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Recently, a new representation model has been proposed to improve the interpretability and accuracy of Computing with Words (CW) processes, the so-called Extended Comparative Linguistic Expressions with Symbolic Translation (ELICIT). It extends the concept of comparative linguistic expressions based on hesitant fuzzy linguistic term sets into a continuous domain by means of the symbolic translation used in the linguistic 2-tuple model. The aggregation of this kind of information is vital when solving decision making problems, but as the field of ELICIT information is still quite new, not many aggregation operators have been defined for it. Therefore, taking into account the need to deal with the fuzzy representation of ELICIT information for its aggregation, we propose the ELICIT type-1 OWA (ELICIT-t1-OWA) operator based on the equivalent α − level type-1 OWA operator to simplify the CW processes by using ELICIT trapezoidal fuzzy representations. The ELICIT-t1-OWA operator will use interval weights induced by an interval-valued linguistic quantifier to aggregate ELICIT expressions and then its properties will be studied. Additionally, a way to deal with both the weights and arguments of the ELICIT-t1-OWA operator is provided in the form of fuzzy numbers. Finally, a decision making model dealing with ELICIT information that carries out the aggregation by using the proposed ELICIT-t1-OWA operator is developed and a numerical example to show its effectiveness is introduced.

This study aims to develop the notion of general fuzzy automata (GFA) to a new one which is known as “ L B -valued general fuzzy automata”. Instead of the term L B -valued general fuzzy automata, for simplicity, L B -valued GFA is used where B is regarded as a set of propositions about the GFA, in which its underlying structure has been a complete infinitely distributive lattice. Further, L B -valued GFA is scrutinized via different operators and also the interrelationship among these operators is examined. Specifically, it is shown that L B -valued successor, L B -valued predecessor and L B -valued residuated operators play an important role in the algebraic study of L B -valued general fuzzy automaton and that under certain conditions these operators are interrelated. In addition, the concept of a homomorphism between L B -valued general fuzzy automata is introduced and studied. Finally, the concepts of equivalence and congruence are defined, the quotient L B -valued GFA with respect to congruence is formulated and the equivalence between L B -valued GFA and its quotient automaton is proved. To clarify the notions and the results obtained in this study, some examples are submitted as well.

3 Although neither Quirk et al. (1985) nor Halliday and Hasan (1976) use the term discourse markers, I take it as non-controversial that, for the most part, the lexical items they discuss may fairly be described as discourse markers. Whereas Quirk et al. and to a lesser extent Halliday and Hasan are more concerned with how markers function as sentence connectors, the notion of discourse marker is intended to capture how markers operate on the propositional, rhetorical and sequential structure of the discourse as a whole.

Multi-term variable-order fractional differential equations (VO-FDEs) are considered to be one of the tools to illustrate the behavior of transient-regime real-life phenomena precisely. The analytical solutions of VO-FDEs are generally very hard to obtain. Therefore, in this study, an approximation method for the solution of multi-term VO-FDEs is proposed using shifted Chebyshev polynomials of the third kind (SCP3). The method employs the operational matrices of SCP3 to proximate the VO-FDEs with a system of algebraic equations. The solution of which also yields the approximate result for the multi-term VO-FDE. An error analysis is also included. The SCP3 method is examined on several examples demonstrating the precision and prowess of the method.

This paper investigates the stability analysis and stabilization problems for fractional order T-S fuzzy systems via fuzzy Lyapunov functions method. A membership-function-dependent fuzzy Lyapunov function instead of the general quadratic Lyapunov function is employed to obtain the stability and stabilization criteria. Different from the general quadratic Lyapunov function, the fuzzy Lyapunov functions contain the product of three term functions. Since the general Leibniz formula cannot be satisfied for fractional derivative, the current results on the fractional derivative for the quadratic Lyapunov functions can not be extended to the fuzzy Lyapunov functions. Therefore, to estimate the fractional derivative of fuzzy Lyapunov functions, the fractional derivative rule for the product of three term functions is proposed. Based on the proposed fractional derivative rule, the corresponding stability and stabilization criteria are established, which extend the existing results. Finally, two simulation examples are presented to illustrate the effectiveness of the proposed theoretical analysis.

The problem of determining whether a term is an instance of another in the simply typed lambda -calculus, i.e. of solving the equation a=b where a and b are simply typed lambda -terms and b is ground, is addressed. An algorithm that decides whether a matching problem in which all the variables are at most third order has a solution is given. The main idea is that if the problem a=b has a solution, then it also has a solution whose depth is bounded by some integer s depending only on the problem a=b, so a simple enumeration of the substitutions whose depth is bounded by s gives a decision algorithm. This result can also be used to bound the depth of the search tree in Huet's semi-decision algorithm and thus to turn it into an always-terminating algorithm. The problems that occur in trying to generalize the proof given to higher-order matching are discussed. >

1. INTRODUCTION. We present a concise and elementary derivation of the complete asymptotic expansion for the factorial function n!, which we will refer to as Stirling’s series. While there have been numerous published proofs of Stirling’s series and of its classical dominant term given by Stirling’s formula lim n→∞ n!e n n n √ 2πn = 1

The number of solutions to $a^2+b^2=c^2+d^2 \le x$ in integers is a well-known result, while if one restricts all the variables to primes Erdos showed that only the diagonal solutions, namely, the ones with $\{a,b\}=\{c,d\}$ contribute to the main term, hence there is a paucity of the off-diagonal solutions. Daniel considered the case of $a,c$ being prime and proved that the main term has both the diagonal and the non-diagonal contributions. Here we investigate the remaining cases, namely when only $c$ is a prime and when both c,d are primes and, finally, when $b,c,d$ are primes by combining techniques of Daniel, Hooley and Plaksin., Comment: Accepted for a publication in J. Number Theory

Beyond generating long and topic-coherent paragraphs in traditional captioning tasks, the medical image report composition task poses more task-oriented challenges by requiring both the highly-accurate medical term diagnosis and multiple heterogeneous forms of information including impression and findings. Current methods often generate the most common sentences due to dataset bias for individual case, regardless of whether the sentences properly capture key entities and relationships. Such limitations severely hinder their applicability and generalization capability in medical report composition where the most critical sentences lie in the descriptions of abnormal diseases that are relatively rare. Moreover, some medical terms appearing in one report are often entangled with each other and co-occurred, e.g. symptoms associated with a specific disease. To enforce the semantic consistency of medical terms to be incorporated into the final reports and encourage the sentence generation for rare abnormal descriptions, we propose a novel framework that unifies template retrieval and sentence generation to handle both common and rare abnormality while ensuring the semantic-coherency among the detected medical terms. Specifically, our approach exploits hybrid-knowledge co-reasoning: i) explicit relationships among all abnormal medical terms to induce the visual attention learning and topic representation encoding for better topic-oriented symptoms descriptions; ii) adaptive generation mode that changes between the template retrieval and sentence generation according to a contextual topic encoder. Experimental results on two medical report benchmarks demonstrate the superiority of the proposed framework in terms of both human and metrics evaluation., To appear in IEEE Transactions on Cybernetics 2021. We attempt to resolve the challenging medical report composition task by i) enforcing the semantic consistency of medical terms to be incorporated into the final reports; and ii) encouraging the sentence generation for rare abnormal descriptions

Let d \subset d' be finite-dimensional Lie algebras, H = U(d), H'=U(d') the corresponding universal enveloping algebras endowed with the cocommutative Hopf algebra structure. We show that if L is a primitive Lie pseudoalgebra over H then all finite irreducible L' = Cur_H^{H'} L-modules are of the form Cur_H^{H'} V, where V is an irreducible L-module, with a single class of exceptions. Indeed, when L = H(d, \chi, \omega), we introduce non current L'-modules that are obtained by modifying the current pseudoaction with an extra term depending on an element t \in \d' \setminus d, which must satisfy some technical conditions. This, along with results from [BDK1, BDK2, BDK3], completes the classification of finite irreducible modules of finite simple Lie pseudoalgebras over the universal enveloping algebra of a finite-dimensional Lie algebra., Comment: 36 pages

In this paper, we presented a method of minimizing the number of overlapped partial products in the accumulation of four-term Karatsuba multiplication. This method reduced the summation of 13 overlapped partial products to 9 and the summation of 40 overlapped partial products to 24 in the case of four-term Karatsuba multiplication and eight-term Karatsuba multiplication, respectively. Moreover, to deal with the problem of negative multiplicands introduced by the choice in the evaluation of four-term Karatsuba multiplication, we further presented a method of converting negative multiplicands to non-negative multiplicands. In this way, our method would lead to the reduction of summation complexity and not using signed multipliers. Compared to the original Karatsuba multiplication designs, our proposed Karatsuba-like multiplication with optimal interpolation would lead to up to 7.7% reduction in ADP (area-delay-product) in ASIC implementations, and up to 20.2% reduction in ADP compared with built-in designs of Synopsys Design Compiler.

We study growth rates of generalised Fibonacci sequences of a particular structure. These sequences are constructed from choosing two real numbers for the first two terms and always having the next term be either the sum or the difference of the two preceding terms where the pluses and minuses follow a certain pattern. In 2012, McLellan proved that if the pluses and minuses follow a periodic pattern and G n is the nth term of the resulting generalised Fibonacci sequence, then lim n → ∞ ⁡ | G n | 1 / n exists. We extend her results to recurrences of the form G m + 2 = α m G m + 1 ± G m if the choices of pluses and minuses, and of the α m follow a balancing word type pattern.

We investigate the dynamics of a delay differential equation obtained by perturbing a vector field f : R n → R n , admitting a stable periodic orbit, by using a delayed feedback control term η g ( x , x ( t − τ ) ) of same regularity, where η is small and τ large so that ητ be bounded but non small. We prove that trajectories starting in a neighborhood (of size independent of the parameters η , τ ) of this original periodic orbit enter asymptotically a periodic regime, and that the number of such distinct periodic regimes increases (almost) linearly when ητ increases infinitely. Our result is based on the construction of an invariant manifold via a process inspired by the Lyapunov-Perron method for integral operators associated to ordinary differential equations, and on the persistence of normally hyperbolic invariant manifolds for semi-flows on Banach spaces. The statement we provide here complements already known results on periodic orbits of delay differential equations.

We obtain approximation ratio 4 + 2 l ≈ 4 + 4 lg ⁡ k lg ⁡ n − lg ⁡ k for the (undirected) k -Connected Subgraph problem, where l = ⌊ lg ⁡ n − lg ⁡ k + 1 2 lg ⁡ k + 1 ⌋ is the largest integer such that 2 l − 1 k 2 l + 1 ≤ n . For large values of n this improves the ratio 6 of Cheriyan and Vegh [4] when n ≥ k 3 (the case l = 1 ). Our result implies an fpt-approximation ratio 4 + ϵ that matches (up to the “+ϵ” term) the best known ratio 4 for k = 6 , 7 for both the general and the easier augmentation versions of the problem. Similar results are shown for the problem of covering an arbitrary symmetric crossing supermodular biset function.

In this paper we present two deterministic distributed algorithms for the Steiner tree (ST) problem in the CONGEST model. The first algorithm computes a 2 ( 1 − 1 / l ) -approximate ST using O ( S + n log ⁎ ⁡ n ) rounds and O ( m S + n 3 / 2 ) messages for a graph of n nodes and m edges, where S is the shortest path diameter of the graph and l is the number of leaf nodes in the optimal ST. It improves the round complexity of the best distributed ST algorithm known so far, which is O ˜ ( S + min { S t , n } ) [34] , where t is the number of terminal nodes. The second algorithm improves the message complexity of the first one by dropping the additive term of O ( n 3 / 2 ) at the expense of a logarithmic multiplicative factor in the round complexity. We also show that for graphs with S = O ( log ⁡ n ) , a 2 ( 1 − 1 / l ) -approximate ST can be deterministically computed using O ˜ ( n ) rounds and O ˜ ( m ) messages and these complexities almost coincide with the results of some of the singularly-optimal minimum spanning tree (MST) algorithms proposed in [15] , [22] , [37] .

The Qur'an is a guide for humanity that contains everything related to all creatures, it was just that in interpreting the meaning of the Qur'an there are still many who do not know and master the meaning of these verses. The word Al-Nafs is a word found in the Qur'an in various forms. The Qur'an mentions the term Al-Nafs as many as 298 mentions in 270 verses contained in 63 letters. Of the many mentions there are different meanings, namely: the Essence of Allah SWT, the Spirit, the inner side of humans, Person, offspring, the human self and something that refers to what is contained in humans that produces behavior. This research focuses on finding out the term Al-Nafs in the interpretation of Al-Sya'rawi, then examining it to find out how it is interpreted in interpreting the verses related to al-Nafs and how efforts to shape and make al-Nafs itself have a good impact on the community. one's self. In this study, the researcher used a qualitative method, this method was used to give birth to a thought figure from one of the commentators who were studied on a selected theme. And describe the character's thoughts by connecting and returning the original meaning carefully to all data, either in the form of opinions or statements. The research sources consist of the interpretation of Al-Sha'rawi and various literature related to this research.

The article is studied for the first time status of terminological phrases with the basic sema "Erythema" in the structure of the Latin medical terminology.Verbal codification of the selected is traced terminological phrases in modern medical encyclopedic dictionaries. Carried out etymological, morphological, syntactic analysis of binary attributive components of functioning terminological phrases in medical oral and written discourse. Methods research. In the study, the method of continuous sampling, which allowed the selection of actual material; descriptive the method by which the inventory and internalinterpretation of selected terminological phrases; structural method for establishing connections and relationships between linguistic elements. Conclusions. According to the study found that the attributive component in the structure of binary terminological phrases with the basic sema "erythema"outlines the etiological sign, symptoms of the disease, form, consequence, clinical expressiveness, ie, attributive component in each case carries outclassification detail of the denoted phenomenon and thus contributes to the specification of clinical forms of erythema and allows avoid misunderstandings when making a diagnosis. Predominant most terminological phrases with sema "Erythema" consists of binary terminological phrases, formed according to the scheme Subst. nom. sing. + Adject. nom. sing .; model formation of terminological phrases according to the scheme Subst. nom. sing. + Subst. gen. sing./gen. plur. is unproductive; terminological phrases using prepositions refer to unproductive model of term formation.

In this paper we study existence and regularity results for solution to a nonlinear and singular parabolic problem. The model is $$\begin{aligned} \left\{ \begin{array}{lll} \dfrac{\partial u}{\partial t}-\text{ div }((a(x,t)+|u|^{q})\nabla u)=\frac{f}{u^{\gamma }} &{} \text{ in } &{} Q,\\ u(x,t)=0 &{} \text{ on } &{} \Gamma ,\\ u(x,0)=u_{0}(x) &{} \text{ in } &{} \varOmega , \end{array} \right. \end{aligned}$$ where $$\varOmega $$ is a bounded open subset of $$\mathbb {R}^{N},$$ $$N\ge 2,$$ Q is the cylinder $$\varOmega \times (0,T),$$ $$T>0,$$ $$\Gamma $$ the lateral surface $$\partial \varOmega \times (0,T),$$ $$q>0,$$ $$\gamma >0,$$ and f is non-negative function belonging to some Lebesgue space $$L^{m}(Q),$$ $$m\ge 1$$ and $$u_{0}\in L^{\infty }(\varOmega )$$ such that $$\begin{aligned} \forall \; \omega \subset \subset \varOmega ,\; \exists \; D_{\omega }>0: \; u_{0}\ge D_{\omega }\;\; \text{ in }\; \omega . \end{aligned}$$

Since Saul Kripke’s and Hilary Putnam’s groundbreaking work in the Seventies, the idea has emerged that natural kind terms are semantically special among common nouns. Stephen P. Schwartz, for example, has argued that an artifactual kind term like “pencil” functions very differently from a natural kind term like “tiger.” This, however, blatantly violates a principle that I call Semantic Uniformity. In this paper, I defend the principle. In particular, I outline a picture of how natural kind terms function based on Kripke’s and Putnam’s considerations, and I use it to rebut Schwartz’s arguments, showing that if it works for natural kind terms, it can work for artifactual kind terms too (and, arguably, for common nouns in general), or at least that Schwartz did not provide good enough reasons to the contrary.

In this paper, we consider a class of quasilinear Schrodinger-Poisson problems of the form $$\left\{ {\matrix{{ - \left( {a + b\int_{{^N}} {{{\left| {\nabla u} \right|}^2}dx} } \right)\Delta u + V(x)u + \phi u - {1 \over 2}u\Delta ({u^2}) - \lambda {{\left| u \right|}^{p - 2}}u = 0} \hfill & {{\rm{in}}\,\,{\mathbb{R}^N},} \hfill \cr { - \Delta \phi = {u^2},\,\,\,\,\,u(x) \to 0,\,\,\,\,\,\left| x \right| \to \infty } \hfill & {{\rm{in}}\,\,{\mathbb{R}^N},} \hfill \cr {\int_{{\mathbb{R}^N}} {{{\left| u \right|}^p}dx = 1,} } \hfill & {} \hfill \cr } } \right.$$ where a > 0, b ⩾ 0, N ⩾ 3, λ appears as a Lagrangian multiplier, and $$4 < p < 2 \cdot {2^\ast} = {{4N} \over {N - 2}}$$ . We deal with two different cases simultaneously, namely lim∣x∣→∞V(x) = ∞ and lim∣x∣→∞V(x) = V∞. By using the method of invariant sets of the descending flow combined with the genus theory, we prove the existence of infinitely many sign-changing solutions. Our results extend and improve some recent work.

In sociolinguistic studies, language is defined as a symbol system, in the form of sound, arbitrary, productive, dynamic, diverse and human. Understanding of language in the big Indonesian dictionary, understanding language in general can be defined as a symbol, and understanding language according to the term is a communication tool in the form of a system of symbols produced by speech organs in humans. Language is also part of culture and it is language that develops culture as we know it today. Language can also act as a tool for social integration as well as a tool for social adaptation, considering that Indonesian has a pluralistic language. Slang is the typical language of teenagers (words that are changed in such a way that it can only be understood between them) can be understood by almost all teenagers in the country who are reached by the mass media. Yet the terms are evolving, changing and increasing almost every day. Slang is a language that has unique terms, while the second definition is made clear again that it is teenagers who use the language and the language will continue to develop. As for the characteristics of slang, the factors that support the prevalence of slang among teenagers, the influence of slang on Indonesian and the impact of the use of slang.

The paper presents an analysis of the sentence “water is H2O” as a significant example for the theory of meaning, scientific realism and philosophy of chemistry. Subsequent chapters introduce Putnam’s theory of the meaning, referring it to the term “water” understood by scientists and ordinary users of language, possible readings of the sentence “water is H2O” and a critique of Putnam’s example. The author also considers the validity of the example and how to interpret the sentence “water is H2O”. The paper aims to show how we can accept Putnam’s example despite the solid and accurate criticism.

The study of solitons and compactons is important in nonlinear physics. In this paper we combined the Adomian polynomials with the multi-step approach to present a new technique called Multi-step Modified Reduced Differential Transform Method (MMRDTM). The proposed technique has the advantage of producing an analytical approximation in a fast converging sequence with a reduced number of calculated terms. The MMRDTM is presented with some modification of the Reduced Differential Transformation Method (RDTM) with multi-step approach and its nonlinear term is replaced by the Adomian polynomials. Therefore, the nonlinear initial value problem can easily be solved with less computational effort. Besides that, the multi-step approach produces a solution in fast converging series that converges the solution in a wide time area. Two examples are provided to demonstrate the capability and benefits of the proposed method for approximating the solution of NKdVEs with compactons. Graphical inputs are used to represent the solution and to demonstrate the precision and validity of the MMRDTM in graphic illustration. From the results, it was found that it is possible to obtain highly accurate results or exact solutions by using the MMRDTM.

We prove uniform versions of two classical results in analytic number theory. The first is an asymptotic for the number of points of a complete lattice $$\Lambda \subseteq \mathbb {R}^d$$ inside the d-sphere of radius R. In contrast to previous works, we obtain error terms with implied constants depending only on d. Secondly, let $$\phi (s) = \sum _n a(n) n^{-s}$$ be a ‘well behaved’ zeta function. A classical method of Landau yields asymptotics for the partial sums $$\sum _{n < X} a(n)$$ , with power saving error terms. Following an exposition due to Chandrasekharan and Narasimhan, we obtain a version where the implied constants in the error term will depend only on the ‘shape of the functional equation’, implying uniform results for families of zeta functions with the same functional equation.

Being one of the basic didactic terms, “learning” is frequently translated by Russianspeaking researchers as either “obuchenie” or “uchenie”. It seems strange, as these two words are not synonyms in Russian. Moreover, in Russian conventional didactics they denote two different phenomena: “obuchenie” refers to the entire educational process consisting of both the teacher’s and the learner’s activities while “uchenie” corresponds to the latter one. Successful international academic communication presupposes that any terms accepted by English-speaking professionals should be adapted to the national didactic concepts of this or that country. Taking this requirement into account, the author concludes that the only possible equivalent of “learning” in Russian is “uchenie”, not “obuchenie”, while the phrase “the shift from teaching to learning” and the term “student-centred learning” should be translated as “sdvig / perekhod ot prepodavaniya k ucheniyu” and “studentotsentrirovannoe uchenie” respectively. The author comes to the conclusion that student-centred learning (SCL) opposed to student-centred teaching can be considered the highest point in the development of student-centred approach currently prevailing in European countries. SCL as a new type of learning means that the student becomes an active participant in educational process having his (her) own needs and interests in the focus of attention. The substitution of the word “uchenie” by the incorrect variant “obuchenie” existing in the Russian academic discourse nowadays prevents Russian-speaking researchers from seeing clearly the essence of SCL.

In this paper, a second-order Godunov-type finite volume technique based upon the wave propagation algorithm has been defined which mainly addresses second-order, one-dimensional, macroscopic traffic flow models. Four widely used models that have fundamental differences in terms of the equations form were chosen to evaluate this formula. These models use Riemann’s solution propagating different jump discontinuity from each finite-volume cell interface. The proposed modified flux-wave formula is well-balanced and includes the related source term within the flux-differencing from each cell interface. Therefore, no additional numerical treatment is required with respect to the source terms. The numerical results obtained herein have been compared with high-order relaxations schemes including fifth-order WENO and second-order MUSCL (for three models in a straight homogeneous road) and Roe decomposition technique (for two models in a ring road). The results show that the defined approach is capable to provide stable and realistic response for the macroscopic traffic models without numerical diffusion. Additionally, a very good agreement achieved with the reference solution and also higher order schemes. It is also inferred that the plausibility and positivity conserving conditions have been maintained for the modified flux wave approach for all of the examined models.

A formula giving the exact error term for convergents of quadratic numbers is given. This formula is applied to Markoff forms and Markoff irrationalities: characterization of the smallest values of the form (the minimum being the corresponding Markoff number), mapped bijectively to the conjugates of the corresponding Christoffel word; a new proof of the result giving the ranks of the good convergents of the Markoff irrationalities; a refinement of Markoff's classification of the latter numbers. Other applications appear in the article.

In this paper, we study the nonlinear Choquard equation $$\begin{aligned} -\Delta {u}+u=\left( |x-y|^{-\mu }*G(u)\right) g(u),\quad \text {in}\ {\mathbb {R}}^N, \end{aligned}$$ where $$0

In 1993, Shub and Smale posed the problem of finding a sequence of univariate polynomials of degree $N$ with condition number bounded above by $N$. In a previous paper by C. Belt\'an, U. Etayo, J. Marzo and J. Ortega-Cerd\`a, it was proved that the optimal value of the condition number is of the form $O(\sqrt{N})$, and the sequence demanded by Shub and Smale was described by a closed formula (for large enough $N\geqslant N_0$ with $N_0$ unknown) and by a search algorithm for the rest of the cases. In this paper we find concrete estimates for the constant hidden in the $O(\sqrt{N})$ term and we describe a simple formula for a sequence of polynomials whose condition number is at most $N$, valid for all $N=4M^2$, with $M$ a positive integer., Comment: 21 pages

The paper aims to improve the terminology used in dependability-related state standards. Examples are given of the use of the terms “estimate” and “definition” in the “Risk management” and “Dependability in technics” series of state standards. The meanings of those terms were clarified based on the existing regulatory documents. Requirements for the integrity of the used terms were defined. Wordings were proposed for the term definitions that feature the words “estimate” and “definition”. Aim. To examine and discuss the common, but not sufficiently substantiated terms “estimate” and “definition” used in state standards, i.e., to consider the legitimacy of their application as part of the above series of state standards. Proposals as to the improvement of such terms’ application were also set forth. Methods. Examples are given of the use of the terms “estimate” and “definition” in state standards. Based on the existing state standards, the actual meanings of the considered terms were clarified: “definition” refers to the way a term is defined, while “estimate” and “estimation” are closely associated with mathematical statistics. The requirements for the integrity of the used terminology are defined and come down to it being unambiguous, consistent within itself and across the relevant state standards. In this context, the shortcomings of the examined terms are shown that are associated with the above requirements, i.e., the meaning, content, essence and key features of such terms are clearly defined. Any comments or references to other regulatory documents are missing as well. Results. In most standards, in the “Terms and definitions” section, the concept of “definition” is used correctly, i.e., terms are defined. However, in other cases, the concept of “definition” is used in a different sense, as nothing is actually being defined. Based on the term integrity requirements and in light of the above shortcomings, proposed replacements for the terms in question were defined. In most cases, instead of the terms “estimate” and “definition”, it is proposed to use the terms “calculation” and “computation”, as well as their cognates, “calculate”, “compute”. It should be noted that along the state standards, theseterms are used in technical documentation, science papers, monographs and textbooks. Conclusions. The use of the examined terms in some standards lacks integrity. The requirements of the standardization recommendations are not observed, the terms are not unambiguous and consistent with other standards. Based on these requirements, the paper proposes improved ways of using the terms “estimate” and “definition”. The suggested terms should be considered as a tentative proposal. Final definitions and/or replacements of these terms are to be developed through extensive discussion and compromise.

There has been much research about regularizing optimal portfolio selections through $$\ell _1$$ norm and/or $$\ell _2$$ -norm squared. The common consensuses are (i) $$\ell _1$$ leads to sparse portfolios and there exists a theoretical bound that limits extreme shorting of assets; (ii) $$\ell _2$$ (norm-squared) stabilizes the computation by improving the condition number of the problem resulting in strong out-of-sample performance; and (iii) there exist efficient numerical algorithms for those regularized portfolios with closed-form solutions each step. When combined such as in the well-known elastic net regularization, theoretical bounds are difficult to derive so as to limit extreme shorting of assets. In this paper, we propose a minimum variance portfolio with the regularization of $$\ell _1$$ and $$\ell _2$$ norm combined (namely $$\ell _{1, 2}$$ -norm). The new regularization enjoys the best of the two regularizations of $$\ell _1$$ norm and $$\ell _2$$ -norm squared. In particular, we derive a theoretical bound that limits short-sells and develop a closed-form formula for the proximal term of the $$\ell _{1,2}$$ norm. A fast proximal augmented Lagrange method is applied to solve the $$\ell _{1,2}$$ -norm regularized problem. Extensive numerical experiments confirm that the new model often results in high Sharpe ratio, low turnover and small amount of short sells when compared with several existing models on six datasets.

Let $${\mathbb{Z}_m}$$ be the additive group of residue classes modulo m. Let s(m, n) denote the number of subgroups of the group $${\mathbb{Z}_m} \times {\mathbb{Z}_n}$$ , where m and n are arbitrary positive integers. For any x ⩽ 1, we consider the asymptotic behavior of $$D_{s}:=\sum\nolimits_{m^{2}+n^{2}\leqslant x}s(m,n)$$ and obtain an asymptotic formula by using the elementary method.

L’actualité des publications en sociologie vient mettre en question sa capacité à expliquer ce qu’elle prend pour objet sans véritablement définir ce que signifie ce mot, expliquer. Le présent article cherche à répondre aux questions suivantes : qu’est-ce donc qu’expliquer ? Que signifie exactement ce terme associé à la science ? En quoi et pourquoi la visée que sous-tend le mot trouve-t-elle difficilement son droit, ou sa pertinence, en sociologie ? Comment se conçoit l’explication en termes opératoires ? Les réponses avancées ici s’appuient d’abord sur les nuances apportées par l’épistémologie contemporaine à la caractérisation de la science associée aux trois maîtres mots que sont décrire, comprendre et expliquer. L’analyse d’une entrevue qualitative vient ensuite illustrer les opérations en vertu desquelles expliquer devient possible dans cette discipline, dès lors susceptible d’être considérée comme une science, elle-même conçue comme une connaissance par objet, par concept et par méthode.

A key component of mathematical reasoning is the ability to formulate interesting conjectures about a problem domain at hand. In this paper, we give a brief overview of a theory exploration system called QuickSpec, which is able to automatically discover interesting conjectures about a given set of functions. QuickSpec works by interleaving term generation with random testing to form candidate conjectures. This is made tractable by starting from small sizes and ensuring that only terms that are irreducible with respect to already discovered conjectures are considered. QuickSpec has been successfully applied to generate lemmas for automated inductive theorem proving as well as to generate specifications of functional programs. We give an overview of typical use-cases of QuickSpec, as well as demonstrating how to easily connect it to a theorem prover of the user's choice., In Proceedings VPT 2021, arXiv:2109.02001

We report on an inversion tool for a class of oriented conditional constructor term rewriting systems. Four well-behaved rule inverters ranging from trivial to full, partial and semi-inverters are included. Conditional term rewriting systems are theoretically well founded and can model functional and non-functional rewrite relations. We illustrate the inversion by experiments with full and partial inversions of the Ackermann function. The case study demonstrates, among others, that polyvariant inversion and input-output set propagation can reduce the search space of the generated inverse systems., Comment: In Proceedings VPT 2021, arXiv:2109.02001

Chord diagrams and 4-term relations were introduced by Vassiliev in the late 1980. Various constructions of weight systems are known, and each of such constructions gives rise to a knot invariant. In particular, weight systems may be constructed from Lie algebras as well as from the so-called 4-invariants of graphs. A Chmutov–Lando theorem states that the value of the weight system constructed from the Lie algebra $$\mathfrak {sl}_2$$ on a chord diagram depends on the intersection graph of the diagram, rather than the diagram itself. This inspired a question due to Lando about whether it is possible to extend the weight system $$\mathfrak {sl}_2$$ to a graph invariant satisfying the four term relations for graphs. We show that for all graphs with up to 8 vertices such an extension exists and is unique, thus answering in affirmative to Lando’s question for small graphs.

The present paper is devoted to the phenomenon of codification and the main inconsistencies between the theoretical requirements for a term and actual terminological units found in terminological dictionaries of law. The paper presents the analysis of terms used in the legal sphere. The objective of the research is to identify and classify the inconsistencies that have a direct impact on codification as the last stage of the creation of a terminological dictionary. Particular attention is paid to the study of the content plane of legal terms listed in English terminological dictionaries as well as their expression plane. The authors conclude that at both levels (those of the content plane and the expression plane) and at the level of functioning the inconsist- encies raise important issues concerning further development of both terminography as a field of science and the dictionary-making process taking place today.

In this paper, we consider the well-posedness of the inhomogeneous nonlinear biharmonic Schrodinger equation with spatial inhomogeneity coefficient K ( x ) behaves like | x | − b for 0 b min ⁡ { N 2 , 4 } . We show the local well-posedness in the whole H s -subcritical case, with 0 s ≤ 2 . The difficulties of this problem come from the singularity of K ( x ) and the lack of differentiability of the nonlinear term. To resolve this, we derive the bilinear Strichartz's type estimates for the nonlinear biharmonic Schrodinger equations in Besov spaces.

A generalization of the well–known Fibonacci sequence is the l-Fibonacci sequence ( F m ( l ) ) m whose first l terms are 0 , … , 0 , 1 and each term afterwards is the sum of the preceding l terms. The k-Pell sequence ( P n ( k ) ) n , which is a generalization of the classical Pell sequence, can be defined similarly. In this paper, we find all coincidences between these two families of sequences. That is, we find all the solutions of the Diophantine equation P n ( k ) = F m ( l ) in positive integers n , k , m , l with k , l ≥ 2 . This paper continues and extends prior results which dealt with the above problem for some particular cases of k and l. In particular, it extends the previous work [2] that found all Fibonacci numbers in the Pell sequence.

There is a growing interest in the phenomenon of co-predication, where a single NP appears with predicates that have incompatible selectional preferences. The phenomenon suggests that a single NP can stand for at least two entities and so that the truth-conditions of a co-predicative sentence are more complicated than what the surface structure indicates. In this paper, two different kinds of proposals concerning this issue are presented and discussed: conservative approaches that commit to there being just one entity that is referred by a co-predicative term; and non-conservative, but more intuitive approaches, that assign conjunctions of simple truth-conditional contents to co-predicative sentences. Meanwhile, it is argued that, although much is still unknown about co-predication, many approaches coincide in signalling that the different senses of the terms that co-predicate in a stable way are linked by particular metaphysical relations.

Making a rank-one modification on the classical BFGS (Broyden–Fletcher–Goldfarb–Shanno) updating formula, we develop a class of augmented BFGS methods. The suggested formula can be considered as a hybridization of the basic BFGS updating formula for Hessian with an additional rank-one term embedded to guarantee a general modified secant equation. By using the well-known Sherman–Morrison formula, the inverse of a memoryless version of the given updating formula is computed to be applied for solving large-scale problems. Convergence analysis is concisely carried out as well. At last, the practical merits of the method are investigated by numerical tests on a set of CUTEr problems as well as the well-known compressed sensing problem. Results show the computational efficiency of the given method.

This paper analyzes nested-abbreviated terms from a linguistic perspective by describing their morphological, syntactic, and semantic features for terminology purposes. Nested-abbreviated terms can be considered as abbreviated forms, either initialisms or acronyms, which have within their meaning another abbreviated term. To carry out the analysis, 433 nested-abbreviated terms were extracted from two specialized dictionaries in English. Data analysis showed that, from the morphological and semantic perspective, nested-abbreviated terms behave like typical abbreviations. Important differences were found from a syntactic standpoint where nested abbreviated terms behave as premodifiers in the noun phrase (NP) in 98.93% of the cases. As this is the first time nested-abbreviated terms are studied, they were not only described but also analyzed and defined. Although the percentage of nested-abbreviated terms obtained from the dictionaries is relatively low, less than 1% of total abbreviations, it was found that it is highly relevant to study this growing phenomenon in specialized languages for terminology extraction, as well as for other purposes.

In this paper, we study two-term tilting complexes for preprojective algebras of non-Dynkin type. We show that there exist two families of two-term tilting complexes, which are respectively parameterized by the elements of the corresponding Coxeter group. Moreover, we provide the complete classification in the case of affine type by showing that any two-term silting complex belongs one of them. For this purpose, we also discuss the Krull-Schmidt property for the homotopy category of finitely generated projective modules over a complete ring., v2. typo corrected, minor changes. 15 pages

This paper presents rules in sequent calculus for a binary quantifier I to formalise definite descriptions: Ix[F, G] means ‘The F is G’. The rules are suitable to be added to a system of positive free logic. The paper extends the proof of a cut elimination theorem for this system by Indrzejczak by proving the cases for the rules of I. There are also brief comparisons of the present approach to the more common one that formalises definite descriptions with a term forming operator. In the final section rules for I for negative free and classical logic are also mentioned.

We provide a novel recursive method, which does not require any assumption, to compute the entries of the kth power of a semicirculant matrix by using a closed-form expression for the mth term of a...

In this manuscript, the authors derive a formula for the double Laplace transform expressed in terms of the Lerch Transcendent. The log term mixes the variables so that the integral is not separable except for special values of k. The method of proof follows the method used by us to evaluate single integrals. This transform is then used to derive definite integrals in terms of fundamental constants, elementary and special functions. A summary of the results is produced in the form of a table of definite integrals for easy referencing by readers.

The subject of the present paper is a material connection that describes the sources of incompatibility in growing solids. There are several possibilities to introduce such a connection on the body manifold, which provides formal description of a body as a continuous collection of material particles. Two of them are discussed in detail. The first sets the geometry of Riemannian manifold, while the second sets Weitzenbock geometry. To derive particular connection functions, related with given evolutionary problem for growing solid, one has to use some intermediate configurations, whose choice is also uncertain. The purpose of this study is to find out how the ambiguity affects on the stress-strain state modelling. The main results are the following. It is proven that the geometrical invariants of considered material connections, namely the invariants of torsion and curvature, are independent on particular choice of intermediate configuration. It is shown that Weitzenbock connection contains all metric information that completely defines Riemannian ones, but, except it, provides additional description for contorsion, which characterizes inhomogeneity by specific term in balance of momentum. Thus, the two connections do not contradict each other. To describe the body’s response to deformation it is sufficient to construct more simpler Riemannian connection, while to completely describe balance laws it is advisable to obtain more complete Weitzenbock connection.

In this article, we study sums related to the Lehmer problem over short intervals, and give two asymptotic formulae for them. The original Lehmer problem is to count the numbers coprime to a prime such that the number and the its number theoretical inverse are in different parities in some intervals. The numbers which satisfy these conditions are called Lehmer numbers. It prompts a series of investigations, such as the investigation of the error term in the asymptotic formula. Many scholars investigate the generalized Lehmer problems and get a lot of results. We follow the trend of these investigations and generalize the Lehmer problem.

The present research featured the family of words as a complex unit within the framework of military terminology. The article introduces a new method for studying high-frequency English-language military terms, where terminological units are systematized by the family of words. English-language military terminology is constantly changing. As a result, it remains understudied and requires structuring. The research objective was to structure military vocabulary as blocks, each representing a certain family of words. Military term blocks were selected from modern lexicographic sources. The study involved etymological, semantic, and word-formation analyses. The family of words proved to be a microsystem that combines grammatical, word-formation, and lexical relations. The authors structured cognate high-frequency English military terms as microsystems, i.e. families of words with peaks -bat- , -defend- , -arm- , etc.

This study aims to describe the nature of the interpretation of maudu'i in etymology, terminology and use of the word maudu'i in the Qur'an and the study of interpretation. Research on the interpretation of maudu'i has been carried out by many reviewers of the Qur'an, both in terms of its meaning in language or terms as well as in terms of its application to a particular theme. The research method used in this research is descriptive-analysis and book research. The results of this study are that the word maudu'i is found in the Qur'an 24 times, with one of its meanings being to determine something that is used in a problem or topic. From this, the term maudu'i can be applied to the study of interpretation with the term maudu'i interpretation or in Indonesian known as thematic interpretation. Maudu'i interpretation is a method of interpreting the Qur'an by collecting verses that have the same theme or topic of discussion and also the same purpose and then analyzing them in detail as contained in the rules of tahlili interpretation, explaining their meaning and imposing the laws in it.