In a recent paper, Aldous, Blanc and Curien asked which distributions can be expressed as the distance between two independent random variables on some separable measured metric space. We show that every nonnegative discrete distribution whose support contains 0 arises in this way, as well as a class of compactly supported distributions with density.

The distance between the effects – ideal and real – of many incentives calls into question the way in which they are granted, monitored, supervised and, often, perpetuated, due to the lack of defined time limits for all federation entities. Over time, they become ineffective and become a “real black hole” of public resources that, if collected, could be better used for the benefit of society. The purpose of this article is to solve this problem of distance between the ideal and the real external effect. The deductive method was used, with bibliographical research of national and international authors, based on the doctoral thesis of Celso Correia Neto on tax exemption. The proposed solution was the performance of the Public Ministry of Accounts as an essential agent in overseeing tax expenditure policies. The example of the Public Ministry of Accounts of Pará (MPC-PA) illustrated this role through Preliminary Procedure No. 2021/0118-6, in which weaknesses in the state incentive policy were identified and recommendations for its improvement were issued, thereby reinforcing the institution’s mission to ensure oversight and corrective action in fiscal management.

Aiming at the problem of long distance laying of casing for connected roadway directional borehole in underground coal mine, the bending capacity and passing capacity of casing were calculated and analyzed with the large diameter casing of Ф219 × 8.94 mm as the research object. The stress situation in the process of casing running was studied, and the supporting pipe jacking machine was developed and the engineering test was carried out. The results show that the limit dog leg of the casing string is 5.512°/30 m. The smaller borehole diameter has high requirements for dogleg control, and the larger borehole diameter increases the drilling difficulty. The preferred borehole diameter is 330 mm. The casing laying scheme of ' drill machine pulling back + pipe jacking machine pushing ' is put forward. The casing pushing and pulling process should be matched with thrust and tension. Focus on the design of horizontal telescopic guide rail propulsion system and mobile centralizer and clamping release system, the supporting pipe jacking machine was developed. The engineering test was carried out in the directional long borehole between Daliuta Mine and Huojitu Mine. The casing running and cementing achieved good results. The research results can provide reference for the implementation of similar projects.

Falconer distance problem on Riemannian manifolds

UDMB is a distributor company of frozen food products in East Kalimantan and North Kalimantan. Time and distance are the biggest obstacles felt by companies in the distribution process. It is because the product must be at a minimum temperature of -18o Celsius so that the product remains in good condition. Meanwhile, the cooling machine on a distribution truck can only maximize working temperature for 6 hours. These travel time and distance problems have occurred more than 12 times a year in out-of-town distribution. Therefore, this research aims to produce an optimal distribution routes with consideration of the fastest time and shortest distance. This problem is solved using the Clarke and Wright Savings Method with the Head and Tail concept and the Cluster First Route Second Method with Sweep Algorithm and Nearest Neighbor. Then, the total distribution time and distance between the results of the two methods are compared. Based on the first results, the total trucks used are 3 units with a total distribution time of 847 minutes and a total distribution distance of 475.8 km. Based on the second results, the total trucks used are 3 units with a total distribution time of 875 minutes and a total distribution distance of 483.8 km. This shows that the Clarke and Wright Savings Method with the Head and Tail concept is the method that produces the most optimal route with the fastest total distribution time and shortest total distribution distance.

Since the well-known breakthrough of L. Guth and N. Katz on the Erdős distinct distances problem in the plane, it aroused mainstream interest by their method and the Elekes–Sharir framework. In short, they study the second moment in the framework. One may wonder if higher moments would be more efficient. In this paper, using number-theoretic methods, we show that any higher moment fails the expectation. We also show that the second moment gives an optimal estimate in higher dimensions. Moreover, we prove the mean second moment attains the maximum for the hexagonal lattice in $\mathbb{R}^2$, which is a parallel result on the distinct distances problem for lattices.

The creation of Nigeria Incentive-based Risk Sharing System for Agricultural Lending (NIRSAL) was exigent on poor credit delivery to agricultural sector in Nigeria occasioned by high percentage financial risks of most formal financial institutions who lent to the sector. The study assessed the role of NIRSAL in de-risking institutional lending to farmers in Cross River State. Specifically, the study assessed the current challenges and risks faced by farmers regarding institutional lending for agricultural purposes; investigated the level of awareness and understanding of farmers concerning NIRSAL and its risk-sharing mechanism; identified the key factors influencing accessibility and utilization of NIRSAL services; and evaluated the effectiveness of NIRSAL in mitigating and de-risking institutional loans to farmers in the study area. Primary and secondary data were used for the study, and 684 respondents were selected for the study. The data obtained were analyzed using a Likert, Ordered Probit Model, Logit Model and Propensity Score Matching models. The study established a significant gender disparity in awareness and access to NIRSAL services, with female farmers facing considerable barriers (p-values =0.060, 0.072, and 0.050, for the Ordered Probit). The study further showed that previous experience (p-value = 0.000) of earlier government schemes/programmes and how far they were from farmers (p-value = 0.000) positively influenced access to these services, but the overall participation rate remained low at 15.76%. Although farmers could gain substantial financial benefits (N208, 750 ≡ 130.47USD per farmer) from NIRSAL's risk-sharing mechanisms, they were often limited by the distance to financial institutions and to NIRSAL. The study, therefore, recommends among others, that NIRSAL collaborate with Non-governmental organizations and Community-based organizations to facilitate training and outreach efforts, ensuring more farmers are informed about its services; create incentive programmes that encourage farmers to engage with it, such as reduced fees for participation or additional support for first-time users; and collaborate with financial institutions to establish agent banking system in the rural farming communities to serve farmers in these areas due to distance problem to urban centers. Keywords: Farm business, agricultural financing, financial management, institutional loans, rural employment, food supply.

Sustainable urban development is profoundly challenged by socio-spatial inequality that systematically disadvantages vulnerable groups across geographical space, directly undermining the Right to the City. Addressing this is critical for achieving SDG 11, yet rapid Sub Saharan African urbanization continuously generates spatial disparities. Using Buea, Cameroon, this study sought to: (1) assess the spatial distribution and multi-dimensional accessibility of healthcare and security services; (2) quantify the resulting inequalities and their implications for population well-being; and (3) analyze the governance policy failures perpetuating this injustice. We employed a robust mixed-methods approach. GIS-based analysis established nominal access metrics. The legal framework was analyzed via thematic content analysis, while the causes of ineffective enactment were explored through thematic analysis of semi-structured interviews. A strati ied household survey then quanti ied the impacts, using Chi-square tests (χ2) to compare service outcomes between settlements, triangulating legal de icit, governance failure, and household experience. Nominal proximity was misleading proxy for true access. While marginalized areas were within a distance norm (400m-800m), the true barrier lies in infrastructural decay and planning failure. Sectoral health and security laws were disconnected from spatial planning mandates, creating a legal vacuum. This governance failure was evident as emergency vehicle access dropped from 97% in planned areas to 45% in unplanned zones (χ2=p<0.041), and average travel time to health centers escalated from 18 minutes to a prohibitive 70 minutes. Political interference was the primary mechanisms preventing law enforcement; ensuring spatial inequality was an enforced outcome of planning paralysis. Hence, spatial inequality in Buea was not merely a technical problem of distance but a direct manifestation of socio-spatial injustice. The projected population dynamics will escalate this crisis by 2030, fundamentally undermining the core tenets of SDG 11. This study proposed shifting to a harmonized, needs-based planning approach that emphasized true access policies, infrastructure development and institutional reform.

We study the Pythagoras numbers py ⁡ ( 3 , 2 d ) \operatorname {py}(3,2d) of real ternary forms, defined for each degree 2 d 2d as the minimal number r r such that every degree 2 d 2d ternary form which is a sum of squares can be written as the sum of at most r r squares of degree d d forms. Scheiderer [Math. Z. 286 (2017), pp. 559–570] showed that d + 1 ≤ py ⁡ ( 3 , 2 d ) ≤ d + 2 d+1\leq \operatorname {py}(3,2d)\leq d+2 . We show that p y ( 3 , 2 d ) = d + 1 py(3,2d) = d+1 for 2 d = 8 , 10 , 12 2d = 8,10,12 . Our approach is to connect the problem with optimality conditions for a Euclidean distance problem. When paired with Diesel’s characterization of height 3 Gorenstein algebras, this allows us to control the syzygies of the forms involved in the decomposition into sums of squares.

The electromechanical braking (EMB) system is an important component of intelligent vehicles and is also the core actuator for longitudinal dynamic control in autonomous driving motion control. Therefore, we propose a new mechanism layout form for EMB and a feedforward second-order linear active disturbance rejection controller based on clamping force. This solves the problem of excessive axial distance in traditional EMB and reduces the axial distance by 30%, while concentrating the PCB control board for the wheels on the EMB housing. This enables the ABS and ESP functions to be integrated into the EMB system, further enhancing the integration of line control and active safety functions. A feedforward second-order linear active disturbance rejection controller (LADRC) based on the clamping force of the brake caliper is proposed. Compared with the traditional clamping force control methods three-loop PID and adaptive fuzzy PID, it improves the response speed, steady-state error, and anti-interference ability. Moreover, the LADRC has more advantages in parameter adjustment. Simulation results show that the response speed is increased by 130 ms, the overshoot is reduced by 9.85%, and the anti-interference ability is increased by 41.2%. Finally, the feasibility of this control algorithm was verified through the EMB hardware-in-the-loop test bench.

Introduction: Increasing network communication area has lot of unstructured routing to create complex structures. The communication structure is non-linear to create connective edges to degrade the communication performance. Many non-linear solutions and distance theory models contains maximum non-liability of variables are taken to solve the problems. But structure difference and dynamic variables are constantly applied to make solution which leads errors and complex solutions. To resolve this problem, to propose a Redundant mathematical solution for complex homotopy structures using Multinomial-Cordial Graph Theory (MCGT) based on Bipartite Chromatic Polynomial Distribution Theory (BCPDT) for solving distance problems. To apply neighbor-based distance coverage model with cordial labeling variable structure to reduce the complexity variable structure problems, this paper explores a novel strategy for encapsulating the non-linear complex homotopy in its entirety by employing graph theory and the concept of cordial labeling. By establishing a connection between algebraic topology and graph theoretical constructs, we formulate a redundant solution that illuminates the intricacies of complex homotopy but also provides practical methodologies for solving distance-related issues prevalent in various mathematical and applied fields as well, compared to the previous models.

ABSTRACTEquitable access to primary healthcare services can considerably improve citizens' health and well‐being. However, most location–allocation models emphasize efficiency, such as minimizing total travel cost and maximizing demand coverage while overlooking spatial equality. Therefore, this study addresses the issue of spatial equality planning for primary healthcare facilities by proposing a new framework for evaluation, optimization, and validation. Using the county‐level city of Changyuan in China as a case study, the researchers adopted an optimal supply–demand allocation model to assess the spatial accessibility of primary healthcare facilities. Moreover, this study examines the capacitated minimum distance and envy location problem (CMDELP) model to recognize optimal locations for new healthcare facilities. The results showed that people prefer to use electric bicycles as their mode of transportation, with 74.95% of the people reaching the nearest healthcare facility within 15 min under the electric bicycle scenario. The Gini coefficient was 0.454. By incorporating the newly proposed facilities, whose optimal locations were determined using the p‐median problem (PMP) model, capacitated p‐median problem (CPMP) model, and CMDELP models, additional people coverage for the electric bicycle scenario could potentially increase by 17.47%, 15.00%, and 18.39%, respectively, while the Gini coefficient decreases to 0.325, 0.332, and 0.277, respectively. The proposed solution for optimizing the layout of public service facilities has the potential to be a useful tool for improving the spatial equality of facilities at the county level.

Finite distance problem on the moduli of non-Kähler Calabi–Yau $$\partial {\bar{\partial }}$$-threefolds

Abstract A problem of current interest, also motivated by applications to Coding theory, is to find explicit equations for maximal curves, that are projective, geometrically irreducible, non-singular curves defined over a finite field $$\mathbb {F}_{q^2}$$ F q 2 whose number of $$\mathbb {F}_{q^2}$$ F q 2 -rational points attains the Hasse-Weil upper bound $$q^2+2\mathfrak {g}q+1$$ q 2 + 2 g q + 1 where $$\mathfrak {g}$$ g is the genus of the curve $$\mathcal {X}$$ X . For curves which are Galois covered of the Hermitian curve, this has been done so far ad hoc, in particular in the cases where the Galois group has prime order and also when has order the square of the characteristic. In this paper we obtain explicit equations of all Galois covers of the Hermitian curve with Galois group of order dp where p is the characteristic of $$\mathbb {F}_{q^2}$$ F q 2 and d is a prime other than p. We also compute the generators of the Weierstrass semigroup at a special $$\mathbb {F}_{q^2}$$ F q 2 -rational point of some of the curves, and discuss some possible positive impacts on the minimum distance problems of AG-codes.

Motivated by recent results on radial projections and applications to the celebrated Falconer distance problem, we study radial projections in the setting of finite fields. More precisely, we extend results due to Mattila and Orponen [Proc. Amer. Math. Soc. 144 (2016), pp. 3419–3430], Orponen [Bull. Lond. Math. Soc. 50 (2018), pp. 1–6], and Liu [Rev. Mat. Iberoam. 37 (2020), pp. 1307–1319] to finite spaces. In some cases, our results are stronger than the corresponding results in the continuous setting. In particular, we solve the finite field analog of a conjecture due to Liu and Orponen on the exceptional set of radial projections of a set of dimension between d − 2 d-2 and d − 1 d-1 .

Genome Rearrangement distance problems are used in Computational Biology to estimate the evolutionary distance between genomes. These problems consist of minimizing the number of rearrangement events necessary to transform one genome into another. Two commonly used rearrangement events are reversal and transposition. The first studied problems ignored nucleotides outside genes (called intergenic regions), or assumed that genomes have a single copy of each gene. Recent works made advancements in more general problems considering the number of nucleotides in intergenic regions, and replicated genes. Nevertheless, genomes tend to have wildly different quantities of nucleotides on their intergenic regions, which poses a problem when comparing these regions exactly. To overcome this limitation, our work considers some flexibility when matching intergenic regions that do not have the same number of nucleotides. We propose new problems seeking the minimum number of reversals, or reversals and transpositions, necessary to transform one genome into another, while considering flexible intergenic region information. We show approximations for these problems by exploring their relationship with the Signed Minimum Common Flexible Intergenic String Partition problem. We also present different heuristics for the partition problem, and conduct experimental tests on simulated genomes to assess the performance of our algorithms.

Tourism plays an important role in the development of a region. Apart from introducing the area to a wider audience, tourism is also a major source of creating jobs and encouraging local economic growth. Pesawaran Regency, which was previously part of South Lampung Regency, is now a newly formed region. Its location close to Bandar Lampung City, the capital of Lampung Province, provides strategic value that can accelerate the development of the region. Distance problems and uncertainty in finding routes often become obstacles for many people when visiting various locations. Pesawaran Regency has a number of interesting tourist destinations, one of which is Pahawang Island, which is one of the leading tourist destinations. To make it easier for tourists, both local and international, the fastest route to these tourist destinations is needed. This research uses the Dijkstra algorithm to calculate the shortest distance from one point to the selected tourist destination in Pesawaran Regency. This article will review the application of the Dijkstra algorithm in finding the most efficient route for searching tourist locations in Pesawaran Regency. The research results show that this system can help tourists reach tourist locations more quickly.

Aiming to address the problem of limited transmission distance in applying reconfigurable intelligent surface (RIS) technology, this study leverages a tunnel simulation platform to investigate RIS-assisted wireless communication systems. Through theoretical derivation, we propose a path loss model formula specifically applicable to tunnel scenarios. Simulation results demonstrate that the proposed model accurately reflects the communication performance characteristics of RIS in tunnel scenarios, verifying the capability of RIS technology to enhance signal transmission distance within tunnels in rail transit engineering applications. This finding highlights the significant engineering potential and value of RIS technology.

ABSTRACT In this article, we study the development of agriculture in the Swedish settlement (‘colony’) in southern Ukraine in the 1800s and first part of the 1900s, including in the early Soviet period. We use unique maps, acquired in the Kherson State archives in southern Ukraine, to show how cultivation expanded away from settlements close to the Dnipro River. Using a variety of historical sources in Swedish, German, Russian and Ukrainian, we detail (1) challenges that settlers had in securing agricultural production; (2) changing agrarian structure and land relations; and (3) how settlers dealt with the problem of distance between settlements and fields. Citing historical debates on farm differentiation, we argue that agrarian structure developed both as a result of demographic and market-related factors and that both pre-Soviet and early Soviet periods showed potential for agricultural development.

The study aimed to analyze and understand the problem of social-spatial distance “in their intricacies and complex intersections to the issue of urban integration” (Elbhiri & Assebane, 2022) between two typologies of families with different paths. The first model refers to families that fall within the framework of the settlement policy, residents of shanty houses. The second model relates to families not targeted by the housing policy and who broke into the housing market due to their economic capital by purchasing the rights of slum residents within the neighborhood. According to the gender approach, the study’s sample consisted of twelve people; there were six males and six females. The qualitative methodology employed in the study included observation and semi-directed interviews. As a result, this study came to several conclusions. For instance, the families who weren’t covered by the resettlement program had no issues with the distance between the housing sites and the work locations. For the families covered by the resettlement policy, the distance between their place of residence and place of employment presents daily challenges because they don’t have access to private transportation, except for one respondent who owns a motorcycle.