Regular Extension Research Articles

Extendability of differential forms via Cartier operators

Let X be a normal variety over a perfect field of positive characteristic and B a reduced divisor on X . We prove that if the Cartier isomorphism on the log smooth locus of (X,B) extends to the entire X , then (X,B) satisfies the logarithmic extension theorem for differential forms. As an application, we show that the logarithmic extension theorem holds for good quotients of smooth varieties by actions of reduced linearly reductive group schemes. In addition, the logarithmic extension theorem for one-forms holds for singularities of higher codimension under assumptions about Serre’s condition. We also prove that tame quotients satisfy the regular extension theorem.

Analysis of Factors Causing Difficulties in Use of Rice Land in the Irrigation Area of the Tojo Region and West Tojo

In one of the areas in Tojo Una-Una Regency, the rice fields are irrigated rice fields with a surface irrigation system, where the water source comes from a river which flows into the rice fields. However, in the dry season, the water demand for rice fields in these two regions cannot evenly meet the water needs of rice fields in both regions, thus affecting farmers' production results. The aim of this research is to find out what factors make it difficult for farmers to utilize rice fields in the irrigation areas of the Tojo and West Tojo regions and to find out the strategies used by farmers to overcome difficulties in utilizing rice fields in the irrigation areas of the Tojo and West Tojo regions . Respondents in this study were 281 respondents including rice field farmers in the Tojo region and farmers in the West Tojo region. Data analysis uses Factor Analysis. The magnitude of the influence resulting from all these factors reached 62,445%, while the remaining 37,555% was influenced by other factors whose influence was not significant. The strategies implemented by farmers to overcome difficulties in utilizing rice fields in the irrigation areas of Tojo and West Tojo regions include repairing irrigation networks, building groundwater irrigation pumps, improving the quality of farmers' human resources through regular extension activities, arranging planting pattern schedules, changing systems. distributing water during the dry season, and reactivating the P3A (Water User Farmers Association).

Farmers’ preferences for adopting agroforestry in the Eastern Province of Rwanda: A choice experiment

Agroforestry is recognized as an effective land restoration strategy in Rwanda. To effectively implement agroforestry practices, it is crucial to examine and address the preferences of farmers. However, there is limited knowledge concerning farmers’ preferences for different agroforestry characteristics and their level of willingness to engage in such systems. This paper examines farmers’ preferences for adopting agroforestry in the Eastern Province of Rwanda using a discrete choice experiment (DCE) conducted among 248 households. The analysis conducted at plot level included a total of eight attributes: number of fruit trees, number of non-fruit trees, root system and canopy, change in maize yield resulting from tree planting, extension assistance, additional labor, distance to the tree nursery, and the cost of tree seedlings. Results indicate that farmers are generally willing to adopt agroforestry practices. They prefer agroforestry systems that incorporate non-fruit and particularly fruit trees, trees with smaller canopies, agroforestry systems with potential to increase maize yields, and regular extension assistance. However, farmers dislike increases in the cost of tree seedlings. Furthermore, findings reveal two distinct latent classes of plots, encompassing 34.5 % (Class 1) and 65.5 % (Class 2) of the plots. Farmers in Class 1 possess plots that are farther away from their homesteads and are indifferent towards the number of trees to be planted but prefer trees that increase maize yields. Farmers in Class 2 exhibit a strong inclination towards planting a greater number of trees that increase maize yields and have a small canopy. The proximity to tree nurseries and the availability of low-cost tree seedlings contribute to the likelihood of tree planting in this class. This study recommends aligning agroforestry-related policies and interventions with the preferences and needs of the farmers, taking into account plot characteristics.

The Effect of Industry Extension Services Project on the Performance of Small and Micro Enterprises

The purpose of the study was to investigate the effect of industry extension service projects on the performance of micro and small enterprises. Thus, the study utilized an explanatory and descriptive research design to achieve the objectives of the research. The study targeted MSEs that had been in operation for more than two years at the time of the study. The research had a total population of 606 MSEs, out of which a sample size of 241 operators was realized using Taro Yamane’s formula. Thus, a stratified sampling technique and simple random sampling were employed to select representative samples. Beside, primary and secondary data were used in the study. The analysis was conducted using SPSS version 20 on 223 fully responded questionnaires. The data was analyzed using descriptive and inferential statistics. In addition to this, correlation and regression models were used to analyze the variables of the study. The finding proved that IESP support provided by TVET trainers to MSEs was not adequate. Regression analysis indicated that entrepreneurship, technology, kaizen, and technical skill support had a positive and significant relationship with the performance of MSEs. Thus, it is recommended that the TVET College should provide regular industry extension service support to MSEs through four packages.

Factors Influencing Adoption of System of Rice Intensification among Smallholder Farmers in Mvomero District, Tanzania

Adoption of the System of Rice Intensification among Smallholder Farmers (SRI) is important due to its extraordinary potential in production and productivity but there are factors which influence its adoption in different places including Tanzania. This research was conducted in Mvomero District, Morogoro, Tanzania to determine the extent of adoption of innovations in paddy production and analyzed factors influencing this adoption. A cross-sectional research design was adopted and 299 respondents were sampled using simple random technique while the Key Informants were sampled purposively. Data were collected using questionnaire and in-depth interviews. Qualitative data were analyzed using content analysis while quantitative data based on the factors influencing adoption of SRI were analyzed using a Two-limit Tobit model. It was found that Marital status, land ownership, availability of paddy markets, knowledge, age and education level had significant influence on adoption of SRI (p0.05). It is concluded farmers’ knowledge is an important variable in adoption of SRI and hence enhancement of paddy production and productivity. Extension workers are advised to deliver regular extension programmes to farmers to enable them adopt new paddy innovations including SRI. In this case, farmers will be well-informed about the introduced innovations to their setting.

Profinite version of the Beckmann-Black problem

The Beckmann-Black problem asks whether any given finite Galois extension E/K of group G is the specialization at some point t 0 ∈ P 1 ( K ) of some finite regular Galois extension F / K ( T ) with the same group. In this paper, we study a generalization of this problem for infinite extensions, via the profinite twisting lemma, and apply the latter in many situations, like abelian infinite extensions and the l -universal Frattini cover of an arbitrary finite group.

On Some Constructions of Regular Linear Extensions of Dynamical Systems on a Torus

On Some Constructions of Regular Linear Extensions of Dynamical Systems on a Torus

LHS-spectral sequences for regular extensions of categories

LHS-spectral sequences for regular extensions of categories

Synchronizing deterministic push-down automata can be really hard

The question if a deterministic finite automaton admits a software reset in the form of a so-called synchronizing word can be answered in polynomial time. In this paper, we extend this algorithmic question to deterministic automata beyond finite automata. We prove that the question of synchronizability becomes undecidable even when looking at deterministic one-counter automata. This is also true for another classical mild extension of regularity, namely, that of deterministic one-turn push-down automata. However, when we combine both restrictions, we arrive at scenarios with a PSPACE-complete (and hence decidable) synchronizability problem. Likewise, we arrive at a decidable synchronizability problem for (partially) blind deterministic counter automata.There are several interpretations of what synchronizability should mean for deterministic push-down automata. This is depending on the role of the stack: should it be empty on synchronization, should it be always the same or is it arbitrary? For the automata classes studied in this paper, the complexity or decidability status of the synchronizability problem is mostly independent of this technicality, but we also discuss one class of automata where this makes a difference.

Temporal logics with language parameters

We develop a generic framework to extend the logics LTL, CTL+ and CTL⁎ by automata-based connectives from formal language classes and analyse this framework with regard to regular languages, visibly pushdown languages, deterministic and non-deterministic context-free languages. More precisely, we consider how the use of different automata classes changes the expressive power of the logics and provide algorithms for the satisfiability and model checking problems induced by the use of different classes of automata. For the model checking problem, we treat not only finite Kripke transition systems, but also visibly pushdown systems and pushdown systems. We provide completeness or undecidability results in all cases and show that the extensions we consider can formulate properties not expressible in classical temporal logics or regular extensions thereof.

Microstructure and mechanical properties of an ultra-high strength steel fabricated by laser hybrid additive manufacturing

35CrMnSiA is a type of ultra-high-strength steel that finds extensive application in key components characterized by geometrically regular structures and complex extensions, such as structural shells. Laser hybrid additive manufacturing (LHAM) is an advanced manufacturing technology that combines the benefits of traditional manufacturing and additive manufacturing. LHAM has the potential for rapid and cost-effective production of these components. However, the formation mechanism of the microstructure in different zones of 35CrMnSiA steel fabricated by LHAM and its impact on the overall tensile performance remain unclear, thereby tremendously restricting its application. To address this issue, this study employed wrought 35CrMnSiA steel as the base material and utilized directed energy deposition (DED) to fabricate defect-free LHAM parts. The microstructure of LHAM-fabricated 35CrMnSiA steel is location-related. The laser deposition zone comprised ferrite with internal and boundary-distributed carbides, whereas the substrate zone comprised martensite. The heat-affected zone exhibited a gradient microstructure between the two. The microstructure in the deposition zone was primarily governed by solidification behavior and thermal history during the deposition process, while the heat-affected zone was mainly influenced by recrystallization. The non-uniform characteristics of the microstructure significantly influenced its mechanical properties, resulting in a “cask effect,” namely, the tensile performance of LHAM-fabricated 35CrMnSiA steel depended on the weakest laser deposition zone. The ultimate tensile strength and elongation of LHAM-fabricated 35CrMnSiA steel are 959 MP and 15.2%, respectively. This study establishes a basis for controlling the microstructure and optimizing the performance of hybrid-manufactured ultra-high-strength steel.

Smoothing filter design: A general framework

Signal filtering/smoothing is a challenging problem arising in many applications ranging from image, speech, radar and biological signal processing. In this paper, we present a general framework to signal smoothing. The key idea is to use a suitable linear (time-variant or time-invariant) differential equation model in the regularization of an optimization problem. The presented approach has many applications in signal processing. Specifically, the quadratic variation (QV) regularization and smoothness priors are special cases of the proposed framework. These two methods are particularly suited for polynomial signal smoothing, as they use the derivatives of the signal in the regularization term of the optimization problem. Therefore, their performance is significantly decreased for signals that cannot be well modeled with a low order polynomial function. The approach presented in this paper was used to overcome this limitation. As proof of other applications, it was employed for designing an extension of QV regularization to remove the baseline wander in electrocardiogram (ECG), simultaneous tracking of powerline interference and baseline wander, and T-wave amplitude computation.

A validation on concept of formula for variable order integral and derivatives

This paper deals and addresses the query that which of the variable order operators are reasonable and regular extension of constant order operators. An irregularity is pointed out in the definition of variable order operators. We generalize some existing results of constant order to variable order using special functions of fractional calculus. It provides a method for considering the existence of solution for variable order fractional differential equations. Some illustrations are presented to support the validity of variable order operators. Further, we consider an application of a class of fractional initial value problems and provide the criteria of existence and uniqueness of its solution with example.

Representing Paths in Graph Database Pattern Matching

Modern graph database query languages such as GQL, SQL/PGQ, and their academic predecessor G-Core promote paths to first-class citizens in the sense that their pattern matching facility can return paths , as opposed to only nodes and edges. This is challenging for database engines, since graphs can have a large number of paths between a given node pair, which can cause huge intermediate results in query evaluation. We introduce the concept of path multiset representations (PMRs) , which can represent multisets of paths exponentially succinctly and therefore bring significant advantages for representing intermediate results. We give a detailed theoretical analysis that shows that they are especially well-suited for representing results of regular path queries and extensions thereof involving counting, random sampling, and unions. Our experiments show that they drastically improve scalability for regular path query evaluation, with speedups of several orders of magnitude.

On the zero bounds of polynomials and regular functions of a quaternionic variable

In this manuscript, we are concerned with the problem of locating the zeros of some special quaternionic polynomials and regular functions with restricted coefficients; namely quaternionic coefficients whose real components or their moduli satisfy suitable inequalities. The obtained results for this subclass of quaternionic polynomials and regular functions produce extensions of the classical Enestr?om-Kakeya theorem and its various variants from complex to the quaternionic setting.

Статистические ряды РЭБ: обследования промышленных предприятий

Industrial indexes of the Russian Economic Barometer cover a wide range of economic indicators of Russia’s industrial enterprises. The article presents the basic statistical data collected on a monthly, quarterly and semi-annual base by the Russian Economic Barometer through direct surveys of industrial enterprises’ managers. Regular extension of rows allows to consider the dynamics of more than 100 series of indicators, to conduct a comparative analysis of data collected since 1991.

REB Indexes

“REB indexes” cover a wide range of economic indicators of Russian industrial enterprises. The article presents basic statistical data collected on a monthly, quarterly and semi-annual base by the Russian Economic Barometer by means of direct questioning of managers of industrial and agricultural enterprises. Regular extension of rows allows seeing dynamics of more than 70 series of indicators and conducting comparative analysis of data collected since 1991.

Статистические ряды РЭБ: обследования промышленных предприятий

Industrial indexes of the Russian Economic Barometer cover a wide range of economic indicators of Russia’s industrial enterprises. The article presents the basic statistical data collected on a monthly, quarterly and semi-annual base by the Russian Economic Barometer through direct surveys of industrial enterprises’ managers. Regular extension of rows allows to consider the dynamics of more than 100 series of indicators, to conduct a comparative analysis of data collected since 1991.

REB Indexes

“REB indexes” cover a wide range of economic indicators of Russian industrial enterprises. The article presents basic statistical data collected on a monthly, quarterly and semi-annual base by the Russian Economic Barometer by means of direct questioning of managers of industrial and agricultural enterprises. Regular extension of rows allows seeing dynamics of more than 70 series of indicators and conducting comparative analysis of data collected since 1991.

PERAN KELOMPOK USAHA BERSAMA (KUBE) DALAM PEMBERDAYAAN MASYARAKAT NELAYAN DI DESA ALUE NAGA KECAMATAN SYIAH KUALA KOTA BANDA ACEH

The Joint Business Group (KUBE) is one of the fishing community institutions that has a role in developing fisheries and empowerment businesses. KUBE as a non governmental organization to improve the insight and competence of its members in preparing planning, management, and financial arrangements to increase fishermen's income. The purpose of the study was to determine the role of the joint business group (KUBE) in empowering fishing communities in building awareness of the Alu Naga village community. The study used descriptive qualitative research types, observational data collection techniques, interviews. Technical data analysis, data presentation, data verification, and conclusion. The results showed that KUBE provided financial assistance, socialization, training, bout assistance. open opportunities in running a business, increase knowledge and skills in catching fish and so on. Meanwhile, efforts to increase awareness of the fishing community are to make regular extension activities and optimize the capacity of potential fishermen groups to be developed, form fishermen institutions, care for the coastal ecosystem environment, training on the use of fishing technology tools, create new livelihoods as a form of increasing the income of the Alu Naga village community