Monomial Structure Research Articles

Syntactic independent sentence without illocutive force

The article deals with the factors which influence the illocutionary force of the sentence. The syntactically independent sentences are in the focus of the discussion. It is shown that illocutionary force is formed by three factors: communicative binary, semantics of the sentence and temporal reference. They are universal. At the level of the deep structure, sentences, which have illocutionary force include three components: topic, focus and modality. The presence of modal component is not possible without the topic. Sentences without any illocutionary force do not have topicalized components and are incompatible with modal indicators. At the level of the surface structure the absence of illocutionary force is marked by the displacement of the predicate to the initial position, the position of the subject after the predicate or the monomial structure of a sentence. Sentences devoid of illocutionary force in the Russian language are always marked. In German the word order is fixed, therefore, in communicatively monomial sentences, the “shift” of the verb to the first position and the displacement of the referential subject is carried out by using the formal subject es in the preposition. In English, in this case, the initial elements there or it can be used. In proposals of this type, local and time indicators are often shifted to the initial position. Neither local nor temporal indicators can be the subject of a statement: at the beginning of a sentence they mark the absence of illocutionary force. Sentences devoid of illocutionary force serve as the background of the main narrative in the text or initiate the text. At the level of semantics, the sentences of this type are characterized by providing descriptions of nature, weather, situation, state, or act as introductory sentences in microtext or text. When describing states and characteristics, we mostly refer to permanent signs or properties of objects/objects/phenomena in the environment. The factors that shape the illocutionary force of a sentence are universal.

Portuguese for Audit and Accounting: Variability in the Monomial Structure

. The paper considers Portuguese for Audit and Accounting as a specific domain of knowledge and studies the terminological expressions, or terminological collocations, subject to Chernovaty’s classification of terms, or according to Chaika (2019, 2020), linguistic monomials as set term clusters in relevant terminologies, or languages for specific purposes (LSP). In order to demonstrate the application of methodology, this time it is Portuguese for Audit and Accounting, which serves to meet the objectives of the current study. The paper aims to reveal certain approaches to analyse the structure of the monomial in linguistics. Such approaches vary from the structural analysis of the set term cluster (monomial) by the number of components / elements in the structure, morphological class of the head term in the monomial structure, to their role in a sentence under a professional setting, as well as syntactic patterns as basic units of syntax, which are logically, grammatically, and semantically arranged. The result is unique inseparable conceptual (semantic) value of such monomials in Portuguese for Audit and Accounting. The list of approaches to study and analysis of the designated field and the respective material is not exhaustive. The examples of monomials in Portuguese for Audit and Accounting are selected from the Glossary of Terms, the Handbook of International Quality Control, Auditing, Review, Other Assurance, and Related Services Pronouncements validated by the International Auditing and Assurance Standards Board (IAASB). It is revealed that distinct similarities identified in the course of work with Portuguese for Audit and Accounting may take to relevant classifications attributable with the same set of criteria for the Ukrainian, English, German, Spanish languages as representatives of the Slavic, Germanic, and Romance families. The further prospect lies in performing comparative and contrastive analyses of the mentioned language material in respective LSP corpora.

Структура спрощених мономів (мономіалів) в українській мові обліку й аудиту

The present paper is work in progress and closely relates to the earlier introduced idea of monomials and polynomials as substitutes of the term in linguistics when applicable to terminologies. The term of monomial is seen with the following features. Firstly, it refers to specialised terms, which are natural to one domain only. Secondly, a monomial can be either one-word term or two-word term, or three-word and multi-word term as required in a relevant terminology. According to the complexity of the monomial structure, monomials break into simple (one-term terms), simplified (bi-term monomials), compound and complex. The two latter refer to three-term and multi-term monomials that include the core term (the head of the term cluster) and modifiers (dependents), on the one hand, and on the other, the complex monomial at least reflects a two-tier syntactic hierarchical subordinate relations between the core and the modifier. This paper focuses on the simplified monomials that consist of two notional terms only, hence the name, as opposed to mono-term monomials, or one-word terms simple by nature (ways of term coinage). The material of the study is made with the examples of monomials from the Handbook of International Quality Control, Auditing, Review, Other Assurance, and Related Services Pronouncements as translated into Ukrainian (official wording when published and distributed by the Audit Chamber of Ukraine). The Ukrainian monomials in the field of audit and accounting demonstrate a clear distinction between the two major groups of their coinage and structure. One group speaks of the compound nounal nature as the morphological class of the constituent terms is a noun. The other group of simplified monomials in Ukrainian for Audit and Accounting doubles the number of the afore-mentioned and is represented by the morphological pattern of adj. + n in most cases under study.

Sensitivity analysis beyond linearity

A wide array of graphical models can be parametrized to have atomic probabilities represented by monomial functions. Such a monomial structure has proven very useful when studying robustness under the assumption of a multilinear model where all monomials have either zero or one exponents. Robustness in probabilistic graphical models is usually investigated by varying some of the input probabilities and observing the effects of these on output probabilities of interest. Here the assumption of multilinearity is relaxed and a general approach for one-way sensitivity analysis in non-multilinear models is presented. It is shown that in non-multilinear models sensitivity functions have a polynomial form, conversely to multilinear models where these are simply linear. The form of various divergences and distances under different covariation schemes is also formally derived. Proportional covariation is proven to be optimal in non-multilinear models under some specific choices of varied parameters. The methodology is illustrated throughout by an educational application.

On degree bounds for the sparse Nullstellensatz

We prove new upper bounds for the degrees in Hilbert's Nullstellensatz and for the Noether exponent of polynomial ideals in terms of the monomial structure of the polynomials involved. Our bounds improve the previously known bounds in the sparse setting and are the first to take into account the different supports of the polynomials.

Polynomial reduction and evaluation of tree- and loop-level CHY amplitudes

We develop a polynomial reduction procedure that transforms any gauge fixed CHY amplitude integrand for $n$ scattering particles into a $\sigma$-moduli multivariate polynomial of what we call the $\textit{standard form}$. We show that a standard form polynomial must have a specific $\textit{ladder type}$ monomial structure, which has finite size at any $n$, with highest multivariate degree given by $(n-3)(n-4)/2$. This set of monomials spans a complete basis for polynomials with rational coefficients in kinematic data on the support of scattering equations. Subsequently, at tree and one-loop level, we employ the global residue theorem to derive a prescription that evaluates any CHY amplitude by means of collecting simple residues at infinity only. The prescription is then applied explicitly to some tree and one-loop amplitude examples.

Computational Design of Stephenson II Six-Bar Function Generators for 11 Accuracy Points

This paper presents a design methodology for Stephenson II six-bar function generators that coordinate 11 input and output angles. A complex number formulation of the loop equations yields 70 quadratic equations in 70 unknowns, which is reduced to a system of ten eighth degree polynomial equations of total degree 810=1.07×109. These equations have a monomial structure which yields a multihomogeneous degree of 264,241,152. A sequence of polynomial homotopies was used to solve these equations and obtain 1,521,037 nonsingular solutions. Contained in these solutions are linkage design candidates which are evaluated to identify cognates, and then analyzed to determine their input–output angles in each assembly. The result is a set of feasible linkage designs that reach the required accuracy points in a single assembly. As an example, three Stephenson II function generators are designed, which provide the input–output functions for the hip, knee, and ankle of a humanoid walking gait.

Finding All Isolated Zeros of Polynomial Systems inCnvia Stable Mixed Volumes

To find all the isolated zeroes of a polynomial system P(x) inCn (as opposed to in (C*)n) via the polyhedral homotopy of Huber and Sturmfels (1997), one first finds all stable mixed cells in a special polyhedral subdivision called a stable mixed subdivision and creates a fine mixed subdivision for each stable mixed cell. The stable mixed subdivision depends solely on the monomial structure of P and a convex geometric lifting process. One then solves a collection of subsystems corresponding to the stable mixed cells, and uses these solutions as starting points for a finite set of nonlinear homotopies. This final set of homotopies give a dramatic computational improvement over earlier homotopy algorithms, but the initial steps of finding the stable mixed cells and their fine mixed subdivisions require many costly recursive liftings. The purpose of this paper is to present a new strategy using a single lifting which quickly (and simultaneously) builds the stable mixed subdivision, the fine mixed subdivisions of the stable mixed cells, and the necessary subsystems.

A Sparse Effective Nullstellensatz

We present bounds for the sparseness in the Nullstellensatz. These bounds can give a much sharper characterization than degree bounds of the monomial structure of the polynomials in the Nullstellensatz in case that the input system is sparse. As a consequence we derive a degree bound which can substantially improve the known ones in case of a sparse system.In addition we introduce the notion of algebraic degree associated to a polynomial system of equations. We obtain a new degree bound which is sharper than the known ones when this parameter is small. We also improve the previous effective Nullstellensätze in case the input polynomials are quadratic.Our approach is completely algebraic, and the obtained results are independent of the characteristic of the base field.

Homotopies Exploiting Newton Polytopes for Solving Sparse Polynomial Systems

This paper is concerned with the problem of finding all isolated solutions of a polynomial system. The BKK bound, defined as the mixed volume of the Newton polytopes of the polynomials in the system, is a sharp upper bound for the number of isolated solutions in $\mathbb{C}_0^n ,\mathbb{C}_0 = \mathbb{C} \backslash \{ 0\} $, of a polynomial system with a sparse monomial structure. First an algorithm is described for computing the BKK bound. Following the lines of Bernshtei˘n’s proof, the algorithmic construction of the cheater’s homotopy or the coefficient homotopy is obtained. The mixed homotopy methods can be combined with the random product start systems based on a generalized Bezout number. Applications illustrate the effectiveness of the new approach.