ordinal sum construction and show that it can always be expressed in the reduced basic form. This means that it is enough to assume only trivial semigroups in the branching set and we can always remove semigroups with duplicate carriers. We also investigate the cardinality of the minimal branching set corresponding to monotone (and non-monotone) functions defined on the unit interval constructed via z-ordinal sum construction.