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Let X be a finite connected poset, K a field of characteristic zero and I (X , K) the incidence algebra of X over K seen as a Lie algebra under the commutator product. In the first part of the paper we show that any 1 2 -derivation of I (X , K) decomposes into the sum of a central-valued 1 2 -derivation, an inner 1 2 -derivation and a 1 2 -derivation associated with a map σ : X < 2 → K that is constant on chains and cycles in X. In the second part of the paper we use this result to prove that any transposed Poisson structure on I (X , K) is the sum of a structure of Poisson type, a mutational structure and a structure determined by λ : X e 2 → K , where X e 2 is the set of (x , y) ∈ X 2 such that x < y is a maximal chain not contained in a cycle. [ABSTRACT FROM AUTHOR]

Let k be an algebraically closed field of characteristic 0. We study some cohomological properties of Lie subalgebras of the Witt algebra W = Der (k [ t , t − 1 ]) and the one-sided Witt algebra W ≥ − 1 = Der (k [ t ]). In the first part of the paper, we consider finite codimension subalgebras of W ≥ − 1. We compute derivations and one-dimensional extensions of such subalgebras. These correspond to Ext U (L) 1 (M , L) , where L is a subalgebra of W ≥ − 1 and M is a one-dimensional representation of L. We find that these subalgebras exhibit a kind of rigidity: their derivations and extensions are controlled by the full one-sided Witt algebra. As an application of these computations, we prove that any isomorphism between finite codimension subalgebras of W ≥ − 1 extends to an automorphism of W ≥ − 1. The second part of the paper is devoted to explaining the observed rigidity. We define a notion of "completely non-split extension" and prove that W ≥ − 1 is the universal completely non-split extension of any of its subalgebras of finite codimension. In some sense, this means that even when studying subalgebras of W ≥ − 1 as abstract Lie algebras, they remember that they are contained in W ≥ − 1. We also consider subalgebras of infinite codimension, explaining the similarities and differences between the finite and infinite codimension situations. Almost all of the results above are also true for subalgebras of the Witt algebra. We summarise results for W at the end of the paper. [ABSTRACT FROM AUTHOR]

This study presents the problem of spreading non fatal disease in a population by using the Morgan-Voyce collocation method. The main aim of this paper is to find the exact solutions of the SIR model with vaccination. The problem may be modelled mathematically with a nonlinear system of ordinary differential equations. The presented method reduces the problem into a nonlinear algebraic system of equations by using unknown coefficient Morgan-Voyce polynomials and expanding approximate solutions. Morgan-Voyce polynomials are used. These unknown coefficients are calculated via the collocation method and matrix operation derivations. Two examples are given to show the feasibility of the method. To calculate the solutions, MATLAB R2021a is used. Additionally, comparing our method to the Homotopy perturbation method (HPM) and the Laplace Adomian decomposition method (LADM) proves the accuracy of the solution. The method studied can be seen as effective from these comparisons. So, it is essential to find solutions for the governing model. The study will contribute to literature since we also discuss the vaccination situation. The results of this study are valuable for controlling an epidemic. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the Lie algebra bundles defined by Jordan algebra bundles of finite type over an arbitrary topological space and observe that such Lie algebra bundles are also of finite type. Also, we examine some ideal bundles of Lie algebra bundles defined by semisimple Jordan algebra bundles of finite type. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study the concept of hyper-instability as a strong version of multiplicative instability. This concept provides a powerful tool to study the multiplicative instability of Banach algebras. It replaces the condition of the iterated limits in the definition of multiplicative instability with conditions that are easier to examine. In particular, special conditions are suggested for Banach algebras that admit bounded approximate identities. Moreover, these conditions are preserved under isomorphisms. This enlarges the class of studied Banach algebras. We prove that many interesting Banach algebras are hyper-unstable, such as C-algebras, Fourier algebras, and the algebra of compact operators on Banach spaces, each under certain conditions. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to investigate the type of monadic bounded L-algebras as L-algebras equipped with two monadic operators, named universal quantifier "∀" and existential quantifier "∃", respectively. First, we investigate the properties of pre-ideals on L-algebras and the pre-ideal generated by a nonempty subset of an L-algebra is defined. Second, we investigate monadic bounded L-algebras and monadic pre-ideals in monadic bounded L-algebras. Moreover, the relation between monadic bounded L-algebras and monadic quantum B-algebras is discussed. Finally, the relations among monadic self-similar L-algebras and other monadic structures are discussed, such as monadic (left) hoops, monadic Wajsberg hoops and monadic MV-algebras. Moreover, we obtain a characterization of monadic bounded L-algebras and monadic bounded self-similar L-algebras by relatively complete subalgebras and m-relatively complete subalgebras, respectively. These results are important to the further study of logical system with monadic operators. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of similarity monadic MTL-algebras and study some of their related basic algebraic properties. Then we introduce and investigate similarity monadic filters of similarity monadic MTL-algebras. In particular, by means of similarity monadic filters, we give some characterizations of representable similarity monadic MTL-algebras. Finally, we introduce the logic of similarity monadic MTL-algebras and prove the completeness of them. [ABSTRACT FROM AUTHOR]

Let 퓟n := H*((ℝP∞)n) ≅ ℤ2[x1, x2, ..., xn] be the graded polynomial algebra over ℤ2, where ℤ2 denotes the prime field of two elements. We investigate the Peterson hit problem for the polynomial algebra 퓟n, viewed as a graded left module over the mod-2 Steenrod algebra, 퓐. For n > 4, this problem is still unsolved, even in the case of n = 5 with the help of computers. In this article, we study the hit problem for the case n = 6 in the generic degree dr = 6(2r − 1) + 4.2r with r an arbitrary non-negative integer. By considering ℤ2 as a trivial 퓐-module, then the hit problem is equivalent to the problem of finding a basis of ℤ2-vector space ℤ2 ⊗퓐퓟n. The main goal of the current article is to explicitly determine an admissible monomial basis of the ℤ2 vector space ℤ2 ⊗퓐퓟6 in some degrees. As an application, the behavior of the sixth Singer algebraic transfer in the degree 6(2r − 1) + 4.2r is also discussed at the end of this paper. [ABSTRACT FROM AUTHOR]

In this paper, we define and study the variety of tense modal pseudocomplemented De Morgan algebras. This variety is a proper subvariety of the variety of tense tetravalent modal algebras. A tense modal pseudocomplemented De Morgan algebra is a modal pseudocomplemented De Morgan algebra endowed with two tense operators G and H satisfying additional conditions. Also, the variety of tense modal pseudocomplemented De Morgan algebras is intimately connected with some well-known varieties of De Morgan algebras with tense operators. [ABSTRACT FROM AUTHOR]

In this paper, we present a modality-free pre-rough algebra. Łukasiewicz Moisil algebra and Wajsberg algebra are equivalent under a transformation. A similar type of equivalence exists in our proposed definition and standard definition of pre-rough algebra. We obtain a few modality-free algebras weaker than pre-rough algebra. Furthermore, it is also established that modality-free versions for other analogous structures weaker than pre-rough algebra do not exist. Both Hilbert-type axiomatization and sequent calculi for all proposed algebras are presented. [ABSTRACT FROM AUTHOR]

Over the past 50 years, Nelson algebras have been extensively studied by distinguished scholars as the algebraic counterpart of Nelson's constructive logic with strong negation. Despite these studies, a comprehensive survey of the topic is currently lacking, and the theory of Nelson algebras remains largely unknown to most logicians. This paper aims to fill this gap by focussing on the essential developments in the field over the past two decades. Additionally, we explore generalisations of Nelson algebras, such as N4-lattices which correspond to the paraconsistent version of Nelson's logic, as well as their applications to other areas of interest to logicians, such as duality and rough set theory. A general representation theorem states that each Nelson algebra is isomorphic to a subalgebra of a rough set-based Nelson algebra induced by a quasiorder. Furthermore, a formula is a theorem of Nelson logic if and only if it is valid in every finite Nelson algebra induced by a quasiorder. [ABSTRACT FROM AUTHOR]

Convolution plays a pivotal role in the domains of signal processing and optics. This paper primarily focuses on studying the weighted convolution for quaternion linear canonical cosine transform (QLCcT) and its application in multiplicative filter analysis. Firstly, we propose QLCcT by combining quaternion algebra with linear canonical cosine transform (LCcT), which extends LCcT to Hamiltonian quaternion algebra. Secondly, we introduce weighted convolution and correlation operations for QLCcT, accompanied by their corresponding theorems. We also explore the properties of QLCcT. Thirdly, we utilize these proposed convolution structures to analyze multiplicative filter models that offer lower computational complexity compared to existing methods based on quaternion linear canonical transform (QLCT). Additionally, we discuss the rationale behind studying such transforms using quaternion functions as an illustrative example. [ABSTRACT FROM AUTHOR]

One of the most relevant topics in web theory is linearization. A particular class of linearizable webs is the Grassmannizable web. Akivis gave a characterization of such a web, showing that Grassmannizable webs are equivalent to isoclinic and transversally geodesic webs. The obstructions given by Akivis that characterize isoclinic and transversally geodesic webs are computed locally, and it is difficult to give them an interpretation in relation to torsion or curvature of the unique Chern connection associated with a web. In this paper, using Nagy's web formalism, Frölisher—Nejenhuis theory for derivation associated with vector differential forms, and Grifone's connection theory for tensorial algebra on the tangent bundle, we find invariants associated with almost-Grassmann structures expressed in terms of torsion, curvature, and Nagy's tensors, and we provide an interpretation in terms of these invariants for the isoclinic, transversally geodesic, Grassmannizable, and parallelizable webs. [ABSTRACT FROM AUTHOR]

In this paper, we define a cohomology theory of a modified λ -differential left-symmetric algebra. Moreover, we introduce the notion of modified λ -differential left-symmetric 2-algebras, which is the categorization of a modified λ -differential left-symmetric algebra. As applications of cohomology, we classify linear deformations and abelian extensions of modified λ -differential left-symmetric algebras using the second cohomology group and classify skeletal modified λ -differential left-symmetric 2-algebra using the third cohomology group. Finally, we show that strict modified λ -differential left-symmetric 2-algebras are equivalent to crossed modules of modified λ -differential left-symmetric algebras. [ABSTRACT FROM AUTHOR]

In this paper, we provide some properties of k-potent elements in algebras obtained by the Cayley–Dickson process over Z p . Moreover, we find a structure of nonunitary ring over Fibonacci quaternions over Z 3 and we present a method to encrypt plain texts, by using invertible elements in some of these algebras. [ABSTRACT FROM AUTHOR]

In this paper we investigate left ideals as codes in twisted skew group rings. The considered rings, which are in most cases algebras over a finite field, allow us to retrieve many of the well-known codes. The presentation, given here, unifies the concept of group codes, twisted group codes and skew group codes. [ABSTRACT FROM AUTHOR]

In this paper, by using the notion of fuzzy points and equality algebras, the notions of fuzzy point equality algebra, equality-subalgebra, and ideal were established. Some characterizations of fuzzy subalgebras were provided by using such concepts. We defined the concepts of (∈, ∈) and (∈, ∈ ∨ q)-fuzzy ideals of equality algebras, discussed some properties, and found some equivalent definitions of them. In addition, we investigated the relation between different kinds of (α, β)-fuzzy subalgebras and (α, β)-fuzzy ideals on equality algebras. Also, by using the notion of (∈, ∈)-fuzzy ideal, we defined two equivalence relations on equality algebras and we introduced an order on classes of X, and we proved that the set of all classes of X by these order is a poset. [ABSTRACT FROM AUTHOR]

This paper presents an integrated color imaging system for taking images in extremely high dynamic range scenes. The system first fuses several differently exposed raw images to acquire more intensity information. The effective dynamic range of the image raw data can be extended to 256 times ~five differently exposed images are fused. Then it runs edge detection iterations to extract the image details in different luminance levels. The proposed tone reproduction algorithm equalizes the histogram of the extracted fine edges which tends to assign larger dynamic range for highly populated regions. Finally, the local contrast enhancement is performed to further refine the image details. The experimental results show that the proposed high dynamic range imaging system has good performance on both tone and color reproduction'. [ABSTRACT FROM AUTHOR]

Problems of finding general rule in the case of linear correspondences are often encountered in the research papers, where they are supplied with iconic means which support induction. And as the researchers report it, students have a tendency to focus solely on the numeric data even when visual patterns are given. The objective of our research is the examination of the influence of various iconic representations designed to help students establish and express general relations between quantities. This research is of empirical nature. The research was based on the testing technique. The obtained results show that iconic representation of the structure of algebraic contents influences greatly students' ability of making generalisations and establishing algebraic relations and simple rules of correspondence. The very activity of drawing and iconic representing of the pattern members can also be seen as potentially significant for the discovering of the rule of correspondence and its generalisation. [ABSTRACT FROM AUTHOR]

Many networked embedded sensing and control systems can be modeled as hybrid systems with interacting continuous and discrete dynamics. These systems present significant challenges for monitoring and diagnosis. Many existing model-based approaches focus on diagnostic reasoning assuming appropriate fault signatures have been generated. However, an important missing piece is the integration of model-based techniques with the acquisition and processing of sensor signals and the modeling of faults to support diagnostic reasoning. This paper addresses key modeling and computational problems at the interface between model-based diagnosis techniques and signature analysis to enable the efficient detection and isolation of incipient and abrupt faults in hybrid systems. A hybrid automata model that parameterizes abrupt and incipient faults is introduced. Based on this model, an approach for diagnoser design is presented. The paper also develops a novel mode estimation algorithm that uses model-based prediction to focus distributed processing signal algorithms. Finally. the paper describes a diagnostic system architecture that integrates the modeling, prediction, and diagnosis components. The implemented architecture is applied to fault diagnosis of a complex electro-mechanical machine, the Xerox DC265 printer, and the experimental results presented validate the approach. A number of design trade-otis that were made to support implementation of the algorithms for online applications are also described. [ABSTRACT FROM AUTHOR]

In the paper we provide some polynomial identities for finite-dimensional algebras. A list of well known single polynomial identities is exposed and the classification of all two-dimensional algebras with respect to these identities is given. [ABSTRACT FROM AUTHOR]

Abstract: In 1.9 of the paper [A. Hahn, A Hermitian Morita theorem for algebras with anti-structure, J. Algebra 93 (1985) 215–235], should be replaced by . This leads to minor changes in the rest of the paper where the ring should be replaced by its opposite and vice versa. [Copyright &y& Elsevier]

In the above referenced paper, misinterpretations led Martin to claim that there are errors in certain equations derived in our paper on the use of Frobenius’ method to solve curved crack problems. This note identifies the misinterpretations and shows that our results are the same as those derived by Martin. [ABSTRACT FROM AUTHOR]

In this paper, we construct a symbol calculus yielding short exact sequences for the dual Toeplitz algebra generated by all bounded dual Toeplitz operators on the Hardy space associated with the polydisk D n in the unitary space C n , that have been introduced and well studied in our earlier paper (Benaissa and Guediri in Taiwan J Math 19: 31–49, 2015), as well as for the C*-subalgebra generated by dual Toeplitz operators with symbols continuous on the associated hypertorus T n . [ABSTRACT FROM AUTHOR]

Let p 1 , p 2 , ... , p r , q be distinct primes, q odd. Let m = ∏ i = 1 r p i , where r ≥ 2 be an integer. In this paper, it is observed that the explicit expressions of primitive idempotents from R p i are sufficient to compute the explicit expressions of primitive idempotent in semisimple ring R m = F q [ x ] / (x m − 1). It is also shown that the results obtained in [A. Sahni and P. T. Sehgal, Minimal cyclic codes of length p n q , Finite Fields Appl. 18(5) (2012) 1017–1036; P. Kumar and S. K. Arora, λ -mapping and primitive idempotents in semisimple ring ℜ m , Comm. Algebra 41(10) (2013) 3679–3694] are simple corollaries to the results obtained in the paper. [ABSTRACT FROM AUTHOR]

This study discusses the use of quaternions and dual quaternions in the description of artificial fish kinematics. The investigation offered here illustrates quaternion and dual quaternion algebra, as well as its implementation in the software chosen. When it comes to numerical stability, quaternions are better than matrices because a normalised quaternion always shows the correct rotation, while a matrix more easily loses its orthogonality due to rounding errors and oversizing. Although quaternions are more compact than rotation matrices, using quaternions does not always provide less numerical computation and the amount of memory needed. In this paper, an algebraic form of quaternion representation is provided which is less memory-demanding than the matrix representation. All the functions that were used to prepare this work are presented, and they can be employed to conduct more research on how well quaternions work in a specific assignment. [ABSTRACT FROM AUTHOR]

In this paper, we study variation-inequality initial-boundary value problems with fouth order p(x)-Kirchhoff operators. First, an operator is constructed based on the Leray Schauder principle, and the existence of solutions is obtained. Secondly, the stability and uniqueness of the solution are analyzed after the conditions are appropriately relaxed on the Kirchhoff operators. [ABSTRACT FROM AUTHOR]

When children are first taught about multiplication of the natural numbers, it is usually presented as repeated addition. Later, learning about raising to an exponent is presented as repeated multiplication. Then the following analogy is obvious: addition is to multiplication as multiplication is to raising to an exponent. An interesting question is to ask what happens if we go in the other direction. That is, multiplication is to addition as addition is to what? In this paper, we will answer this question, and show that there are several possible operations that could be used to answer the question. Some of them will be presented in connection with algebraic semirings. A semiring is a set, together with two operations, semiring addition and semiring multiplication, satisfying certain properties. We will define several semirings, such that the semiring multiplication is ordinary addition. In each case, the semiring addition will then be an answer to the question in the title of this paper. [ABSTRACT FROM AUTHOR]

In an unpublished work of Fasel–Rao–Swan the notion of the relative Witt group W E (R , I) is defined. In this paper, we will give the details of this construction. Then we study the injectivity of the relative Vaserstein symbol V R , I : U m 3 (R , I) / E 3 (R , I) → W E (R , I). We establish injectivity of this symbol if R is a non-singular affine algebra of dimension 3 over a perfect C 1 -field and I is a local complete intersection ideal of R. It is natural to ask whether the Vaserstein symbol is injective for a singular 3-dimensional affine algebra. At the end of the paper, we will give an example of a singular 3-dimensional algebra over a perfect C 1 -field for which the Vaserstein symbol is injective. [ABSTRACT FROM AUTHOR]

In this paper, we generalize known results of nonabelian embedding tensor to the Hom setting. We introduce the concept of Hom-Leibniz-Lie algebra, which is the basic algebraic structure of nonabelian embedded tensors on Hom-Lie algebras and can also be regarded as a nonabelian generalization of Hom-Leibniz algebra. Moreover, we define a cohomology of nonabelian embedding tensors on Hom-Lie algebras with coeffcients in a suitable representation. The first cohomology group is used to describe infinitesimal deformations as an application. In addition, Nijenhuis elements are used to describe trivial infinitesimal deformations. [ABSTRACT FROM AUTHOR]

In this paper, we continue to introduce new properties of principal MS -algebras deal with congruence relations via MS -congruence pairs. Necessary and sucient conditions for a pair of congruences (θ1; 12) 2 Con(Loo) x Conlat(D(L)) to become an MS -congruence pair of a principal MS -algebra (principal Stone algebra) L are obtained. We describe the lattice of all MS -congruence pairs of a principal MS -algebra L which induced by the Boolean elements of L. We introduce certain special congruence on a principal MS -algebra and its related properties which are useful for the topic of this paper. A characterization of 2-permutable congruences using MS -congruence pairs of principal MS -algebras is established. Finally, a characterization of n-permutability of congruences of principal MS -algebras is given, which is a generalization of the characterization of 2-permutability of congruences of such algebras. [ABSTRACT FROM AUTHOR]

A new three-dimensional Lie algebra and its loop algebra are proposed by us, whose commutator is a vector product. Based on this, a positive flow and a negative flow are obtained by introducing a new kind of spectral problem expressed by the vector product, which reduces to a generalized KdV equation, a generalized Schrödinger equation, a sine-Gordon equation, and a sinh-Gordon equation. Next, the well-known Tu scheme is generalized for generating isospectral integrable hierarchies and non-isospectral integrable hierarchies. It is important that we make use of the variational method to create a new vector-product trace identity for which the Hamiltonian structure of the isospectral integrable hierarchy presented in the paper is worded out. Finally, we further enlarge the three-dimensional loop algebra into a six-dimensional loop algebra so that a new isospectral integrable hierarchy which is a type of extended integrable model is produced whose bi-Hamiltonian structure is also derived from the vector-product trace identity. This new approach presented in the paper possesses extensive applications in the aspect of generating integrable hierarchies of evolution equations. [ABSTRACT FROM AUTHOR]

In [Finite solvable groups with exactly two nonlinear non-faithful irreducible characters, J. Algebra Appl. 18(5) (2019) 1950091], the first author studied directly indecomposable, solvable groups with exactly two nonlinear non-faithful irreducible characters. In this paper, we study the decomposable case and give a classification of decomposable groups possessing exactly two nonlinear non-faithful irreducible characters. In particular, nilpotent groups with this property are also classified. [ABSTRACT FROM AUTHOR]

In this paper, we give an alternative construction of a certain class of deformed double current algebras. These algebras are deformations of |$ U(\textrm {End}(\Bbbk ^r)[x,y]) $| and they were initially defined and studied by N. Guay in his papers. Here, we construct them as algebras of endomorphisms in Deligne category. We do this by taking an ultraproduct of spherical subalgebras of the extended Cherednik algebras of finite rank. [ABSTRACT FROM AUTHOR]

The author briefly reviews studies on the math teaching of secondary school students with mild intellectual disabilities. Then, the author demonstrates ways to teach secondary‐level mathematics to students with mild intellectual disabilities. In this article, readers will learn about how to use manipulatives, diagrams, and gestures to support students' thinking. Readers will also learn how to make connections between new and challenging math content to students' experiences inside and outside of school to support them as they think through mathematics. [ABSTRACT FROM AUTHOR]

In Alase et al (2022 J. Phys. A: Math. Theor. 55 244003), Alase et al wrote that 'the constraint of quasi-Hermiticity on observables' is not 'sufficient to extend the standard quantum theory' because 'such a system is equivalent to a standard quantum system.' Three addenda elucidating the current state of the art are found necessary. The first one concerns the project: in the related literature the original 'aim of extending standard quantum theory' has already been abandoned shortly after its formulation. The second comment concerns the method, viz., the study in 'the framework of general probabilistic theories' (GPT). It is noticed that a few other, mathematically consistent GPT-like theories are available. The authors do not mention, in particular, the progress achieved, under the quasi-Hermiticity constraint, in the approach using the effect algebras. We add that this approach already found its advanced realistic applications in the quasi-Hermitian models using the unbounded operators of observables acting in the infinite-dimensional Hilbert spaces. Thirdly, the 'intriguing open question' about 'what possible constraints, if any, could lead to such a meaningful extension' (in the future) is given an immediate tentative answer: the possibility is advocated that the desirable constraint could really be just the quasi-Hermiticity of the observables, provided only that one has in mind its recently developed non-stationary version. [ABSTRACT FROM AUTHOR]

The variety DHMSH of dually hemimorphic semi-Heyting algebras was introduced in 2011 by the second author as an expansion of semi-Heyting algebras by a dual hemimorphism. In this paper, we focus on the variety DHMSH from a logical point of view. The paper presents an extensive investigation of the logic corresponding to the variety of dually hemimorphic semi-Heyting algebras and of its axiomatic extensions, along with an equally extensive universal algebraic study of their corresponding algebraic semantics. Firstly, we present a Hilbertstyle axiomatization of a new logic called "Dually hemimorphic semi-Heyting logic" (DHMSH, for short), as an expansion of semi-intuitionistic logic SI (also called SH) introduced by the first author by adding a weak negation (to be interpreted as a dual hemimorphism). We then prove that it is implicative in the sense of Rasiowa and that it is complete with respect to the variety DHMSH. It is deduced that the logic DHMSH is algebraizable in the sense of Blok and Pigozzi, with the variety DHMSH as its equivalent algebraic semantics and that the lattice of axiomatic extensions of DHMSH is dually isomorphic to the lattice of subvarieties of DHMSH. A new axiomatization for Moisil's logic is also obtained. Secondly, we characterize the axiomatic extensions of DHMSH in which the "Deduction Theorem" holds. Thirdly, we present several new logics, extending the logic DHMSH, corresponding to several important subvarieties of the variety DHMSH. These include logics corresponding to the varieties generated by two-element, three-element and some four-element dually quasi-De Morgan semi- Heyting algebras, as well as a new axiomatization for the 3-valued Lukasiewicz logic. Surprisingly, many of these logics turn out to be connexive logics, only a few of which are presented in this paper. Fourthly, we present axiomatizations for two infinite sequences of logics namely, De Morgan Gödel logics and dually pseudocomplemented Gödel logics. Fifthly, axiomatizations are also provided for logics corresponding to many subvarieties of regular dually quasi-De Morgan Stone semi-Heyting algebras, of regular De Morgan semi-Heyting algebras of level 1, and of JI-distributive semi-Heyting algebras of level 1. We conclude the paper with some open problems. Most of the logics considered in this paper are discriminator logics in the sense that they correspond to discriminator varieties. Some of them, just like the classical logic, are even primal in the sense that their corresponding varieties are generated by primal algebras. [ABSTRACT FROM AUTHOR]

Multi-layer metamodeling is a metamodeling method that provides great flexibility for domain prototyping, while it also ensures rigid validation of domain rules. Visualization of multi-layer models would be essential in order to promote this new modeling technique in industrial setups; however, the traditional way of representing model entities is not sufficient here. Dynamic Multi-Layer Algebra is a multi-layer metamodeling approach that addressed the challenges of multi-layer modeling, but uses a text-based language to create models. This paper presents Dynamo, a visual notation for Dynamic Multi-Layer Algebra, which is also applicable to other multi-layer metamodeling approaches. The paper elaborates the graphical syntax and the design decisions. [ABSTRACT FROM AUTHOR]

Suppose that S T 1 is a class of close-to-star functions. In this paper, we investigated the estimate of Zalcman functional on the logarithmic coefficients and the third Hankel determinant for the class S T 1 with the determinant entry of logarithmic coefficients. Also, we obtained the sharp bounds of Zalcman functional J 2 , 4 f and J 3 , 3 f for the class S T 1 . [ABSTRACT FROM AUTHOR]

The present paper is devoted to the study of 2-local derivations on the Schrödinger-Virasoro Algebra, which is an infinite-dimensional Lie algebra with three outer derivations. We prove that all 2-local derivations on the Schrödinger-Virasoro Algebra are derivations. [ABSTRACT FROM AUTHOR]

In this paper, we give a complete classification of all free $ U(\mathbb {C}L_0 \oplus \mathbb {C}Y_0\oplus \mathbb {C}M_0) $ U (C L 0 ⊕ C Y 0 ⊕ C M 0) -modules of rank 1 over a Schrödinger-Virasoro type algebra $ \mathfrak {tsv} $ tsv . [ABSTRACT FROM AUTHOR]

This paper concerns with convergence properties of an inertial proximal algorithm that contains a Tikhonov term regularization, time scale parameter, and a Hessian-driven damping in a Hilbert space. More precisely, we prove the strong convergence of the proximal algorithm obtained by temporal discretization of a continuous dynamic that we treated earlier in a previous work. We also obtain the convergence of the values to the global minimum of the objective function, and a strong convergence of the gradient and the velocity towards zero. Finally, we present a numerical example to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we exploit necessary/sufficient optimality conditions for ε-quasi positively properly efficient solutions of the semi-infinite multiobjective optimization problems with data uncertainty. We also consider Wolfe type dual problems/Mond--Weir type dual problems under the assumptions of generalized convexity. Finally, several illustrative examples are also provided. [ABSTRACT FROM AUTHOR]

To elucidate the combinatorial architecture of neural codes, the neural ideal , an algebraic object, was introduced. Represented in its canonical form, provides a succinct characterization of the inherent receptive field architecture within the code. The polynomials in are also instrumental in determining the relationships among the neurons' receptive fields. Consequently, the computation of the collection of canonical forms is pivotal. In this paper, based on the study of relations between pseudo-monomials, the authors present a computationally efficient iterative algorithm for the canonical forms of the neural ideal. Additionally, we introduce a new relationship among the neurons' receptive fields, which can be characterized by if-and-only-if statements, relating both to and to a larger ideal of a code . [ABSTRACT FROM AUTHOR]

We describe some recent computer investigations with the 'Constraint Logic Programming over Finite Domains' library in the Prolog programming environment to search for new simple Lie algebras over the field \operatorname {GF}(2) of 2 elements. Motivated by a paper of Grishkov et al., we specifically look for those with a thin decomposition , and we settle one of their conjectures. We extrapolate from our results the existence of two new infinite families of simple Lie algebras, in addition to finding seven new sporadic examples in dimension 31. We also better contextualise some previously discovered simple algebras, putting them into families which do not seem to have ever appeared in the literature, and give an updated table of those currently known. [ABSTRACT FROM AUTHOR]

In this paper, we prove a result similar to results of Itoh [J. Algebra 150 (1992), pp. 101–117] and Hong-Ulrich [J. Lond. Math. Soc. (2) 90 (2014), pp. 861–878], proving that integral closure of an ideal is compatible with specialization by a general element of that ideal for ideals of height at least two in a large class of rings. Moreover, we show integral closure of sufficiently large powers of the ideal is compatible with specialization by a general element of the original ideal. In a polynomial ring over an infinite field, we give a class of squarefree monomial ideals for which the integral closure is compatible with specialization by a general linear form. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study a poset isomorphism between two support \tau-tilting posets. We take several information from combinatorial properties of support \tau-tilting posets and give an analogue of Happel-Unger's reconstruction theorem. [ABSTRACT FROM AUTHOR]

Building on work of Ruelle and Putnam in the Smale space case, Thomsen defined the homoclinic and heteroclinic C^\ast-algebras for an expansive dynamical system. In this paper we define a class of expansive dynamical systems, called synchronizing dynamical systems, that exhibit hyperbolic behavior almost everywhere. Synchronizing dynamical systems generalize Smale spaces (and even finitely presented systems). Yet they still have desirable dynamical properties such as having a dense set of periodic points. We study various C^\ast-algebras associated with a synchronizing dynamical system. Among other results, we show that the homoclinic algebra of a synchronizing system contains an ideal which behaves like the homoclinic algebra of a Smale space. [ABSTRACT FROM AUTHOR]

Let K be a field of characteristic zero and x a free variable. A K - ℰ -derivation of K [ x ] is a K -linear map of the form I , − , ϕ for some K -algebra endomorphism ϕ of K [ x ] , where I denotes the identity map of K [ x ]. In this paper, we study the image of an ideal of K [ x ] under some K -derivations and K - ℰ -derivations of K [ x ]. We show that the LFED conjecture proposed in [W. Zhao, Some open problems on locally finite or locally nilpotent derivations and ℰ -derivations, Commun. Contem. Math. 20(4) (2018) 1750056] holds for all K - ℰ -derivations and all locally finite K -derivations of K [ x ]. We also show that the LNED conjecture proposed in [W. Zhao, Some open problems on locally finite or locally nilpotent derivations and ℰ -derivations, Commun. Contem. Math. 20(4) (2018) 1750056] holds for all locally nilpotent K -derivations of K [ x ] , and also for all locally nilpotent K - ℰ -derivations of K [ x ] and the ideals u K [ x ] such that either u = 0 , or deg u ≤ 1 , or u has at least one repeated root in the algebraic closure of K. As a bi-product, the homogeneous Mathieu subspaces (Mathieu–Zhao spaces) of the univariate polynomial algebra over an arbitrary field have also been classified. [ABSTRACT FROM AUTHOR]