Search results for: lexical invariant

Authors: S. Pesina, T. Solonchak

Abstract:

Lexical invariants, being a sort of stereotypes within the frames of ordinary consciousness, are created by the members of a language community as a result of uniform division of reality. The invariant meaning is formed in person’s mind gradually in the course of different actualizations of secondary meanings in various contexts. We understand lexical the invariant as abstract language essence containing a set of semantic components. In one of its configurations it is the basis or all or a number of the meanings making up the semantic structure of the word.

Keywords: lexical invariant, invariant theories, polysemantic word, cognitive linguistics

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Authors: Yukiko Sasaki Alam

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This research aims at finding out the causes that led to wrong lexical selections in machine translation (MT) rather than categorizing lexical errors, which has been a main practice in error analysis. By manually examining and analyzing lexical errors outputted by a MT system, it suggests what knowledge would help the system reduce lexical errors.

Keywords: machine translation, error analysis, lexical errors, evaluation

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Authors: Reza Aghayan

Abstract:

Numerically invariant signatures were introduced as a new paradigm of the invariant recognition for visual objects modulo a certain group of transformations. This paper shows that the current formulation suffers from noise and indeterminacy in the resulting joint group-signatures and applies the n-difference technique and the m-mean signature method to minimize their effects. In our experimental results of applying the proposed numerical scheme to generate joint group-invariant signatures, the sensitivity of some parameters such as regularity and mesh resolution used in the algorithm will also be examined. Finally, several interesting observations are made.

Keywords: Euclidean and affine geometry, differential invariant G-signature curves, numerically invariant joint G-signatures, object recognition, noise, indeterminacy

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Authors: S. Pesina, T. Solonchak

Abstract:

Phenomenological analysis is not based on natural language, but ideal language which is able to be a carrier of ideal meanings – eidos representing typical structures or essences. For this purpose, it’s necessary to release from the spatio-temporal definiteness of a subject and then state its noetic essence (eidos) by means of free fantasy generation. Herewith, as if a totally new objectness is created - the universal, confirming the thesis that thinking process takes place in generalizations passing by numerous means through the specific to the general and from the general through the specific to the singular.

Keywords: lexical eidos, phenomenology, noema, polysemantic word, semantic core

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Authors: Georgios Alexandropoulos

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The purpose of this study is to examine the historical text of Alexiad by Anna Comnena using computational tools for the extraction of lexical bundles containing the name of her father, Alexius Comnenus. For this reason, in this research we apply corpus linguistics techniques for the automatic extraction of lexical bundles and through them we will draw conclusions about how these lexical bundles serve her support provided to her father.

Keywords: lexical bundles, computational literature, critical discourse analysis, Alexiad

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Authors: Zainab Al-Maamari, Yassir Dinar

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The orbit space of an irreducible representation of a finite group is a variety with the ring of invariant polynomials as a coordinate ring. The invariant ring is a polynomial ring if and only if the representation is a reflection representation. Boris Dubrovin shows that the orbits spaces of irreducible real reflection representations acquire the structure of polynomial Frobenius manifolds. Dubrovin's method was also used to construct different examples of Frobenius manifolds on certain reflection representations. By successfully applying Dubrovin’s method on non-polynomial invariant rings of linear representations of dicyclic groups, it gives some results that magnify the relation between invariant theory and Frobenius manifolds.

Keywords: invariant ring, Frobenius manifold, inversion, representation theory

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Authors: Reza Aghayan

Abstract:

This paper illustrates that numerically invariant joint signatures suffer biases in the resulting signatures. Next, we classify the arising biases as Bias Type 1 and Bias Type 2 and show how they can be removed.

Keywords: Euclidean and affine geometries, differential invariant signature curves, numerically invariant joint signatures, numerical analysis, numerical bias, curve analysis

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Authors: Khalid Soussi

Abstract:

The study at hand has attempted to describe the acquisition of three EFL lexical knowledge aspects - meaning, synonymy and collocation – across three academic levels: Baccalaureate, second year and fourth year university levels in Morocco. The research also compares the development of the three lexical knowledge aspects between knowledge (reception) and use (production) and attempts to trace their order of acquisition. This has led to the use of three main data collection tasks: translation, acceptability judgment and multiple choices. The study has revealed the following findings. First, L1 and EFL mental lexicons are connected at the lexical knowledge depth. Second, such connection is active whether in language reception or use. Third, the connectivity between L1 and EFL mental lexicons tends to relatively decrease as the academic level of the learners increases. Finally, the research has revealed a significant 'order' of acquisition between the three lexical aspects, though not a very strong one.

Keywords: vocabulary acquisition, EFL lexical knowledge, mental lexicon, vocabulary knowledge depth

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Authors: Mariana T. Teixeira, Joana P. Luz

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This paper is based on assumptions of psycholinguistics and investigates the processing of ambiguous sentences in Brazilian Portuguese. Specifically, it aims to verify if there is a difference in processing time between sentences with lexical ambiguity and sentences with structural (or syntactic) ambiguity. We hypothesize, based on the Garden Path Theory, that the two types of ambiguity entail different cognitive efforts, since sentences with structural ambiguity require that two structures be processed, whereas ambiguous phrases whose root of ambiguity is in a word require the processing of a single structure, which admits a variation of punctual meaning, within the scope of only one lexical item. In order to test this hypothesis, 25 undergraduate students, whose average age was 27.66 years, native speakers of Brazilian Portuguese, performed a self-monitoring reading task of ambiguous sentences, which had lexical and structural ambiguity. The results suggest that unambiguous sentence processing is faster than ambiguous sentence processing, whether it has lexical or structural ambiguity. In addition, participants presented a mean reading time greater for sentences with syntactic ambiguity than for sentences with lexical ambiguity, evidencing a greater cognitive effort in sentence processing with structural ambiguity.

Keywords: Brazilian portuguese, lexical ambiguity, sentence processing, syntactic ambiguity

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Authors: Rami Al-Sadi

Abstract:

The assignment of lexical stress in English to its correct syllable is an enormous challenge to EFL learners, especially if their first language (L1) phonology is very different from English phonology. Arabic-speaking EFL learners not only stumble very frequently when it comes to placing the lexical stress in a given word, but they also seem to relegate the role of lexical stress as unimportant, mainly because in Arabic, unlike in English, lexical stress is not phonemic. This study aims at exploring the possible benefits of utilizing spectrographic representations of English words correctly pronounced, for the purpose of finding out how these spectrograms can provide a visual aid to the learners and help them rectify their stress placement errors as they see in real time spectrograms of the correct pronunciations juxtaposed on a computer screen with spectrograms of their own pronunciations for easy comparison. The study involved 120 students from the English Department at Prince Sattam bin Abdulaziz University in Saudi Arabia. 60 participants were taught the English lexical stress rules and also received spectrographic guidance on pronunciation; the other 60 received only verbal instruction on the stress rules and verbal feedback on their pronunciations. Statistical results showed that when the learners had the opportunity to ‘see’ their pronunciation mistakes, they were three times more likely to rectify their placement of lexical stress.

Keywords: Arabic-speaking EFL learners, lexical stress, pronunciation, spectrographic representation, stress placement

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Authors: M. Berrehail, F. Benamira

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We study the quantum motion of a particle in the presence of a time- dependent linear potential using an operator invariant that is quadratic in p and linear in q within the framework of the Lewis-Riesenfeld invariant, The special invariant operator proposed in this work is demonstrated to be an Hermitian operator which has an Airy wave packet as its Eigenfunction

Keywords: airy wave packet, ivariant, time-dependent linear potential, unitary transformation

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Authors: Nadya Inda Syartanti

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This research aims to identify, classify, and analyze descriptively the aspects of grammatical and lexical cohesion in the speech text of Japan’s Prime Minister Shinzo Abe entitled Nihon wa Modotte kimashita delivered in Washington DC, the United States on February 23, 2013, as a research data source. The method used is qualitative research, which uses descriptions through words that are applied by analyzing aspects of grammatical and lexical cohesion proposed by Halliday and Hasan (1976). The aspects of grammatical cohesion consist of references (personal, demonstrative, interrogative pronouns), substitution, ellipsis, and conjunction. In contrast, lexical cohesion consists of reiteration (repetition, synonym, antonym, hyponym, meronym) and collocation. Data classification is based on the 6 aspects of the cohesion. Through some aspects of cohesion, this research tries to find out the frequency of using grammatical and lexical cohesion in Shinzo Abe's speech text entitled Nihon wa Modotte kimashita. The results of this research are expected to help overcome the difficulty of understanding speech texts in Japanese. Therefore, this research can be a reference for learners, researchers, and anyone who is interested in the field of discourse analysis.

Keywords: cohesion, grammatical cohesion, lexical cohesion, speech text, Shinzo Abe

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Authors: Saroj Bijarnia, Preety Singh

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We propose a simple and effective biometrics system based on face verification across aging using a new variant of texture feature, Pyramid Binary Pattern. This employs Local Binary Pattern along with its hierarchical information. Dimension reduction of generated texture feature vector is done using Principal Component Analysis. Support Vector Machine is used for classification. Our proposed method achieves an accuracy of 92:24% and can be used in an automated age-invariant face verification system.

Keywords: biometrics, age invariant, verification, support vector machine

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Authors: A. Suparmi, C. Cari, M. Yunianto, B. N. Pratiwi

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D-dimensional Dirac equations of q-deformed shape invariant potentials were solved using supersymmetric quantum mechanics (SUSY QM) in the case of exact spin symmetry. The D dimensional radial Dirac equation for shape invariant potential reduces to one-dimensional Schrodinger type equation by an appropriate variable and parameter change. The relativistic energy spectra were analyzed by using SUSY QM and shape invariant properties from radial D dimensional Dirac equation that have reduced to one dimensional Schrodinger type equation. The SUSY operator was used to generate the D dimensional relativistic radial wave functions, the relativistic energy equation reduced to the non-relativistic energy in the non-relativistic limit.

Keywords: D-dimensional dirac equation, non-central potential, SUSY QM, radial wave function

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Authors: Fatima Muhammad Shitu

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This study seeks to investigate the effect of the keyword strategy on lexico–semantic acquisition, recognition, retention and comprehension in an ESL context. The aim of the study is to determine whether the keyword strategy can be used to enhance acquisition. As a quasi- experimental research, the objectives of the study include: To determine the extent to which the scores obtained by the subjects, who were trained on the use of the keyword strategy for acquisition, differ at the pre-tests and the post–tests and also to find out the relationship in the scores obtained at these tests levels. The sample for the study consists of 300 hundred undergraduate ESL Students in the Federal College of Education, Kano. The seventy-five lexical items for acquisition belong to the lexical field category known as register, and they include Medical, Agriculture and Photography registers (MAP). These were divided in the ratio twenty-five (25) lexical items in each lexical field. The testing technique was used to collect the data while the descriptive and inferential statistics were employed for data analysis. For the purpose of testing, the two kinds of tests administered at each test level include the WARRT (Word Acquisition, Recognition, and Retention Test) and the CCPT (Cloze Comprehension Passage Test). The results of the study revealed that there are significant differences in the scores obtained between the pre-tests, and the post–tests and there are no correlations in the scores obtained as well. This implies that the keyword strategy has effectively enhanced the acquisition of the lexical items studied.

Keywords: keyword, lexical, semantics, strategy

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Authors: Siti Noor Farwina Anwar, Hailiza Kamarulhaili

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In this paper, we present the idea of implementing the Integer Sub-Decomposition (ISD) method on elliptic curves with j-invariant 1728. The ISD method was proposed in 2013 to compute scalar multiplication in elliptic curves, which remains to be the most expensive operation in Elliptic Curve Cryptography (ECC). However, the original ISD method only works on integer number field and solve integer scalar multiplication. By extending the method into the complex quadratic field, we are able to solve complex multiplication and implement the ISD method on elliptic curves with j-invariant 1728. The curve with j-invariant 1728 has a unique discriminant of the imaginary quadratic field. This unique discriminant of quadratic field yields a unique efficiently computable endomorphism, which later able to speed up the computations on this curve. However, the ISD method needs three endomorphisms to be accomplished. Hence, we choose all three endomorphisms to be from the same imaginary quadratic field as the curve itself, where the first endomorphism is the unique endomorphism yield from the discriminant of the imaginary quadratic field.

Keywords: efficiently computable endomorphism, elliptic scalar multiplication, j-invariant 1728, quadratic field

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Authors: Tayebeh Norouzi

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This study aims to investigate the acquisition process of intonation. It examines the intonation structure of Tokyo Japanese and its realization by Iranian learners of Japanese. Seven Iranian learners of Japanese, differing in fluency, and two Japanese speakers participated in the experiment. Two sentences were used to test the phonological and phonetic characteristics of lexical pitch-accent as well as the intonation patterns produced by the speakers. Both sentences consisted of similar words with the same number of syllables and lexical pitch-accents but different syntactic structure. Speakers were asked to read each sentence three times at normal speed, and the data were analyzed by Praat. The results show that lexical pitch-accent, Accentual Phrase (AP) and AP boundary tone realization vary depending on sentence type. For sentences of type XdeYwo, the lexical pitch-accent is realized properly. However, there is a rise in AP boundary tone regardless of speakers’ level of fluency. In contrast, in sentences of type XnoYwo, the lexical pitch-accent and AP boundary tone vary depending on the speakers’ fluency level. Advanced speakers are better at grouping words into phrases and produce more native-like intonation patterns, though they are not able to realize downstep properly. The non-native speakers tried to realize proper intonation patterns by making changes in lexical accent and boundary tone.

Keywords: intonation, Iranian learners, Japanese prosody, lexical accent, second language acquisition.

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Authors: Natalia M. Nepomniashchikh

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The research focuses on Russian and English linguoculturemes Caucasian mountaineer and Scottish Highlander, the effort of comparative-contrastive analysis was made. In order to reach the aim, the analysis of the vocabulary definitions of the concepts under consideration was taken, which made it possible to build the lexical-semantic fields of both lexical items in Russian and English. This stage of research helped to turn to the linguistic-cultural fields construction. To build these fields, literary pieces containing the concepts under consideration and the items directly related to them were taken from the works about the Caucasus mountains and mountaineers living there by M. Yu. Lermontov and the ones by W. Scott devoted to the Scottish Highlands and their inhabitants. All collected data was systematized in schemes and tables reflecting the differences and intercrossing areas.

Keywords: lexemes, lexical items, lexical-semantic field, linguistic-cultural field, linguoculturemes

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Authors: Pam Bitrus Marcus

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Compounds in Berom, a Niger-Congo language that is spoken in parts of central Nigeria, have been understudied, and the semantics of N-V nominal compounds have not been sufficiently delineated. This study describes the lexical classification of compounds in Berom and, specifically, examines the semantics of nominal compounds with N-V constituents. The study relied on a data set of 200 compounds that were drawn from Bere Naha (a newsletter publication in Berom). Contrary to the nominalization process in defining the lexical class of compounds in languages, the study revealed that verbal and adjectival classes of compounds are also attested in Berom and N-V nominal compounds have an agentive or locative interpretation that is not solely determined by the meaning of the constituents of the compound but by the context of the usage.

Keywords: berom, berom compounds, nominal compound, N-V compounds

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Authors: Huma Javed

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Stylistics is a broad term that is concerned with both literature and linguistics, due to which the significance of the stylistics increases. This research aims to analyze Qaisra Shahraz's short story ‘The Escape’ from the stylistic analysis viewpoint. The focus of this study is on three aspects grammar category, lexical category, and figure of speech of the short story. The research designs for this article are both explorative and descriptive. The analysis of the data shows that the writer has used more nouns in the story as compared to other lexical items, which suggests that story has a descriptive style rather than narrative.

Keywords: The Escape, stylistics, grammatical category, lexical category, figure of speech

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Authors: Eleonora Sasso

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This paper takes as its starting point the notions of cognitive linguistics and lexical blending, and uses both these theoretical concepts to advance a new reading of Margaret Atwood’s latest writings, one which sees them as paramount literary examples of norm and usage in bilingual Canadian lexicography. Atwood’s prose seems to be imbued with Canadianisms and neologisms, lexical blends of zoomorphic forms, a kind of meeting-point between two conceptual structures which follow the principles of lexical economy and asyntactic relation. Atwood’s neologisms also attest to the undeniable impact on language exerted by Canada’s aboriginal peoples. This paper aims to track through these references and with the aid of the Eskimo-English dictionary look at the linguistic issues – attitudes to contaminations and hybridisations, questions of lexical blending in literary examples, etc – which they raise. Atwood’s fiction, whose cognitive linguistic strategy employs ‘the virtues of scissors and matches’, always strives to achieve isomorphism between word form and concept.

Keywords: Atwood, Canadianisms, cognitive science, Eskimo/English dictionary

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Authors: Wei Feilong

Abstract:

In this study, an local invariant generalized Houghtransform (LI-GHT) method is proposed for integrated circuit (IC) visual positioning. The original generalized Hough transform (GHT) is robust to external noise; however, it is not suitable for visual positioning of IC chips due to the four-dimensionality (4D) of parameter space which leads to the substantial storage requirement and high computational complexity. The proposed LI-GHT method can reduce the dimensionality of parameter space to 2D thanks to the rotational invariance of local invariant geometric feature and it can estimate the accuracy position and rotation angle of IC chips in real-time under noise and blur influence. The experiment results show that the proposed LI-GHT can estimate position and rotation angle of IC chips with high accuracy and fast speed. The proposed LI-GHT algorithm was implemented in IC visual positioning system of radio frequency identification (RFID) packaging equipment.

Keywords: Integrated Circuit Visual Positioning, Generalized Hough Transform, Local invariant Generalized Hough Transform, ICpacking equipment

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Authors: Khaled Barkaoui

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Research on second-language (L2) learning tends to focus on comparing students with different levels of proficiency at one point in time. However, to understand L2 development, we need more longitudinal research. In this study, we adopt a longitudinal approach to examine changes in three indicators of L2 ability, complexity, accuracy, and fluency (CAF), as reflected in the writing of L2 learners when writing on different tasks before and after a period L2 instruction. Each of 85 Chinese learners of English at three levels of English language proficiency responded to two writing tasks (independent and integrated) before and after nine months of English-language study in China. Each essay (N= 276) was analyzed in terms of numerous CAF indices using both computer coding and human rating: number of words written, number of errors per 100 words, ratings of error severity, global syntactic complexity (MLS), complexity by coordination (T/S), complexity by subordination (C/T), clausal complexity (MLC), phrasal complexity (NP density), syntactic variety, lexical density, lexical variation, lexical sophistication, and lexical bundles. Results were then compared statistically across tasks, L2 proficiency levels, and time. Overall, task type had significant effects on fluency and some syntactic complexity indices (complexity by coordination, structural variety, clausal complexity, phrase complexity) and lexical density, sophistication, and bundles, but not accuracy. L2 proficiency had significant effects on fluency, accuracy, and lexical variation, but not syntactic complexity. Finally, fluency, frequency of errors, but not accuracy ratings, syntactic complexity indices (clausal complexity, global complexity, complexity by subordination, phrase complexity, structural variety) and lexical complexity (lexical density, variation, and sophistication) exhibited significant changes after instruction, particularly for the independent task. We discuss the findings and their implications for assessment, instruction, and research on CAF in the context of L2 writing.

Keywords: second language writing, Fluency, accuracy, complexity, longitudinal

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Authors: Teoman Ozer, Ozlem Orhan

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This study deals with symmetry group properties and conservation laws of partial differential equations. We give a geometrical interpretation of notion of μ-prolongations of vector fields and of the related concept of μ-symmetry for partial differential equations. We show that these are in providing symmetry reduction of partial differential equations and systems and invariant solutions.

Keywords: λ-symmetry, μ-symmetry, classification, invariant solution

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Authors: Maba Boniface Matadi

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This paper analyses the model of Malaria endemic from the point of view of the group theoretic approach. The study identified new independent variables that lead to the transformation of the nonlinear model. Furthermore, corresponding determining equations were constructed, and new symmetries were found. As a result, the findings of the study demonstrate of the integrability of the model to present an invariant solution for the Malaria model.

Keywords: group theory, lie symmetry, invariant solutions, malaria

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Authors: Yuliya E. Leshchenko, Tatyana S. Ostapenko

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Language variation is a widespread linguistic phenomenon which can affect different levels of a language system: phonological, morphological, lexical, syntactic, etc. It is obvious that the scope of possible standard alternations within a particular language is limited by a variety of its norms and regulations which set more or less clear boundaries for what is possible and what is not possible for the speakers. The possibility of lexical variation (alternate usage of lexical items within the same contexts) is based on the fact that the meanings of words are not clearly and rigidly defined in the consciousness of the speakers. Therefore, lexical variation is usually connected with unstable relationship between words and their referents: a case when a particular lexical item refers to different types of referents, or when a particular referent can be named by various lexical items. We assume that the scope of lexical variation in bilingual speech is generally wider than that observed in monolingual speech due to the fact that, besides ‘lexical item – referent’ relations it involves the possibility of cross-language variation of L1 and L2 lexical items. We use the term ‘cross-language variation’ to denote a case when two equivalent words of different languages are treated by a bilingual speaker as freely interchangeable within the common linguistic context. As distinct from code-switching which is traditionally defined as the conscious use of more than one language within one communicative act, in case of cross-language lexical variation the speaker does not perceive the alternate lexical items as belonging to different languages and, therefore, does not realize the change of language code. In the paper, the authors present research of lexical variation of adult Komi-Permyak – Russian bilingual speakers. The two languages co-exist on the territory of the Komi-Permyak District in Russia (Komi-Permyak as the ethnic language and Russian as the official state language), are usually acquired from birth in natural linguistic environment and, according to the data of sociolinguistic surveys, are both identified by the speakers as coordinate mother tongues. The experimental research demonstrated that alternation of Komi-Permyak and Russian words within one utterance/phrase is highly frequent both in speech perception and production. Moreover, our participants estimated cross-language word combinations like ‘маленькая /Russian/ нывка /Komi-Permyak/’ (‘a little girl’) or ‘мунны /Komi-Permyak/ домой /Russian/’ (‘go home’) as regular/habitual, containing no violation of any linguistic rules and being equally possible in speech as the equivalent intra-language word combinations (‘учöтик нывка’ /Komi-Permyak/ or ‘идти домой’ /Russian/). All the facts considered, we claim that constant concurrent use of the two languages results in the fact that a large number of their words tend to be intuitively interpreted by the speakers as lexical variants not only related to the same referent, but also referring to both languages or, more precisely, to none of them in particular. Consequently, we can suppose that bilingual mental lexicon includes an extensive ‘fused’ zone of lexical representations that provide the basis for cross-language variation in bilingual speech.

Keywords: bilingualism, bilingual mental lexicon, code-switching, lexical variation

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Authors: Chamindi Dilkushi Senaratne

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Borrowing is the morphological, syntactic and (usually) phonological integration of lexical items from one language into the structure of another language. Borrowings show complete linguistic integration and due to the frequency of use become fossilized in the recipient language differentiating them from switches and mixes. Code mixes are different to borrowings. Code mixing takes place when speakers use lexical items in casual conversation to serve a variety of functions. This study presents an analysis of lexical items used in English newspapers in Sri Lanka in 2017 which reveal characteristics of borrowing or code mixes. Both phenomena arise due to language contact. The study will also use data from social media websites that comment on newspaper articles available on the web. The study reiterates that borrowings are distinguishable from code mixes and that they are two different phenomena that occur in language contact situations. The study also shows how existing morphological processes are used to create new vocabulary in language use. The study sheds light into how existing morphological processes are used by the bilingual to be creative, innovative and convey a bilingual identity.

Keywords: borrowing, code mixing, morphological processes

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Authors: Matthaios Katsanikas

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We study the structure of the invariant manifolds of complex unstable periodic orbits of a family of periodic orbits, in a 3D autonomous Hamiltonian system of galactic type, after a transition of this family from stability to complex instability (Hamiltonian Hopf bifurcation). We consider the case of a supercritical Hamiltonian Hopf bifurcation. The invariant manifolds of complex unstable periodic orbits have two kinds of structures. The first kind is represented by a disk confined structure on the 4D space of section. The second kind is represented by a complicated central tube structure that is associated with an extended network of tube structures, strips and flat structures of sheet type on the 4D space of section.

Keywords: dynamical systems, galactic dynamics, chaos, phase space

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Authors: Michele Aleandri, Matteo Colangeli, Davide Gabrielli

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We study a generalization to a continuous setting of the classical Markov chain tree theorem. In particular, we consider an irreducible diffusion process on a metric graph. The unique invariant measure has an atomic component on the vertices and an absolutely continuous part on the edges. We show that the corresponding density at x can be represented by a normalized superposition of the weights associated to metric arborescences oriented toward the point x. A metric arborescence is a metric tree oriented towards its root. The weight of each oriented metric arborescence is obtained by the product of the exponential of integrals of the form ∫a/b², where b is the drift and σ² is the diffusion coefficient, along the oriented edges, for a weight for each node determined by the local orientation of the arborescence around the node and for the inverse of the diffusion coefficient at x. The metric arborescences are obtained by cutting the original metric graph along some edges.

Keywords: diffusion processes, metric graphs, invariant measure, reversibility

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Authors: Kankeyanathan Kannan

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On approximation properties of group C* algebras is everywhere; it is powerful, important, backbone of countless breakthroughs. For a discrete group G, let A(G) denote its Fourier algebra, and let M₀A(G) denote the space of completely bounded Fourier multipliers on G. An approximate identity on G is a sequence (Φn) of finitely supported functions such that (Φn) uniformly converge to constant function 1 In this paper we prove that approximation property pass to free product.

Keywords: approximation property, weakly amenable, strong invariant approximation property, invariant approximation property

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