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We study cohomology of morphisms of Lie-Yamaguti algebras. As an application, we establish that this cohomology 'controls' the formal deformations. Additionally, we demonstrate its connection to the abelian extensions of morphisms of Lie-Yamaguti algebras. [ABSTRACT FROM AUTHOR]

Although the category of instinct is included in almost every discourse in which animal behavior is analyzed, a closer look at the phenomenon that creates its specificity shows its elusiveness. One gets the impression that something called instinctive behavior is simply not significantly different from other non-instinctive behaviors. Firstly, instinct understood as innate, pre-programmed behavior partially loses its features of automaticity and rigid schematicity when its features are compared with the features of other behaviors acquired through learning. Secondly, the genesis of the instinct, which is at least partly to be found in epigenetics and the mechanisms of individual development, shows that the differences between it and other behaviors not inherited genetically are not as large as may be assumed at first glance. Third, a promising explanation for the origin of instinctive beha vior is the ecological theory originally formulated by Eleanor Gibson and James J. Gibson for perception, as it allows us to understand the role of environmental factors in the development of patterns of instinctive action. [ABSTRACT FROM AUTHOR]

Although the category of instinct is inscribed in almost every discourse in which the behavior of animals is analyzed, a closer look at the phenomenon that creates its specificity reveals its elusiveness. One gets the impression that something like instinctive behavior is simply not significantly different from other non-instinctive behavior. First, instinct as an innate, pre-programmed behavior disappears when its characteristics are compared with those of other behaviors acquired through learning. Secondly, the genesis of the instinct, which should be sought in epigenetics and the mechanisms of individual development, shows that it does not differ fundamentally from other behaviors not inherited by genetics. Third, the best explanation for the origin of instinctive behavior is the ecological theory originally formulated by Eleanor Gibson and James J. Gibson for perception, as it allows us to understand the role of environmental factors in the formation of instinctive action patterns.

Birational properties of generically finite morphisms X→Y$X\rightarrow Y$ of algebraic varieties can be understood locally by a valuation of the function field of X. In finite extensions of algebraic local rings in characteristic zero algebraic function fields which are dominated by a valuation, there are nice monomial forms of the mapping after blowing up enough, which reflect classical invariants of the valuation. Further, these forms are stable upon suitable further blowing up. In positive characteristic algebraic function fields, it is not always possible to find a monomial form after blowing up along a valuation, even in dimension two. In dimension two and positive characteristic, after enough blowing up, there are stable forms of the mapping which hold upon suitable sequences of blowing up. We give examples showing that even within these stable forms, the forms can vary dramatically (erratically) upon further blowing up. We construct these examples in defect Artin–Schreier extensions which can have any prescribed distance. [ABSTRACT FROM AUTHOR]

The cohomology algebra of the space H∗ (X) defines neither cohomology modules of the loop space H∗ (ΩX) nor cohomologies of the free loop space H∗ (ΛX). But by the author's minimality theorem, there exists a structure of A(∞)-algebra (H∗ (X), {mi}) on H∗ (X), which determines H∗ (ΩX). Here will be shown that the same A(∞)-algebra (H∗(X), {mi}) determines also cohomology modules H∗ (ΛX). [ABSTRACT FROM AUTHOR]

We prove that every non-degenerate toric variety, every homogeneous space of a connected linear algebraic group without non-constant invertible regular functions, and every variety covered by affine spaces admit a surjective morphism from an affine space. [ABSTRACT FROM AUTHOR]

In this paper, given a morhism φ with its pseudo core inverse φ Ⓓ and a morphism η such that 1 X + φ Ⓓ η is invertible, a necessary and sufficient condition and two sufficient conditions are presented under which the additive property, namely (φ + η) Ⓓ = (1 X + φ Ⓓ η) − 1 φ Ⓓ holds. Several interesting results about additive properties of core inverses of bounded linear operators presented in Huang et al. are generalized to the case of pseudo core inverse of morphism. Also, many results regarding additive properties of core-EP inverses of complex matrices studied by Ma and Stanimirović are extended to the cases of morphism. [ABSTRACT FROM AUTHOR]

In this paper, we obtain that all filters and the empty set of every effect algebra could naturally form a convex structure, which is called a filter convex structure, and morphism (resp., monomorphism) between two effect algebras is convexity-preserving (resp., convex-to-convex) correspondingly constructed convexity spaces. Then we introduce the concept of nets (convergent nets) in convexity spaces that is compatible with convexity-preserving mappings and investigate some properties of convergent nets. Moreover, we prove that the partial subtraction − for the first position is convexity-preserving and the partial addition + is separately convexity-preserving with respect to filter convex structures by nets. Finally, we discuss convexity-preserving properties of the partial subtraction − for the first position and that the partial addition + is separately convexity-preserving in quotient (resp., finite product) of filter convex structures. For finite product, we also investigate the opposite direction for the partial subtraction. [ABSTRACT FROM AUTHOR]

In this note, we introduce the notion of a morphism between two hyperbolic iterated function systems. We prove that the graph of such a morphism is the attractor of an iterated function system, giving a closed graph theorem, and demonstrate how it can be used to approach the topological conjugacy problem for iterated function systems. [ABSTRACT FROM AUTHOR]

A set of words, also called a language, is letter-balanced if the number of occurrences of each letter only depends on the length of the word, up to a constant. Similarly, a language is factor-balanced if the difference of the number of occurrences of any given factor in words of the same length is bounded. The most prominent example of a letter-balanced but not factor-balanced language is given by the Thue–Morse sequence. We establish connections between the two notions, in particular for languages given by substitutions and, more generally, by sequences of substitutions. We show that the two notions essentially coincide when the sequence of substitutions is proper. For the class of Thue–Morse–Sturmian languages, we give a full characterisation of factor-balancedness. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a notion of morphism between two groupoid defined in terms of groupoid actions and we prove that groupoids as objects and equivalence classes of certain type of such morhisms form category which is equivalent to the category introduced in [2].

We show that there exists an infinite word over the alphabet {0, 1, 3, 4} containing no three consecutive blocks of the same size and the same sum. This answers an open problem of Pirillo and Varricchio from 1994. [ABSTRACT FROM AUTHOR]

Eicosanoids are a class of functionally bioactive lipid mediators derived from the metabolism of long-chain polyunsaturated fatty acids (PUFAs) mediated by multiple enzymes of three main branches, including cyclooxygenases (COXs), lipoxygenases (LOXs), and cytochrome P450s (CYPs). Recently, the role of eicosanoids derived by COXs and LOXs pathways in the control of physiological and pathological processes associated with cancer has been well documented. However, the role of CYPs-mediated eicosanoids, such as epoxyeicosatrienoic acids (EETs), epoxyoctadecenoic acids (EpOMEs), epoxyeicosatetraenoic acids (EpETEs), and epoxydocosapentaenoic acids (EDPs), as well as hydroxyeicosatetraenoic acids (HETEs), in tumorigenesis and cancer progression have not been fully elucidated yet. Here we summarized the association of polymorphisms of CYP monooxygenases with cancers and the pleiotropic functions of CYP monooxygenase-mediated eicosanoids (EETs, EpOMEs, EpETE, EDPs, and 20-HETE) in the tumorigenesis and metastasis of multiple cancers, including but not limited to colon, liver, kidney, breast and prostate cancers, which hopefully provides valuable insights into cancer therapeutics. We believe that manipulation of CYPs with or without supplement of ω-3 PUFAs to regulate eicosanoid profile is a promising strategy to prevent and/or treat cancers.

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Some scholars have proposed homomorphisms between information systems based on consistent functions. However, the binary relations in the codomain induced by consistent functions thoroughly depend on the binary relations induced by the original domain systems. This paper introduces the concept of core knowledge to analyze the intrinsical topology structures of binary approximation spaces, binary knowledge bases and binary information systems. Because of the three different categories, we use the term "morphism" from category theory to depict the communication into the three categories. A morphism can be regarded as the composition of a natural projection induced by core knowledge and an embedding, which are more general than homomorphisms. What's more, this paper proposes the notion of isomorphism and shows that the two isomorphic categories can be seen as one category based on the topological invariance. Considering that the reduction of knowledge and attributes should be based on the premise of maintaining the structure of core knowledge, isomorphisms will provide the theoretical basis of the reduction. [ABSTRACT FROM AUTHOR]

• Given an alphabet A , and an (anti-)automorphism θ , a set L ⊆ A ⁎ is θ -invariant if θ (L) = L. • In the framework of θ -invariant sets, a defect effect is highlighted. • Several non-trivial examples of finite complete θ -invariant codes are presented. • Over a finite alphabet, any regular non complete θ -invariant code can be embedded into a complete one. • Given a thin θ -invariant code, being a maximal code, or being maximal in the family of θ -invariant codes, or being complete are equivalent properties. Let A be an arbitrary alphabet and let θ be an (anti-)automorphism of A ⁎ (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under θ (θ -invariant for short) that is, languages L satisfying θ (L) ⊆ L. We establish an extension of the famous defect theorem. With regard to the so-called notion of completeness, we provide a series of examples of finite complete θ -invariant codes. Moreover, we establish a formula which allows to embed any non-complete θ -invariant code into a complete one. As a consequence, in the family of the so-called thin θ -invariant codes, maximality and completeness are two equivalent notions. [ABSTRACT FROM AUTHOR]

The problem we consider is the following: Given an infinite word w on an ordered alphabet, construct the sequence ν w = (ν [ n ]) n , equidistributed on [ 0 , 1 ] and such that ν [ m ] < ν [ n ] if and only if σ m (w) < σ n (w) , where σ is the shift operation, erasing the first symbol of w. The sequence ν w exists and is unique for every word with well-defined positive uniform frequencies of every factor, or, in dynamical terms, for every element of a uniquely ergodic subshift. In this paper we describe the construction of ν w for the case when the subshift of w is generated by a morphism of a special kind; then we overcome some technical difficulties to extend the result to all binary morphisms. The sequence ν w in this case is also constructed with a morphism. At last, we introduce a software tool which, given a binary morphism φ , computes the morphism on extended intervals and first elements of the equidistributed sequences associated with fixed points of φ. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a notion of morphism between two groupoid defined in terms of groupoid actions and we prove that groupoids as objects and equivalence classes of certain type of such morhisms form category which is equivalent to the category introduced in [2]. [ABSTRACT FROM AUTHOR]

We consider the paracomplex version of the notion of mixed linear spaces introduced by M. Jurchescu in [4] by replacing the complex unit i with the paracomplex unit j, j2 = 1. The linear algebra of these spaces is studied with a special view towards their morphisms.

Bounding the number of morphisms between compact Riemann surfaces is a long standing problem coming from complex and algebraic geometry. We show that linear algebra techniques allow to improve the known results when we assume a kind of condition number bound for the period matrix. [ABSTRACT FROM AUTHOR]

Let S be a finite subset of Z n. A vector sequence (z i) is an S -walk if and only if z i + 1 − z i is an element of S for all i. Gerver and Ramsey showed in 1979 that for S ⊂ Z 3 there exists an infinite S -walk in which no 5 11 + 1 = 48 , 828 , 126 points are collinear. Here, we use the same general approach, but with the aid of a computer search, to improve the bound to 189. [ABSTRACT FROM AUTHOR]

Graf berarah dapat dipandang sebagai pasangan 4-tupel yang terdiri dari dua himpunan serta dua pemetaan dan disebut sebagai quiver . Untuk suatu quiver dapat didefinisikan representasi quiver . Representasi quiver merupakan penempatan ruang vektor pada setiap titik-titik dari quiver dan pemetaan linier pada setiap panah-panahnya. Sebuah representasi yang tidak memiliki subrepresentasi sejati selain nol disebut sebagai representasi sederhana. Pada makalah ini, dipelajari sifat-sifat dari suatu representasi quiver sederahana. Selanjutnya sifat-sifat tersebut digunakan untuk menyelidiki syarat perlu dan cukup dari suatu representasi sederhana.A directed graph can be viewed as a 4-tuple where are finite sets of vertices and arrows respectively, and are two maps from to . A directed graph is often called a quiver. For a quiver , we can define a quiver representation . A representation of a quiver is an assignment of a vector space to each vertex and a linear mapping to each arrow. A representation which has no proper subrepresentation except zero is called a simple representation. In this paper, we study the properties of a simple representation of quiver. These properties will be used to investigate the necessary and sufficient condition of a simple representation of quiver.

Let be an additive category with an involution. Suppose that is a morphism with kernel in , then is core invertible if and only if has a cokernel and both and are invertible. In this case, we give the representation of the core inverse of. We also give the corresponding result about dual core inverse. [ABSTRACT FROM AUTHOR]

We introduce the concept of a morphism from the set of Butson Hadamard matrices over k th roots of unity to the set of Butson matrices over ℓ th roots of unity. Tensor products give many examples of morphisms in which k divides ℓ. More interesting are constructions where k does not divide ℓ. Examples where this occurs include Turyn's construction of real Hadamard matrices from Butson matrices over the 4th roots and the work of Compton, Craigen and de Launey on 'unreal' Butson matrices over the 6th roots. We give a unified treatment of these constructions in terms of the eigenvalues and minimal polynomials of associated Butson matrices. We produce a new family of morphisms from sets of mutually unbiased bases constructed by Gow. We also classify all morphisms from the set of n × n Butson matrices over k th roots of unity to the set of 2 n × 2 n Butson matrices over ℓ th roots of unity where ℓ < k. [ABSTRACT FROM AUTHOR]

Let 𝒞 be a category with an involution ∗. Suppose that φ : X → X is a morphism and (φ 1 , Z , φ 2) is an (epic, monic) factorization of φ through Z , then φ is core invertible if and only if (φ ∗) 2 φ 1 and φ 2 φ 1 are both left invertible if and only if ((φ ∗) 2 φ 1 , Z , φ 2) , (φ 2 ∗ , Z , φ 1 ∗ φ ∗ φ) and (φ ∗ φ 2 ∗ , Z , φ 1 ∗ φ) are all essentially unique (epic, monic) factorizations of (φ ∗) 2 φ through Z. We also give the corresponding result about dual core inverse. In addition, we give some characterizations about the coexistence of core inverse and dual core inverse of an R -morphism in the category of R -modules of a given ring R. [ABSTRACT FROM AUTHOR]

Properties of words that are finite sequences of symbols from a finite set, con-stitute an interesting topic of investigation in the field of "combinatorics on words". Parikh matrix of a word w over an ordered alphabet is a relatively new notion introduced by Ma-teescu et al. (2000). The entries above the main diagonal in this upper triangular Parikh matrix provide counts of certain subwords in the word w that are subsequences of w. On the other hand several morphisms on words have also been explored for their properties. Here we consider a morphism, called Prouhet morphism and establish several properties of images of words under this morphism in the context of subwords and Parikh matrices. [ABSTRACT FROM AUTHOR]