Unary Operation Research Articles

Asymmetric interval numbers: A new approach to modeling uncertainty

This paper introduces Asymmetric Interval Numbers (AINs), a novel type of interval numbers that combines the straightforward identification characteristic of classical interval numbers with the advanced capability for modeling uncertainty found in fuzzy sets, all while maintaining simplicity. AINs incorporate the expected value within the interval, providing a more accurate representation of the uncertainty of the data compared to the classical interval numbers. We define basic arithmetic operations for AINs, discuss their properties, and provide proofs. Additionally, we present theorems on symmetry and asymmetry for fundamental binary and unary operations, enhancing the mathematical framework for AINs. Several illustrative examples demonstrate the practical application of AINs. Although challenges remain, such as exploring performance with different distributions and reducing overestimation, AINs present a promising advancement in interval arithmetic. This study underscores the practical and theoretical implications of AINs, paving the way for further research and application in diverse scientific and industrial contexts.

Per Segment Plane Sweep Line Segment Intersection on the GPU

Polygon overlay operations are used for various purposes such as GIS searches and queries, VLSI and basic geometric operations of intersection, union and difference. There have been recent research articles presenting algorithms using the GPU to perform line segment intersection for geometric operations. We present two parallel algorithms implemented on the GPU that focus on the active list portion of the traditional serial plane sweep algorithm. The first algorithm uses a single block of threads to simulate the active list data structure in hardware; this algorithm is slow due to GPU thread block size limitations and synchronization points, but demonstrates favorable time complexity. The second algorithm uses dynamic parallelism to remove synchronization and scales to utilize available GPU hardware (single GPU). We perform experiments on both synthetic and real world data sets. The presented results show improvement in execution time with respect to recent algorithms, and low memory usage compared to recent algorithms. We achieve speedups of up to 38.8 over the serial sweep line algorithm on real world data.

Specifics of the Constitutional Right to Establish and Operate the Trade Unions

Introduction. In the framework of the legal regulation of the trade union activities in Russia, a number of regulations cause certain contradictions with regard to establishment of the social and labour relations. Difficulties in interaction of the trade unions with the employers and the state, supplemented by the competition with the private labour, arise the problem of preserving the institution under study as the one aimed at the formation of a system of social partnership, development of the labour environment, national economy and social equality. Therefore, the research strives to investigate the constitutional requirements for establishment and operation of the trade unions to enable harmonization of the social and labour relations. By finding the legislative gaps in the process of implementing the rights of citizens to establish and operate the trade unions, it is possible to modernize the regulatory legal institutions in this field. The aim of the research is to study the specifics of the constitutional right to establish and operate the trade unions.Materials and Methods. The methodological framework was organised based on the selection, analysis and systematisation of the relevant regulatory and legal data and research works in the subject area. The use of a set of general scientific (dialectical, logical, systemic) and specific scientific methods of cognition (comparative legal, dogmatic legal, sociolegal) made it possible to study the principles of state regulation of the trade union activities, identify the gaps in their work and shortcomings due to be eliminated, as well as to summarise the factors of applicability of the constitutional operational procedure to the activities of the trade union organisations in Russia.Results. The constitutional right to establish and operate the trade unions has been analysed. It has been acknowledged that determination of the legal advantages of the trade union members does not correlate with the process of declining the popularity of this institution in the Russian Federation. It has been revealed that this trend is caused by the several problems, i.e.: the multiplicity of the legislative requirements creates a number of contradictions in the relations between the trade unions and employers preventing the full freedom of organisations’ activities; the process of establishing the trade unions is complicated by the need to incorporate the legal entity, the legislative predetermination and formality do not give freedom to the organisations in compiling the charter and making changes to it without permission of the state; the principles of the internal relations regulation must comply with the standard provisions of the Labour Code of the Russian Federation, which also limits the trade union activity; the court defence of the rights of the trade union members needs to be revised and modernized to eliminate the ambiguous provisions and reduce the bureaucratic processes. The use of the variable collective agreements and principles of social partnership aimed at harmonisation of the social and labour relations have been proposed as the solutions to the identified problems.Discussion and Conclusion. The study has identified the key issues and underdeveloped aspects of the constitutional regulation of the trade union activities in the Russian Federation, which could be solved through the optimisation of the excessive legislative requirements, issuing the updated provisions on court defence of the trade union members, establishing the full independence and autonomy of such organisations in the matters of internal regulation, as well as through the development of the system of social partnership. The theoretical and practical conclusions drawn in the paper could be used for further research in the field of improving the legal literacy of the trade union members.

Double domination number of graphs generated from unary products

A subset $S$ of $V(G)$ is a double dominating set of a graph $G$ if $S$ dominates every vertex of $G$ at least twice. The minimum cardinality of a double dominating set denoted by $\gamma_{2\times}(G)$, is the double domination number of $G$. In this paper, we identified the double domination number of graphs generated by applying various unary operations on standard graph classes.

Modal weak Kleene logics: axiomatizations and relational semantics

Abstract Weak Kleene logics are three-valued logics characterized by the presence of an infectious truth-value. In their external versions, as they were originally introduced by Bochvar [4] and Halldén [30], these systems are equipped with an additional connective capable of expressing whether a formula is classically true. In this paper we further expand the expressive power of external weak Kleen logics by modalizing them with a unary operator. The addition of an alethic modality gives rise to the two systems $\textsf{B}_{\text{e}}^{\square }$ and $\textsf{PWK}^{\Box }_{\text{e}} $, which have two different readings of the modal operator. We provide these logics with a complete and decidable Hilbert-style axiomatization w.r.t. a three-valued possible worlds semantics. The starting point of these calculi are new axiomatizations for the non-modal bases $\textsf{B}_{\text{e}}$ and $\textsf{PWK}_{\text{e}}$, which we provide using the recent algebraization results about these two logics. In particular, we prove the algebraizability of $\textsf{PWK}_{\text{e}}$. Finally some standard extensions of the basic modal systems are provided with their completeness results w.r.t. special classes of frames.

Binary distinguishability operation

This paper analyzes a new distinguishability operation for finite deterministic machines and languages. The research was inspired by the “Gedanken experiments” on sequential machines performed by Moore in 1956, and extends the study of the unary distinguishability operation to a binary one. Besides studying the new operation's properties, we give a tight bound of its state complexity on regular languages, including the case for finite languages.

“Beyond the literal meaning” processing implied emotion in second language discourse: an ERP study

ABSTRACT Emotion is processed incrementally during sentence comprehension in a first language (L1) due to unification operations. Since processing multiple types of information is cognitively more demanding in a second language (L2), we investigated implied emotion processing in L1 and L2 using event-related brain potentials. We presented native Spanish speakers with sentences whose context rendered neutral words either negative-congruent, neutral-congruent or neutral-incongruent in Spanish (L1) and English (L2). Results showed differences in early emotion processing across languages: a larger N100 for neutral than negative sentences in L1 and a more positive P300 for negative than neutral sentences in L2. Effects in the N400 and LPP time windows were not language dependent. An N400 semantic incongruity effect was present in both languages. A gradual LPP effect was larger for negative than incongruent sentences in both languages, with neutral sentences in between. Results indicate early time-window differences in implied emotion processing across languages.

New Type of Extended Soft Set Operation: Complementary Extended Union Operation

Soft set theory was proposed by Molodtsov in 1999 to model some problems involving uncertainty. It has a wide range of theoretical and practical applications. Soft set operations constitute the basic building blocks of soft set theory. Many kinds of soft set operations have been described and applied in various ways since the inception of the theory. In this paper, to contribute to the theory, a new soft set operation, called complementary extended union operation, is defined, its properties are discussed in detail to obtain the relationship of each operation with other soft set operations, and the distributions of these operations over other soft set operations are examined. We obtain that the complementary extended union operation along with other certain types of soft set operations construct some well-known algebraic structure such as Boolean Algebra, De Morgan Algebra, semiring, and hemiring in the set of soft sets with a fixed parameter set. Since Boolean Algebra is fundamental in digital logic design, computer science, information retrieval, set theory and probability; De Morgan Algebra in logic and set theory, computer science, artificial intelligence, circuit design; semirings in theoretical computer science, optimization problems, economics, cryptography and coding theory, and hemirings in combinatorics, mathematical economics, theoretical computer science, these algebraic structures provide essential tools for various applications, facilitating the analysis, design, and optimization of systems across many disciplines, and thus this study is expected to contribute to decision-making methods and cryptography based on soft sets.

Decompositions of multiplicative semigroups of m-domain rings and reduced Rickart rings

The main result of this article is that the multiplicative semigroup of an m-domain ring is a strong semilattice of certain subsemigroups, each of which turns out to be a \rcancellative\ monoid, and that this presentation of the semigroup as a strong semilattice of \rcancellative\ semigroups is essentially unique. As a consequence, it is shown that, given an m-domain ring $ \ang{R,+,\cdot} $ with the unary operation $ \dop{} $ mapping every element to its minimal idempotent duplicator (in the sense of N.V.~Subrahmanyam), the algebra $ \ang{R,\cdot,\dop{}} $ is a strong semilattice of \rcancellative\ \dsemigroup s (in the sense of T.~Stokes), also essentially unique. Implications for reduced Rickart rings, which can be seen as a subclass of m-domain rings, are also described.

Unary Operations on Homogeneous Coordinates in the Plane of a Triangle

Suppose that X is a triangle center with homogeneous coordinates (barycentric or trilinear) x:y:z. Eight unary operations discussed in this paper include u1(X)=(y−z)/x:(z−x)/y:(x−y)/z. For each ui, there exist, formally, two points, P and U, such that ui(P)=ui(U)=X. To such pairs of inverses are applied nine binary operations, each resulting in a triangle center. If L is a line, then formally, ui(L) is a cubic curve that passes through the vertices A,B,C. If L passes through the point 1:1:1 (the centroid or incenter, assuming that the coordinates are barycentric or trilinear), then the cubic is degenerate as the union of a parabola and the line at infinity. The methods in this work are largely algebraic and computer-dependent.

Renovation of the content and mode of operation of the Ho Chi Minh communist youth union contributes to improving the quality of young human resources in the context of digital transformation

Renovation of the content and mode of operation of the Ho Chi Minh communist youth union contributes to improving the quality of young human resources in the context of digital transformation

Varieties defined by basic equations have the amalgamation property

A variety is a class of algebraic structures axiomatized by a set of equations. An equation is basic if there is at most one occurrence of a nonnullary operation symbol on each side. We show that a variety axiomatized by basic equations has the strong amalgamation property. Suppose further that the language has no constant symbol and, for each equation, either one side is operation-free, or exactly the same variables appear on both sides. Then also the joint embedding property holds, hence if the language is finite we get the existence of Fraïssé limits for finite algebras. Examples include virtually all the varieties defining classical Maltsev conditions. In a few special cases, the above properties are preserved when further unary operation symbols appear in the equations.

How a System Is Closing the Evidence-Based Data Management Gap.

To translate raw data into information that is understandable and actionable, healthcare leaders must leverage decision-making tools that can drive strategic innovation, improve processes, and shape the future of healthcare. Continuous changes in healthcare delivery require constant monitoring of an expanding range of data. Population demographics, psychographics, and availability of care all must be considered, as well as provider practice patterns, patient utilization, clinical and service quality, costs, and many other key variables over time. RWJBarnabas Health is navigating significant changes in its approach to managing data. A unified operating model is driving standardization, continuous quality improvement, and cost reductions across the system. The solution is based on an electronic health record system designed to meet the needs of the entire system, an array of carefully selected external data sources, and a business intelligence tool to enable leaders to quickly draw insights from all the available data.

How Should the Benefits and Burdens Arising from the Eurozone Be Distributed amongst Its Member States?

How Should the Benefits and Burdens Arising from the Eurozone Be Distributed amongst Its Member States?

Advanced Sea Ice Modeling for Short-Term Forecasting for Alaska’s Coasts

Abstract In Alaska’s coastal environment, accurate information of sea ice conditions is desired by operational forecasters, emergency managers, and responders. Complicated interactions among atmosphere, waves, ocean circulation, and sea ice collectively impact the ice conditions, intensity of storm surges, and flooding, making accurate predictions challenging. A collaborative work to build the Alaska Coastal Ocean Forecast System established an integrated storm surge, wave, and sea ice model system for the coasts of Alaska, where the verified model components are linked using the Earth System Modeling Framework and the National Unified Operational Prediction Capability. We present the verification of the sea ice model component based on the Los Alamos Sea Ice Model, version 6. The regional, high-resolution (3 km) configuration of the model was forced by operational atmospheric and ocean model outputs. Extensive numerical experiments were conducted from December 2018 to August 2020 to verify the model’s capability to represent detailed nearshore and offshore sea ice behavior, including landfast ice, ice thickness, and evolution of air–ice drag coefficient. Comparisons of the hindcast simulations with the observations of ice extent presented the model’s comparable performance with the Global Ocean Forecast System 3.1 (GOFS3.1). The model’s skill in reproducing landfast ice area significantly outperformed GOFS3.1. Comparison of the modeled sea ice freeboard with the Ice, Cloud, and Land Elevation Satellite-2 product showed a mean bias of −4.6 cm. Daily 5-day forecast simulations for October 2020–August 2021 presented the model’s promising performance for future implementation in the coupled model system. Significance Statement Accurate sea ice information along Alaska’s coasts is desired by the communities for preparedness of hazardous events, such as storm surges and flooding. However, such information, in particular predicted conditions, remains to be a gap. This study presents the verification of the state-of-art sea ice model for Alaska’s coasts for future use in the more comprehensive coupled model system where ocean circulation, wave, and sea ice models are integrated. The model demonstrates comparable performance with the existing operational ocean–ice coupled model product in reproducing overall sea ice extent and significantly outperformed it in reproducing landfast ice cover. Comparison with the novel satellite product presented the model’s ability to capture sea ice freeboard in the stable ice season.

On undecidability of unary non-nested PFP-operators for one successor function theory

We investigate the decidability of first-order logic extensions. For example, it is established in A. S. Zolotov’s works that a logic with a unary transitive closure operator for the one successor theory is decidable. We show that in a similar case, a logic with a unary partial fixed point operator is undecidable. For this purpose, we reduce the halting problem for the counter machine to the problem of truth of the underlying formula. This reduction uses only one unary non-nested partial fixed operator that is applied to a universal or existential formula.

MATHEMATICAL MODEL OF ECONOMIC INFORMATION

This article shows that economic information can be formally described using an information field, which is a topological space with an introduced system of subsets that is closed with respect to the union operation. This system of subsets consists of information quanta - sets of information that can be used by a subject when making economic decisions. On this information field, a set function is introduced, defined on information quanta, which has the meaning of the economic value of the information quanta when the subject solves an economic problem. Many economic problems can be described by optimization problems, when a subject need to make a certain choice from a set of feasible solutions, and by game-theoretic models, when it is necessary to choose the best strategy in the face of opposition from other subjects. For these models, it is shown how a function can be constructed to evaluate the economic usefulness of information quanta.

On the Network Index of MAS with Layered Lattice-like Structures of Multiple Vertex-Related Parameters

In this article, a robust index named first-order network coherence (FONC) for the multi-agent systems (MASs) with layered lattice-like structure is studied via the angle of the graph spectra theory. The union operation of graphs is utilized to construct two pairs of non-isomorphic layered lattice-like structures, and the expression of the index is acquired by the approach of Laplacian spectra, then the corresponding asymptotic results are obtained. It is found that when the cardinality of the node sets of coronary substructures with better connectedness tends to infinity, the FONC of the whole network will have the same asymptotic behavior with the central lattice-like structure in the considered classic graph frameworks. The indices of the networks were simulated to illustrate the the asymptotic results, as described in the last section.

A practical algorithm for the design of multiple-sized porous scaffolds with triply periodic structures

In this study, we present a practical volume-merging method for generating multiple-sized porous structures that exhibit geometries with triply periodic minimal surface (TPMS) lattice structures. The proposed method consists of three stages: (1) designing the physical models with a signed distance field, (2) performing a merging operation for the porous scaffolds, and (3) assembling different units into a composite structure. The significant advantages of the proposed algorithm can be summarized as follows: Our method is independent of the model shape; the designed structures maintain a smooth surface with a constant mean curvature, and the mathematical computational complexity is low. We can join two different-sized triply periodic minimal surface lattices in the radial direction, where the transition region is obtained by smooth interpolation between the two lattice structures with different cell sizes or types. However, constructing large-sized models is only conceptually possible due to computational cost and memory storage constraints. To overcome these limitations, we present a practical method that can efficiently assemble large-scaled models at a low computational cost. The proposed method is based on a Boolean union operation of basic units of TPMS. Thus, it is simple to generate large-scale three-dimensional multiple-sized porous volumes based on our proposed method, which can be applied to many applications in mechanical and electrical engineering. The produced multi-scale compound scaffolds have smooth surfaces without fractures, making them suitable for straightforward application in additive manufacturing. Several numerical tests are conducted to validate the efficiency of the proposed algorithm.

Varieties of unary-determined distributive $\ell$-magmas and bunched implication algebras

A distributive lattice-ordered magma ($d\ell$-magma) $(A,\wedge,\vee,\cdot)$ is a distributive lattice with a binary operation $\cdot$ that preserves joins in both arguments, and when $\cdot$ is associative then $(A,\vee,\cdot)$ is an idempotent semiring. A $d\ell$-magma with a top $\top$ is unary-determined if $x{\cdot} y=(x{\cdot}\!\top\wedge y)$ $\vee(x\wedge \top\!{\cdot}y)$. These algebras are term-equivalent to a subvariety of distributive lattices with $\top$ and two join-preserving unary operations $\mathsf p,\mathsf q$. We obtain simple conditions on $\mathsf p,\mathsf q$ such that $x{\cdot} y=(\mathsf px\wedge y)\vee(x\wedge \mathsf qy)$ is associative, commutative, idempotent and/or has an identity element. This generalizes previous results on the structure of doubly idempotent semirings and, in the case when the distributive lattice is a Heyting algebra, it provides structural insight into unary-determined algebraic models of bunched implication logic. We also provide Kripke semantics for the algebras under consideration, which leads to more efficient algorithms for constructing finite models. We find all subdirectly irreducible algebras up to cardinality eight in which $\mathsf p=\mathsf q$ is a closure operator, as well as all finite unary-determined bunched implication chains and map out the poset of join-irreducible varieties generated by them.