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We discuss the notion of vague subbisemiring, level sets of vague subbisemirings and vague normal subbisemiring of a bisemiring. Also, we investigate some properties related to these subbisemirings. The homomorphic image of vague subbisemirings is also vague subbisemirings. The homomorphic preimage of vague subbisemirings is also vague subbisemirings. To illustrate our results and examples are given. [ABSTRACT FROM AUTHOR]

Reversible data hiding in encrypted images (RDHEI) is a technique that allows for secret data to be embedded in images while preserving the privacy of the image content when the image owner and the data hider are different entities. This paper proposes a new reversible data hiding scheme in encrypted images, in which the data hider does not need a data hiding key in the data embedding process. We first reserve embedding room before image encryption based on the congruence relations of pixel values within image blocks. Then, the pre-processed original image is encrypted using a multi-secret sharing based image encryption algorithm that satisfies additive homomorphism. Using the homomorphism of the image encryption, we embed the secret data into the reserved embedding room directly in the encrypted images without a data hiding key. The receiver can extract the secret data by checking the congruence relation between pixel values in a decrypted image block and then recover the original image. We analyze the security of the proposed scheme and embedding capacity with different block sizes and different parameters of transformation. The experimental results and analysis show that the proposed scheme achieves a high embedding capacity with a suitable block size especially in smooth images. [ABSTRACT FROM AUTHOR]

We discuss the notion of intuitionistic fuzzy subbisemiring, level sets of intuitionistic fuzzy subbisemirings and intuitionistic fuzzy normal subbisemiring of a bisemiring. Also, we investigate some of the properties related to these subbisemirings. To illustrate our results examples are given. [ABSTRACT FROM AUTHOR]

There exist two known types of ultrafilter extensions of first-order models, both in a certain sense canonical. One of them (Goranko in Filter and ultrafilter extensions of structures: universal-algebraic aspects, preprint, 2007) comes from modal logic and universal algebra, and in fact goes back to Jónsson and Tarski (Am J Math 73(4):891–939, 1951; 74(1):127–162, 1952). Another one (Saveliev in Lect Notes Comput Sci 6521:162–177, 2011; Saveliev in: Friedman, Koerwien, Müller (eds) The infinity project proceeding, Barcelona, 2012) comes from model theory and algebra of ultrafilters, with ultrafilter extensions of semigroups (Hindman and Strauss in Algebra in the Stone–Čech Compactification, W. de Gruyter, Berlin, 2012) as its main precursor. By a classical fact of general topology, the space of ultrafilters over a discrete space is its largest compactification. The main result of Saveliev (Lect Notes Comput Sci 6521:162–177, 2011; in: Friedman, Koerwien, Müller (eds) The infinity project proceeding, Barcelona, 2012), which confirms a canonicity of this extension, generalizes this fact to discrete spaces endowed with an arbitrary first-order structure. An analogous result for the former type of ultrafilter extensions was obtained in Saveliev (in On two types of ultrafilter extensions of binary relations. arXiv:2001.02456). Results of such kind are referred to as extension theorems. After a brief introduction, we offer a uniform approach to both types of extensions based on the idea to extend the extension procedure itself. We propose a generalization of the standard concept of first-order interpretations in which functional and relational symbols are interpreted rather by ultrafilters over sets of functions and relations than by functions and relations themselves, and define ultrafilter models with an appropriate semantics for them. We provide two specific operations which turn ultrafilter models into ordinary models, establish necessary and sufficient conditions under which the latter are the two canonical ultrafilter extensions of some ordinary models, and obtain a topological characterization of ultrafilter models. We generalize a restricted version of the extension theorem to ultrafilter models. To formulate the full version, we propose a wider concept of ultrafilter models with their semantics based on limits of ultrafilters, and show that the former concept can be identified, in a certain way, with a particular case of the latter; moreover, the new concept absorbs the ordinary concept of models. We provide two more specific operations which turn ultrafilter models in the narrow sense into ones in the wide sense, and establish necessary and sufficient conditions under which ultrafilter models in the wide sense are the images of ones in the narrow sense under these operations, and also are two canonical ultrafilter extensions of some ordinary models. Finally, we establish three full versions of the extension theorem for ultrafilter models in the wide sense. The results of the first three sections of this paper were partially announced in Poliakov and Saveliev (in: Kennedy, de Queiroz (eds) On two concepts of ultrafilter extensions of first-order models and their generalizations, Springer, Berlin, 2017). [ABSTRACT FROM AUTHOR]

In this work, we intend to introduce and study another algebraic structure of single-valued neutrosophic sets called neutrosophic field as a continuation of our investigations on neutrosophic algebraic structures. For this goal, we define the concept of neutrosophic fields and observe some of their basic characteristics and properties. Then we give the definition of a neutrosophic linear space over the proposed neutrosophic field and consider its fundamental properties. [ABSTRACT FROM AUTHOR]

In this paper we investigate quasigroups isotopic to groups [1]. The need for such a detailed study follows from the fact that the center of a quasigroup is a T􀀀quasigroup [3], and therefore the structure of quasigroups is based on T􀀀quasigroups [2]. T􀀀quasigroups are an special case of IG􀀀quasigroups. [ABSTRACT FROM AUTHOR]

A homomorphism quasi-order between algebraic structures A and B of the same type is defined as follows: 𝒜 ≤ ℬ if there is a homomorphism of 𝒜 to ℬ . The paper deals with the class L of all connected monounary algebras. Let ∼ be the equivalence corresponding to the relation ≤ and let L = L ∼ . We prove that L is a lattice. Next it is shown that the lattice L is distributive. For the purpose of the proof, to each connected monounary algebra without a cycle, an increasing sequence of ordinals is assigned. Finally, we deal with the special case of increasing sequences, namely, such that the sequence contains only positive integers. [ABSTRACT FROM AUTHOR]

We present the notion of Pythagorean Fuzzy Weak Bi-Ideals (PFWBI) and interval valued Pythagorean fuzzy weak biideals of G-near-rings and studies some of its properties. We present the notion of interval valued Pythagorean fuzzy weak bi-ideal and establish some of its properties. We study interval valued Pythagorean fuzzy weak bi-ideals of G-nearring using homomorphism. [ABSTRACT FROM AUTHOR]

In this article, we develop some more of the theory of (m, n)-semirings. In particular, we study ideals, primary ideals, and subtractive ideals of (m, n)-semirings and 「-(m, n)-semirings. We describe the functions between (m, n)-semirings that preserve the (m, n)-semiring structure. Also, we look at another way of forming new (m, n)-semiring from existing ones. [ABSTRACT FROM AUTHOR]

The notion of ideals is introduced in transitive BE-algebras. Some characterization theorems of ideals of transitive BE-algebras are derived. The notion of semi-ideals is introduced and studied a relationship between semi-ideals and ideals. Properties of ideals are studied with the help of homomorphisms and congruences. [ABSTRACT FROM AUTHOR]

In this paper, a derivative for functions f:G→H, where G is any metric divisible group and H is a metric Abelian group with a group metric, is defined. Basic differentiation theorems are stated and demonstrated. In particular, we obtain the Chain Role.

This paper studies information structures in a fuzzy β-covering information system. We introduce the concepts of a fuzzy β-covering information system and homomorphism between them, and investigate related properties. The concept of information structure of a fuzzy β-covering information system is given. We discuss the relationships between information structures from the view of dependence and separation. Then granularity measures for a fuzzy β-covering information system are studied. Finally, we discuss invariance of fuzzy β-covering information systems under homomorphism and illustrate its application on data compression. [ABSTRACT FROM AUTHOR]

For n ≥ 2 , an additive map f between two rings A and B is called an n-Jordan homomorphism, or an n-homomorphism if f (a n) = f (a) n , for all a ∈ A , or f (a 1 a 2 ⋯ a n) = f (a 1) f (a 2) ⋯ f (a n) , for all a 1 , a 2 , ... , a n ∈ A , respectively. In particular, if n = 2 then f is simply called a Jordan homomorphism or a homomorphism, respectively. The notion of n-Jordan homomorphism between rings was introduced in 1956 by Herstein and the concept of n-homomorphism between algebras was introduced in 2005 by Hejazian et al. Properties of n-Jordan homomorphisms as well as n-homomorphisms have been studied by many authors since then. One of the main questions is that, "under what conditions n- Jordan homomorphisms are n-homomorphism?". Another natural question is that "under what conditions certain properties of homomorphisms may be extended to n-homomorphisms". We provide conditions under which these questions have affirmative answers. We also study the continuity problem for n-Jordan homomorphisms on Banach algebras, while extending some known results in this field. [ABSTRACT FROM AUTHOR]

In order to investigate the derivation theory on MV-algebras further more, we give the notion of τ-additive derivations as a generalization of additive derivations in [29]. Then we discuss some related properties and characterizations of τ-additive derivations, and obtain the condition for a τ- additive derivation to be an endomorphism. Furthermore, some properties of τ-additive derivations related with the fixed set Δd(A) are given. [ABSTRACT FROM AUTHOR]

In this paper, we investigate some properties of homomorphisms and deductive systems of generalized BE-semigroups. In particular, we show that through every deductive system, we may get factor generalized BE-semigroup. [ABSTRACT FROM AUTHOR]

In this paper, a Sheffer stroke BG-algebra, a subalgebra and a normal subset of a Sheffer stroke BG-algebra are given. After determining a filter of Sheffer stroke BG-algebra, a congruence relation on a Sheffer stroke BG-algebra is defined by means of its filter, and quotient of a Sheffer stroke BG-algebra by a congruence relation on this algebra is built. Besides, a homo- morphism between Sheffer stroke BG-algebras is introduced and it is presented that their features are preserved under this homomorphism. [ABSTRACT FROM AUTHOR]

Peter Cameron introduced the concept of the circular altitude of graphs, a parameter which was shown by Bamberg et al. that provides a lower bound on the circular chromatic number. In this paper, we investigate this parameter and show that the circular altitude of a graph is equal to the maximum of circular altitudes of its blocks. Also, we show that homomorphically equivalent graphs have the same circular altitudes. Finally, we prove that the circular altitude of the Cartesian product of two graphs is equal to the maximum of circular altitudes of its factors. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to associate a family of groupoids and morphisms to a discrete nonautonomous system that does not necessarily satisfy the semigroup property. This approach provides a unifying framework to study discrete nonautonomous systems and to uncover similarities between seemingly unrelated systems. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce and study 2-absorbing fuzzy ideals of commutative semirings. Some basic operations on them are defined and some of its characterizations are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of denumerably many positive solutions for singular iterative system of fractional order boundary value problem involving Riemann--Liouville integral boundary conditions with increasing homeomorphism and positive homomorphism operator by using Hölder's inequality and Krasnoselskii's cone fixed point theorem in a Banach space. [ABSTRACT FROM AUTHOR]

The existent algebraic models of the genetic code contribute to the understanding of the physio-chemical characteristics of the amino acids. However, the process of translating a gene into a phenotype is highly complex. Moreover, the intricacy of gene expression gets further multiplied due to the biases in the codon usage. This paper explores an algebraic structure called module on the set of codons as well as on that of RNA sequences. We study the potential implications of these structures on gene expression and the G C content of an RNA sequence. The base order { C , U , G , A } appears to possess greater biological significance than many of the orders previously studied. We have developed a novel algorithm to generate RNA sequences with high G C content, aiming to enhance the thermostability of biomolecules. The insights gained from this investigation may have applications in biomolecular modeling and docking, protein engineering, drug development, and related fields. • A module structure is constructed on genetic code and studied its implications. • Developed a novel algorithm to increase the G C content of RNA sequences. • This study may be utilized in computational protein engineering. [ABSTRACT FROM AUTHOR]

An oriented k − coloring of an oriented graph G⃗ is a partition of V(G⃗) into k color classes such that no two adjacent vertices belong to the same color class, and all the arcs linking the two color classes have the same direction. The oriented chromatic number of an oriented graph G⃗ is the minimum order of an oriented graph H⃗ to which G⃗ admits a homomorphism to H⃗. The oriented chromatic number of an undirected graph G is the maximum oriented chromatic number of all possible orientations of the graph G. In this paper, we show that every edge amalgamation of cycle graphs, which also known as a book graph, has oriented chromatic number less than or equal to six.

A new form of the hidden discrete logarithm problem, proposed as primitive of the post-quantum public-key cryptoschemes, is defined over the 6-dimensional finite non-commutative associative algebra with a large set of the left-sided global units. The considered computationally difficult problem uses the mutual commutativity of the exponentiation operation and homomorphism mapping defined relatively a fixed unit element of the algebra. The related properties of the introduced algebra are described. Novel public key-agreement and zero-knowledge protocols based on the hidden logarithm problem are introduced as post-quantum cryptoschemes.

A BN-algebra is a non-empty set X with a binary operation “∗” and a constant 0 that satisfies the following axioms: (B1) x∗x=0, (B2) x∗0=x, and (BN) (x∗y)∗z=(0∗z)∗(y∗x) for all x, y, z ∈X. A non-empty subset I of X is called an ideal in BN-algebra X if it satisfies 0∈X and if y∈I and x∗y∈I, then x∈I for all x,y∈X. In this paper, we define several new ideal types in BN-algebras, namely, r-ideal, k-ideal, and m-k-ideal. Furthermore, some of their properties are constructed. Then, the relationships between ideals in BN-algebra with r-ideal, k-ideal, and m-k-ideal properties are investigated. Finally, the concept of r-ideal homomorphisms is discussed in BN-algebra.

The Constraint Satisfaction Problem (CSP) and its counting counterpart appears under different guises in many areas of mathematics, computer science, and elsewhere. Its structural and algorithmic properties have been shown to play a crucial role in many of those applications. For instance, in the decision CSPs, structural properties of the relational structures involved—like, for example, dismantlability—and their logical characterizations have been instrumental for determining the complexity and other properties of the problem. Topological properties of the solution set such as connectedness are related to the hardness of CSPs over random structures. Additionally, in approximate counting and statistical physics, where CSPs emerge in the form of spin systems, mixing properties and the uniqueness of Gibbs measures have been heavily exploited for approximating partition functions and free energy. In spite of the great diversity of those features, there are some eerie similarities between them. These were observed and made more precise in the case of graph homomorphisms by Brightwell and Winkler, who showed that dismantlability of the target graph, connectedness of the set of homomorphisms, and good mixing properties of the corresponding spin system are all equivalent. In this paper we go a step further and demonstrate similar connections for arbitrary CSPs. This requires much deeper understanding of dismantling and the structure of the solution space in the case of relational structures, and new refined concepts of mixing introduced by Briceño. In addition, we develop properties related to the study of valid extensions of a given partially defined homomorphism, an approach that turns out to be novel even in the graph case. We also add to the mix the combinatorial property of finite duality and its logic counterpart, FO-definability, studied by Larose, Loten, and Tardif. [ABSTRACT FROM AUTHOR]

Let X be a finite partially ordered set, R a commutative domain and σ an endomorphism of R. We define the skew incidence ring I (X , R , σ) and we prove that each Jordan isomorphism of I (X , R , σ) onto an associative ring S is a near-sum of a homomorphism and an anti-homomorphism. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study some basic properties of the orbits of elements in dynamical systems defined by groups. The relation between orbit of an element and the orbit of its inverse element has been established. The nature of the orbit of the identity element in the dynamical system has been studied and a singleton set containing the identity element itself has been obtained. It is observed that the set of all fixed points in the dynamical system is strongly invariant (Sinvariant) and is a closed subgroup of the group. By using the topological conjugacy between dynamical systems defined by groups, a relation between the orbit of an element and the orbit of its image element in the other dynamical system has been obtained. Finally, we obtained that if an element is in the kernel of the homomorphism, then it must be eventually fixed at the identity element of the group. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the concept of homomorphism from BE-semigroups to generalized BE-semigroups. In order to show the existence, we construct some examples. Furthermore, we characterize generalized BE-semigroups by using homomorphism. In particular, we show that through every homomorphism, we may get factor generalized BE-semigroup. [ABSTRACT FROM AUTHOR]

Recently, Location Based Services (LBS) is widely used in mobile technology. Location Based Services (LBS) is one of the new emerging mobile technologies in smart grid. In smart grid, however, the use of these technologies has resulted to new challenges. The privacy issues related with these services are becoming main concerns because of the leakage of user's locations and query contents on smart meters. The most recent studies that have been done for privacy preserving solutions such as temporal and spatial cloaking based methods are not enough to protect user's location privacy and hence hackers are hacking information, making changes to readings on smart meter too. This is because preserving privacy for LBS, is a very hard task. For instance, preserving privacy for a continuous query that is issued on road network environment and where location semantics are known well remains a serious challenge. Moreover, use of cloud computing result to very serious privacy leakages in this environment. The study designed a protocol and a Semantically-Aware Query Cloaking (SQC) in smart grid. To achieve this, the paper proposed to secure a real continuous query for location based services with queries that are semantically-aware. The authors bring in anonymity to hide the location of the smart grid and use homomorphism encryption mechanisms to secure services over the cloud. Finally, the study analyzed the security of the proposed algorithm and protocol. [ABSTRACT FROM AUTHOR]

Let G be an abelian group, let M 2 (C) be the algebra of complex 2 × 2 matrices, and let φ : G → G be an endomorphism that need not be involutive. We determine the solutions Φ : G → M 2 (C) of the matrix functional equation Φ (x + y) + Φ (x + φ (y)) 2 = Φ (x) Φ (y) , x , y ∈ G. This enables us to characterize the solutions g : G → C 2 and Φ : G → M 2 (C) of the following functional equation g (x + y) + g (x + φ (y)) = 2 Φ (y) g (x) , x , y ∈ G , under the invariant condition Φ ∘ φ = Φ . [ABSTRACT FROM AUTHOR]

A reformulation of the four color theorem is to say that K 4 is the smallest graph to which every planar (loop-free) graph admits a homomorphism. Extending this theorem, the second author has proved (using the four color theorem) that the Clebsch graph (a well known triangle-free graph on 16 vertices) is a smallest graph to which every triangle-free planar graph admits a homomorphism. As a further generalization he has proposed that the projective cube of dimension 2 k , P C (2 k) , (that is the Cayley graph (Z 2 2 k , { e 1 , e 2 , ... , e 2 k , J } , where the e i 's are the standard basis and J = e 1 + e 2 + ⋯ + e 2 k) is a smallest graph of odd-girth 2 k + 1 to which every planar graph of odd-girth at least 2 k + 1 admits a homomorphism. This conjecture is related to a conjecture of P. Seymour who claims that the fractional edge-chromatic number of a planar multigraph determines its edge-chromatic number (more precisely, Seymour conjectured that χ ′ (G) = ⌈ χ f ′ (G) ⌉ for any planar multigraph G). Note that the restriction of Seymour's conjecture to cubic (planar) graphs is Tait's reformulation of the four color theorem. Both these conjectures are believed to be true for the larger class of K 5 -minor-free graphs (which includes the class of planar graphs). Motivated by these conjectures and in extension of a recent work of L. Beaudou, F. Foucaud and the second author, which studies homomorphism bounds for the class of K 4 -minor-free graphs, in this work we first give a necessary and sufficient condition for a graph B of odd-girth 2 k + 1 to admit a homomorphism from any partial t -tree of odd-girth at least 2 k + 1. Applying our results to the class of partial 3-trees, which is a rich subclass of K 5 -minor-free graphs, we prove that P C (2 k) is in fact a smallest graph of odd-girth 2 k + 1 to which every partial 3-tree of odd-girth at least 2 k + 1 admits a homomorphism. We then apply this result to show that every planar (2 k + 1) -regular multigraph G whose dual is a partial 3-tree, and whose fractional edge-chromatic number is 2 k + 1 , is (2 k + 1) -edge-colorable. Both these results are the best known supports for the general cases of the above mentioned conjectures in extension of the four color theorem. [ABSTRACT FROM AUTHOR]

The purpose of this work is to use the concepts of reachability and coreachability maps to provide a solution of a well-known characterization for L-valued multiset regular languages. In between, we associate two deterministic L-valued multiset automata with a given deterministic L-valued multiset automaton (DLMA) and show that the reachability and coreachability maps of the given DLMA turn out to be morphisms in the category of deterministic L-valued multiset automata. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Computer Engineering & Applications is the property of Beijing Journal of Computer Engineering & Applications Journal Co Ltd. 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.)

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She 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.)

Neutrosophic graphs are employed as a mathematical key to hold an imprecise and unspecified data. Vague sets gives more intuitive graphical notation of vague information, that delicates crucially better analysis in data relationships, incompleteness and similarity measures. In this paper, the neutrosophic vague line graphs are introduced. The necessary and sufficient condition for a line graph to be neutrosophic vague line graph is provided. Further, homomorphism, weak vertex and weak line isomorphism are discussed. The given results are illustrated with suitable example. [ABSTRACT FROM AUTHOR]

Several results concerning the homomorphism functional equation f x ∨ y = f x ∨ f y , in the class of semilattices, as well as other similar equations, are presented in the paper. [ABSTRACT FROM AUTHOR]

In this article, we establish the existence of countably infinitely many positive solutions for singular fractional order Boundary value problem involving Riemann-Stieltjes integral boundary condition with increasing homeomorphism and positive homomorphism operator by using Hölder's inequality and Krasnoselskii's fixed-point theorem (in cone) in a Banach spaces. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a novel concept of groupoid action and to obtain a characterization of a groupoid homomorphism as an action that commutes with the multiplication on the range. We also define the corresponding fuzzy concepts. This approach allows the study within a unified framework of various fuzzy structures viewed as fuzzy subgroupoids of appropriate groupoids. [ABSTRACT FROM AUTHOR]