Regular Maps Research Articles

A classification of regular maps with Euler characteristic a negative prime cube

A classification of regular maps with Euler characteristic a negative prime cube

A new noise source modelling tool for shooting sheds using novel edge diffraction methodology

Shooting ranges may have a shooting shed to protect the shooter against weather and to reduce noise to neighbours. The noise reduction depends on both shielding and reflection effects and can be difficult to measure due to complex surroundings. In this paper, a new tool will be presented to predict the influence of the shed on the emitted noise. The tool produces a substitute source which models the combined effect of the weapon and the shed, meant for efficient use in regular noise mapping software. It combines advanced edge diffraction methodology for the body of the shed, with a boundary element solution for minor areas representing openings or absorbers in the shed. With this approach we cover the full spectral range (up to 10 kHz) at low calculation time, with an intended precision comparable to traditional models based on boundary element methods. The tool is also intended for opposite use, by reciprocity, for instance to model quietness on the backside of a house by a road.

Effective Communication Strategies for Business Analysts to Bridge the Gap between IT and Finance

As organizations depend more on technology to stay ahead of the competition, their information technology (IT) and business departments must work together closely. However, cultural differences and understanding between the specialized fields often make it hard for them to work together effectively. If these issues are fixed, they could make it easier to finish projects, stick to budgets, and agree on the company's goals. Many companies use business analysts to help people talk to each other by acting as liaisons knowledgeable in technology and finances. However, there is limited information in the literature about how analysts can connect the tasks. This study fills that gap by looking into the problems when IT and finance work together and suggesting specific steps analysts can take to improve strategic alignment. Looking at past studies shows that common differences make it hard for people to work together. IT and finance use different vocabularies for technical terms and project-based versus financial terms, leading to misunderstandings. They also set other priorities. It emphasizes speed of innovation and technical practicality, while finance emphasizes reducing risk, accuracy, and returns. There are also differences in the amount of knowledge and skill that people in IT and finance have regarding technical solution details and financial effects. They also use different ways to make decisions. IT bases judgments on technological factors, while finance assesses business impact. Besides, cultural norms diverge between the flexible and creative IT culture and the rigorous and methodical finance culture. Business analysts should utilize several focused communication strategies to close these gaps. Creating a shared vocabulary helps terms from diverse fields fit. Regular mapping and stakeholder conversations help you grasp other perspectives. Actively listening, repeating, asking questions, and summarizing shows you comprehend. Educating on decision-making variables and expertise broadens perspectives. Discussing cultural meanings and making sure individuals understand questions improves discussion. Using shared goals like increasing sales or lowering costs is another way to unite people around similar goals. By using these specific methods, business experts can help IT and finance work together despite cultural differences. Mapping and teaching regularly help keep relationships strong even as needs and staff change. By focusing on active listening, aligning vocabulary, and highlighting shared interests, you can build good working relationships necessary to get strategic benefits from technology investments.

Soluble quotients of triangle groups

This paper helps explain the prevalence of soluble groups among the automorphism groups of regular maps (at least for ‘small’ genus), by showing that every non-perfect hyperbolic ordinary triangle group Δ+(p,q,r)=〈x,y|xp=yq=(xy)r=1〉 has a smooth finite soluble quotient of derived length c for some c≤3, and infinitely many such quotients of derived length d for every d>c.

On Symmetrical Equivelar Polyhedra of Type {3, 7} and Embeddings of Regular Maps

On Symmetrical Equivelar Polyhedra of Type {3, 7} and Embeddings of Regular Maps

Fixed points of regular set-valued mappings in quasi-metric spaces

Metric fixed point theory is becoming increasingly significant across various fields, including data science and iterative methods for solving optimization problems. This paper aims to introduce new fixed point theorems for set-valued mappings under novel regularity conditions, such as orbital regularity and orbital pseudo-Lipschitzness. Instead of traditional metric spaces, we adopt the framework of quasi-metric spaces, motivated by the need to address problems in spaces that are not necessarily metric, such as function spaces of homogeneous type. We also explore the stability of the set of fixed points under variations of the set-valued mapping. Additionally, we provide estimates for the distances from a given point to the set of fixed points and between two sets of fixed points. Building on these findings, we extend the discussion to similar problems involving fixed, coincidence, and cyclic/double fixed points within this framework. Our results generalize recent findings from the literature, including those in Ait Mansour M, Bahraoui MA, El Bekkali A. [Metric regularity and Lyusternik-Graves theorem via approximate fixed points of set-valued maps in noncomplete metric spaces. Set-Valued Var Anal. 2022;30(1):233–256. doi: 10.1007/s11228-020-00553-1], Dontchev AL, Rockafellar RT. [Implicit functions and solution mappings. a view from variational analysis. Dordrecht: Springer; 2009. Springer Monographs in Mathematics], Ioffe AD. [Variational analysis of regular mappings. Springer, Cham; 2017. Springer Monographs in Mathematics; theory and applications. doi: 10.1007/978-3-319-64277-2], Lim TC. [On fixed point stability for set-valued contractive mappings with applications to generalized differential equations. J Math Anal Appl. 1985;110(2):436–441. doi: 10.1016/0022-247X(85)90306-3] and Tron NH. [Coincidence and fixed points of set-valued mappings via regularity in metric spaces. Set-Valued Var Anal. 2023;31(2):22. Paper No. 17. doi: 10.1007/s11228-023-00680-5].

Magnetic properties of the umbral boundary during sunspot decay

Context. In recent years, the magnetic properties of the umbra-penumbra boundary of sunspots and the boundary of pores at various evolutionary stages have been characterised using datasets from different instruments. Aims. We aim to study the intrinsic differences between the intensity and vector magnetic field properties derived from Hinode/SP and SDO/HMI observations of a decaying sunspot. Methods. We analysed the sunspot embedded in active region NOAA 12797 during six days in 30 SP/Hinode scans and 704 HMI/SDO for both regular maps and maps corrected for scattered light, HMIdcon. We studied the correlation of the magnetic properties and continuum intensity in the datasets within the spot, and we investigated the differences at the umbra-penumbra boundary. We examined the decaying process in detail using the full temporal resolution of the HMIdcon maps. Results. We find a good one-to-one correspondence between the magnetic properties in the SP and HMIdcon maps, but the continuum intensity of the spots in the SP maps is found to be 0.04 IQS brighter than in the HMIdcon maps. The considerable influence of scattered light in the HMI maps makes it the least ideal dataset for studying the boundary of spots without a penumbra. The properties at the umbra-penumbra boundary evolve slowly during the sunspot decay stage, while the penumbra still provides some stability. In contrast, they respond more abruptly to areal changes in the naked-spot stage. During the sunspot decay, we find linear decay in the area and in the magnetic flux. Moreover, the umbra shows two characteristic decaying processes: a slow decay during the first three days, and a sudden fast decay during the final dissipation of the penumbra. We find indications of a 3.5 h lag between the dissipation of the vertical fields in the umbral region and the photometric decay of the umbral area. Conclusions. The differences found in the continuum intensity and in the vertical component of the magnetic field, Bver, between the analysed datasets explain the discrepancies among the Bver values found at the boundaries of umbrae in previous studies.

Enhancing Tuberculosis Care in Madhya Pradesh Through Public-Private Partnerships: An Evaluation of the Patient Provider Support Agency (PPSA) Model

BackgroundThe quality of care that patients receive in the private sector has been reported to be poor. Madhya Pradesh began adopting the PPSA model in September 2020, initially covering 44 districts. By April 2022, the state achieved 100% coverage, becoming the first state in the country to implement PPSA across all 52 districts. Although PPSA is now operational in every district, health indicators in the private sector have shown little improvement, and notifications from the private sector remain significantly below the annual targets The patient provider support agency (PPSA) pilot program has demonstrated newer strategies for private sector engagement to be able to deliver significant outcomes. the study explores the strengths and limitations of the private sector engagement model from the healthcare providers’ perspective MethodsThis was a mixed–methods study in which both quantitative and qualitative data were simultaneously collected. Quantitative data collection (using routinely collected programmatic data) is supported by qualitative data collection (in-depth interviews).This study was conducted to study the impact of the PPSA service implementation model on notification status, patient care activities and outcomes through record review among all 52 districts of Madhya Pradesh between October 2020- December 2022 as well as to explore the strengths and limitations of the PPSA model from the healthcare providers’ perspectives using a mixed-methods approach. ResultThere was a increase in the number of TB patients notified in the private sector (62%), number of patients receiving benefits of the Nikshay Poshan Yojna through Direct Bank Transfer (91%), number of patients tested for Human Immunodeficiency Virus (100%), Diabetes, and universal drug susceptibility testing (25%), as well as successful treatment outcomes in the post-PPSA period as compared to the pre-PPSA period. Seventeen in-depth interviews of health care providers from the public (n=8) and private sector (n=9) highlighted the operational challenges and solutions to implementation of the PPSA. Inadequate Human resource, poor coordination with NTEP Staff, poor mapping of PP’s, mobile based counselling & limited home visit to TB patients were the perceived challenges and regular support to the private health facilities and MIS data, trainings and hand-holding, supportive supervision from the State, and strict need based tendering policies were few of the suggestions to improve the PPSA model were some of the solutions. ConclusionThe implementation of the Patient Provider Support Agency (PPSA) model in Madhya Pradesh has not only improved notification rates and successful treatment outcomes but also strengthened the overall engagement of private healthcare providers in TB management. Enhanced collaboration, regular facility mapping, and sustained educational efforts have led to a more robust approach to TB care that extends across both public and private sectors. While challenges such as funding inconsistencies and service delivery fluctuations highlight areas for further improvement, the overall success of the PPSA model in Madhya Pradesh provides a promising framework for other regions aiming to enhance TB care through public-private partnerships. Future efforts should focus on addressing the identified gaps and scaling up these successful practices to ensure high-quality care for all TB patients, irrespective of where they seek treatment.

Algebraic homotopy classes

We prove several positive results regarding representation of homotopy classes of spheres and algebraic groups by regular mappings. Most importantly we show that every mapping from a sphere to an orthogonal or a unitary group is homotopic to a regular one. Furthermore we prove that algebraic homotopy classes of spheres form a subgroup of the homotopy group, and that a similar result holds also for cohomotopy groups of arbitrary varieties.

Peak frequency mapping usefulness and utilization for typical AVNRT ablation

Abstract Background Accurate identification of slow pathway for the AVNRT ablation is important to achieve successful result and avoid complications mainly AV nodal block. There were some developments to produce precise image to locate this such as identify low voltage bridge (LVB) using electro-anatomical mapping and visualization of direct slow pathway capture (DCSP). The peak frequency (PF) associated with bipolar EGMs is a novel parameter which may serve to distinguish near filed (NF) from far field (FF) electrocardiogram (EGM) components. This technique can be used to differentiate sub-components derived from high density mapping. Previous study suggested this mapping appears to assist in substrate differentiation, pathway localization, and contact assessment. However, this approach has been never evaluated clinically in AVNRT ablation Objective This study conducted to evaluate the usefulness and utilization of the peak frequency mapping to identify the slow pathway location. Method The study conducted in November to December 2023 where twenty consecutive patients with common AVNRT were included in the study. Regular bipolar voltage and activation maps were generated with a regular 4 mm tip catheter. Following this, peak frequency maps (PF) were computed online prior ablation and displayed on the activation map with shadowed areas where PF was <200 Hz (figure, left panel). Focal radiofrequency application (RFa) was directed to the areas of late activation (figure, left panel) and low frequency (figure, right panel) (LA-LF). Successful ablation reached if junctional rhythm was recorded during RFa and AVNRT was no longer inducible afterwards. Results Twenty patients (48 ±15 years, 75% female) were enrolled in the study. A late activation low frequency area of 0.92±0.48 cm2 was found in 18 of them. This study revealed that there was a difference between PF in the slow pathway area compared to the adjacent area where the mean PF at the slow pathway area was 175.5 ± 37.1 Hz (analysis per patient) and 170.1 ± 48.10 Hz (analysis per recording site) which was lower and differed significantly than the PF recorded at the adjacent atrial area (279.71 ± 28.11 Hz per patient, 279.91 ± 69.47 Hz per recording site) (P<0.0001). Following the mapping, RFa were successfully applied at these late activation low-frequency (LA-LF) area induced junctional rhythm in 17 patients. AVNRT was no longer inducible after the ablation in all 17 patients. Additional RFa were often given to reinforce the result (11 ± 9 RFa, 4.03 ± 3.35 min RFa time). Conclusion The peak frequency mapping could be performed to map the slow nodal pathway which is often located in an area of late activation and low frequency.

Improved A* Navigation Path-Planning Algorithm Based on Hexagonal Grid

Navigation systems are extensively used in everyday life, but the conventional A* algorithm has several limitations in path planning applications within these systems, such as low degrees of freedom in path planning, inadequate consideration of the effects of special regions, and excessive nodes and turns. Addressing these limitations, an enhanced A* algorithm was proposed using regular hexagonal grid mapping. First, the approach to map modeling using hexagonal grids was described. Subsequently, the A* algorithm was refined by optimizing the calculation of movement costs, thus allowing the algorithm to integrate environmental data more effectively and flexibly adjust node costs while ensuring path optimality. A quantitative method was also introduced to assess map complexity and adaptive heuristics that decrease the number of traversed nodes and increase the search speed. Moreover, a turning penalty measure was implemented to minimize unnecessary turns on the planned paths. Simulation results confirmed that the improved A* algorithm exhibits superior performance, which can dynamically adjust movement costs, enhance search efficiency, reduce turns, improve overall path planning quality, and solve critical path planning issues in navigation systems, greatly aiding the development and design of these systems and making them better suited to meet modern navigation requirements.

An E³ embedding of Coxeter’s regular map {8, 4 | 3} results in a regular Leonardo polyhedron

An E³ embedding of Coxeter’s regular map {8, 4 | 3} results in a regular Leonardo polyhedron

Assessing Seasonal and Inter-Annual Changes in the Total Cover of Submerged Aquatic Vegetation Using Sentinel-2 Imagery

Remote sensing is a valuable tool for surveying submerged aquatic vegetation (SAV) distribution patterns at extensive spatial and temporal scales. Only regular mapping over successive time periods (e.g., months, years) allows for a quantitative assessment of SAV loss or recolonization extent. Still, there are only a limited number of studies assessing temporal changes in SAV patterns. ESA Sentinel-2 (S2) has a high revisiting frequency permitting the multi-temporal assessment of SAV dynamics both seasonally and inter-annually. In the current study, a physics-based IDA (Image Data Analysis) model was used for the reconstruction of past SAV percent cover (%cover) patterns in the Baltic Sea coastal waters based on S2 archived images. First, we aimed at capturing and quantifying intra-annual spatiotemporal SAV dynamics happening during a growing season. Modeling results showed that significant changes took place in SAV %cover: the extent of low-cover (0–30% coverage) and intermediate-cover (30–70% coverage) areas decreased, while high-cover (70–100% coverage) areas increased during the growing period. Secondly, we also aimed at detecting SAV %cover spatiotemporal variations inter-annually (over the years 2016–2022). Inter-annual variability in %cover patterns was greater in the beginning of the vegetation period (May). The peak of the growing period (July/August) showed greater stability in the areal extent of the %cover classes.

On Reverse Derivations in d-algebras

In the present paper, we apply the concept of reverse derivation in rings on the concept of d − algebra to obtain the concept called a left-right (resp. right-left) reverse derivations of d−algebra X (briefly, (l, r) resp. (r, l)− reverse derivation of d − algebra ), we will also, define some concepts such as regular map, composition two maps and study the related properties. Moreover, the notions of partial ordered edge d − algebra as well as d − subalgebra and their relation to our current study are obtained. In addition, some illustrative examples and counterexamples are discussed.

On almost regular mappings

Ioffe's criterion and various reformulations of it have become a standard tool in proving theorems guaranteeing various regularity properties such as metric regularity, i.e. the openness with a linear rate around the reference point, of a (set-valued) mapping. We derive an analogue of it guaranteeing the almost openness with a linear rate of mappings acting in incomplete spaces and having non-closed graphs, in general. The main tool used is an approximate version of Ekeland's variational principle for a function that is not necessarily lower semi-continuous and is defined on an abstract (possibly incomplete) space. Further, we focus on the stability of this property under additive single-valued and set-valued perturbations.

Regularity of CR maps into uniformly pseudoconvex hypersurfaces and applications to proper holomorphic maps

We study regularity properties of CR maps in positive codimension valued in pseudoconvex manifolds which carry a nontrivial Levi foliation. We introduce an invariant which can be used to deduce that any sufficiently regular CR map from a minimal manifold into such a foliated target is either generically smooth or geometrically highly constrained, and to show generic smoothness of sufficiently regular CR transversal CR maps between pseudoconvex hypersurfaces. As an application, we discuss boundary regularity of proper holomorphic maps into bounded symmetric domains.

A Review on the Structure of Fuzzy Regular Proper Mappings in Fuzzy Topological Spaces and Their Properties

The purpose of this paper is construct the concept of fuzzy regular proper mapping in fuzzy topological spaces. We give some characterization of fuzzy regular compact mapping and fuzzy regular coercive mapping. We study the relation among the concepts of fuzzy regular proper mapping, fuzzy regular compact mapping and fuzzy regular coercive mapping and we obtained several properties.

ЧУВСТВО ЛЮБВИ В МЕТАФОРИЧЕСКОМ ПРОСТРАНСТВЕ РУССКОГО ЯЗЫКА: ОСНОВНЫЕ ПРОЕКЦИИ И МОДЕЛИ

The authors analyze the metaphorical representation of love basing their observations on dictionary data. The object of the study is the metaphorical lexicon of love (249 items, 37% of the total amount of words related to the semantics of love). The subject of the study is the regular metaphorical mappings of the feeling of love and their categorization in relation to the source domain, which serves as a basis for further classification of metaphorical models (M-models). The goal of the study is to identify metaphorical mappings of the feeling of love, to define the structure of denotative ideographic spheres and groups that fill the position of the source domain and form the metaphorical representation of love. The authors suggest an analysis algorithm that consists of the following steps: 1) collection of the corpus of love metaphors; 2) categorization of the words with metaphorical meanings; 3) identification of the core M-models and regular metaphorical mappings; 4) statistical description of the M-models in the “field” format; 5) interpretation of the metaphorical representation of love. The authors conducted paradigmatic analysis of the thematic groups serving as the source domain of the metaphors of love and identified 10 metaphorical mappings on the supercategorical level and 44 M-models on the level of basic categories. As a result, the structure of the metaphorical space has been arranged with regards to the priorities of the metaphorical mappings, and the inventory of the M-models has been itemized. The metaphorical space of love is demonstrated to be polycentric, with the bulk of it being formed by the lexical groups belonging to the denotative spheres of “Concrete Physical Activity”, “Inanimate Nature”, “Public and State”, “Animate Nature”, “Supernatural”. The lexical content of the M-models demonstrates the priorities of filling specific fragments of the metaphorical representation of love.

Strict fixed point and Ulam-Hyers stability of multivalued asymptotically regular mappings

In this paper, we establish the existence and uniqueness of strict fixed point for an asymptotically regular multivalued mapping in a metric space. We also study the Ulam-Hyers stability, well-posedness and data dependence of the associated strict fixed point problem. We give an example to illustrate our results. Our work extends and complements important results existing in the literature.

On the lack of compactness in the axisymmetric neo-Hookean model

Abstract We provide a fine description of the weak limit of sequences of regular axisymmetric maps with equibounded neo-Hookean energy, under the assumption that they have finite surface energy. We prove that these weak limits have a dipole structure, showing that the singular map described by Conti and De Lellis is generic in some sense. On this map, we provide the explicit relaxation of the neo-Hookean energy. We also make a link with Cartesian currents showing that the candidate for the relaxation we obtained presents strong similarities with the relaxed energy in the context of $\mathbb {S}^2$ -valued harmonic maps.