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• Numerical performances of IDEAL and SIMPLERR are analyzed and compared. • SIMPLERR can be regarded as a special form of IDEAL. • The robustness of IDEAL is much better than SIMPLERR. • In general, the performance of IDEAL is superior to SIMPLERR. In this paper, the numerical performances of the algorithm IDEAL proposed by the present authors in 2008, and the recently proposed (2017) SIMPLERR are systematically analyzed and compared via six incompressible fluid flow and heat transfer problems. It is found that the two algorithms are almost identical when the second inner iteration number of IDEAL is fixed at 2. In general, the robustness and convergence of IDEAL are much better than SIMPLERR. The reason why the performance of SIMPLERR deteriorates with the increase of the first inner iteration number is analyzed and detailed comparisons in the robustness and computing time are presented. [ABSTRACT FROM AUTHOR]

In this paper we extend the theory of neutrosophy to study left almost semigroup shortly LAsemigroup. We generalize the concepts of LA-semigroup to form that for neutrosophic LA-semigroup. We also extend the ideal theory of LA-semigroup to neutrosophy and discuss different kinds of neutrosophic ideals. We also find some new type of neutrosophic ideal which is related to the strong or pure part of neutrosophy. We have given many examples to illustrate the theory of neutrosophic LA-semigroup and display many properties of neutrosophic LA-semigroup in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we continue our investigations in line of our recent papers, Savas and Das [16] and Das, Savas and Ghosal [5]. We introduce the notion of AI-statistical convergence which includes the new summability methods studied in [16] and [5] as special cases and make certain observations on this new and more general summability method. [ABSTRACT FROM AUTHOR]

In this paper we use the Hall -- Dilworth gluing construction to obtain multiple congruences of a lattice L. For any finite lattice L, Gm(L,Bn), the gluing of L and n B over F and I, both F and I are isomorphic to 2 C . For any lattice L, the congruences of Gm(L,Bn) is 2(n-1) times the congruences of L where F be the filter of L and I be an ideal of n B and are isomorphic to C2. We call Gm(L,Bn) the congruence multiple operator. [ABSTRACT FROM AUTHOR]

In this paper, we study the Cohen-Macaulay of ideal I2 (G), where I2 (G) = hxyz ∣ x − y − z is 2 − path in G>. Also, we determined the 2-projective dimension R- module, R/I2 (G) denoted by pd2 (G) of some graphs. [ABSTRACT FROM AUTHOR]

The present paper is devoted to the study of some subclasses of H-rings, i.e., rings in which all subrings are ideals. In the description of H-rings an important role is played by almost null rings. We classify, up to isomorphism, torsion almost null rings of bounded exponent. [ABSTRACT FROM AUTHOR]

In this paper, the notion of a QI-algebra is introduced which is a generalization of a BI-algebra and there are studied its properties. We considered ideals, congruence kernels in a QI-algebra and characterized congruence kernels whenever a QI-algebra is right distributive. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the intuitionistic fuzzy Zweier I-convergent double sequence spaces 2Ƶ I(μ,ν) (M) and 2ƵI0(μ,ν) (M) defined by Orlicz function and study the fuzzy topology on the said spaces. [ABSTRACT FROM AUTHOR]

In this paper we discuss p-algebras and some of their subclasses. A notion of DM-algebras is introduced which is an important subclass of p-algebras. We give some characterizations of subclasses of p-algebras. We also give some characterizations of p-ideals of a p-algebra. [ABSTRACT FROM AUTHOR]

The notions of mn-Ig-closed sets and mn-TI spaces in an ideal bi m-space are introduced and investigated by Sanabria et al. [18]. In this paper, we introduce the notion of (Λ, mn*)-closed sets and obtain a decomposition of n*-closed sets and a characterization of mn-TI spaces [18] by using mn-Ig-closed sets and (Λ, mn*)-closed sets. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of (semi)topological BCC-algebras and derive here conditions that imply a BCC-algebra to be a (semi)topological BCC-algebra. We prove that for each cardinal number α there is at least a (semi)topological BCC-algebra of order α. Also we study separation axioms on (semi)topological BCC-algebras and show that for any infinite cardinal number α there is a Hausdorff (semi)topological BCC-algebra of order α with nontrivial topology. [ABSTRACT FROM AUTHOR]

In this paper, the notions of (para, quasi, semi) topological MV-algebras are defined and their related properties are studied. Also, topologies with which an MV-algebra can be a (para, semi) topological MV-algebra are obtained. Clearly, a topological MV-algebra is a (para, quasi, semi) topological MV-algebra, but the converse is not true, as shown by an example. In addition, we study ideals and filters in (para, quasi) topological MV-algebras, and we show that a quasitopological MV-algebra is a topological MV-algebra if the ideal {0}, or equivalently, the filter {1} is open. [ABSTRACT FROM AUTHOR]

(Bounded integral) residuated lattices (which need not be commutative) form a large class of algebras containing some classes of algebras behind many-valued and fuzzy logics. Congruences of such algebras are usually defined and investigated by means of their normal filters. In the paper we introduce and investigate ideals of residuated lattices. We show that one can define, in some cases, congruences also using ideals and that the corresponding quotient residuated lattices are involutive. [ABSTRACT FROM AUTHOR]

In this paper, the notion of derivation on partially ordered sets is introduced and studied. Several characterization theorems on derivations are presented. The properties of the fixed points based on the derivations are investigated. Finally, the properties of ideals and operations related with derivations are studied. [ABSTRACT FROM AUTHOR]

The aim of this paper is to construct a new rough relation structure for a given ideal and to study many of their properties. Further, definitions of lower and upper approximations via ideal have been introduced. These new definitions are compared with Pawlak's definitions. It's therefore shown that the current definitions are more generally. [ABSTRACT FROM AUTHOR]

Let R be a prime ring with center Z(R), C the extended centroid of R, d a derivation of R and n; k be two fixed positive integers. In the present paper we investigate the behavior of a prime ring R satisfying any one of the properties (i) d([x, y]k)n = [x, y]k (ii) if char(R) ≠ 2, d([x; y]k) - [x; y]k ∈ Z(R) for all x; y in some appropriate subset of R. Moreover, we also examine the case when R is a semiprime ring. [ABSTRACT FROM AUTHOR]

We say that an ideal $${\mathcal{I}}$$ on $${\omega}$$ is homogeneous, if its restriction to any $${\mathcal{I}}$$ -positive subset of $${\omega}$$ is isomorphic to $${\mathcal{I}}$$ . The paper investigates basic properties of this notion - we give examples of homogeneous ideals and present some applications to topology and ideal convergence. Moreover, we answer questions related to our research posed in [1]. [ABSTRACT FROM AUTHOR]

In this paper, following a very recent and new approach of [1], we discuss a relation between two kinds of I-convergence of sequences, namely, I-statistical convergence of weight g and I-lacunary statistical convergence of weight g, where g : ℕ → [0,∞) is a function satisfying lim/ n→∞ g (n)=∞and n/g(n) ↛ 0 as n→ ∞ for fuzzy numbers. These methods are based on the methods of statistical convergence and lacunary statistical summability for sequences. Analogs of inclusion and consistency theorems for the sequential methods are established. [ABSTRACT FROM AUTHOR]

In this paper we explore the connections between fuzzy congruence relations, fuzzy ideals and homomorphisms of hyperlattices. Indeed, we introduce the concept of fuzzy quotient set of hyperlattices as it was done in the case of rings [19]. We prove that a fuzzy congruence induces a fuzzy ideal of the fuzzy quotient hyperlattice. In particular, we establish necessary and sufficient conditions for a zero-fuzzy congruence class to be a fuzzy ideal of a hyperlattice. [ABSTRACT FROM AUTHOR]

To evaluate the goodness-of-fit of a statistical model to given data, calculating a conditional p value by a Markov chain Monte Carlo method is one of the effective approaches. For this purpose, a Markov basis plays an important role because it guarantees the connectivity of the chain, which is needed for unbiasedness of the estimation, and therefore is investigated in various settings such as incomplete tables or subtable sum constraints. In this paper, we consider the two-way change-point model for the ladder determinantal table, which is an extension of these two previous works, i.e., works on incomplete tables by Aoki and Takemura (2005, J. Stat. Comput. Simulat.) and subtable some constraints by Hara, Takemura and Yoshida (2010, J. Pure Appl. Algebra). Our main result is based on the theory of Gröbner basis for the distributive lattice. We give a numerical example for actual data. [ABSTRACT FROM AUTHOR]

In this paper, we proved that for every subset X of U there is a corresponding ideal JX of the rough semiring (T, ∆, ∇) also we gave a characterization theorem for the ideals in the rough semiring (T, ∆, ∇) by proving every ideal in (T, ∆, ∇) will be of the form JX for some subset X of U and the properties of these ideals are discussed with suitable examples. [ABSTRACT FROM AUTHOR]

In this paper we discuss the following Tkachuk's question in the sense of ideal convergence [16,18] : Is any Tychonoff connected sequential space a quotient image of a connected metric space? It is proved that let I be an ideal on the set N then a topological space X is an I -connected space with an I - csf -network if and only if X is a continuous I -covering image of a connected metric space. It follows that a topological space X is a connected I -sequential space with an I - csf -network if and only if X is a quotient I -covering image of a connected metric space. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the intuitionistic fuzzy I-convergent sequence spaces S(μ, ν)I(T) and S0(μ, ν)I(T) defined by compact operator and study the fuzzy topology on the above said spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of sBCI/sBCK/eBCI/eBCK-algebras as a generalization of the notion of BCI/BCK-algebras. This structure is studied in detail. Also we introduce a way to make an eBCK-algebra from a BCK-algebra and vice versa. [ABSTRACT FROM AUTHOR]

No matter how insufficient it is to fully respect and accept others in accordance with one's own system of references, tolerance is seen as a universal norm for existence and one of the main modes of human sociability. It is not the product of only one culture or a characteristic of only one, such as modern, epoch. Tolerance presents, mutatis mutandis, an important component of the spiritual and socio-cultural tissue of all developed nations with histories of their own. The idea of tolerance draws its roots from the ancient cultures. It has been modeled by the intuition of the Holy and the spirit of metaphysics while being permeated by their primordial religious meaning. This paper develops a discourse on tolerance as a perennial ideal, a universal norm and a relationship of fundamental importance to human existence. Tolerance is seen here as a key possibility and duty, a condition for as well as a form of the survival of contemporary people and their world. [ABSTRACT FROM AUTHOR]

Let R be a ring and I is a nonzero ideal of R. A mapping F : R → R is called a multiplicative generalized derivation if there exists a mapping g : R → R such that F(xy) = F(x)y + xg(y), for all x, y ∈ R. In the present paper, we shall prove that R contains a nonzero central ideal if any one of the following holds: i) F([x, y]) = 0, ii) F(xoy) = 0, iii) F([x, y]) = ±[x, y], iv) F(xoy) = ±(xoy), v) F([x, y]) = ±(xoy), v) F([x, y]) = ±(xoy), for all x, y ∈ I. vii) F([x, y]) = ±[F(x), y], viii) F(xoy) = ±(F(x)oy), ix) F(xy) ± xy ∈ Z, x) F(xy) ± yx ∈ Z, xi) F(xy) ± [x, y] ∈ Z, xii) F(xy) ± (xoy) ∈ Z,. [ABSTRACT FROM AUTHOR]

In this paper, we introduce generalized difference sequence spaces via ideal convergence, lacunary of χ2 sequence spaces over p-metric spaces defined by Musielak function, and examine the Musielak-Orlicz function which satisfies uniform Δ2 condition, and we also discuss some topological properties of the resulting spaces of χ2 with respect to ideal structures which is solid and monotone. Hence, given an example of the space χ2, this is not solid and not monotone. This theory is very useful for statistical convergence and also is applicable to rough convergence. [ABSTRACT FROM AUTHOR]

In this paper we show that if I is an ideal of a commutative semigroup C such that the separator SepI of I is not empty then the factor semigroup $$S=C/P_I$$ ( $$P_I$$ is the main congruence of C defined by I) satisfies Condition $$(*)$$ : S is a commutative monoid with a zero; The annihilator A( s) of every non identity element s of S contains a non zero element of S; $$A(s)=A(t)$$ implies $$s=t$$ for every $$s, t\in S$$ . Conversely, if $$\alpha $$ is a congruence on a commutative semigroup C such that the factor semigroup $$S=C/\alpha $$ satisfies Condition $$(*)$$ then there is an ideal I of C such that $$\alpha =P_I$$ . Using this result for the multiplicative semigroup $$D_{mult}$$ of a unique factorization domain D, we show that $$P_{J(m)}=\tau _m$$ for every nonzero element $$m\in D$$ , where J( m) denotes the ideal of D generated by m, and $$\tau _m$$ is the relation on D defined by $$(a, b)\in \tau _m$$ if and only if $$gcd(a, m)\sim gcd(b, m)$$ ( $$\sim $$ is the associate congruence on $$D_{mult}$$ ). We also show that if a is a nonzero element of a unique factorization domain D then $$d(a)=|D'/P_{J([a])}|$$ , where d( a) denotes the number of all non associated divisors of a, $$D'=D/\sim $$ , and [ a] denotes the $$\sim $$ -class of $$D_{mult}$$ containing a. As an other application, we show that if d is one of the integers $$-1$$ , $$-2$$ , $$-3$$ , $$-7$$ , $$-11$$ , $$-19$$ , $$-43$$ , $$-67$$ , $$-163$$ then, for every nonzero ideal I of the ring R of all algebraic integers of an imaginary quadratic number field $${\mathbb Q}[\sqrt{d}]$$ , there is a nonzero element m of R such that $$P_I=\tau _m$$ . [ABSTRACT FROM AUTHOR]

In this paper, we enumerate self-dual AG-groupoids up to order 6; and classify them on the basis of commutativity and associativity. A self-dual AG-groupoid-test is introduced to check an arbitrary AG-groupoid for a self-dual AG-groupoid. We also respond to an open problem regarding cancellativity of an element in an AG-groupoid. Some features of ideals in self-dual AG-groupoids are explored. Some desired algebraic structures are constructed from the known ones subject to certain conditions and some subclasses of self-dual AG-groupoids are introduced. [ABSTRACT FROM AUTHOR]

Let R be a *-prime ring with center Z(R), d a non-zero (σ,τ)- derivation of R with associated automorphisms σ and τ of R, such that σ,τ and d commute with '*'. Suppose that U is an ideal of R such that U* = U, and Cσ,τ = {c ∈ R | cσ(x) = τ(x)c for all x ∈ R}. In the present paper, it is shown that if characteristic of R is different from two and [d(U); d(U)]σ,τ = {0}, then R is commutative. Commutativity of R has also been established in case if [d(R),d(R)]σ,τ ⊆ Cσ,τ. [ABSTRACT FROM AUTHOR]

In this paper, we have introduced the idea of I-convergence of filters and studied its various properties. We have proved the necessary and sufficient condition for a filter to be I-convergent. [ABSTRACT FROM AUTHOR]

At the heart of Kant's legal-political philosophy lies a liberal, republican ideal of justice understood in terms of private independence (non-domination) and subjection to public laws securing freedom for all citizens as equals. Given this basic commitment of Kant's, it is puzzling to many that he does not consider democracy a minimal condition on a legitimate state. In addition, many find Kant ideas of reform or improvement of the historical states we have inherited vague and confusing. The aim of this paper is to untangle both puzzles by exploring Kant's idea of self-governance. I argue that Kant's idea of self-governance gives us a very good starting point for thinking about how to leave room for a variety of political systems--different ideals--that have grown out of and responding to different contingent historical and cultural circumstances. It also helps us identify those areas where we want to take extra care to build in safeguards to secure stability and to take sufficiently seriously humankind's truly nasty sides. [ABSTRACT FROM AUTHOR]

This paper is a sequel of our previous paper [1]. In this paper, we introduce the notions of regular ideal and partial ideal (p-ideal) in a ternary semiring and using these two notions we characterize regular ternary semiring. [ABSTRACT FROM AUTHOR]

The paper presents a formula for the γ-interior of a set under special conditions for γ :expX→expX, more general than those in the previous paper [Acta Math. Hungar. 80 (1998) 89–93]. There are also some applications. [Copyright &y& Elsevier]

This paper interprets the fairytale Snow White (Bruder Grimm 1857) in terms of the realization of absolute beauty. Jung's understanding that 'in myths and fairytales, as in dreams, the soul speaks about itself' (Jung 1945, para. 400), underpins such an approach. From this perspective a fantasy image is not about us, not about our unconsciousness, but is essentially about itself. The idea of absolute beauty first arises in the Queen's mind as a wish. Despite the Queen's strong desire to be named as the most beautiful person in the world, her mirror reflects that it is actually her daughter Snow White who is the fairest. Snow White might be regarded in the language of Giegerich as her internal other. Effectively they are separated into the Real that conceives the idea of absolute beauty and the Ideal that embodies it. The exchange that takes place between the two - mediated by mirror and window - generates the corpse of surpassing beauty that never decays but lies inaccessible behind the glass coffin. However the loving and penetrating gaze of the Prince, representing masculinity, succeeds in reanimating Snow White. Thus the Prince as the Other that is completely external and unknown to both the Queen and Snow White, specifically to their femininity, facilitates the realization of absolute beauty as the Ideal in the Real. [ABSTRACT FROM AUTHOR]

In this paper, we study the notion of S-paracompact spaces in ideal topological spaces. We provide some characterizations of these spaces and investigate relationships to other classes of spaces. Moreover, we study the invariance of such spaces under some special types of functions. [ABSTRACT FROM AUTHOR]

Motivated by the earlier study on the notion of signed total graph of a commutative ring, in this paper, we characterize all the commutative rings with unity for which signed total graph is -consistent and sign-compatible. To do this, first, we derive a formula to determine the degree of each vertex in (induced subgraph of the total graph), when and , where each 's is a field of characteristic , is an odd prime, and . [ABSTRACT FROM AUTHOR]

In [3] Dündar introduced the notion of rough I2-convergence and obtained two criteria for rough I2-convergence. In the present paper we introduce some new rough ideal convergent sequence spaces of Musielak-Orlicz functions and four dimensional boundedregular matrices. We study some topological and algebraic properties of these spaces. We also establish some inclusion relations between these spaces. Finally, we examine that these spaces are normal as well as monotone and sequence algebras. [ABSTRACT FROM AUTHOR]

In the present paper we introduce some applications of I-statistical convergence to form some new spaces of sequences using a sequence of Orlicz functions and matrix transformation over n-normed spaces. We also make an effort to study several properties relevant to the topological and algebraic structure of these spaces. We investigate some inclusion relations involving these spaces. [ABSTRACT FROM AUTHOR]

A Γ-so-ring is a structure possessing a natural partial ordering, an infinitary partial addition and a ternary multiplication, subject to a set of axioms. The partial functions under disjoint-domain sums and functional composition is a Γ-so-ring. In this paper we introduce the notions of partial ideal of partial Γ-semiring and ideal of Γ-so-ring and study the ideal theory of Γ-so-rings. [ABSTRACT FROM AUTHOR]

This paper is primarily concerned with a natural extension of the notion of a total graph $$T(\varGamma (R))$$ in the realm of signed graph for a finite commutative ring R. First, we characterize the rings for which the signed total graph $$T_{\varSigma }(\varGamma (R))$$ and its line signed graph $$L(T_{\varSigma }(\varGamma (R)))$$ are balanced. Second, we characterize the rings for which the negation of a signed total graph $$\eta (T_{\varSigma }(\varGamma (R)))$$ is balanced. Several new directions for further research are also indicated. [ABSTRACT FROM AUTHOR]

Following the concept of topological theory of S.E. Rodabaugh, this paper introduces a new approach to (lattice-valued) bornology, which is based in bornological theories, and which is called variety-based bornology. In particular, motivated by the notion of topological system of S. Vickers, we introduce the concept of variety-based bornological system, and show that the category of variety-based bornological spaces is isomorphic to a full reflective subcategory of the category of variety-based bornological systems. [ABSTRACT FROM AUTHOR]

We study the eigenscheme of a matrix which encodes information about the eigenvectors and generalized eigenvectors of a square matrix. The two main results in this paper are a decomposition of the eigenscheme of a matrix into primary components and the fact that this decomposition encodes the numeric data of the Jordan canonical form of the matrix. We also describe how the eigenscheme can be interpreted as the zero locus of a global section of the tangent bundle on projective space. This interpretation allows one to see eigenvectors and generalized eigenvectors of matrices from an alternative viewpoint. [ABSTRACT FROM AUTHOR]

A Γ-so-ring is a structure possessing a natural partial ordering, an infinitary partial addition and a ternary multiplication, subject to a set of axioms. The partial functions under disjoint-domain sums and functional composition is a Γ-so-ring. In this paper we introduce the notions of partial ideal of partial Γ-semiring and ideal of Γ-so-ring and study the ideal theory of Γ-so-rings. [ABSTRACT FROM AUTHOR]

The rough approximations on a complete completely distributive lattice L based on binary relation were introduced by Zhou and Hu (Inf Sci 269:378-387, 2014), where the binary relation was defined on the set of non-zero join-irreducible elements. This paper extends Zhou and Hu's rough set model by defining new approximation operators via ideal. When I is the least ideal of L and R is a reflexive binary relation, these two approximations coincide. We present the essential properties of new approximations and also discuss how the new one relates to the old one. Finally, the topological and lattice structures of the approximations are given. [ABSTRACT FROM AUTHOR]

In this paper we follow the line of recent works of Das [4,5,7] (see also [3] for similar investigation), where a more general approach was made to study certain results on open covers and selection principles by using the notion of ideals and ideal convergence, which automatically extends similar classical results (where finite sets are used), and also recent statistical variants studied by Di Maio and Kočinac [10] . Here we further introduce the notions of cω -covers and I -large covers which extend the notions of ω -covers and large covers in a topological space. We then study the I -groupability of different open covers and some of its consequences. [ABSTRACT FROM AUTHOR]

Let R be a prime ring with characteristic different from two, I be a nonzero ideal of R, and F be a generalized derivation associated with a nonzero derivation d of R. In the present paper we investigate the commutativity of R satisfying the relation F([x, y]k)n = ([x, y]k)l for all x, y ∈ I, where l, n, k are fixed positive integers. Moreover, let R be a semiprime ring, A = O(R) be an orthogonal completion of R, and B = B(C) be the Boolean ring of C. Suppose F([x, y]k)n = ([x, y]k)l for all x, y ∈ R, then there exists a central idempotent element e of B such that d vanishes identically on eA and the ring (1-e)A is commutative. [ABSTRACT FROM AUTHOR]