Basis Of Space Research Articles

Uniform Sobolev Inequality along the Sasaki–Ricci Flow

In this paper we prove a uniform Sobolev inequality along the Sasaki–Ricci flow. In the process, we develop the theory of basic Lebesgue and Sobolev function spaces, and prove some general results about the decomposition of the heat kernel for a class of elliptic operators on a Sasaki manifold.

Forward Causality in Basic Communicative Spaces Networks: The -Ese and -Nikka Constructions in Korean

Forward Causality in Basic Communicative Spaces Networks: The -Ese and -Nikka Constructions in Korean

Cohomologies of spaces of Schwartz test functions

We calculate cohomologies of the Schwartz algebras D and S, which are basic spaces (test-function spaces) of the distribution theory. In the process, we find special cohomologies of the quotient algebras E/D and M/S (E andMare also test-function spaces), which are quite unusual from the standpoint of the standard functional analysis and are interesting for theoretical and mathematical physics.

Singular homology on hypergestures

In this paper, we interpret the basic cubic chain spaces of singular homology in terms of hypergestures in a topological space over a series of copies of the arrow digraph ↑. This interpretation allows for a generalized homological setup. The generalization is (1) to topological categories instead of to topological spaces and (2) to any sequence of digraph (Γ n ) n∈ℤ instead of to the constant series of ↑. We then define the corresponding chain complexes and prove the core boundary operator equation ∂2=0, enabling the associated homology modules over a commutative ring R. We discuss some geometric examples and a musical one, interpreting contrapuntal rules in terms of singular homology.

TOPOLOGY OF 3-COSYMPLECTIC MANIFOLDS

We continue the programme of Chinea, De León and Marrero who studied the topology of cosymplectic manifolds. We study 3-cosymplectic manifolds that are the closest odd-dimensional analogue of hyper-Kähler structures. We show that there is an action of the Lie algebra so(4, 1) on the basic cohomology spaces of a compact 3-cosymplectic manifold with respect to the Reeb foliation. This implies some topological obstructions to the existence of such structures which are expressed by bounds on the Betti numbers. It is known that every 3-cosymplectic manifold is a local Riemannian product of a hyper-Kähler factor and an abelian three-dimensional Lie group. Nevertheless, we present a non-trivial example of a compact 3-cosymplectic manifold that is not the global product of a hyper-Kähler manifold and a flat 3-torus.

Responsible subjects and discourse causality. How mental spaces and perspective help identifying subjectivity in Dutch backward causal connectives

The Basic Communicative Spaces Network (BCSN –Sanders et al., 2009) accounts for crucial semantic–pragmatic characteristics of causal relations expressed by frequently used Dutch causal connectives. BCSN integrates subjectivity theory, domain theory, and mental spaces theory to explain their linguistic categorization. Starting with the original three-way classification of content, epistemic, and speech act use, BCSN represents different uses in separate but connected and embedded mental spaces that are linked to the Subject of Consciousness (SoC), who is present as an actor or concluder in many causal relations. The analytic structure of BCSN explains the contrasts between the backward Dutch causal connectives WANT ‘because/for/since’, signaling speech act and epistemic relations in which the speaker is the implicit SoC, and OMDAT ‘because (of the fact that)’, typically expressing content relations with an explicit SoC. This division of labor corresponds to a cognitive categorization in terms of BCSN. On a more general level, BCSN offers a model for the recursive patterning that characterizes perspective alternation in natural discourse, since the BCSN represents both the author's subjectivity and the subjectivity of other actors in the discourse (such as speakers and characters in a narration), as well as the blends between these perspectives. The analysis is illustrated with corpus examples.

Coherent and finiteness spaces

This short note presents a new relation between coherent spaces and finiteness spaces. This takes the form of a functor from COH to FIN commuting with the additive and multiplicative structure of linear logic. What makes this correspondence possible and conceptually interesting is the use of the infinite Ramsey theorem. Along the way, the question of the cardinality of the collection of finiteness spaces on N is answered. Basic knowledge about coherent spaces and finiteness spaces is assumed.

보육시설 평면사례분석을 통한 시설규모별 소요실 및 면적특성 분석

The purpose of this study is to find out the characteristics of area and spatial elements according to the building size and provide the guidelines for space planning of the child care center. This study used the content analysis method and analysis was made on the floor plans for 51 cases and the floor plans were converted to Autocad drawings to analyze the area. The results of this study were as follows; 1) Child care centers over 70% were single-attached building types which made it possible for creating outdoor environments for children. However, most small-size centers which had under 50 children did not have the facilities for outdoor activities. 2) In terms of spatial elements, the basic spaces of the small-size center were the classroom, bathroom, kitchen, office and reference room. The medium or large size centers had extra rooms for special activities and service spaces in addition to the basic spaces. 3) Classroom area per child was 2.65 m2 on average. Space composition ratio on average for care, staff, and service was programmed by 57%, 9%, 34% respectively. Small-size center had relatively more care space when compared to the others. In the case of large-size centers, there was a tendency that service space was increased, but care space was decreased.

Lorentz martingale spaces and interpolation

In this article, the authors introduce some new Lorentz spaces for martingales, which are extensions of Hardy spaces of martingales. Then they discuss their basic properties, embedding relationships, and interpolation spaces between them, during which the use of rearrangement good-λ-inequality plays an important role.

Basic hypergeometric functions and covariant spaces for even-dimensional representations of Uq[osp(1/2)

Representations of the quantum superalgebra Uq[osp(1/2)] and their relations to the basic hypergeometric functions are investigated. We first establish Clebsch–Gordan decomposition for the superalgebra Uq[osp(1/2)] in which the representations having no classical counterparts are incorporated. Formulae for these Clebsch–Gordan coefficients are derived, and is observed that they may be expressed in terms of the Q-Hahn polynomials. We next investigate representations of the quantum supergroup OSpq(1/2) which are not well defined in the classical limit. Employing the universal -matrix, the representation matrices are obtained explicitly, and found to be related to the little Q-Jacobi polynomials. Characteristically, the relation Q = −q is satisfied in all cases. Using the Clebsch–Gordan coefficients derived here, we construct new noncommutative spaces that are covariant under the coaction of the even-dimensional representations of the quantum supergroup OSpq(1/2).

Three-dimensional microcomputed tomography imaging of basic multicellular unit-related resorption spaces in human cortical bone

This study employed microcomputed tomography (micro-CT) as a novel means for visualizing the morphology and quantifying the range (length) of basic multicellular unit (BMU)-related resorption spaces in human cortical bone. We tested the hypotheses that the density and range of spaces vary with age and sex. The sample included 82 human (18-92 years) anterior femoral midshaft samples. The morphology of the spaces (n = 99) was varied, including unidirectional, bidirectional, branched, and even highly clustered forms. The density of resorption spaces was negatively correlated with age for the combined sexes and females, with Spearman's rho values of -0.355 (P < 0.001) and -0.522 (P = 0.002), respectively. The density of spaces did not differ significantly between the sexes (P = 0.735). Mean range +/- SD for the combined sexes, females, and males was 2,706 +/- 1,177, 2,681 +/- 1,247, and 2,718 +/- 1,150 microm, respectively. Numerical simulation of the effect of the 7,000 microm scan field of view suggested that the actual mean range of the spaces for the pooled sample was actually on the order of 3,770 microm. Range did not correlate significantly with age for the combined sexes (P = 0.587) or females (P = 0.345) and males (P = 0.896) considered separately and was not significantly different (P = 0.883) between the sexes. These results suggest that the range of BMUs is not affected by age. The age-dependent decrease in resorption space density for the females and pooled sexes was most likely a consequence of cortical rarefaction, leading to difficulty detecting resorption spaces with micro-CT, rather than a decrease in overall remodeling activity.

On Harmonic Theory in Flows

AbstractRecently [8], a harmonic theory was developed for a compact contact manifold from the viewpoint of the transversal geometry of contact flow. A contact flow is a typical example of geodesible flow. As a natural generalization of the contact flow, the present paper develops a harmonic theory for various flows on compact manifolds. We introduce the notions of H-harmonic and H*-harmonic spaces associated to a Hörmander flow. We also introduce the notions of basic harmonic spaces associated to a weak basic flow. One of our main results is to show that in the special case of isometric flow these harmonic spaces are isomorphic to the cohomology spaces of certain complexes. Moreover, we find an obstruction for a geodesible flow to be isometric.

Spin Groups Over a Commutative Ring and the Associated Root Data

Usual constructions of spin and Clifford groups, restricted to the case where the basic quadratic spaces is hyperbolic, are examined as those of group schemes over a commutative ring. Not surprisingly they yield indeed smooth and reductive group schemes, but the proof involves a lot of calculation and uses a connection with Jordan pairs. Maximal tori and their associated root data are also constructed explicitly.

Virtual auditorium concepts for exhibition halls

Many communities lack good performance facilities for symphonic music, opera, dramatic and musical arts, but have basic convention, exhibition or assembly spaces. It should be possible to develop performance space environments within large multipurpose facilities that will accommodate production and presentation of dramatic arts. Concepts for moderate-cost, temporary enhancements that transform boxy spaces into more intimate, acoustically articulated venues will be presented. Acoustical criteria and design parameters will be discussed in the context of creating a virtual auditorium within the building envelope. Physical, economic, and logistical limitations affect implementation. Sound reinforcement system augmentation can supplement the room conversion. Acceptable control of reflection patterns, reverberation, and to some extent, ambient noise, may be achieved with an array of nonpermanent reflector and absorber elements. These elements can sculpture an enclosure to approach the shape and acoustic characteristics of an auditorium. Plan and section illustrations will be included.

Properties of the solution set of a fuzzy relation equation from the viewpoint of attainability

In a fuzzy relation equation, many properties of the solution set are known, especially when the basic spaces are all finite sets. However, when the basic spaces are infinite, only a few properties are known. In this paper, we introduce a new binary relation that is weaker than the ordinary one defined on fuzzy sets, and we show that an unattainable solution is partly characterized by the proposed binary relation.

A casa e a aldea: espacios primarios de vida en San Xoán de Poio

We emphasize home and hamlet to be life's basic spaces in traditional society and the way, which everybody knows reality. We make reference to the identities of the community's members and their socialization habits through their activities and behaviours. Many of these activities and behaviours take place in the home and hamlet and provide us with an outline of the community's mentality. We also point out the changes and differences between traditional and present society, which are caused by modernity, including changes in the physical structure of the home and hamlet.

Analysis of the suprabullar and retrobullar recesses for endoscopic sinus surgery.

Presently, the basic structures and spaces of the paranasal sinuses are more clearly understood by otolaryngologists than ever before. Yet, the more subtle and complex ethmoid features, especially of the ethmoidal pre-recesses and recesses, still elude many otolaryngologists. One of the most nebulous, elusive, and difficult-to-understand recesses is the sinus lateralis, or as it is more correctly called, the retrobullar and suprabullar recesses. The primary purpose of this investigation was to ascertain the prevalence of the sinus lateralis in humans. The secondary purpose was to better characterize this subtle feature of ethmoid anatomy. Human cadaver sinonasal complexes were meticulously dissected by both gross and endoscopic techniques. The hiatus semilunaris superior and sinus lateralis were present in all specimens. A separate and discrete retrobullar recess was present in 93.8%. Typically, a crestlike projection from the basal lamella to the lamina papyracea was noted within the posterior aspect of the retrobullar recess. A single, discrete, well-developed suprabullar recess was present in 70.9%, and a rudimentary suprabullar recess was present in 22.9%. In 7.2%, a single large cleft collectively excavated the retrobullar and suprabullar recess areas; separate retrobullar and suprabullar tracts were not present in this subgroup. Typically, the suprabullar recess was separate from and did not communicate with the frontal recess. The data from this investigation indicate that the separate terms retrobullar recess and suprabullar recess more accurately designate the anatomy and are recommended over the term sinus lateralis.

明治期地形図からメッシュ人口データ推定

This paper discusses possibility of the estimation of the past population distribution pattern from old topographical maps. This estimation aims to make Basic Grid Square Spaces (BGSS) population distribution data that can be available in GIS. In the past, no reliable statistical material exists except topographical maps published in many regions, which are showing villages clearly. An efficient method of the estimation of the past population pattern from the maps will provide the way to analyze long time-space population movement in detail.We tried to estimate population distribution in the Meiji-Era at the selected area of East-Biwako area (Koto Plain) in Shiga-Prefecture, firstly by point sampling of buildings drawn in the maps, then using GIS (ArcView). The result shows that it is possible to estimate population distribution at that time with pretty accuracy and adapt it to other time and other regions.

Quantitative Approximation to the Ordered Dirichlet Distribution under Varying Basic Probability Spaces

An approximate expansion of a sequence of ordered Dirichlet densities is given under the set-up with varying dimensions of the relating basic probability spaces. The problem is handled as the approximation to the joint distribution of an increasing number of selected order statistics based on the random sample drawn from the uniform distribution U(0, 1). Some inverse factorial series to the expansion of logarithmic function enable us to give quantitative error evaluations to our problem. With the help of them the relating modified K-L information number, which is defined on an approximate main domain and different from the usual ones, is accurately evaluated. Further, the proof of the approximate joint normality of the selected order statistics is more systematically presented than those given in existing works. Concerning the approximate normality the modified affinity and the half variation distance are also evaluated.

Unattainable solutions of a fuzzy relation equation

In a fuzzy relation equation, the properties of the solution set have been investigated especially when the basic spaces are all finite sets. However, when the basic spaces are infinite, a few properties are known. In this paper, we use the concepts of attainability and unattainability of a solution to clarify some properties of the solution set and show the condition for existence of a partially attainable solution and an unattainable one.