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We explore functors between operator space categories, some properties of these functors, and establish relations between objects in these categories and their images under these functors, in particular regarding injectivity and injective envelopes. We also compare the purely categorical definition of injectivity with the ‘standard’ operator theoretical definition. An appendix by D. P. Blecher discusses the unitization of an operator space and its injective envelope. [ABSTRACT FROM AUTHOR]

Although critical discourse analysis (CDA) sets out to investigate both oppressive and progressive discourses, the vast bulk of published studies seem to prioritize the former. This paper is a response to scholarly calls to engage with (non)oppressive discourses by integrating positive impulses in critical discourse analysis, and thus contribute to the growth of positive discourse analysis (PDA), a complement to CDA, which attends to the emancipatory mechanisms of resistance. Using a combination of theoretical tools, this paper takes a case study approach to explore the potentials of 'complexification' [Macgilchrist, F. (2007). Positive discourse analysis: Contesting dominant discourses by reframing the issues. Critical Approaches to Discourse Analysis Across Disciplines, 1(1), 74–94], a counter-discursive strategy for propelling marginal discourses into the dominant official school discourse. Specifically, the paper discusses three layers of complexification found in a selected Moroccan EFL textbook which has been developed, approved and distributed by the Moroccan Ministry of Education, and has been required to be used in every school, public or private. The analysis highlights the role this textbook plays in promoting emancipatory and progressive discourses about Amazigh social actors, and hence, signals a new shift in analytic focus by illuminating a concrete application of PDA in education curricula. [ABSTRACT FROM AUTHOR]

We present some more foundations for a theory of real structure in operator spaces and algebras, in particular concerning the real case of the theory of injectivity, and the injective, ternary, and C ∗ -envelope. We consider the interaction between these topics and the complexification. We also generalize many of these results to the setting of operator spaces and systems acted upon by a group. [ABSTRACT FROM AUTHOR]

A recent publication in Nature has generated much heated discussion about evolution, its tendency towards increasing diversity and complexity, and its potential status above and beyond the known laws of fundamental physics. The argument at the heart of this controversy concerns assembly theory, a method to detect and quantify the influence of higher-level emergent causal constraints in computational worlds made of basic objects and their combinations. In this short essay, I briefly review the theory, its basic principles and potential applications. I then go on to critically examine its authors' assertions, concluding that assembly theory has merit but is not nearly as novel or revolutionary as claimed. It certainly does not provide any new explanation of biological evolution or natural selection, or a new grounding of biology in physics. In this regard, the presentation of the paper is starkly distorted by hype, which may explain some of the outrage it created. [ABSTRACT FROM AUTHOR]

In this paper, we continue investigation of the lateral order on vector lattices started in [25]. We consider the complexification EC$E_{\mathbb {C}}$ of a real vector lattice E and introduce the lateral order on EC$E_{\mathbb {C}}$. Our first main result asserts that the set of all fragments Fv$\mathfrak {F}_v$ of an element v∈EC$v\in E_{\mathbb {C}}$ of the complexification of an uniformly complete vector lattice E is a Boolean algebra. Then, we study narrow operators defined on the complexification EC$E_{\mathbb {C}}$ of a vector lattice E, extending the results of articles [22, 27, 28] to the setting of operators defined on complex vector lattices. We prove that every order‐to‐norm continuous linear operator T:EC→X$\mathcal {T}: E_{\mathbb {C}} \rightarrow X$ from the complexification EC$E_{\mathbb {C}}$ of an atomless Dedekind complete vector lattice E to a finite‐dimensional Banach space X is strictly narrow. Then, we prove that every C‐compact order‐to‐norm continuous linear operator T$\mathcal {T}$ from EC$E_{\mathbb {C}}$ to a Banach space X is narrow. We also show that every regular order‐no‐norm continuous linear operator from EC$E_{\mathbb {C}}$ to a complex Banach lattice (ℓp(D)C$(\ell _p(\mathcal {D})_{\mathbb {C}}$ is narrow. Finally, in the last part of the paper we investigate narrow operators taking values in symmetric ideals of compact operators. [ABSTRACT FROM AUTHOR]

This paper focuses on the investigation of the dynamics of novel 2-DOF coupled oscillators. The system consists of a linear oscillator (main structure) and an attached lightweight nonlinear oscillator, called a nonlinear energy sink (NES), under harmonic forcing in the regime of 1:1:1 resonance. The studied NES has geometrically nonlinear stiffness and damping. Due to the degeneracies that the NES brings to the system, diverse bifurcation structures and rich dynamical phenomena such as nonlinear beating and strongly modulated response occur. The latter two phenomena represent different patterns of energy transfer. To capture the bifurcation structure, the slow flow of the system can be acquired with the use of the complex-averaging method. Furthermore, by applying the bifurcation analysis technique, we get curve boundaries of several bifurcation points in the parameter space. These boundaries will induce different types of folding structures, which can lead to complicated patterns of strongly modulated responses, in which intense energy transfer from the main structure to NES occurs. To study the necessary parameter conditions of strongly modulated responses, we analyzed the dynamics of different time scales of the slow flow in detail and determined the corresponding parameter ranges finally. It is worth noting that the small parameter ε may have a qualitative impact on the dynamics of the system. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the problem of Schwarzschild space time in which the notion of density is substituted by that of a "fractal mass measure" defined over sets in the framework of the Fractional Action Like Variational Approach with time-dependent exponent. On a hypersphere of radius R centered at a point P, we assume that the mass enclosed behaves like: M (R) ∝ R β (β is a fractal dimension) if P is fractal and is equal to zero otherwise. Furthermore, we conjecture that the Newtonian's gravitational coupling constant increase with R like G N (R) ∝ R ζ , ζ ∈ R ≪ 1 for short distances which is one of the main consequences of the exhaustive examination of non-perturbatively renormalizable or asymptotically safe quantum gravity which envisages a fractal space time structure at sub-Planckian distances whose effective dimensionality is 2. Many interesting features are revealed and discussed in some details, in particular the emergence of complexified space-time, complexified gravity and Schwarzschild space-time metric deformation. [ABSTRACT FROM AUTHOR]

This study investigated the applicability of complexification and ecosystem leadership theories in sharing responsibility for underprivileged students. The complexification theory advocates for the breaking down of complex education systems into smaller, interconnected components to effectively understand and manage issues related to underprivileged students. The ecosystem leadership theory, on the other hand, emphasizes collaboration and shared responsibility among different stakeholders to address complex issues. By utilizing these models, education systems can develop better approaches to sharing responsibility for underprivileged students with a focus on collaboration, shared understanding, and a commitment to achieving shared goals. To make education equitable for students experiencing poverty, the Guimaras State University must adopt ecosystem leadership, collaborate with others, and take collective responsibility for every student's well-being. Educational leaders must prioritize addressing the root causes of poverty by creating an inclusive approach that empowers students and promotes their overall well-being. Adopting ecosystem leadership and prioritizing collective well-being can create an inclusive and equitable educational experience for all students. [ABSTRACT FROM AUTHOR]

We classify derived-discrete algebras over the real numbers up to Morita equivalence, using the classification of complex derived-discrete algebras in D. Vossieck, (J. Algebra, 243, 168–176 2001). To this end, we investigate the quiver presentation of the complexified algebra of a real algebra given by a modulated quiver and an admissible ideal. [ABSTRACT FROM AUTHOR]

While proponents of Chinese IR pursue a national school based on the identification of Chineseness with the Chinese national culture, its critics find a limited value in the 'Chinese' school as a mere temporary site for non-Western agencies. In contrast, I argue a distinctive and enduring Chinese IR is possible if it adopts a non-national and non-essentialised transcultural conception of Chineseness. This transcultural Chinese IR is based first on the contested and transcultural conception of Chineseness and second on the ontology of Chineseness as immanent humanity. Chineseness has been a fiction of a privileged descent from antiquity, which various contestants claimed by redefining the meaning of Chineseness. The shi elites, in particular, developed Chineseness as an aspirational ethos that propelled it to transcend its cultural boundary by incorporating foreign influences and thereby rendered Chineseness transcultural. Also, drawing on the ontological turn and Roy Wagner's work in anthropology, I show how Chineseness as immanent humanity transcends the category of culture, transforming the division of innate nature and constructed culture. The transcultural Chinese IR, with its own complexity and universal aspiration, uses its history and ontology to complexify both its tradition internally and other IR traditions externally, promoting the pluralisation of IR. [ABSTRACT FROM AUTHOR]

Bilateration is one of the localization methods that provides the location information of the target node using two anchors’ location information and two distances between the target node and each anchor. This paper shows that bilateration with different configurations in a three-anchor positioning system gives better precision than trilateration and the same precision as the nonlinear least square (NLS) method when the target is outside the convex hull of the anchors, and also that the combinatorial use of bilaterations gives the same level of precision as the NLS method or tilateration even when the target is inside the convex hull of the anchors. For the rigorous proof of this claim, we first develop a theory that the bilateration method can be naturally modeled and understood by adopting a pair of distances as a complex variable and the mapping in the bilateration method as a complex-valued sine function with a complex variable, respectively. We explain why the proposed complexification is more intuitive and applicable to real-world problems than the real-valued bilateration method. Since the complex sine function has many nice properties and one-to-one correspondence, it can be regarded as a fundamental transformation from the measurement space to position space in a two-dimensional positioning system. Next, based on the complex-valued function theory for bilateration, we describe the error propagation and show that a nonlinear least square method can be replaced with the closed formula in the bilateration localization system. The error propagation of the bilateration has a unique property: the error in position space propagates only in the horizontal direction with anchors and is unchanged in the other direction regardless of the target’s position.

This article presents the results of a quantitative study in which the complexity levels of dialectal varieties belonging to the South Slavic dialect continuum are measured and analyzed. The sample comprises 919 data points, pertaining to the Bulgarian–Macedonian and Serbo-Croatian dialect continua. Complexity is viewed in this study as a property demonstrating variation across areas and subject to diachronic change which can be associated either with language-internal processes or with language contact. This study discusses which linguistic processes produced varying levels of complexity in the modern South Slavic varieties. In particular, a correlation of complexity with altitude and distance to the Albanian border, two factors which can be associated with degree of isolation versus contact of speech communities, is investigated for a subset of varieties spoken across the areas with bi- and multilingual population. Suggestions on which constellations of societal features could act as determinants of linguistic change are made for several areas within the South Slavic continuum. Particular attention is paid to the contact-related developments in the South Slavic varieties spoken in the areas of intensive past and present contact, such as the west of North Macedonia, the south of Montenegro, Kosovo, and Southeast Serbia. [ABSTRACT FROM AUTHOR]

In this paper, we give a pedagogical presentation of the irreducible unitary representations of ℂ 4 ⋊ S p i n (4 , ℂ) , that is, of the universal cover of the complexified Poincaré group ℂ 4 ⋊ S O (4 , ℂ). These representations were first investigated by Roffman in 1967. We provide a modern formulation of his results together with some facts from the general Wigner–Mackey theory which are relevant in this context. Moreover, we discuss different ways to realize these representations and, in the case of a non-zero "complex mass", we give a detailed construction of a more explicit realization. This explicit realization parallels and extends the one used in the classical Wigner case of ℝ 4 ⋊ S p i n 0 (1 , 3). Our analysis is motivated by the interest in the Euclidean formulation of Fermionic theories. [ABSTRACT FROM AUTHOR]

Poverty is a clustered and corrosive disadvantage that affects students throughout their lives. The education system has been positioned as an opportunity to break the cycle of poverty. Yet, the education system continues to fail to achieve its potential. We conceptually explore how educational leaders could perceive their responsibility in assisting children experiencing poverty and in leveraging the education ecosystem to fulfill the promise of full capability functioning through self-agency and empowerment. We call for an education leadership shift from an outcomes-based paradigm to a student-focused paradigm that embraces the complexity of poverty, develops students’ opportunities for self-agency and empowerment, and ultimately leads to a higher quality of life. We propose an interdisciplinary model of leadership. [ABSTRACT FROM AUTHOR]

This paper considers hyperbolic wave equations with non-local in time conditions involving integrals with respect to time. It is shown that regularity of the solution can be achieved for complexified problem with integral conditions involving harmonic complex exponential weights. The paper establishes existence, uniqueness, and regularity of the solutions. [ABSTRACT FROM AUTHOR]

This article analyses attempts to enact complexity in postgenomic experimentations using the case of epigenetic research on biomarkers of psychosocial stress. Enacting complexity in this research means dissecting multiple so-called biosocial processes of health differentiation in the face of stressful experiences. To characterize enactments of biosocial complexity, the article develops the concepts of complexity work and complexification . The former emphasizes the social, technical, and material work that goes into the production of mixed biological and social representations of stress in epigenetics. The latter underlines how complexity can be assembled differently across distinct configurations of experimental work. Specifically, complexification can be defined as producing, stabilizing, and normalizing novel experimental systems that are supposed to improve techno-scientific enactments of complexity. In the case of epigenetics, complexification entails a reconfiguration of postgenomic experimental systems in ways that some actors deem 'better' at enacting health as a biosocial process. This study of complexity work and complexification shows that biosocial complexity is hardly a univocal enterprise in epigenetics. Consequently, the article calls for abandoning analysis of these research practices using clear-cut dichotomies of reductionism vs. holism, as well as simplicity vs. complexity. More broadly, the article suggests the relevance of a sociology of complexification for STS approaches to complexity in scientific practices. Complementing the existing focus on complexity as instrumental rhetoric in contemporary sciences, complexification directs analytical attention to the pragmatic opportunities that alternative (biosocial) complexities offer to collective, societal, and political thinking about science in society., Competing Interests: Declaration of conflicting interestsThe author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Aiming at classifying the polarities over aspects, aspect-based sentiment analysis (ABSA) is a fine-grained task of sentiment analysis. The vector representations of current models are generally constrained to real values. Based on mathematical formulations of quantum theory, quantum language models have drawn increasing attention. Words in such models can be projected as physical particles in quantum systems, and naturally represented by representation-rich complex-valued vectors in a Hilbert Space, rather than real-valued ones. In this paper, the Hilbert Space representation for ABSA models is investigated and the complexification of three strong real-valued baselines are constructed. Experimental results demonstrate the effectiveness of complexification and the outperformance of our complex-valued models, illustrating that the complex-valued embedding can carry additional information beyond the real embedding. Especially, a complex-valued RoBERTa model outperforms or approaches the previous state-of-the-art on three standard benchmarking datasets. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new approach that allows to identify the Gelfand spectrum of weighted Fourier algebras as a subset of an abstract complexification of the corresponding group for a wide class of groups and weights. This generalizes recent related results of Ghandehari-Lee-Ludwig-Spronk-Turowska [11] about the spectrum of Beurling-Fourier algebras on some Lie groups. In the case of discrete groups we show that the spectrum of Beurling-Fourier algebra is homeomorphic to the group itself. [ABSTRACT FROM AUTHOR]

We study glued tensor and free products of compact matrix quantum groups with cyclic groups – so-called tensor and free complexifications. We characterize them by studying their representation categories and algebraic relations. In addition, we generalize the concepts of global colourization and alternating colourings from easy quantum groups to arbitrary compact matrix quantum groups. Those concepts are closely related to tensor and free complexification procedures. Finally, we also study a more general procedure of gluing and ungluing. [ABSTRACT FROM AUTHOR]

Biological life and living organisms appeared about 4 billion years ago. They have become increasingly complex in the course of evolution. The human Self is the current culmination of this incredible complexification. This process and its results are presented in this paper. First the double origin of the Self, biological and social, will be presented. Then the structural development of the Self with its five functions - from bottom to top: Energetic, Sensorial, Muscular, Emotional andRepresentational functions-will be explained. This complex development of the human Self underlies the "ESMERModel". Then, the functional development of the Self will be presented as well as the developmental problems that arise. Evolutionmanaged to organize the Self into an integrated and self-regulated systemby developing four kinds of interconnections between the five functions of the Self. And finally, these four kinds of interconnections will be at the origin of fourmodes of interpersonal relationships. [ABSTRACT FROM AUTHOR]

Let X ⊂ R n be a (global) real analytic surface. Then every positive semidefinite meromorphic function on X is a sum of 10 squares of meromorphic functions on X. As a consequence, we provide a real Nullstellensatz for (global) real analytic surfaces. [ABSTRACT FROM AUTHOR]

Aims and Objectives/Purpose/Research Questions: The Alorese in eastern Indonesia are an Austronesian community who have inhabited two Papuan-speaking islands for approximately 600 years. Their language presents a paradox: contact with the neighbouring Papuan languages has led to both complexification and simplification. This article argues that these opposite outcomes of contact result from two distinct scenarios, and formulates a hypothesis about a shift in multilingual patterns in Alorese history. Design/Methodology/Approach: To formulate a hypothesis about the discontinuity of multilingual patterns, this article first sketches the past and present multilingual patterns of the Alorese by modelling language contact outcomes in terms of bilingual optimisation strategies. This is followed by a comparison of the two scenarios to pinpoint similarities and differences. Data and Analysis: Previous research shows that two types of contact phenomena are attested in Alorese: (a) complexification arising from grammatical borrowings from Papuan languages, and (b) morphological simplification. The first change is associated with prolonged child bilingualism and is the result of Papuan-oriented bilingual strategies, while the latter change is associated with adult second language (L2) learning and is the result of universal communicative strategies. Findings/Conclusions: Complexification and simplification are the results of two different layers of contact. Alorese was first used in small-scale bilingual communities, with widespread symmetric multilingualism. Later, multilingualism became more asymmetric, and the language started to undergo a simplification process due to the considerable number of L2 speakers. Originality: This article is innovative in providing a clear case study showing discontinuity of multilingual patterns, supported by linguistic and non-linguistic evidence. Significance/Implications: This article provides a plausible explanation for the apparent paradox found in Alorese, by showing that different outcomes of contact in the same language are due to different patterns of acquisition and socialisation. This discontinuity should be taken into account by models of language contact. [ABSTRACT FROM AUTHOR]

Qualitative methodological development has produced canonical tendencies that over-complexify and fix a fluid and lived social world. Meanwhile, critical theory has produced critiques on methodology but without enough attention to the qualitative tradition. I bridge these gaps by using an Adornoian position to interrogate the concepts of systematicity, rigidification, complexification, and their problems in ethnographic research and qualitative methodology. I conduct an urban ethnography and autoethnography of the metropolitan blasé as a public attitude of indifference to articulate an alternative, quotidian approach to ethnography that better captures social embeddedness, meaning-creation, and how contexts should drive data collection, analysis, and method-selection. [ABSTRACT FROM AUTHOR]

Aiming at classifying the polarities over aspects, aspect-based sentiment analysis (ABSA) is a fine-grained task of sentiment analysis. The vector representations of current models are generally constrained to real values. Based on mathematical formulations of quantum theory, quantum language models have drawn increasing attention. Words in such models can be projected as physical particles in quantum systems, and naturally represented by representation-rich complex-valued vectors in a Hilbert Space, rather than real-valued ones. In this paper, the Hilbert Space representation for ABSA models is investigated and the complexification of three strong real-valued baselines are constructed. Experimental results demonstrate the effectiveness of complexification and the outperformance of our complex-valued models, illustrating that the complex-valued embedding can carry additional information beyond the real embedding. Especially, a complex-valued RoBERTa model outperforms or approaches the previous state-of-the-art on three standard benchmarking datasets.

We first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompact (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we prove that every unital endomorphism of real Lipschitz algebras of complex-valued functions on compact metric spaces with Lipschitz involutions is a composition operator. Finally, we study some properties of quasicompact and Riesz unital endomorphisms of these algebras.

Every norm ‖ ⋅ ‖ on a real Banach space X induces a minimal norm on the complex linear space C X = X + i X = { x + i y : x , y ∈ X } by ‖ x + i y ‖ C = sup ⁡ { ‖ x cos ⁡ θ + y sin ⁡ θ ‖ : θ ∈ [ 0 , 2 π ] }. In this note we show that if X is finite-dimensional there is a decomposition X = X 1 ⊕ ⋯ ⊕ X k into subspaces such that the isometry group of ‖ ⋅ ‖ C is generated by that of ‖ ⋅ ‖ and operators of the form e i θ 1 I n 1 ⊕ ⋯ ⊕ e i θ k I n k acting on C X = C X 1 ⊕ ⋯ ⊕ C X k. Various applications are given, in particular to isometries of numerical radius. [ABSTRACT FROM AUTHOR]

This paper proposes to integrate the diachronic dimension to the typological study of gender complexity, and focuses on the morphosyntactic encoding of gender distinctions via agreement patterns. After investigating the processes of language change that foster the reduction, loss, expansion and emergence of gender agreement in a sample of fifteen sets of closely related languages (N= 36 languages), we discuss how gender agreement systems in decline and on the rise pattern in terms of complexity. We show that declining and emerging gender agreement systems may exhibit increase or decrease in complexity and discuss how this relates to the fact that they represent transitional stages between absence of gender and full-fledged gender systems. In our analysis, we make use of typological implicational hierarchies in the domain of agreement as a tool to account for diachronic variation and for the patterns of simplification/complexification in the agreement systems of the sampled languages. [ABSTRACT FROM AUTHOR]

In this work, we study some algebraic and topological properties of the ring of global analytic functions on the normalization of a reduced complex analytic space. If is a Stein space, we characterize in terms of the (topological) completion of the integral closure of the ring of global holomorphic functions on X (inside its total ring of fractions) with respect to the usual Fréchet topology of. This shows that not only the Stein space but also its normalization is completely determined by the ring of global analytic functions on X. This result was already proved in 1988 by Hayes–Pourcin when is an irreducible Stein space, whereas in this paper we afford the general case. We also analyze the real underlying structures and of a reduced complex analytic space and its normalization. We prove that the complexification of provides the normalization of the complexification of if and only if is a coherent real analytic space. Roughly speaking, coherence of the real underlying structure is equivalent to the equality of the following two combined operations: (1) normalization + real underlying structure + complexification, and (2) real underlying structure + complexification + normalization. [ABSTRACT FROM AUTHOR]

We derive formulas for characterizing bounded orthogonally additive polynomials in two ways. Firstly, we prove that certain formulas for orthogonally additive polynomials derived in Kusraeva (Vladikavkaz Math J 16(4):49-53, 2014) actually characterize them. Secondly, by employing complexifications of the unique symmetric multilinear maps associated with orthogonally additive polynomials, we derive new characterizing formulas. [ABSTRACT FROM AUTHOR]

Highlights • Chemical composition space helpfully summarizes chemical disequilibria • Life states are metastable attractors that convert food and energy into their key components • New life likely originates at interfaces between low and high diffusion phases (e.g., submerged mineral surfaces) • Chance changes in composition can move a life state to a new, potentially fitter, state • Adaptive evolution in surface-associated life predicts and the origin of cells Abstract Life can be viewed as a localized chemical system that sits in the basin of attraction of a metastable dynamical attractor state that remains out of equilibrium with the environment. To explore the implications of this conception, I introduce an abstract coordinate system, chemical composition (CC Space), which summarizes the degree to which chemical systems are out of equilibrium with the bulk environment. A system's chemical disequilibrium (CD) is defined to be proportional to the Euclidean distance between the composition of a small region of physical space, a pixel, and the origin of CC space. Such a model implies that new living states arise through chance changes in local chemical concentration (“mutations”) that cause chemical systems to move in CC space and enter the basin of attraction of a life state. The attractor of a life state comprises an autocatalytic set of chemicals whose essential (“keystone”) species are produced at a higher rate than they are lost to the environment by diffusion, such that spatial growth of the life state is expected. This framework suggests that new life states are most likely to form at the interface between different physical phases, where the rate of diffusion of keystone species is tied to the low-diffusion regime, whereas food and waste products are subject to the more diffusive regime. Once life nucleates, for example on a mineral surface, it will tend to grow and generate variants as a result of additional mutations that find alternative life states. By jumping from life state to life state, systems can eventually occupy areas of CC space that are too far out of equilibrium with the environment to ever arise in a single mutational step. Furthermore, I propose that variation in the capacity of different surface associated life states to persist and compete may systematically favor states that have higher chemical disequilibrium. The model also suggests a simple and predictable path from surface-associated life to cell-like individuation. This dynamical systems theoretical framework provides an integrated view of the origin and early evolution of life and supports novel empirical approaches. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

Considering tensor products of special commutative algebras and general real Clifford algebras, we arrive at extended Clifford algebras. We have found that there are five types of extended Clifford algebras. The class of extended Clifford algebras is closed with respect to the tensor product. [ABSTRACT FROM AUTHOR]

The Interface Hypothesis (IH) (Sorace, 2011; Sorace & Filiaci, 2006; Sorace & Serratrice, 2009) proposes that structures involving an interface between syntax and other modules are less likely to be fully acquired. Whereas some studies have found evidence in favor of the IH (Michnowicz, 2015), others have reported that adult 2L1 and L2 speakers of differing proficiencies are equally efficient in acquiring the pragmatic constraints conditioning Subject Pronoun Expression (SPE) (Carvalho & Bessett, 2015; Prada-Pérez, 2015). In light of these contradictory results, this study tests the IH by exploring the acquisition of Basque SPE using naturally-occurring speech from 25 Basque-Spanish bilinguals. Results show that Basque L2-learners are responsive to discourse-pragmatic constraints. In fact, L2-Basque SPE is conditioned by a more complex set of constraints than native Basque SPE, for which we propose that L2 SPE results from a process of complexification (Dahl, 2004), triggered by transfer effects from Spanish. [ABSTRACT FROM AUTHOR]

The article discusses the premises of the systemic typology of Gennadij Prokop'evič Mel'nikov in comparison with the precepts of the sociolinguistic typology of Peter Trudgill. The author, in particular, looks into the correlation of linguistic patterning and societal structures as presented in the two theories, and offers a detailed synopsis of the societal factors and their valuables (external determinants) used in the respective disciplines. Detailed discussion of the societal factors as presented in the systemic and social typologies is offered. Major differences between their classifications in Mel'nikov and Trudgill are substantiated. Finally, based on the postulates of Mel'nikov's typology, the paper dwells on the concept of internal determinant or, the communicative scope which optimizes all the levels of language system, while co-varying types of social structures with types of linguistic patterning. [ABSTRACT FROM AUTHOR]

This paper offers further insights on the role of language contact in the reorganization of grammar based on data from two Modern Greek contact-induced dialects: Italiot varieties in contact with both the local Romance varieties and Standard Italian, and Cappadocian, in contact with Turkish. A contrastive investigation reveals interesting correlations and particularities in the reorganization of inflection of the examined systems. Acknowledging that simplification is not triggered solely by contact, we claim that the attested phenomena can be accounted for as temporary complexifications that head toward and ultimately result in simplification within the paradigmatic relations. The amount and type of complexity diverge significantly depending on the (in)compatibility factor among the systems in contact. Furthermore, in terms of loss, addition and replacement of features, our data show that, although replacement and loss are the most prevalent strategies used at the level of morphology, addition is also very likely to occur when structural incompatibility is involved. [ABSTRACT FROM AUTHOR]