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A pseudo-Riemannian Lie group is a connected Lie group endowed with a left-invariant pseudo-Riemannian metric of signature (p , q). In this paper, we study pseudo-Riemannian Lie groups (G , 〈 ⋅ , ⋅ 〉) with non-Killing left-invariant conformal vector fields. Firstly, we prove that if h is a Cartan subalgebra for a semisimple Levi factor of the Lie algebra g , then dim ⁡ h ≤ max ⁡ { 0 , min ⁡ { p , q } − 2 }. Secondly, we classify trans-Lorentzian Lie groups (i.e., min ⁡ { p , q } = 2) with non-Killing left-invariant conformal vector fields, and prove that [ g , g ] is at most three-step nilpotent. Thirdly, based on the classification of the trans-Lorentzian Lie groups, we show that the corresponding Ricci operators are nilpotent, and consequently the scalar curvatures vanish. As a byproduct, we prove that four-dimensional trans-Lorentzian Lie groups with non-Killing left-invariant conformal vector fields are necessarily conformally flat, and construct a family of five-dimensional ones which are not conformally flat. [ABSTRACT FROM AUTHOR]

A study was conducted to understand consumption patterns and factors influencing consumption pattern of meat and meat products in and around Nagpur city. A proportionate random sampling method was used to conduct a survey (sample size of 400) using a bilingual (Marathi and English) questionnaire comprising questions related to the socioeconomic particulars of the consumers, meat and meat products consumption patterns, and factors influencing on it. The study revealed that most respondents were 15 to 30 years (52.5%) and college graduates (35.8%). About 43% of the respondents reported a family income of more than six lakhs. Most of the consumers ate meat for taste (54.4%) and health benefits (27.0%) and responded that they usually consume meat once a week (50.3%). The most preferred meat in and around Nagpur city was poultry meat (50.8%), followed by chevon (27.5%) and Fish & seafood (18.7%). Most respondents (66.8%) were unwilling to pay more for lean meat. The results indicated that most respondents consider safety, nutritional value, taste, market price, availability, and children's meat preference as essential factors influencing meat consumption. [ABSTRACT FROM AUTHOR]

In this study we analyse the spatial distribution patterns of professionals and related workers in high‐skilled occupations and elementary workers in low‐skilled occupations in the Seoul metropolitan area and explore their geographical factors. Spatial autocorrelation relates to the formation and clustering of hot spots according to each occupational characteristic. Geographic factors affecting the distribution of workplaces and residences in professionals‐related occupations and elementary‐related occupations act differently for each middle occupational classification. However, some occupations show similar spatial distribution patterns. In particular, we found that industrial economic drivers have influence more significant than other regional factors in determining the distribution of workplace and residence by occupation. The spatial coefficient of geographical adjacency varies with the attributes of each occupation and tends to be larger in professional jobs. Findings from the study will help prepare policies related to local talents for specialisation and advancement of the occupational structure and will be of wider interest. [ABSTRACT FROM AUTHOR]

We implement the Boolean valued analysis of Baer -algebras and Jordan–Banach algebras. These algebras transform into - and -factors. Presentation of the factors as operator algebras leads to Kaplansky–Hilbert modules. We overview the basic properties of these objects. [ABSTRACT FROM AUTHOR]

We obtain an effective analytic formula, with explicit constants, for the number of distinct irreducible factors of a polynomial $f \in \mathbb {Z}[x]$. We use an explicit version of Mertens' theorem for number fields to estimate a related sum over rational primes. For a given $f \in \mathbb {Z}[x]$ , our result yields a finite list of primes that certifies the number of distinct irreducible factors of f. [ABSTRACT FROM AUTHOR]

A criterion is given for the Lie algebra of infinitesimal holomorphic automorphisms of the direct product of two germs of real analytic generic CR manifolds to be equal to the direct sum of the algebras of the factors. In particular, this equality holds if the algebra of the direct product is finite-dimensional (for example, in the case of the product of holomorphically nondegenerate germs of finite Bloom–Graham type). The notion of the sum of Bloom–Graham types is introduced. It is shown that the type of a direct product is equal to the sum of the types of factors. [ABSTRACT FROM AUTHOR]

The aim of this study is to examine the procedural relationship between the psychosocial factors of mathematics learning such as attitudes, motivation and satisfaction and academic achievement in redesigned college-level algebra course sections. Evaluation reports on the redesigned courses show that they have achieved a level of academic achievement equivalent to and / or better than traditionally taught courses, including university-level mathematics introductory courses. However, the reasons for equal or higher academic achievement are not fully documented in the literature. In this context, the academic success of the university-level algebra course designed using the Emporium model was chosen as the focus of this research study. In this manuscript, in addition to the psychosocial factors of mathematics learning, mathematics achievement in the context of university algebra was also examined. The data related to the psychosocial variables were obtained from a likert scale developed by the researcher, and academic achievement data from the final exam grades of the algebra course. Hierarchical multiple regression analysis was used to analyze the collected data. The results of the study indicaed that satisfaction from mathematics teaching was the only significant predictor of mathematics achievement in college-level algebra; learner motivation and satisfaction were determined as important predictors of attitude towards mathematics, and attitude towards mathematics played the role of mediating variable in the relationship between student satisfaction and motivation in introductory level redesigned university algebra courses. [ABSTRACT FROM AUTHOR]

In real‐world applications, large amounts of data from multiple sources come in the form of streams. This makes multi‐view feature learning cost much time when new instances rise incrementally. Dealing with these growing multi‐view data becomes a challenging problem. Some single‐view methods focus on processing the data dynamically, but they are not suitable for multi‐view data. Some online multi‐view methods are proposed to tackle it, but they ignore the influence of uncorrelated items in each view. Therefore, in this study, the authors propose a new algorithm, called Incremental Multi‐view Correlated Feature Learning (IMCFL) based on non‐negative matrix factorisation, to learn the common feature across views. By separating uncorrelated items of new instances and constructing incremental joint learning of correlated and uncorrelated features, the proposed IMCFL can eliminate the influence of uncorrelated information in the individual view and improve the effectiveness of incremental multi‐view common feature learning. Extensive experiments on real‐world datasets confirm its superiority by comparing it with other state‐of‐the‐art incremental and non‐incremental methods. [ABSTRACT FROM AUTHOR]

For the centrally extended Heisenberg double of SL2, its center is determined, the central factor algebras are described, and classifications of simple Harish-Chandra modules, simple Whittaker modules, and simple quasi-Whittaker modules are obtained. Two classes of simple weight modules with infinite-dimensional weight spaces are given. We also give a classification of simple modules that decompose into a direct sum of simple finite-dimensional s l 2 -modules with finite multiplicities. [ABSTRACT FROM AUTHOR]

The Grigorchuk and Gupta-Sidki groups play fundamental role in modern group theory. They are natural examples of self-similar finitely generated periodic groups. The first author constructed their analogue in case of restricted Lie algebras of characteristic 2 [50] , Shestakov and Zelmanov extended this construction to an arbitrary positive characteristic [68]. Thus, we have examples of finitely generated restricted Lie algebras with a nil p -mapping. In characteristic zero, similar examples of Lie and Jordan algebras do not exist by results of Martinez and Zelmanov [43] and [78]. The first author constructed analogues of the Grigorchuk and Gupta-Sidki groups in the world of Lie superalgebras of arbitrary characteristic, the virtue of that construction is that Lie superalgebras have clear monomial bases [51] , they have slow polynomial growth. As an analogue of periodicity, Z 2 -homogeneous elements are ad-nilpotent. A recent example of a Lie superalgebra is of linear growth, of finite width 4, just infinite but not hereditary just infinite [13]. By that examples, an extension of the result of Martinez and Zelmanov [43] for Lie superalgebras of characteristic zero is not valid. Now, we construct a just infinite fractal 3-generated Lie superalgebra Q over arbitrary field, which gives rise to an associative hull A , a Poisson superalgebra P , and two Jordan superalgebras J and K , the latter being a factor algebra of J. In case char K ≠ 2 , A has a natural filtration, which associated graded algebra has a structure of a Poisson superalgebra such that gr A ≅ P , also P admits an algebraic quantization using a deformed superalgebra A (t). The Lie superalgebra Q is finely Z 3 -graded by multidegree in the generators, A , P are also Z 3 -graded, while J and K are Z 4 -graded by multidegree in four generators. By virtue of our construction, these five superalgebras have clear monomial bases and slow polynomial growth. We describe multihomogeneous coordinates of bases of Q , A , P in space as bounded by "almost cubic paraboloids". We determine a similar hypersurface in R 4 that bounds monomials of J and K. Constructions of the paper can be applied to Lie (super)algebras studied before to obtain Poisson and Jordan superalgebras as well. The algebras Q , A , and the algebras without unit P o , J o , K o are direct sums of two locally nilpotent subalgebras and there are continuum such decompositions. Also, Q = Q 0 ¯ ⊕ Q 1 ¯ is a nil graded Lie superalgebra, so, Q again shows that an extension of the result of Martinez and Zelmanov for Lie superalgebras of characteristic zero is not valid. In case char K = 2 , Q has a structure of a restricted Lie algebra with a nil p -mapping. The Jordan superalgebra K is nil finely Z 4 -graded, in contrast with non-existence of such examples (roughly speaking, analogues of the Grigorchuk group) of Jordan algebras in characteristic distinct from 2 [78]. Also, K is of slow polynomial growth, just infinite, but not hereditary just infinite. We call the superalgebras Q , A , P , J , K fractal because they contain infinitely many copies of themselves. [ABSTRACT FROM AUTHOR]

Let (g,[p]) be a restricted Lie algebra over an algebraically closed field k of characteristic p ≥ 3. Motivated by the behavior of geometric invariants of the so-called (g,[p])-modules of constant j-rank (j ∈ {1, . . . , p−1}), we study the projective variety E(2,g) of two-dimensional elementary abelian subalgebras. If p ≥ 5, then the topological space E(2,g/C(g)), associated to the factor algebra of g by its center C(g), is shown to be connected. We give applications concerning categories of (g,[p])-modules of constant j-rank and certain invariants, called j-degrees. [ABSTRACT FROM AUTHOR]

We give a full description of associative algebras over an arbitrary field, whose subalgebra lattice is distributive. All such algebras are commutative, their nil-radical is at most two-dimensional, and the factor algebra with respect to the nil-radical is an algebraic extension of the base field. [ABSTRACT FROM AUTHOR]

In commutative invariant theory, a classical result due to Auslander says that if R = k x 1 , ... , x n and G is a finite subgroup of Au t gr (R) ≅ GL (n , k) which contains no reflections, then there is a natural graded isomorphism R # G ≅ End R G (R). In this paper, we show that a version of Auslander's Theorem holds if we replace R by an Artin-Schelter regular algebra A of global dimension 2, and G by a finite subgroup of Au t gr (A) which contains no quasi-reflections. This extends work of Chan–Kirkman–Walton–Zhang. As part of the proof, we classify all such pairs (A , G) , up to conjugation of G by an element of Au t gr (A). In all but one case, we also write down explicit presentations for the invariant rings A G , and show that they are isomorphic to factors of AS regular algebras. [ABSTRACT FROM AUTHOR]

Considering their share in total public revenues, the most important source of income used by states for financing their economic activities are taxes. Due to their sovereign power, they collect taxes free of charge and compulsory. The algebra factor in taxation can naturally play a determining role on the level of happiness of a query on taxpayers. In this way, it helps the tax to transform the social and psychological aspects of the tax in order to realize the intended effects of tax policies and to manage the positive or negative reactions against the tax. When asked to be asked in this context, that is, through social consensus, information about taxpayers will become a source of social happiness. However, this is associated with a society-acceptable tax burden. This high tax burden impact on happiness of spatial econometric models for 2013 and 2015 were investigated life in Turkey. A negative effect of tax burden on happiness level was observed in all models estimated. Regardless of the calculation method of the tax burden; tax burden reduces the happiness levels of the provinces. Accordingly, it has emerged that the total tax burden should be reduced and public services should be clearly explained to the public. [ABSTRACT FROM AUTHOR]

Arch-shaped axially magnetized bodies tend to appear frequently in electrical machine analysis such as in the overhang parts of the classical radial-flux machines as well as in the main parts of the axial-flux machines. The calculation of the 3-D fields originating from these bodies is demanding. The 3-D FEA suffers from high computational burden as well as no knowledge of the field origin. Analytic techniques involve the use of elliptic integrals and complex numbers for numerical evaluation, which makes them significantly slower than the 3-D FEA. In this article, a new analytical technique is proposed to speed up the computation by a factor of 20 for the global magnetic field created by a generic magnetized body by removing complex numbers and reducing the analytic equations significantly without any loss of precision. As a result, it can compete with the conventional 3-D FEA. In addition, integral methods may contribute to the wider use of parallel processing techniques. The original expressions for the vector potential are also provided, which has its own benefits and applications. Finally, the showcased magnetized body is assessed against 3-D FEA and discussed in terms of practical applications. [ABSTRACT FROM AUTHOR]

[Objective] The paper was to screen out the dominant species of Trichogramma sp. parasitized on Ostrinia nubilalis eggs and to evaluate the field control effect of Trichogramma sp.. [Method] Six kinds of fresh egg masses of Trichogramma sp. parasitized on O. nubilalis were used to screen out three dominant species of Trichogramma sp., and the single factor experimental design was used to evaluate field control effect. The dominant species were determined by combining yield, recovery yield loss rate and yield increase rate. [Result] T. ostriniae had the highest parasitic rate on O. nubilalis; the parasitic rate of egg masses was 74.0%, and the parasitic rate of egg granules was 65.4%. The second was T. dendrolimi; the parasitic rate of egg masses was 62.0%, and the parasitic rate of egg granules was 59.5%. The parasitic rates of egg masses and egg granules of T. chilonis were 58.0% and 47.1%, respectively. The three Trichogramma sp. were the dominant bee species parasitized on O. nubilalis eggs. The average control effect of T. ostrinae parasitized on 0. nubilalis in the field was 73.86%; the average control effect of T. dendrolimi was 68.47%; and the average control effect of T. chilonis was 47.97%. The recovery yield loss rates was 9.58%, 7.02% and 4.02%, and the yield increase rates were 9.65%, 7.47% and 4.52%, respectively. [Conclusion] Considering the control effect and cost control comprehensively, T. dendrolimi should be used to control O. nubilalis in actual production. [ABSTRACT FROM AUTHOR]

We shall give some results for an integer divisible by its unitary totient. [ABSTRACT FROM AUTHOR]

Reservoir evaluation of tight sandstone involves the determination of reservoir properties from samples and logs. In the calculation of water saturation, Archie formula is an important fundamental and connection between log evaluation and petrophysics. Highly accurate parameters of Archie formula are the key to the log evaluation of gas-bearing tight sandstone. At present, there are two methods of the rock-electric experiment to measure parameters of Archie formula: water increment (imbibition) and water decrement (centrifugation). In this paper the experimental measurement of a group of tight sandstone has been designed and the results of the two experimental ways are quite different. In the experiment, the distribution of brine is a main factor affecting the electrical properties of rocks. Fluid distribution model during imbibition and drainage is used to explain the results of rock electrical experiments, and the results are verified by nuclear magnetic resonance measurement. In the end, the Pickett chart method of actual data is used to compute the ranges of the saturation exponent n approximately, then to verify the correctness of the theoretical analysis. The results demonstrate that the centrifugal method is more applicable. In the log evaluation of tight sandstone, the appropriate choice of the method which can get accurate rock electrical parameters is important. Reliable evaluation will provide support for future development of gas-bearing tight sandstone. [ABSTRACT FROM AUTHOR]

This commentary attempts to briefly but critically discuss some of the potential factors that have made the 2005 article 'City Branding: An effective assertion of identity or a transitory marketing trick?' a well‐known and extensively cited article in the field of place branding. It includes an account of the major sources of inspiration and the main intentions of the article, as well as a necessarily personal reflection on its shortcomings. [ABSTRACT FROM AUTHOR]

The aim of the paper is to prove two conjectures from the paper [V. V. Bavula, The algebra of integro-differential operators on a polynomial algebra, J. London Math. Soc. (2) 83 (2011) 517–543, arXiv:math.RA/0912.0723] that the (left and right) global dimension of the algebra 𝕀 n : = K 〈 x 1 , ... , x n , ∂ ∂ x 1 , ... , ∂ ∂ x n , ∫ 1 , ... , ∫ n 〉 of polynomial integro-differential operators and the Jacobian algebra 𝔸 n is equal to n (over a field of characteristic zero). The algebras 𝕀 n and 𝔸 n are neither left nor right Noetherian and 𝕀 n ⊂ 𝔸 n . Furthermore, they contain infinite direct sums of nonzero left/right ideals and are not domains. An analogue of Hilbert's Syzygy Theorem is proven for the algebras 𝕀 n , 𝔸 n and their factor algebras. It is proven that the global dimension of all prime factor algebras of the algebras 𝕀 n and 𝔸 n is n and the weak global dimension of all the factor algebras of 𝕀 n and 𝔸 n is n. [ABSTRACT FROM AUTHOR]

We defined the notion of the quantum double inclusion [S. De, J. Math. Phys. 60, 071701 (2019)] associated with a finite-index and finite-depth subfactor, which is closely related to that of Ocneanu's asymptotic inclusion, and studied the quantum double inclusion associated with the Kac algebra subfactor RH ⊂ R, where H is a finite-dimensional Kac algebra acting outerly on the hyperfinite II1 factor R and RH denotes the fixed-point subalgebra. In this article, we analyze quantum double inclusions associated with the family of Kac algebra subfactors given by { R H ⊂ R ⋊ H ⋊ H * ⋊ ⋯ ︸ m times : m ≥ 1 }. For each m > 2, we construct a model N m ⊂ M for the quantum double inclusion of R H ⊂ R ⋊ H ⋊ H * ⋊ ⋯ ︸ m − 2 times , where N m = ((⋯ ⋊ H − 2 ⋊ H − 1 ) ⊗ ( H m ⋊ H m + 1 ⋊ ⋯ )) ′ ′ , M = (⋯ ⋊ H − 1 ⋊ H 0 ⋊ H 1 ⋊ ⋯ ) ′ ′ , and for any integer i, the notation Hi stands for H or H* according as i is odd or even. In this article, we give an explicit description of the subfactor planar algebra associated with N m ⊂ M (m > 2) which turns out to be a planar subalgebra of P * (m) ( H m ) (the adjoint of the m-cabling of the planar algebra of Hm). We then show that for each m > 2, the depth of N m ⊂ M is always two. Observing that N m ⊂ M is reducible for all m > 2, we study in great detail the weak Kac algebra structure of the relative commutant ( N m ) ′ ∩ M 2 . [ABSTRACT FROM AUTHOR]

Empirical evaluations can be conducted with students or professionals as subjects. Students are much more accessible than professionals and they are inexpensive, allowing a greater number of empirical studies to be conducted. Professionals are preferred over students due to concerns regarding the external validity of student-based experiments. Professionals are believed to perform differently, most likely better than students. But with respect to evaluating the cognitive effectiveness of software engineering notations, are professionals really better? The literature has suggested that the presentation of information is just as critical as the content it conveys, hence necessitating this type of empirical studies. If professionals are not much better than students, then such important finding can be a springboard to many much-needed empirical evaluations in this field. In this paper, we report on an experiment that compare the performances of professionals and students with respect to syntactical model comprehension, which is a core factor for evaluating the cognitive effectiveness of notations. The experiment involved two groups of professionals and two student groups, totaling 74 professionals and 75 students. The results of the experiment indicate that students can be used as an adequate replacement to professionals in such type of empirical studies. [ABSTRACT FROM AUTHOR]

We study the stable category of the graded Cohen–Macaulay modules of the factor algebra of the preprojective algebra associated with an element w of the Coxeter group of a quiver. We show that there exists a silting object M(w)| of this category associated with each reduced expression w of w and give a sufficient condition on w such that M(w) is a tilting object. In particular, the stable category is triangle equivalent to the derived category of the endomorphism algebra of M(w)⁠. Moreover, we compare it with a triangle equivalence given by Amiot–Reiten–Todorov for a cluster category. [ABSTRACT FROM AUTHOR]

Distinguishing certain and uncertain information is of crucial importance both in the scientific field in the strict sense and in the popular scientific domain. In this paper, by adopting an epistemic stance perspective on certainty and uncertainty, and a mixed procedure of analysis, which combines a bottom-up and a top-down approach, we perform a comparative study (both qualitative and quantitative) of the uncertainty linguistic markers (verbs, non-verbs, modal verbs, conditional clauses, uncertain questions, epistemic future) and their scope in three different corpora: a historical corpus of 80 biomedical articles from the British Medical Journal (BMJ) 1840–2007; a corpus of 12 biomedical articles from BMJ 2013, and a contemporary corpus of 12 scientific popular articles from Discover 2013. The variables under observation are time, structure (IMRaD vs no-IMRaD) and genre (scientific vs popular articles). We apply the Generalized Linear Models analysis in order to test whether there are statistically significant differences (1) in the amount of uncertainty among the different corpora, and (2) in the categories of uncertainty markers used by writers. The results of our analysis reveal that (1) in all corpora, the percentages of uncertainty are always much lower than that of certainty; (2) uncertainty progressively diminishes over time in biomedical articles (in conjunction with their structural changes–IMRaD–and to the increase of the BMJ Impact Factor); and (3) uncertainty is slightly higher in scientific popular articles (Discover 2013) as compared to the contemporary corpus of scientific articles (BMJ 2013). Nevertheless, in all corpora, modal verbs are the most used uncertainty markers. These results suggest that not only do scientific writers prefer to communicate their uncertainty with markers of possibility rather than those of subjectivity but also that science journalists prefer using a third-person subject followed by modal verbs rather than a first-person subject followed by mental verbs such as think or believe. [ABSTRACT FROM AUTHOR]

Follow-up experiment is widely applied to various fields such as science and engineering, since it is an indispensable strategy, especially when some additional resources or information become available after the initial design of experiment is carried out. Moreover, some extra factors may be added in the follow-up experiment. One may augment the number of runs and/or factors for the purpose of application. In this paper, the issue of the uniform row augmented designs and column augmented designs with mixed two- and three-level is investigated. The uniformity of augmented designs is discussed under the Lee discrepancy, some lower bounds of Lee discrepancy for the augmented designs are obtained. The construction algorithm of the uniform augmented designs is given. Some numerical examples indicate that uniform augmented designs can be constructed with high efficiency. [ABSTRACT FROM AUTHOR]

We present the High-Elective Resolution Modelling Emission System version 3 (HERMESv3), an open source, parallel and stand-alone multi-scale atmospheric emission modelling framework that computes gaseous and aerosol emissions for use in atmospheric chemistry models. HERMESv3 is coded in Python and consists of a global_regional module and a bottom_up module that can be either combined or executed separately. In this contribution (Part 1) we describe the global_regional module, a customizable emission processing system that calculates emissions from different sources, regions and pollutants on a user-specified global or regional grid. The user can flexibly define combinations of existing up-to-date global and regional emission inventories and apply country-specific scaling factors and masks. Each emission inventory is individually processed using user-defined vertical, temporal and speciation profiles that allow obtaining emission outputs compatible with multiple chemical mechanisms (e.g. Carbon-Bond 05). The selection and combination of emission inventories and databases is done through detailed configuration files providing the user with a widely applicable framework for designing, choosing and adjusting the emission modelling experiment without modifying the HERMESv3 source code. The generated emission fields have been successfully tested in different atmospheric chemistry models (i.e. CMAQ, WRF-Chem and NMMB-MONARCH) at multiple spatial and temporal resolutions. In a companion article (Part 2; Guevara et al., 2019) we describe the bottom_up module, which estimates emissions at the source level (e.g. road link) combining state-of-the-art bottom–up methods with local activity and emission factors. [ABSTRACT FROM AUTHOR]

The development of libraries in any country is critical for its socio-economic transformation, especially in the 21st century where access to information and knowledge has become the key factor in production. In support of this thinking, the International Federation of Library Associations and Institutions (IFLA) launched its Global Vision project in 2017, which has attracted the participation of over 190 countries worldwide. For most nations, this project has indeed created platforms for championing strong and united library associations that contribute towards developing literate, informed and participative societies. A number of countries in Africa have taken the initiative to participate in the IFLA Global Vision project, and Zimbabwe is no exception. This article seeks to examine the challenges and opportunities for Zimbabwe as a participant. It also scrutinises the road travelled by librarians in Zimbabwe in their pursuit of a vision to reposition their libraries in the global library landscape. The article studies the factors affecting the development of a unified library sector in Zimbabwe. In addition, it explores how Zimbabwe's national professional association, the Zimbabwe Library Association (ZIMLA), can unite librarians and contribute towards the IFLA Global Vision for a unified library profession. The article proposes a strategy to enhance unity among library professionals for the actualisation of the IFLA Global Vision. [ABSTRACT FROM AUTHOR]

A pair of orthogonal one-factorizations F and G of the complete graph Kn is C4-free if for any two factors F∈F and G∈G the union F∪G does not include a cycle of length four. Such a concept was introduced by Blokhuis et al. (J Combin Theory B 82: 1-18, 2001), who used it to improve the upper bound for two-round rainbow colorings of Kn. In this paper, we focus on constructions for a pair of orthogonal C4-free one-factorizations of the complete graph Kn. Some infinite classes of such orthogonal decompositions are obtained. [ABSTRACT FROM AUTHOR]

Abstract Given a finite dimensional algebra over a perfect field the text introduces covering functors over the mesh category of any modulated Auslander–Reiten component of the algebra. This is applied to study the composition of irreducible morphisms between indecomposable modules in relation with the powers of the radical of the module category. [ABSTRACT FROM AUTHOR]

On the background of structural changes recorded in the past ten years and the micro and macro-prudential policy mix, the Romanian banking sector has seen an improvement of the main financial and prudential indicators. At the same time, it was emphasized the linkage between the risk associated with the banking sector and the related government sector. The regulatory system in the banking field has experienced significant changes, including for the purposes of consumer protection, with a direct effect on the profitability of this sector. Commercial banks' strategies have led to changes in the balance sheet of commercial banks, as well as at the market level, by reducing their number, increasing competitiveness, reducing the vulnerability associated with the currency risk, changes in the structure of credits granted by reducing the credit intake in foreign currency in total credits, increasing the level of lending in the population sector, notably by supporting the mortgage credit, reducing external financial dependence, improvement solvency. This article aims to highlight the evolution of the profitability of the banking sector in the last decade and the main factors that have influenced the level of financial profitability. [ABSTRACT FROM AUTHOR]

In this paper, we explicitly work out the subfactor planar algebra P (N ⊂ Q) for an intermediate subfactor N ⊂ Q ⊂ M of an irreducible subfactor N ⊂ M of finite index. We do this in terms of the subfactor planar algebra P (N ⊂ M) by showing that if T is any planar tangle, the associated operator Z T (N ⊂ Q) can be read off from Z T (N ⊂ M) by a formula involving the so-called biprojection corresponding to the intermediate subfactor N ⊂ Q ⊂ M and a scalar α (T) carefully chosen so as to ensure that the formula defining Z T (N ⊂ Q) is multiplicative with respect to composition of tangles. Also, the planar algebra of Q ⊂ M can be obtained by applying these results to M ⊂ M 1 . We also apply our result to the example of a semi-direct product subgroup-subfactor. [ABSTRACT FROM AUTHOR]

Abstract Inspired by Edward Witten's questions, we compute the mutual information associated with free fermions, and we deduce many results about entropies for chiral CFT's which are embedded into free fermions, and their extensions. Such relative entropies in CFT are here computed explicitly for the first time in a mathematical rigorous way, and Our results agree with previous computations by physicists based on heuristic arguments; in addition we uncover a surprising connection with the theory of subfactors, in particular by showing that a certain duality, which is argued to be true on physical grounds, is in fact violated if the global dimension of the conformal net is greater than 1. [ABSTRACT FROM AUTHOR]

Let P : C n → C be an m -homogeneous polynomial given by P ( x ) = ∑ 1 ≤ j 1 ≤ … ≤ j m ≤ n c j 1 … j m x j 1 … x j m . Defant and Schlüters defined a non-symmetric associated m -form L P : ( C n ) m → C by L P ( x ( 1 ) , … , x ( m ) ) = ∑ 1 ≤ j 1 ≤ … ≤ j m ≤ n c j 1 … j m x j 1 ( 1 ) … x j m ( m ) . They estimated the norm of L P on ( C n , ‖ ⋅ ‖ ) m by the norm of P on ( C n , ‖ ⋅ ‖ ) times a ( c log ⁡ n ) m 2 factor for every 1-unconditional norm ‖ ⋅ ‖ on C n . A symmetrization procedure based on a card-shuffling algorithm which (together with Defant and Schlüters' argument) brings the constant term down to ( c m log ⁡ n ) m − 1 is provided. Regarding the lower bound, it is shown that the optimal constant is bigger than ( c log ⁡ n ) m / 2 when n ≫ m . Finally, the case of ℓ p -norms ‖ ⋅ ‖ p with 1 ≤ p < 2 is addressed. [ABSTRACT FROM AUTHOR]

We show that Shlyakhtenko's free Araki-Woods factors are strongly solid, meaning that for any diffuse amenable von Neumann subalgebra that is the range of a normal conditional expectation, the normalizer remains amenable. This provides the first class of nonamenable strongly solid type III factors. [ABSTRACT FROM AUTHOR]

Abstract: It is well known that a nontrivial commutator in a free group is never a proper power. We prove a theorem that generalizes this fact and has several worthwhile corollaries. For example, an equation [ x 1 , y 1 ] … [ x k , y k ] = z n, where n ⩾ 2 k, in the free product F of groups without nontrivial elements of order ⩽ n implies that z is conjugate to an element of a free factor of F. If a nontrivial commutator in a free group factors into a product of elements which are conjugate to each other then all these elements are distinct. [ABSTRACT FROM AUTHOR]

We study the Ollivier{Ricci curvature of graphs as a function of the chosen idleness. We show that this idleness function is concave and piecewise linear with at most three linear parts, and at most two linear parts in the case of a regular graph. We then apply our result to show that the idleness function of the Cartesian product of two regular graphs is completely determined by the idleness functions of the factors. [ABSTRACT FROM AUTHOR]

An interpretation of quantum mechanics is discussed. It is assumed that quantum is energy. An algorithm by means of the energy interpretation is discussed. An algorithm, based on the energy interpretation, for fast determining a homogeneous linear function f(x) := s.x = s1x1 + s2x2 + ⋯ + sNxN is proposed. Here x = (x1, …, xN), xj ∈ R and the coefficients s = (s1, …, sN), sj ∈ N. Given the interpolation values (f(1),f(2),...,f(N))=y→, the unknown coefficients s=(s1(y→),…,sN(y→)) of the linear function shall be determined, simultaneously. The speed of determining the values is shown to outperform the classical case by a factor of N. Our method is based on the generalized Bernstein-Vazirani algorithm to qudit systems. Next, by using M parallel quantum systems, M homogeneous linear functions are determined, simultaneously. The speed of obtaining the set of M homogeneous linear functions is shown to outperform the classical case by a factor of N × M. [ABSTRACT FROM AUTHOR]

Results of a recent paper by A. V. Vasin, S. V. Kislyakov, and the author are extended to the case of outer functions in the upper half-plane. As in the case of the disk, it can only be guaranteed that the smoothness of an outer function is at least one half of that for its modulus, but the quantitative manifestation of this effect is different; in particular, it depends on the position of the point at which the smoothness is measured. Bibliography: 8 titles. [ABSTRACT FROM AUTHOR]

This paper deals with the mutual relationships between the factor group G/ζ(G) (respectively G/ζk(G)) and G′ (respectively γk+1(G) and GN). It is proved that if G/ζ(G) (respectively G/ζk(G)) has finite 0-rank, then G′ (respectively γk+1(G) and GN) also have finite 0-rank. Furthermore, bounds for the 0-ranks of G′,γk+1(G) and GN are obtained. [ABSTRACT FROM AUTHOR]

The structure of groups which have at most two isomorphism classes of central factors (B2-groups) are investigated. A complete description of B2-groups is obtained in the locally finite case and in the nilpotent case. In addition detailed information is obtained about soluble B2-groups. Also structural information about insoluble B2-groups is given, in particular when such a group has the derived subgroup satisfying the minimal condition. [ABSTRACT FROM AUTHOR]

We prove that the Kloosterman sum S(1, 1; c) changes sign infinitely often as c runs over squarefree numbers with at most 7 prime factors, which improves the previous results of Fouvry and Michel, Sivak-Fischler, Matomäki, and the author. [ABSTRACT FROM AUTHOR]

Two edges and in a graph are said to be adjacent if they have a vertex in common, and distance two apart if they are nonadjacent but both are adjacent to a common edge. An -edge-labeling of a graph is an assignment of nonnegative integers, called labels, to the edges of such that the difference between labels of any two adjacent edges is at least , and the labels of any two edges that are distance two apart are different. The span of an -edge-labeling of a graph is the difference between the maximum and minimum labels. The minimum span over all -edge-labelings of a graph is called the -edge-labeling number of , denoted by . For , the edge-path-replacement of a graph , denoted by , is a graph obtained by replacing each edge of with a path on vertices. This paper investigates the -edge-labeling number of the edge-path-replacement of a graph for . We get the following main results: Let be a graph with maximum degree and be an integer not less than , then if is odd, and otherwise . Let be a graph with maximum degree . Then when is even, and when is odd. [ABSTRACT FROM AUTHOR]

In this article, we study a form of free transport for the interpolated free group factors, extending the work of Guionnet and Shlyakhtenko for the usual free group factors [11] . Our model for the interpolated free group factors comes from a canonical finite von Neumann algebra M ( Γ , μ ) associated to a finite, connected, weighted graph ( Γ , V , E , μ ) [12,13] . With this model, we use an operator-valued version of Voiculescu's free difference quotient introduced in [13] to state a Schwinger–Dyson equation which is valid for the generators of M ( Γ , μ ) . We construct free transport for appropriate perturbations of this equation. Also, M ( Γ , μ ) can be constructed using the machinery of Shlyakhtenko's operator-valued semicircular systems [24] . [ABSTRACT FROM AUTHOR]

This paper is devoted to investigate the symmetry and monotonicity properties for positive solutions of fractional Laplacian equations. Especially, we consider the following fractional Laplacian equation with homogeneous Dirichlet condition: Here is a domain (bounded or unbounded) in which is convex in -direction. is the nonlocal fractional Laplacian operator which is defined as Under various conditions on and on a solution it is shown that is strictly increasing in in the left half of , or in . Symmetry (in ) of some solutions is proved. [ABSTRACT FROM AUTHOR]