Search

In this paper, we study the following prescribed Gaussian curvature problem: K = f ~ ⁢ (θ) ϕ ⁢ (ρ) α − 2 ⁢ ϕ ⁢ (ρ) 2 + | ∇ ¯ ⁢ ρ | 2 , a generalization of the Alexandrov problem ( α = n + 1 ) in hyperbolic space, where f ~ is a smooth positive function on S n , 휌 is the radial function of the hypersurface, ϕ ⁢ (ρ) = sinh ⁡ ρ and 퐾 is the Gauss curvature. By a flow approach, we obtain the existence and uniqueness of solutions to the above equations when α ≥ n + 1 . Our argument provides a parabolic proof in smooth category for the Alexandrov problem in H n + 1 . We also consider the cases 2 < α ≤ n + 1 under the evenness assumption of f ~ and prove the existence of solutions to the above equations. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some Korovkin type approximation theorems for double sequences of positive linear operators on two-dimensional weighted spaces via statistical type convergence method with respect to power series method. Additionally, we calculate the rate of convergence. As an application, we provide an approximation using the generalization of Gadjiev-Ibragimov operators for Pp-statistical convergence. Our results are meaningful and stronger than those previously given for two-dimensional weighted spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the f-operator radius of Hilbert space operators as a generalization of the Euclidean operator radius and the q-operator radius. The properties of the newly defined radius are discussed, emphasizing how it extends some known results in the literature. [ABSTRACT FROM AUTHOR]

The issue of modelling observations generated in matrix form over time is key in economics, finance and many domains of application. While it is common to model vectors of observations through standard vector time series analysis, original matrix-valued data often reflect different types of structures of time series observations which can be further exploited to model interdependencies. In this paper, we propose a novel matrix autoregressive model in a bilinear form which, while leading to a substantial dimensionality reduction and enhanced interpretability: (a) allows responses and potential covariates of interest to have different dimensions; (b) provides a suitable estimation procedure for matrix autoregression with lag structure; (c) facilitates the introduction of Bayesian estimators. We propose maximum likelihood and Bayesian estimation with Independent-Normal prior formulation, and study the theoretical properties of the estimators through simulated and real examples. [ABSTRACT FROM AUTHOR]

Let k ≥ 2. A generalization of the well-known Pell sequence is the k-Pell sequence whose first k terms are 0,..., 0, 1 and each term afterwards is given by the linear recurrence p n (k) = 2 P n − 1 (k) + P n − 2 (k) + ⋯ + P n − k (k) . The goal of this paper is to show that 11, 33, 55, 88 and 99 are all repdigits expressible as sum or difference of two k-Pell. The proof of our main theorem uses lower bounds for linear forms in logarithms of algebraic numbers and a modified version of Baker-Davenport reduction method (due to Dujella and Pethő). This extends a result of Bravo and Herrera [Repdigits in generalized Pell sequences, Arch. Math. (Brno) 56(4) (2020), 249–262]. [ABSTRACT FROM AUTHOR]

The reversible property of rings was introduced by Cohn and has important generalizations in noncommutative ring theory. In this paper, reversibility of rings is investigated in relation with quasinilpotents and idempotents, and our argument is spread out based on this. We call a ring RQnil e-reversible if for any a , b ∈ R , being a ⁢ b = 0 implies b ⁢ a ⁢ e ∈ R qnil for a prescribed idempotent e ∈ R , where R qnil denotes the set of all quasinilpotent elements of R. In the first, we determine the set R qnil for some classes of rings to investigate the structure of Qnil e-reversible rings. In the second, we use R qnil to define Qnil e-reversibility of rings. The notion of Qnil e-reversible ring is a proper generalization of that of e-semicommutative ring, Qnil-semicommutative ring, e-reversible ring and right (left) quasi-duo ring. We obtain some relations between a ring and its quotient rings in terms of Qnil e-reversibility. Applications via some ring extensions and examples illustrating our results are provided. [ABSTRACT FROM AUTHOR]

To complement existing synchronic typological studies of the marking strategies of (past) habituality, this paper details the diachronic paths leading to and from past habitual constructions. The rich corpus evidence from the diachrony of Ancient Greek demonstrates at least four source constructions: (1) past counterfactual mood (in optative and indicative), (2) futures in the past, (3) iteratives (with -sk) and (4) lexical sources with semantic affinity to habituality (volition, habit, love). It is argued that the former two acquire habitual meaning through an invited inference of epistemic certainty of the statement by the speaker: what certainly would have happened in the knowable past is implied to be characteristic of the past. The past forms with the so-called iterative -sk (3) suffix follow the cross-linguistically frequent evolution of pluractional constructions through a form of semantic bleaching: past iterative > frequentative > habitual > habitual imperfective. Lexical sources (4) first acquire habitual meaning in the present after which only the more heavily grammaticalized ones receive past habitual usage through semantic bleaching and generalization of usage (as reflected by host class expansions). The paper is concluded with a diachronic map of these paths into habituality and the paths leading from past habituality into other domains such as genericity. [ABSTRACT FROM AUTHOR]

Feedforward multilayer perceptron models (MLPs) have been applied to power distribution system state estimation (DSSE) in the past. Existing methods usually employ an ad-hoc or trial and error approach to MLP hyperparameter selection, and thus a systematic way of selecting the optimal hyperparameters including the number of neurons per hidden layer, learning rate, number of training epochs and training batch size is desirable and needed. This paper presents an approach based on Bayesian Optimization with Gaussian Processes for selecting MLP model hyperparameters for state estimation purposes. Results of the optimized MLP models are presented alongside the unoptimized models to compare performance of training, testing, and validation in terms of root-mean-squared-error (RMSE). Additionally, machine learning pipelines were employed and total execution time (seconds) for each trial is presented. The study shows that the MLP models obtained through the proposed optimization method outperform unoptimized models in terms of generalization capability for unseen, new cases. [ABSTRACT FROM AUTHOR]

In this paper, we study the following prescribed Gaussian curvature problem: K = f ~ ⁢ (θ) ϕ ⁢ (ρ) α − 2 ⁢ ϕ ⁢ (ρ) 2 + | ∇ ¯ ⁢ ρ | 2 , a generalization of the Alexandrov problem ( α = n + 1 ) in hyperbolic space, where f ~ is a smooth positive function on S n , 휌 is the radial function of the hypersurface, ϕ ⁢ (ρ) = sinh ⁡ ρ and 퐾 is the Gauss curvature. By a flow approach, we obtain the existence and uniqueness of solutions to the above equations when α ≥ n + 1 . Our argument provides a parabolic proof in smooth category for the Alexandrov problem in H n + 1 . We also consider the cases 2 < α ≤ n + 1 under the evenness assumption of f ~ and prove the existence of solutions to the above equations. [ABSTRACT FROM AUTHOR]

In this paper, by using the notions of λ-density, (V , λ) -summability and Orlicz function ϕ, we introduce a new concept of convergence, namely λ-statistically ϕ-convergence, as a generalization of the λ-statistical convergence and statistically ϕ-convergence. Based on this concept, we introduce a new sequence space S λ - ϕ and investigate some of its properties. Also, we find its relations with statistically ϕ-convergence, [ C , 1 ] ϕ -summability and [ V , λ ] ϕ -summability. Finally, we introduce and investigate the concept of S λ - ϕ Cauchy sequences. [ABSTRACT FROM AUTHOR]

This paper aims at studying the Iwasawa λ-invariant of the p-primary Selmer group. We study the growth behavior of p-primary Selmer groups in p-power degree extensions over non-cyclotomic ℤ p -extensions of a number field. We prove a generalization of Kida's formula in such a case. Unlike the cyclotomic ℤ p -extension, where all primes are finitely decomposed, in the ℤ p -extensions we consider primes may be infinitely decomposed. In the second part of this paper, we study the relationship of Iwasawa invariants with respect to congruences, obtaining refinements of the results of Greenberg, Vatsal and Kidwell. As an application, we provide an algorithm for constructing elliptic curves with large anticyclotomic λ-invariant. Our results are illustrated by explicit computation. [ABSTRACT FROM AUTHOR]

In many life time scenarios, life of one component or system nested in other components or systems. To model these complex structures some so called nested models are required rather than conventional models. This paper introduces the generalization of the method of generating continuous distribution proposed by N. Eugene, C. Lee, and F. Famoye, "Beta-normal distribution and its applications," Commun. Stat. Theor. Methods, vol. 31, no. 4, pp. 497–512, 2002 and A. Alzaatreh, C. Lee, and F. Famoye, "A new method for generating families of continuous distributions," Metron, vol. 71, no. 1, pp. 63–79, 2013 which nest one model in other to cope with complex systems. Some important characteristics of the proposed family of generalized distribution have been studied. The famous Beta, Kumaraswami and Gamma generated distributions are special cases of our suggested procedure. Some new distributions have also been developed by using the suggested methodology and their important properties have been discussed as well. A variety of real life data sets are used to demonstrate the efficacy of new suggested distributions and illation is made with baseline models. [ABSTRACT FROM AUTHOR]

Millikan's (1984. Language, Thought, and Other Biological Categories: New Foundations for Realism. MIT Press) selected effects theory of functions states that functions are effects for which the ancestors of a trait were selected for. As the function is an effect a thing's ancestors produced, only things that are reproductions in some sense can have functions. Against this reproduction requirement, Garson (2019. What Biological Functions Are and Why They Matter. Cambridge University Press) argues that not only processes of differential reproduction but also processes of differential persistence can lead to new functions. Since such "persistence functions" have the same explanatory power as traditional selected effects functions, selected effects theorists should include them in their theory. In this paper, I will defend Millikan's theory against this argument. I will show that the proponents of the generalized theory have yet to provide a working notion of populations that avoids a liberality problem. Further, I will argue that persistence functions are at best a marginal case of functions due to their restricted explanatory power. [ABSTRACT FROM AUTHOR]

This is the first in a series of papers concerned with Morse quasiflats, which are a generalization of Morse quasigeodesics to arbitrary dimension. In this paper we introduce a number of alternative definitions, and under appropriate assumptions on the ambient space we show that they are equivalent and quasi-isometry invariant; we also give a variety of examples. The second paper proves that Morse quasiflats are asymptotically conical and have canonically defined Tits boundaries; it also gives some first applications. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the generalization of finitary 2-representation theory of finitary 2-categories to finitary birepresentation theory of finitary bicategories. In previous papers on the subject, the classification of simple transitive 2-representations of a given 2-category was reduced to that for certain subquotients. These reduction results were all formulated as bijections between equivalence classes of 2-representations. In this paper, we generalize them to biequivalences between certain 2-categories of birepresentations. Furthermore, we prove an analog of the double centralizer theorem in finitary birepresentation theory. [ABSTRACT FROM AUTHOR]

This paper studies an environment in which a decision maker choosing between acts may initially be unaware of certain consequences. We follow the approach of Karni and Vierø (2013) to modeling increasing awareness, which allows for the decision maker's state space to expand as she becomes aware of new possible consequences. We generalize the main result in Karni and Vierø (2013) by allowing the discovery of new consequences to nullify some states that were non-null before the discovery. We also provide alternative assumptions which strengthen the predictions of the belief updating model. [ABSTRACT FROM AUTHOR]

We prove a sharp quantitative form of isocapacitary inequality in the case of a general p. This work is a generalization of the author's paper with Guido De Philippis and Michele Marini, where we treated the case of 2-capacity. [ABSTRACT FROM AUTHOR]

This article discusses phonological generalisations concerning Podhale Goralian, a dialect of Polish spoken in southern Lesser Poland. It is argued that Podhale Goralian has a process called Final Tensing, which changes ɔ → o before word-final voiced consonants and glides. Final Tensing interacts with other rules of the dialect, leading to both major types of opacity: underapplication and overapplication. The descriptive generalisations are first stated in terms of rules and then reanalysed in terms of OT constraints. Even though both frameworks deliver the correct results, it is argued that the OT-based analysis is by a small margin superior to the rule-based analysis. Furthermore, the sources of the opacity exhibited by the discussed processes are classified according to Baković's (2007, 2011) revised typology of opacity. I am particularly grateful to Jerzy Rubach for his discussion, guidance and support. I would also like to thank Jakub Dunin-Borkowski and Grzegorz Lara, who read an earlier version of this paper and provided inspiring feedback. My gratitude goes also to the three PSiCL referees for their helpful criticism, which led to considerable improvement of both the content and the presentation of my analysis. Last but not least, I have a special debt of gratitude to my native speaker consultants for their help and patience: Józef Bąk, Andrzej Kamiński, Stanisław Kamiński, Józef Kula, Anna Łuszczek, Małgorzata Łuszczek, Wojciech Łuszczek, Dorota Pająk, Martyna Pająk, Tomasz Płaza, Leszek Stasiwolak, Katarzyna Szwajnos, Maria Szwajnos, Monika Szwajnos and Andrzej Zarycki. Needless to say, the responsibility for this article is solely mine. [ABSTRACT FROM AUTHOR]

This paper explores the pedagogical implications and implementations of a Cognitive Construction Grammar (Goldberg, Adele E. 2006. Constructions at work: The nature of generalization in language. New York: Oxford University Press) approach for the teaching of construal in the L2 class of Spanish at an advanced level. To this end, this paper focuses on instances of secondary predication (involving a direct object and an object-related XPCOMP) with decir "say" and other verbs of saying and calling in present-day Spanish, under the rubric of the denominative subjective-transitive construction. This construction comprises a number of lower-level configurations involving a reflexive direct object (the reflexive subjective-transitive construction), and an imperative verb (the imperative subjective-transitive construction). The verb decir is also frequently attested in the reflex passive construction (the impersonal subjective-transitive construction), under which two different, though closely connected, lexically-filled lo que se dice XPCOMP configurations can be posited, which may function as a focusing/emphasizer subjunct or as a summative conjunct in present-day Spanish. A default inheritance system of the type invoked in Cognitive Construction Grammar is shown to capture broad and specific generalizations at a horizontal level (among the verbs attested in the (sub-)construction(s)) and a vertical level (among constructions of varying degrees of specificity) and can thus be informally used to optimize the pedagogical efficiency of the input for the explicit instruction of grammar in the advanced Spanish L2 class. [ABSTRACT FROM AUTHOR]

The motion by curvature of networks is the generalization to finite union of curves of the curve shortening flow. This evolution has several peculiar features, mainly due to the presence of junctions where the curves meet. In this paper we show that whenever the length of one single curve vanishes and two triple junctions coalesce, then the curvature of the evolving networks remains bounded. This topological singularity is exclusive of the network flow and it can be referred as a "Type-0" singularity, in contrast to the well known "Type-I" and "Type-II" ones of the usual mean curvature flow of smooth curves or hypersurfaces, characterized by the different rates of blow-up of the curvature. As a consequence, we are able to give a complete description of the evolution of tree–like networks till the first singular time, under the assumption that all the "tangents flows" have unit multiplicity. If the lifespan of such solutions is finite, then the curvature of the network remains bounded and we can apply the results from [T. Ilmanen, A. Neves and F. Schulze, On short time existence for the planar network flow, J. Differential Geom. 111 2019, 1, 39–89] and [J. Lira, R. Mazzeo, A. Pluda and M. Saez, Short–time existence for the network flow, preprint 2021] to "restart" the flow after the singularity. [ABSTRACT FROM AUTHOR]

A generalized metric type space is a generic name for various spaces similar to hyperconvex metric spaces or extensions of them. The purpose of this article is to introduce some KKM theoretic works on generalized metric type spaces and to show that they can be improved according to our abstract convex space theory. Most of these works are chosen on the basis that they can be improved by following our theory. Actually, we introduce abstracts of each work or some contents, and add some comments showing how to improve them. [ABSTRACT FROM AUTHOR]

The applications of q-calculus in the approximation theory is a very interesting area of research in the recent years, several new q-operators were introduced and their behaviour were discussed by many researchers. This paper is the extension of the paper [15], in which Durrmeyer type generalization of q-Baskakov-Stancu type operators were discussed by using the concept of q-integral operators. Here, we propose to study the Stancu variant of q-Baskakov-Stancu type operators. We establish an estimate for the rate of convergence in terms of modulus of continuity and weighted approximation properties of these operators. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study the notion of an 푆-weakly prime ideal which is a generalization of a weakly prime ideal. Let 퐴 be a commutative ring and 푆 a multiplicative set of 퐴. We define a proper ideal 푃 of 퐴 to be 푆-weakly prime if there exists s ∈ S such that, for all a , b ∈ A with 0 ≠ a ⁢ b ∈ P , then s ⁢ a ∈ P or s ⁢ b ∈ P . We describe the behavior of an 푆-weakly prime property across various ring-theoretic constructions such as direct product, homomorphic image, localization, trivial ring extensions and amalgamation rings. [ABSTRACT FROM AUTHOR]

This paper investigates frequency effects in the L2 acquisition of the catenative verb construction by German learners of English from a usage-based perspective by presenting findings from two experimental studies and a complementary corpus study. It was examined if and to what extent the frequency of the verb in the catenative verb construction affects the choice of the target-like complement type and if the catenative verb construction with a to-infinitive complement, which is highly frequent in English, is more accurately acquired and entrenched than the less frequent variant with an -ing complement. In all three studies, the more frequent construction with a to-infinitive yielded higher numbers of target-like complement choices. Furthermore, it was shown that the verb's faithfulness to the construction made a significant prediction of a target-like complement preference. It is argued that a higher faithfulness promotes a target-like entrenchment of the construction and motivates a taxonomic generalisation across related exemplars. Furthermore, the results provide support for the idea that the mental representation of language is comprised of item-specific as well as more abstract schema knowledge, where frequency determines the specificity with which the construction is entrenched. [ABSTRACT FROM AUTHOR]

This paper investigates the distinct functions associated with the copula morpheme and their distribution across Sinitic languages. Based on fieldwork on five Sinitic languages, an empirical generalization will be presented regarding the scope and variation of copular multifunctionality. Specifically, language-specific variation is witnessed in topic and conditional marking as well as verum marking. Conversely, it is found that Sinitic languages converge on employing the copula in constructions expressing phrasal and clausal level focus. The paper further explores whether these copular constructions should receive a uniform syntax, or should be conceived of as having a set of underlaid heterogeneous structures. [ABSTRACT FROM AUTHOR]

In this paper, we consider the solvability over non-negative integers of certain Diophantine equations coming from representations of integers as sums of pentagonal numbers (counting the number of dots in a regular pentagon). We study a general method to obtain generalized versions of Cauchy's lemma. Using this, we show the "pentagonal theorem of 63", which states that a sum of pentagonal numbers represents every non-negative integer if and only if it represents the integers 1 , 2 , 3 , 4 , 6 , 7 , 8 , 9 , 11 , 13 , 14 , 17 , 18 , 19 , 23 , 28 , 31 , 33 , 34 , 39 , 42 , 63. We further show that these integers form a unique minimal universality criterion set. [ABSTRACT FROM AUTHOR]

Let K be a number field and S a set of primes of K. We write K S / K {K_{S}/K} for the maximal extension of K unramified outside S and G K , S {G_{K,S}} for its Galois group. In this paper, we prove the following generalization of the Neukirch–Uchida theorem under some assumptions: "For i = 1 , 2 {i=1,2} , let K i {K_{i}} be a number field and S i {S_{i}} a set of primes of K i {K_{i}}. If G K 1 , S 1 {G_{K_{1},S_{1}}} and G K 2 , S 2 {G_{K_{2},S_{2}}} are isomorphic, then K 1 {K_{1}} and K 2 {K_{2}} are isomorphic." Here the main assumption is that the Dirichlet density of S i {S_{i}} is not zero for at least one i. A key step of the proof is to recover group-theoretically the l-adic cyclotomic character of an open subgroup of G K , S {G_{K,S}} for some prime number l. [ABSTRACT FROM AUTHOR]

In this paper, we prove that a two-dimensional self-shrinker, homeomorphic to the sphere, immersed in the three-dimensional Euclidean space ℝ 3 {{\mathbb{R}}^{3}} is a round sphere, provided its mean curvature and the norm of the its position vector have an upper bound in terms of the norm of its traceless second fundamental form. The example constructed by Drugan justifies that the hypothesis on the second fundamental form is necessary. We can also prove the same kind of rigidity results for surfaces with parallel weighted mean curvature vector in ℝ n {{\mathbb{R}}^{n}} with radial weight. These results are applications of a new generalization of Cauchy's Theorem in complex analysis which concludes that a complex function is identically zero or its zeroes are isolated if it satisfies some weak holomorphy. [ABSTRACT FROM AUTHOR]

In this paper, we propose a refinement of Sims' conjecture concerning the cardinality of the point stabilizers in finite primitive groups, and we make some progress towards this refinement. In this process, when dealing with primitive groups of diagonal type, we construct a finite primitive group 퐺 on Ω and two distinct points α , β ∈ Ω \alpha,\beta\in\Omega with G α ⁢ β ⊴ G α G_{\alpha\beta}\unlhd G_{\alpha} and G α ⁢ β ≠ 1 G_{\alpha\beta}\neq 1 , where G α G_{\alpha} is the stabilizer of 훼 in 퐺 and G α ⁢ β G_{\alpha\beta} is the stabilizer of 훼 and 훽 in 퐺. In particular, this example gives an answer to a question raised independently by Cameron and by Fomin in the Kourovka Notebook. [ABSTRACT FROM AUTHOR]

Theorem C in [S. Dolfi, M. Herzog, G. Kaplan and A. Lev, The size of the solvable residual in finite groups, Groups Geom. Dyn.1 (2007), 4, 401–407] asserts that, in a finite group with trivial Fitting subgroup, the size of the soluble residual of the group is bounded from below by a certain power of the group order and that the inequality is sharp. Inspired by this result and some of the arguments in the above article, we establish the following generalisation: if 픛 is a subgroup-closed Fitting formation of full characteristic which does not contain all finite groups and X ¯ \overline{\mathfrak{X}} is the extension-closure of 픛, then there exists an (explicitly known and optimal) constant 훾 depending only on 픛 such that, for all non-trivial finite groups 퐺 with trivial 픛-radical, | G X ¯ | > | G | γ \lvert G^{\overline{\mathfrak{X}}}\rvert>\lvert G\rvert^{\gamma} , where G X ¯ G^{\overline{\mathfrak{X}}} is the X ¯ \overline{\mathfrak{X}} -residual of 퐺. When X = N \mathfrak{X}=\mathfrak{N} , the class of finite nilpotent groups, it follows that X ¯ = S \overline{\mathfrak{X}}=\mathfrak{S} , the class of finite soluble groups; thus we recover the original theorem of Dolfi, Herzog, Kaplan, and Lev. In the last section of our paper, building on J. G. Thompson's classification of minimal simple groups, we exhibit a family of subgroup-closed Fitting formations 픛 of full characteristic such that S ⊂ X ¯ ⊂ E \mathfrak{S}\subset\overline{\mathfrak{X}}\subset\mathfrak{E} , where 픈 denotes the class of all finite groups, thus providing applications of our main result beyond the reach of the above theorem. [ABSTRACT FROM AUTHOR]

Let G be a finite group, and let 𝔉 be a hereditary saturated formation. We denote by 𝐙𝔉(G) the product of all normal subgroups N of G such that every chief factor H/K of G below N is 𝔉-central in G, that is, (H / K) ⋊ (G / 𝐂 G ⁢ (H / K)) ∈ 𝔉 {(H/K)\rtimes(G/\mathbf{C}_{G}(H/K))\in\mathfrak{F}}. A subgroup A ⩽ G {A\leqslant G} is said to be 𝔉 {\mathfrak{F}} -subnormal in the sense of Kegel, or K- 𝔉 {\mathfrak{F}} -subnormal in G, if there is a subgroup chain A = A0 ⩽ A1 ⩽ ⋯ ⩽ An = G such that either Ai-1 ⁢ ⊴ ⁢ Ai or Ai/(Ai-1)Ai ∈ 𝔉 for all i = 1 , . . . , n. In this paper, we prove the following generalization of Schenkman's theorem on the centraliser of the nilpotent residual of a subnormal subgroup: Let F be a hereditary saturated formation containing all nilpotent groups, and let S be a K-F-subnormal subgroup of G. If ZF(E) = 1 for every subgroup E of G such that S ⩽ E , then CG(D) ⩽ D, where D = SF is the F-residual of S. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some new fixed point theorems in generalized metric spaces for maps satisfying an implicit relation. The obtained results unify, generalize, enrich, complement and extend a multitude of related fixed point theorems from metric spaces to generalized metric spaces. [ABSTRACT FROM AUTHOR]

Let A be a unital algebra, δ be a linear mapping from A into itself and m, n be fixed integers. We call δ an (m, n)-derivable mapping at Z, if mδ(AB) + nδ(BA) = mδ(A)B + mAδ(B) + nδ(B)A for all A,B ∈ A with AB = Z. In this paper, (m, n)-derivable mappings at 0 (resp. IA ⊕ 0, I) on generalized matrix algebras are characterized. We also study (m, n)-derivable mappings at 0 on CSL algebras. We reveal the relationship between this kind of mappings with Lie derivations, Jordan derivations and derivations. [ABSTRACT FROM AUTHOR]

This paper offers an integrated framework of one- and two-sector optimal .growth models for the dynamic analysis of the joint effects of distorting taxes and production externalities. We investigate how capital and labor income tax rates influence local dynamics near a steady state depending on the sizes of externalities. Our results clarify how tax rates on factor income affect the range of the sizes of externalities that induce indeterminacy. We find that the possibility of indeterminacy is significantly higher for given values of externalities, the labor supply elasticity and the elasticity of intertemporal substitution in consumption if capital income tax rates are increased from zero to values similar to those in many countries. [ABSTRACT FROM AUTHOR]

In this paper we obtain rigidity results for a non-constant entire solution u of the Allen–Cahn equation in ℝn, whose level set {u = 0} is contained in a half-space. If n ≤ 3, we prove that the solution must be one-dimensional. In dimension n ≥ 4, we prove that either the solution is one-dimensional or stays below a one-dimensional solution and converges to it after suitable translations. Some generalizations to one phase free boundary problems are also obtained. [ABSTRACT FROM AUTHOR]

In 1977, Colville, Davis, and Keimel [Positive derivations on f-rings, J. Aust. Math. Soc. Ser. A 23 1977, 3, 371–375] proved that a positive derivation on an Archimedean f-algebra A has its range in the set of nilpotent elements of A. The main objective of this paper is to obtain a generalization of the above Colville, Davis and Keimel result to general derivations. Moreover, we give a new version of the Singer–Wermer conjecture for the class of second-order derivations acting on uniformly complete almost f-algebras. [ABSTRACT FROM AUTHOR]

Approximation using linear positive operators is a well-studied research area. Many operators and their generalizations are investigated for their better approximation properties. In the present paper, we construct and investigate a variant of modified (p , q) (p,q) -Baskakov operators, which reproduce the test function x 2 x^{2}. We have determined the order of approximation of the operators via K-functional and second order, the usual modulus of continuity, weighted and statistical approximation properties. In the end, some graphical results which depict the comparison with (p , q) (p,q) -Baskakov operators are explained and a Voronovskaja type result is obtained. [ABSTRACT FROM AUTHOR]

Classical Castelnuovo Lemma shows that the number of linearly independent quadratic equations of a nondegenerate irreducible projective variety of codimension c is at most (c + 1 2) {{{c+1}\choose{2}}} and the equality is attained if and only if the variety is of minimal degree. Also G. Fano's generalization of Castelnuovo Lemma implies that the next case occurs if and only if the variety is a del Pezzo variety. Recently, these results are extended to the next case in [E. Park, On hypersurfaces containing projective varieties, Forum Math. 27 2015, 2, 843–875]. This paper is intended to complete the classification of varieties satisfying at least (c + 1 2) - 3 {{{c+1}\choose{2}}-3} linearly independent quadratic equations. Also we investigate the zero set of those quadratic equations and apply our results to projective varieties of degree ≥ 2 ⁢ c + 1 {\geq 2c+1}. [ABSTRACT FROM AUTHOR]

A persistent issue for the Prosodic Hierarchy is what repertory of prosodic constituents is needed to define the commonly recurring domains for phonological processes. Even though there is a long tradition of work arguing in favor of up to three subphrasal constituents (Composite Group (CG), PWord and PStem), a body of recent work has argued in favor of a more parsimonious view of the repertory, making the strong claim that, at the subphrasal level, the Prosodic Hierarchy contains only one constituent, Phonological Word (PWord). Any additional subphrasal domains required by the phonology must be defined as recursions of PWord. This paper argues that PStem must find a place even in a parsimonious Prosodic Hierarchy. It cannot easily be replaced by recursive PWord or by a CG-PWord distinction. The cross-linguistic validity of a PStem-PWord distinction is supported by showing that it accounts for a robust cross-linguistic generalization concerning subphrasal phonological domains. Alternatives to PStem not only miss this generalization but also prove to be formally inadequate. [ABSTRACT FROM AUTHOR]

Studies in grammaticalization have established that processes of grammatical change frequently have lexical items as their source, and more specifically nouns and verbs. But there is at least one potential exception: As argued by Holger Diessel in a number of publications, demonstratives cannot be historically derived from other entities, such as lexical items. Based on a survey of languages from different parts of the world and belonging to different language families, the present paper argues that this generalization is in need of reconsideration. [ABSTRACT FROM AUTHOR]

In joint work with E. Dubuc and D. Mundici, the first author extended Stone duality for boolean algebras to locally finite MV-algebras. On the topological side of the duality, one has to assign to each point of a boolean space a generalized natural number by way of a multiplicity, so as to make the assignment continuous with respect to the Scott topology of the lattice of generalized natural numbers. The continuous maps between such generalized multisets are to be multiplicity-decreasing with respect to the divisibility order of generalized natural numbers. In this paper we extend these results to the class of MV-algebras that are locally weakly finite, i.e., such that all their finitely generated subalgebras split into a finite direct product of simple MV-algebras. Using the Scott topology on the lattice of subalgebras of the real unit interval (regarded with its natural MV-algebraic structure), we construct a `real-valued multiset' over the (boolean) space of maximal ideals of a locally weakly finite MV-algebra. Building on this, we obtain a duality for locally weakly finite MV-algebras that includes as a special case the above-mentioned duality for locally finite MV-algebras. We give an example that shows that the duality established in this paper via the Scott topology cannot be extended, without non-trivial modifications, to larger classes of algebras. [ABSTRACT FROM AUTHOR]

In this paper, we are mainly interested to study the generalization of typically real functions in the unit disk. We study some coefficient inequalities concerning this class of functions. In particular, we find the Zalcman conjecture for generalized typically real functions. [ABSTRACT FROM AUTHOR]

While many linguists view language as either a cognitive or a social phenomenon, it is clearly both: a language can live only in individual minds, but it is learned from examples of utterances produced by speakers engaged in communicative interaction. In other words, language is what (Keller 1994. On language change: The invisible hand in language. London: Taylor & Francis) calls a "phenomenon of the third kind", emerging from the interaction of a micro-level and a macro-level. Such a dual perspective helps us understand some otherwise puzzling phenomena, including "non-psychological" generalizations, or situations where a pattern which is arguably present in a language is not explicitly represented in most speakers' minds. This paper discusses two very different examples of such generalizations, genitive marking on masculine nouns in Polish and some restrictions on questions with long-distance dependencies in English. It is argued that such situations are possible because speakers may represent "the same" knowledge at different levels of abstraction: while a few may have extracted an abstract generalization, others approximate their behaviour by relying on memorised exemplars or lexically specific patterns. Thus, a cognitively realistic usage-based construction grammar needs to distinguish between patterns in the usage of a particular speech community (a social phenomenon) and patterns in speakers' minds (a cognitive phenomenon). [ABSTRACT FROM AUTHOR]

In the first part of the paper we study the sets of boundedness and of convergence and divergence to infinity of sequences of real closed-graph functions. Generalization on ideal convergence of such sequences is discussed. Limits and ideal-limits of sequences of functions with closed graphs are considered in the last part of the article. [ABSTRACT FROM AUTHOR]

In this paper we derive convergence rates results for Landweber iteration in Hilbert scales. The assumptions that are necessary to prove these results are less restrictive than the ones given in an earlier paper. The relaxed conditions enlarge the range of applicability to a much wider class of nonlinear problems. The theory is applied to nonlinear Hammerstein operators. [ABSTRACT FROM AUTHOR]

Copyright of Technisches Messen is the property of De Gruyter and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we define a new class of posets which are complemented and ideal-distributive, we call these posets strong Boolean. This definition is a generalization of Boolean lattices on posets, and is different from Boolean posets. We give a topology on the set of all prime Frink ideals in order to obtain the Stone's topological representation for strong Boolean posets. A discussion of a duality between the categories of strong Boolean posets and BP-spaces is also presented. [ABSTRACT FROM AUTHOR]

When investigating the complexity of implementing Boolean functions, it is usually assumed that the basis inwhich the schemes are constructed and the measure of the complexity of the schemes are known. For them, the Shannon function is introduced, which associates with each Boolean function the least complexity of implementing this function in the considered basis. In this paper we propose a generalization of such a Shannon function in the form of an upper bound that is taken over all functionally complete bases. This generalization gives an idea of the complexity of implementing Boolean functions in the "worst" bases for them. The conceptual content of the proposed generalization is demonstrated by the example of a conjunction. [ABSTRACT FROM AUTHOR]

Motivated by our subfactor generalization of Wall's conjecture and interest about completely rational conformal nets in general, in this paper we show that there is a one-to-one correspondence between intermediate conformal nets in a pair of completely rational nets with finite index and certain class of fusion rings. As a consequence we show that our conjecture for the pair is reduced to a conjecture about fusion rings, and our result also gives a method of enumerating all intermediate conformal nets. [ABSTRACT FROM AUTHOR]

We consider for integers k ≥ 2 the k–generalized Fibonacci sequences F(k) := (F n (k) ) n ≥ 2 − k , $\begin{array}{} (F_n^{(k)})_{n\geq 2-k}, \end{array} $ whose first k terms are 0, …, 0, 1 and each term afterwards is the sum of the preceding k terms. In this paper, we show that there does not exist a quadruple of positive integers a1 < a2 < a3 < a4 such that aiaj + 1 (i ≠ j) are all members of F(k). [ABSTRACT FROM AUTHOR]