Magnifying Elements Research Articles

Abundance and magnifying elements in transformation semigroups that preserve order and equivalence

Let [Formula: see text] be a nontrivial equivalence relation on a totally ordered set [Formula: see text] and [Formula: see text] be the semigroup of all transformations of [Formula: see text] that preserve [Formula: see text]. In this paper, we consider a subsemigroup of [Formula: see text] defined by [Formula: see text] and present a necessary and sufficient condition under which the semigroup [Formula: see text] is abundant. Also, we describe all the left and right magnifying elements in [Formula: see text].

On magnifying elements in semigroups of transformations restricted by an equivalence relation with a restricted range

On magnifying elements in semigroups of transformations restricted by an equivalence relation with a restricted range

A Survey of Advances in Magnifying Elements in Semigroups

An element s of a semigroup S is said to be a right (resp. left) magnifying (magnifier) element if there exists a proper subset M of S such that Ms=S [resp. sM=S]. If M is a proper subsemigroup of S, then s in S is called strong right (resp. strong left) magnifying element. In this paper, we present a panorama of various research articles in magnifying elements in semigroups from its inception in 1963. We present this via the various existing notions and related results.

Magnifying Elements in Semigroups of Fixed Point Set Transformations Restricted by an Equivalence Relation

Let X be a nonempty set and ρ be an equivalence relation on X . For a nonempty subset S of X , we denote the semigroup of transformations restricted by an equivalence relation ρ fixing S pointwise by E F S X , ρ . In this paper, magnifying elements in E F S X , ρ will be investigated. Moreover, we will give the necessary and sufficient conditions for elements in E F S X , ρ to be right or left magnifying elements.

Factorizable Ordered Hypergroupoids with Applications

In this study, we propose the concept of factorizable ordered hypergroupoids (semihypergroups) and present several of its properties. Our goal is to construct ordered hypergroupoid from blood groups together with some other information. Finally, we discuss right magnifying elements for further research.

Magnifying elements in linear transformation semigroups with restricted range which nullity or co-rank are infinite

In this paper, we characterize left (right) magnifying elements in the semigroups of linear transformations with restricted range which nullity or co-rank are infinite. Furthermore, we also show that every left (right) magnifier in these semigroups is very good.

Left and right magnifying elements in some generalized partial transformation semigroups

An element a of a semigroup S is called left [right] magnifying if there exists a proper subset M of S such that S = aM [S = Ma]. Let P(X) be a semigroup of all partial transformations on a set X under the composition of maps. A number of results concerning the necessary and sufficient conditions for elements in some interesting generalized semigroups of partial transformations to be left or right magnifiers are presented.

Left and Right Magnifying Elements in the Semigroup of all Binary Relations

An element a of a semigroup S is called left [right] magnifying if there exists a proper subset M of S such that S = aM [S = M a]. Let X be a nonempty set and BX the semigroup of binary relations on X. In this paper, we give necessary and sufficient conditions for elements in BX to be left or right magnifying.

Magnifying elements and factorization of ordered semigroups

This note defines the left magnifying and the strongly left magnifying elements in an ordered groupoid and discusses their properties. It is shown that in an ordered semigroup, every left magnifying element is of infinite order. The concept of factorizable ordered semigroups has been also introduced and, using the infinite order property, it is shown that every ordered semigroup having a strongly left magnifying element is factorizable.

Magnifying elements in semigroups of linear transformations with invariant subspaces

Let L(V) be the linear transformation semigroup on a vector space V. It is well-known that L(V) contains left [right] magnifying elements if and only if the dimension of V is infinite. In case its dimension is infinite, α ϵ L(V) is left magnifying if and only if it is surjective and not injective and it is right magnifying if and only if it is injective and not surjective. To generalize this result, let W be a subspace of V and S(V, W) = {f ∈ L(V) | (W) f ⊆ W}. Then S(V, W) is a subsemigroup of L(V) and if W = V, then S(V, W) = S(V, V) = L(V). Our purpose in this paper is to give necessary and sufficient conditions for elements in S(V, W) to be left [right] magnifying.

Left (right) magnifying elements of a partial transformation semigroup

An element [Formula: see text] of a semigroup [Formula: see text] is a called a left (respectively right) magnifying element of [Formula: see text] if [Formula: see text] (respectively [Formula: see text]) for some proper subset [Formula: see text] of [Formula: see text]. In this paper, left magnifying elements and right magnifying elements of a partial transformation semigroup will be characterized. The results obtained generalize the results of Magill [K. D. Magill, Magnifying elements of transformation semigroups, Semigroup Forum, 48 (1994) 119–126].

Left and Right Magnifying Elements in Generalized Semigroups of Transformations by Using Partitions of a Set

An element a of a semigroup S is called left [right] magnifying if there exists a proper subset M of S such that S = aM [S = Ma]. Let X be a nonempty set and T(X) be the semigroup of all transformation from X into itself under the composition of functions. For a partition P = {X_α | α ∈ I} of the set X, let T(X,P) = {f ∈ T(X) | (X_α)f ⊆ X_α for all α ∈ I}. Then T(X,P) is a subsemigroup of T(X) and if P = {X}, T(X,P) = T(X). Our aim in this paper is to give necessary and sufficient conditions for elements in T(X,P) to be left or right magnifying. Moreover, we apply those conditions to give necessary and sufficient conditions for elements in some generalized linear transformation semigroups.

Journal of Tourism & Hospitality

Mega-events play an accelerating role in the transformation of host cities with renewed image, pride, and the construction of infrastructure to sustain economic development. Given the high investment costs and risks associated with mega-events for the host city, local authorities try to catalyze their efforts for improved infrastructure and durable legacies. Contrary to the assumption, tourism doesn’t necessarily grow during the event and even shows disappointing results in the post-event years. Evaluating the tangible and intangible benefits of mega-events in the long run remains a challenge for a destination. Events are considered to have a short lifecycle and melt like ice cream, hence the term “ice cream economy”. The purpose of this conceptual paper is to analyze the relationship between host city planning, mega-events and tourism sustainability. It discusses internal and external changes that affect host destinations and how tourism makes uses of the legacies of mega-events. The paper reviews the current literature and then takes a case study approach to compare mega-events and their impacts in selected cities with significant tourism planning outcomes. Findings show that mega-events bring specific magnifying elements to urban economies. Cities that have allowed tourism strategies and policies a more central role in the mega-event planning have shown more successful results over time. They have connected the strong infrastructure development of mega-events with enhanced tourism products and uses. This paper concludes with recommendations for tourism management and ice cream economy, integration in planning by destinations that host mega-events. This includes strategies to integrate these innovative tourism policies to city management.

Laboratory X-ray microtomographs with the use of monochromatic radiation

The possibility and expediency of designing X-ray microtomographs based on X-ray diffractometers have been analyzed. Some biomedical objects have been investigated. It has been demonstrated that it is possible to achieve a resolution of the order 10 μm with a field of view of the order of 20 mm without recourse to magnifying X-ray optical elements.

Transformation-designed optical elements

We describe transformation design of optical elements which, in addition to image transfer, perform useful operations. For one class of operations, including translation, rotation, mirroring and inversion, an image can be generated that is ideal in the sense of the perfect lens (combining both near- and far-field components in a flat, unit transfer function, up to the limits imposed by material imperfection). We also describe elements that perform magnification, free from geometric aberrations, even while providing free-space working distance on both the input and output sides. These magnifying elements also operate in the near- and far-field, allowing them to transfer near field information into the far field, as with the hyper lens and other related devices, however in contrast to those devices, insertion loss can be much lower, due to the matching properties accessible with transformation design. The devices here described inherently require dispersive materials, thus chromatic aberration will be present, and the bandwidth limited.

Semigroups with strong and nonstrong magnifying elements

The question if there exist semigroups containing both strong and nonstrong magnifying elements was recently raised up by K.D. Magill Jr. in [3] and by F. Catino and F. Migliorini in [1]. In this note we give an affirmative answer to this question.

Magnifying elements of transformation semigroups

An element a of a semigroup S is a left (right) magnifying element if aM = S (Ma = S) for some proper subset M of S. It is a strong left (right) magnifying element if aT = S (Ta = S) for a proper subsemigroup T of S. The notion of a magnifying element was introduced by E.S. Ljapin [7] and that of a strong magnifying element by K. Tolo [ll]. For a list of other papers dealing with magnifying elements, see the first paragraph of [1]. V.M. Klimov has shown that any Bear-Levi semigroup consists of nonstrong left magnifying elements and we will see that there is an abundance of semigroups with the property that all magnifying elements are strong. It is noted in [1], however, that no one has yet produced an example of a semigroup which contains both strong and nonstrong left (right) magnifying elemcnts. In Section 2, we gather together several elementary results about magnifying elements in abstract semigroups which will be of use to us in our subsequent discussion. In Section 3, we investigate magnifying elements for quite general transformation semigroups. Among other things, we characterize those transformation semigroups with identities which have magnifying elements and we characterize those magnifying elements. The results are then applied in Section 4 to such transformation semigroups as the semigroup of all linear transformations of a vector space and S(X) , the semigroup of all continuous selfmaps of the topological space X. We are able to show, for example, that if X is any local dendrite with finite branch number, then the subsemigroup of all left magnifying elements of S(X) is isomorphic to the dual of the semigroup of all monomorphisms which map S(X) properly into S(X) and the subsemigroup of all right magnifying elements is a homomorphic image of that semigroup.

Some researches on semigroups with magnifying elements

Some researches on semigroups with magnifying elements