Natural Equivalence Research Articles

On state monadic MV-algebras

Monadic MV-algebras are an algebraic model of the predicate calculus of the Łukasiewicz infinite valued logic in which only a single individual variable occurs. In this paper, we extend monadic MV-algebras with a state operator that describes algebraic properties of states. The resulting variety of algebras will be called state monadic MV-algebras. First, we introduce state monadic MV-algebras and establish a natural equivalence between the category of state monadic MV-algebras and the category of state monadic ℓ-groups with strong units. Moreover, we prove that the class of all state monadic ideals in state monadic MV-algebras is a complete Heyting algebra. In particular, by studying extended state monadic ideals, we prove that the set of all stable state monadic ideals in state monadic MV-algebras is a complete Heyting algebra. Also, the class of all involutory state monadic ideals in state monadic MV-algebras is a complete Boolean algebra. Finally, we introduce and characterize some members in the variety of state monadic MV-algebras, which are subdirectly irreducible, simple, semisimple, local and semilocal, respectively.

Translation of Long Sentences in Engineering Contracts under the Theory of Functional Equivalence: Taking FIDIC Conditions of Contract for Construction (Red Book) as an Example

The FIDIC (Fédération lnternationale Des lngénieurs Conseils) Conditions of Contract for Construction are widely used in international engineering contracts, and their translation also plays an active role in the construction of China's own engineering contract texts. Due to the complexity and variety of the logical levels and modifiers, understanding and translation have become a major challenge. This paper will use functional equivalence theory as the theoretical guide, take the English and Chinese versions of FIDIC Conditions of Contract for Construction (1999 Red Book) as the main research text, analyze the long sentences of FIDIC Conditions of Contract for Construction and its translation techniques in Chinese translation, and explore how Chinese translation can deal with complex long sentences to achieve the closest and most natural equivalence between the target language and the source language.

Прескриптивный и дескриптивный перевод идиоматических выражений с русского языка на английский

The aim of the paper is to study the patterns and distinctive features of prescriptive and descriptive translation forms of idiomatic transfer from Russian into English. The scientific novelty lies in the identification of fundamental differences regarding the prescriptive and descriptive approaches to the translation of idiomatic expressions from Russian into English. This makes it possible to present translation as a constant process of renewal, affecting the gap between said compared languages and cultures. As a result, some issues in the understanding of the theory of natural and artificial (arbitrary, directed) equivalence are identified. Thus, equivalence in prescriptive translation studies is considered as natural, while in descriptive – as directed/oriented. At the same time, in descriptive translation studies, the theory of equivalence is controversial in many aspects, since the norms of adaptive translation in the linguistic and cultural space of intercultural communication are not fully defined. If two components are the most important for prescriptive translation: similarity and difference, then in descriptive translation, a key role is assigned to mediation in intercultural interaction.

Equivalences of words in source and target languages ​​in translation (په ژباړه کې د مبدا او موخنې ژبې د کلمو تعادل)

In translation, the principle of equivalence is still significant, and this principle is divided into details, one of which is the equivalence of words. Linguistic elements and especially words cannot study simply and singly, but are related to the culture, values, experiences, and environment of a language, because of this, the discussion of the equivalence of words in translation becomes complicated. Words have different meanings, sometimes words convey the primary meaning, sometimes their meaning becomes implicated, and when it comes to other words change their meaning. Sometimes it happens that the same word has opposite meanings in two places, so it is important for the translator to understand these meanings and find an alternative for them in the target language. In the discussion of word equivalence, it is not necessary to find one word for the source language word in the target language, but the important thing is that the cooperation of one or more words has the same role and meaning value as in the source language, it must also have in the target language. Accordingly, sometimes a word of the source language becomes several words in the target language, sometimes it becomes a sentence or sentences and even long descriptions. Sometimes the translator needs to borrow the word of the source language and sometimes needs to explain this borrowed word. It also happens that a word of the source language is equivalent to a word of the target language, but it is necessary to add an adverb or another word. Accordingly, the translator should understand all these nuances and use them for a better translation. Keywords: Equivalence, natural equivalence, lateral equivalence, source language, target language, meaning of words

On natural invariants and equivalence of differential operators

We give a description of the field of rational natural differential invariants for a class of nonlinear differential operators of order k≥2 on an n-dimensional manifold, n≥2, and apply the results to the equivalence problem of such operators.

The smallest bimolecular mass-action system with a vertical Andronov–Hopf bifurcation

We present a three-dimensional differential equation, which robustly displays a degenerate Andronov–Hopf bifurcation of infinite codimension, leading to a center, i.e., an invariant two-dimensional surface that is filled with periodic orbits surrounding an equilibrium. The system arises from a three-species bimolecular chemical reaction network consisting of four reactions. In fact, it is, up to a natural equivalence, the only such mass-action system that admits a center via an Andronov–Hopf bifurcation.

Natural Differential Invariants and Equivalence of Third Order Nonlinear Differential Operators

Natural Differential Invariants and Equivalence of Third Order Nonlinear Differential Operators

Geodesic Growth of Numbered Graph Products

In this paper, we study geodesic growth of numbered graph products; these are a generalization of right-angled Coxeter groups, defined as graph products of finite cyclic groups. We first define a graph-theoretic condition called link-regularity, as well as a natural equivalence amongst link-regular numbered graphs, and show that numbered graph products associated to link-regular numbered graphs must have the same geodesic growth series. Next, we derive a formula for the geodesic growth of right-angled Coxeter groups associated to link-regular graphs. Finally, we find a system of equations that can be used to solve for the geodesic growth of numbered graph products corresponding to link-regular numbered graphs that contain no triangles and have constant vertex numbering.

The smallest bimolecular mass action reaction networks admitting Andronov–Hopf bifurcation

We address the question of which small, bimolecular, mass action chemical reaction networks (CRNs) are capable of Andronov–Hopf bifurcation (from here on abbreviated to ‘Hopf bifurcation’). It is easily shown that any such network must have at least three species and at least four irreversible reactions, and one example of such a network with exactly three species and four reactions was previously known due to Wilhelm. In this paper, we develop both theory and computational tools to fully classify three-species, four-reaction, bimolecular CRNs, according to whether they admit or forbid Hopf bifurcation. We show that there are, up to a natural equivalence, 86 minimal networks which admit nondegenerate Hopf bifurcation. Amongst these, we are able to decide which admit supercritical and subcritical bifurcations. Indeed, there are 25 networks which admit both supercritical and subcritical bifurcations, and we can confirm that all 25 admit a nondegenerate Bautin bifurcation. A total of 31 networks can admit more than one nondegenerate periodic orbit. Moreover, 29 of these networks admit the coexistence of a stable equilibrium with a stable periodic orbit. Thus, fairly complex behaviours are not very rare in these small, bimolecular networks. Finally, we can use previously developed theory on the inheritance of dynamical behaviours in CRNs to predict the occurrence of Hopf bifurcation in larger networks which include the networks we find here as subnetworks in a natural sense.

The Hurwitz existence problem for surface branched covers

To a branched cover f:Σ ˜→Σ between closed surfaces one can associate a combinatorial datum given by the topological types of Σ ˜ and Σ, the degree d of f, the number n of branching points of f, and the n partitions of d given by the local degrees of f at the preimages of the branching points. This datum must satisfy the Riemann-Hurwitz condition plus some extra ones if either Σ or both Σ and Σ ˜ are non-orientable. A very old question posed by Hurwitz [14] in 1891 asks whether a combinatorial datum satisfying these necessary conditions is actually realizable (namely, associated to some existing f) or not (in which case it is called exceptional). Or, more generally, to count the number of realizations of the datum up to a natural equivalence relation. Many partial answers have been given to the Hurwitz problem over the time, but a complete solution is still missing. In this short course we will report on ancient and recent results and techniques employed to attack the question.

The explanatory power of descriptive translation studies in the machine translation era

ABSTRACT Machine translation (MT) accounts for the largest, and increasingly growing, proportion of translated text produced today, yet the most influential theoretical frameworks developed in translation studies had preceded the contemporary MT era by decades. The question arises as to whether these theories are well-equipped to capture the makeup of today's corpus-based MT. The current article examines and compares the explanatory power of different theoretical frameworks with regard to MT processes and phenomena. The article discusses the incongruences between corpus-based MT algorithms and major paradigms of (human) translation such as natural equivalence, Skopos theory, and poststructuralist approaches. The article then argues that Descriptive Translation Studies (DTS), in its classic formulation introduced and advanced by Gideon Toury, is the theoretical approach that best corresponds to, and is the most useful framework for conceptualizing, the features of corpus-based MT – and, consequently, of an overwhelming proportion of the translation produced today for multilingual communication and understanding.

Comparing the Reasoning Capabilities of Equilibrium Theories and Answer Set Programs

Answer Set Programming (ASP) is a well established logical approach in artificial intelligence that is widely used for knowledge representation and problem solving. Equilibrium logic extends answer set semantics to more general classes of programs and theories. When intertheory relations are studied in ASP, or in the more general form of equilibrium logic, they are usually understood in the form of comparisons of the answer sets or equilibrium models of theories or programs. This is the case for strong and uniform equivalence and their relativised and projective versions. However, there are many potential areas of application of ASP for which query answering is relevant and a comparison of programs in terms of what can be inferred from them may be important. We formulate and study some natural equivalence and entailment concepts for programs and theories that are couched in terms of inference and query answering. We show that, for the most part, these new intertheory relations coincide with their model-theoretic counterparts. We also extend some previous results on projective entailment for theories and for the new connective called fork.

On uniform f −statistical convergence of sequences of functions

We introduce the notions of uniform f −statistical convergence of sequences and uniform f −statistical Cauchy sequences of functions. The natural equivalence between these two notions, in Banach spaces, is proved. In doing so, we generalize and improve results of Gökhan and Güngör.

Super Graphs on Groups, I

Let G be a finite group. A number of graphs with the vertex set G have been studied, including the power graph, enhanced power graph, and commuting graph. These graphs form a hierarchy under the inclusion of edge sets, and it is useful to study them together. In addition, several authors have considered modifying the definition of these graphs by choosing a natural equivalence relation on the group such as equality, conjugacy, or equal orders, and joining two elements if there are elements in their equivalence class that are adjacent in the original graph. In this way, we enlarge the hierarchy into a second dimension. Using the three graph types and three equivalence relations mentioned gives nine graphs, of which in general only two coincide; we find conditions on the group for some other pairs to be equal. These often define interesting classes of groups, such as EPPO groups, 2-Engel groups, and Dedekind groups. We study some properties of graphs in this new hierarchy. In particular, we characterize the groups for which the graphs are complete, and in most cases, we characterize the dominant vertices (those joined to all others). Also, we give some results about universality, perfectness, and clique number.

Natural differential invariants and equivalence of nonlinear second order differential operators

We give a description of the field of rational natural differential invariants for a class of nonlinear differential operators of the second order and show their application to the equivalence problem of such operators.

On the Subgroups Lattice and Fuzzy Subgroups of Finite Groups U 6n

In this paper, we treat accounting for the number of fuzzy (normal) subgroups of finite groups . In order to do this, we use the natural equivalence relation on the set of fuzzy (normal) subgroups of , which has a consistent group theoretical foundation. In fact, the corresponding equivalence classes of fuzzy (normal) subgroups of are closely connected to the structure of (normal) subgroups lattice of and chains of subgroups of , which terminate in . In this regards, the Inclusion-Exclusion principle plays an essential role and in some situations leads to recurrence relations, whose their solutions can be easily found.

Internal Cat-1 and XMod

In this study, internal categories in the category of cat-1 groups, 1-cat, are determined, and it is investigated whether there is a natural equivalence between the category of these categories and the category of internal categories within the category of crossed modules of groups, XMod.

$${ \mathsf {TQ} }$$-completion and the Taylor tower of the identity functor

The goal of this short paper is to study the convergence of the Taylor tower of the identity functor in the context of operadic algebras in spectra. Specifically, we show that if $A$ is a $(-1)$-connected $\mathcal{O}$-algebra with $0$-connected $\mathsf{TQ}$-homology spectrum $\mathsf{TQ}(A)$, then there is a natural weak equivalence $P_\infty$(id)$A\simeq A_\mathsf{TQ}^\wedge$ between the limit of the Taylor tower of the identity functor evaluated on $A$ and the $\mathsf{TQ}$-completion of $A$. Since, in this context, the identity functor is only known to be $0$-analytic, this result extends knowledge of the Taylor tower of the identity beyond its "radius of convergence."

On monic abelian cubics

In this paper, we prove the assertion that the number of monic cubic polynomials $F(x) = x^3 + a_2 x^2 + a_1 x + a_0$ with integer coefficients and irreducible, Galois over ${\mathbb {Q}}$ satisfying $\max \{|a_2|, |a_1|, |a_0|\} \leq X$ is bounded from above by $O(X (\log X)^2)$. We also count the number of abelian monic binary cubic forms with integer coefficients up to a natural equivalence relation ordered by the so-called Bhargava–Shankar height. Finally, we prove an assertion characterizing the splitting field of 2-torsion points of semi-stable abelian elliptic curves.

Rings of Multisets and Integer Multinumbers

In the paper, we consider a ring structure on the Cartesian product of two sets of integer multisets. In this way, we introduce a ring of integer multinumbers as a quotient of the Cartesian product with respect to a natural equivalence. We examine the properties of this ring and construct some isomorphisms to subrings of polynomials and Dirichlet series with integer coefficients. In addition, we introduce finite rings of multinumbers “modulo (p,q)” and propose an algorithm for construction of invertible elements in these rings that may be applicable in Public-key Cryptography. An analog of the Little Fermat Theorem for integer multinumbers is proved.