Semi-invariant Riemannian submersions from nearly Kaehler manifolds

We study semi-invariant Riemannian submersions from a nearly Kaehler manifold to a Riemannian manifold. It is well known that the vertical distribution of a Riemannian submersion is always integrable therefore, we derive condition for the integrability of horizontal distribution of a semi-invariant Riemannian submersion and also investigate the geometry of the foliations. We discuss the existence and nonexistence of semi-invariant submersions such that the total manifold is a usual product manifold or a twisted product manifold. We establish necessary and sufficient conditions for a semi-invariant submersion to be a totally geodesic map. Finally, we study semi-invariant submersions with totally umbilical fibers.

Neutrosophic Components Semigroups and Multiset Neutrosophic Components Semigroups

Neutrosophic components (NC) under addition and product form different algebraic structures over different intervals. In this paper authors for the first time define the usual product and sum operations on NC. Here four different NC are defined using the four different intervals: (0, 1), [0, 1), (0, 1] and [0, 1]. In the neutrosophic components we assume the truth value or the false value or the indeterminate value to be from the intervals (0, 1) or [0, 1) or (0, 1] or [0, 1]. All the operations defined on these neutrosophic components on the four intervals are symmetric. In all the four cases the NC collection happens to be a semigroup under product. All of them are torsion free semigroups or weakly torsion free semigroups. The NC defined on the interval [0, 1) happens to be a group under addition modulo 1. Further it is proved the NC defined on the interval [0, 1) is an infinite commutative ring under addition modulo 1 and usual product with infinite number of zero divisors and the ring has no unit element. We define multiset NC semigroup using the four intervals. Finally, we define n-multiplicity multiset NC semigroup for finite n and these two structures are semigroups under + modulo 1 and { M ( S ) , + , × } and { n - M ( S ) , + , × } are NC multiset semirings. Several interesting properties are discussed about these structures.

Tensor products of modal logics

We consider shifted products of modal algebras and logics first introduced by Y. Hasimoto in 2000. For logics this operation is similar to the well-known usual product but it is logically invariant. We prove the conjecture of D. Gabbay that shifted products act on Boolean algebras exactly as tensor products, so we call them tensor products of modal algebras. We also propose a filtration technique for models based on tensor products and obtain some decidability results.

RECOVERING OLD STEREOSCOPIC NEGATIVES AND PRODUCING DIGITAL 3D MODELS OF FORMER APPEARANCES OF HISTORIC BUILDINGS

Three-dimensional models with photographic textures have become a usual product for the study and dissemination of elements of heritage. The interest for cultural heritage also includes evolution along time; therefore, apart from the 3D models of the current state, it is interesting to be able to generate models representing how they were in the past. To that end, it is necessary to resort to archive information corresponding to the moments that we want to visualize. <br><br> This text analyses the possibilities of generating 3D models of surfaces with photographic textures from old collections of analog negatives coming from works of terrestrial stereoscopic photogrammetry of historic buildings. The case studies presented refer to the geometric documentation of a small hermitage (done in 1996) and two sections of a wall (year 2000). <br><br> The procedure starts with the digitization of the film negatives and the processing of the images generated, after which a combination of different methods for 3D reconstruction and texture wrapping are applied: techniques working simultaneously with several images (such as the algorithms of Structure from Motion – SfM) and single image techniques (such as the reconstruction based on vanishing points). Then, the features of the obtained models are described according to the geometric accuracy, completeness and aesthetic quality. In this way, it is possible to establish the real applicability of the models in order to be useful for the aforementioned historical studies and dissemination purposes. <br><br> The text also wants to draw attention to the importance of preserving the documentary heritage available in the collections of negatives in archival custody and to the increasing difficulty of using them due to: (1) problems of access and physical conservation, (2) obsolescence of the equipment for scanning and stereoplotting and (3) the fact that the software for processing digitized photographs is discontinued.

Maps preserving 2-idempotency of certain products of operators

Let A,B be standard operator algebras on complex Banach spaces X and Y of dimensions at least 3, respectively. In this paper we give the general form of a surjective (not assumed to be linear or unital) map ? : A ? B such that ?2 : M2(C)?A ? M2(C)?B defined by ?2((sij)2x2) = (?(sij))2x2 preserves nonzero idempotency of Jordan product of two operators in both directions. We also consider another specific kinds of products of operators, including usual product, Jordan semi-triple product and Jordan triple product. In either of these cases it turns out that ? is a scalar multiple of either an isomorphism or a conjugate isomorphism.

An Alternative Estimator for Estimating the Finite Population Mean Using Auxiliary Information in Sample Surveys

This paper suggests a class of estimators for estimating the finite population mean of the study variable using known population mean of the auxiliary variable . Asymptotic expressions of bias and variance of the suggested class of estimators have been obtained. Asymptotic optimum estimator (AOE) in the class is identified along with its variance formula. It has been shown that the proposed class of estimators is more efficient than usual unbiased, usual ratio, usual product, Bahl and Tuteja (1991), and Kadilar and Cingi (2003) estimators under some realistic conditions. An empirical study is carried out to judge the merits of suggested estimator over other competitors practically.

Sulfate Formation During Corrosion of Copper Alloy Objects

ABSTRACTThe copper sulfate minerals chalcanthite (CuSO4.5H20), antlerite (Cu3SO4(OH)4), and brochantite (Cu4SO4(OH)6) are observed as corrosion products on copper alloy objects such as statues which are exposed to weathering. The usual product in aqueous corrosion is brochantite, though posnjakite (Cu4SO4(OH)6H20) is also known. No copper sulfate mineral is commonly found in artifacts recovered from near-surface burial. These observations can be explained in terms of stability diagrams and microbiological activity.

How Far Should Global Products Go?

Some authorities in international business have suggested that international markets are becoming increasingly homogeneous, causing more firms to offer global products. Vachani and Wells based on a study of the product decisions of Indian subsidiaries of five multinationals argue that there remain important consumer segments that have special needs which are not met by global products. According to Vachani and Wells, decisions of multinationals and local firms to cater to the special needs of various consumer segments in developing countries depend on four variables: the structure and competitive conditions of their industry segments, the ability to use their traditional competitive advantage in different segments, the ease with which their usual product lines can be extended into new segments, and the availability of more special products elsewhere within the multinational enterprise.

Antichains and Finite Sets that Meet all Maximal Chains

This paper is inspired by two apparently different ideas. Let P be an ordered set and let M(P) stand for the set of all of its maximal chains. The collection of all sets of the formandwhere x ∊ P, is a subbase for the open sets of a topology on M(P). (Actually, it is easy to check that the B(x) sets themselves form a subbase.) In other words, as M(P) is a subset of the power set 2|p| of P, we can regard M(P) as a subspace of 2|p| with the usual product topology. M. Bell and J. Ginsburg [1] have shown that the topological space M(P) is compact if and only if, for each x ∊ P, there is a finite subset C(x) of P all of whose elements are noncomparable to x and such that {x} ∪ C(x) meets each maximal chain.