Quasi-uniform Structures Research Articles

Evolution of suspended sediment concentration profiles in the partially and periodically stratified Changjiang Estuary during dry season

A better understanding of how the vertical profile of suspended sediment concentration (SSC) is influenced by multiple factors is required to better understand the hydrodynamics and sediment dynamics of estuaries. Based on in situ measurements obtained during a spring-neap cycle in the estuarine turbidity maximum (ETM) of the Changjiang Estuary in January 2015, we investigate the intratidal evolution and controlling mechanisms of SSC profiles. The results show that during the dry season the ETM was characterized by periodic salinity stratification, low SSC, suspended sediments with reduced grain size, and low sediment availability for resuspension. Three types of SSC profiles were identified, i.e., profiles with two-layer, linear and quasi-uniform structures. The shapes of the SSC profiles varied with time and generally deviated from the equilibrium profile due to the highly variable hydrodynamic and sediment conditions. During ebbs of spring and intermediate tides, the SSC profiles generally evolved from a two-layer to a quasi-uniform structure via a linear structure. Analysis shows that the linear and quasi-uniform profiles occurred under the combination of vertically well-mixed salinity, negligible resuspension, low settling velocity associated with very fine grains, and shallow water depth. Such an evolution pattern can be well reproduced using a one-dimensional numerical model, with the diffusion coefficient being parabolically distributed in the water column and the four factors mentioned above. The findings reported here imply a high variability of SSC profiles in estuarine environments.

Quasi-uniform structures determined by closure operators

We demonstrate a one-to-one correspondence between idempotent closure operators and the so-called saturated quasi-uniform structures on a category C. Not only this result allows to obtain a categorical counterpart P of the Császár-Pervin quasi-uniformity P, that we characterize as a transitive quasi-uniformity compatible with an idempotent interior operator, but also permits to describe those topogenous orders that are induced by a transitive quasi-uniformity on C. The categorical counterpart P⁎ of P−1 is characterized as a transitive quasi-uniformity compatible with an idempotent closure operator. When applied to other categories outside topology P allows, among other things, to generate a family of idempotent closure operators on Grp, the category of groups and group homomorphisms, determined by the normal closure.

Some applications of the open mapping theorem in locally convex cones

UDC 515.12 We show that a continuous open linear operator preserves the completeness and barreledness in locally convex cones. Specially, we prove some relations between an open linear operator and its adjoint in uc-cones (locally convex cones which their convex quasi-uniform structures are generated by one element).

Quasi-uniform and syntopogenous structures on categories

We introduce and study an abstract notion of Császár's syntopogenous structure which provides a convenient setting to investigate a quasi-uniformity on a category. We show that a quasi-uniformity is a family of categorical closure operators. In particular, it is shown that every idempotent closure operator is quasi-uniformity.Various notions of completeness of objects and precompactness with respect to a quasi-uniformity defined in a natural way are also studied.

Maximality, fixed points and variational principles for mappings on quasi-uniform spaces

By making use of maximality on some appropriate preorderings, some classical results stated in the context of metric spaces are extended to spaces endowed with quasi-uniform structures. Indeed, various results on fixed point theory and variational principles have been proved by arguments using order relations in metric spaces. In this work, some of the mentioned results are extended to spaces having a quasi-uniform structure, by means of appropriate preorderings. The concept of w-distance is used to this purpose. Moreover, equivalences of maximality are stated for general preorderings.

Relationships between L-fuzzy quasi-uniform structures and L-fuzzy topologies

In this paper, we investigated the properties of two L-fuzzy interior operators and two L-fuzzy topologies induced by L-quasi-uniformity in complete residuated lattices. We study the relations among L-fuzzy quasi-uniformities, L-fuzzy interior operators and L-fuzzy topologies. We give their examples.

Locally Convex Product and Direct Sum Cones

In Motallebi and Saiflu [3], products and direct sums of cones have been investigated based on convex quasi-uniform structures. In this paper, we define the notion of product and direct sum cone topologies based on a suitable order relation and discuss the duality properties. Using the polars of neighborhoods, we define some of the X-topologies which are isomorphic to each other. In the condition of the strict separation property, these topologies will be isomorphic to a product (or direct sum) cone topology. This leads us to study weak-topologies, topologies of pointwise convergence and the finest X-topologies.

Stratified L-ordered quasiuniform limit spaces

By making use of the intrinsic lattice-valued inclusion orders of L-subsets and that of stratified L-filters, a concept of stratified L-ordered quasiuniform limit structure is proposed, which is asymmetric and available to establish a framework of asymmetric structures. Then the category of stratified L-ordered quasiuniform limit spaces is introduced and its categorical properties are shown. The next objective of the paper is to propose a concept of stratified L-ordered principle quasiuniform limit space, and we prove that the category of stratified L-quasiuniform spaces can be embedded into the category of stratified L-quasiuniform limit spaces as a bireflective subcategory. Moreover, two ways of inducing stratified L-ordered limit structures from stratified L-ordered quasiuniform structures are presented, and the method of obtaining stratified [0,1]-ordered quasiuniform structures from [0,1]-ordered probabilistic quasiuniform limit structures and fuzzy quasi-metrics is introduced in the paper.

Locally convex cones and the Schröder-Simpson theorem

This paper paper has two goals: Firstly, to present the conceptual proof of the Schröder-Simpson theorem. The Schröder-Simpson theorem is stated in terms of domain theory and uses directed complete partially ordered cones and Scott-continuous maps. These structures are used to model probabilistic phenomena in denotational semantics. The proof presented here relies on another generalization of vector spaces to an asymmetric setting – cones with convex quasiuniform structures – which has not been used in the semantic community until now. The second goal of this paper is to introduce these two parallel developments of asymmetric generalizations of topological vector spaces in the style of a survey. There are the order theoretical and topological point of view on one hand, and the quasiuniform aspect on the other hand. Both developments had been pursued in parallel until now. The aim is to point out the close connection of these developments to the community working on asymmetric normed and asymmetric locally convex spaces.

Standard fuzzy uniform structures based on continuous t-norms

This paper deals with fuzzy uniform structures previously introduced by the authors [Fuzzy uniform structures and continuous t-norms, Fuzzy Sets Syst. 161 (2009) 1011–1021]. Our approach involves a covariant functor Ψ from the category of fuzzy uniform spaces and fuzzy uniformly continuous mappings (in our sense) to the category of uniform spaces and uniformly continuous mappings. We show that Ψ is well-behaved with respect to some significant fuzzy uniform concepts, and its behavior provides a method to introduce notions of fine fuzzy uniform structure and Stone–Čech fuzzy compactification in this context. Our method also applies to obtain fuzzy versions of some classical results on topological algebra and hyperspaces. The case of quasi-uniform structures is also analyzed.

A Survey on Wallman Bases

Wallman bases are frequently used in compactification processes of topological spaces. However, they are also related with quasi–uniform structures and they are useful to characterize some topological properties. We present a brief survey on the subject which supports these statements.

Initial L-fuzzy quasi-uniform structures

We prove the existence of initial L-fuzzy (quasi-)uniform structures. From this fact, we can define subspaces and products of L-fuzzy (quasi-)uniform spaces.

Bcl-2 blocks a caspase-dependent pathway of apoptosis activated by herpes simplex virus 1 infection in HEp-2 cells.

Earlier reports have shown that herpes simplex virus 1 (HSV-1) mutants induce programmed cell death and that wild-type virus blocks the execution of the cell death program triggered by expression of viral genes, by the Fas and tumor necrosis factor pathways, or by nonspecific stress agents. In particular, an earlier report from this laboratory showed that the mutant virus d120 lacking the genes encoding infected cell protein 4 (ICP4), the major regulatory protein of the virus, induces a caspase-3-independent pathway of apoptosis in human SK-N-SH cells. Here we report that the pathway of apoptosis induced by the d120 mutant in human HEp-2 cells is caspase dependent. Specifically, in HEp-2 cells infected with d120, (i) a broad-range inhibitor of caspase activity, z-vad-FMK, efficiently blocked DNA fragmentation, (ii) cytochrome c was released into the cytoplasm, (iii) caspase-3 was activated inasmuch as poly(ADP-ribose) polymerase was cleaved, and (iv) chromatin condensation and fragmentation of cellular DNA were observed. In parallel studies, HEp-2 cells were transfected with a plasmid encoding human Bcl-2 and a clone (VAX-3) expressing high levels of Bcl-2 was selected. This report shows that Bcl-2 blocked all of the manifestations associated with programmed cell death caused by infection with the d120 mutant. Consistent with their resistance to programmed cell death, VAX-3 cells overproduced infected cell protein 0 (ICP0). An unexpected observation was that ICP0 encoded by the d120 mutant accumulated late in infection in small, quasi-uniform vesicle-like structures in all cell lines tested. Immunofluorescence-based colocalization studies indicated that these structures were not mitochondria or components of the endoplasmic reticulum or the late endosomal compartment. These studies affirm the conclusion that HSV can induce programmed cell death at multiple steps in the course of its replication, that the d120 mutant can induce both caspase-dependent and -independent pathways of programmed cell death, and that virus-induced stimuli of programmed cell death may differ with respect to the pathway that they activate.

Topological Formation of Small Scales in Magnetohydrodynamics: A Fast Dissipation Mechanism

The dissipation of Alfvén wave packets propagating in an inhomogeneous three-dimensional magnetic field is numerically studied in the Wentzel-Kramers-Brillouin (WKB) approximation. The dissipation rate is found to scale proportionally to the logarithm of viscosity and/or resistivity, i.e., much faster than the scaling found for two-dimensional configurations (phase mixing, resonance absorption). This phenomenon is related to the exponential separation of neighboring rays; estimations of the corresponding rate are consistent with the behavior of the Kolmogorov entropy in this kind of structure. The scaling law td ∝ ln S (td is the e-folding dissipation time and S is the Reynolds number) holds not only in an irregular magnetic field (which was studied by Similon & Sudan), but is also verified in quasi-uniform magnetic structures, which contain very small chaotic regions. This study can apply to the heating of low-collision plasmas, e.g., in astrophysical contexts such as the solar corona.

Quasi-uniform Structures in Linear Lattices

Quasi-uniform Structures in Linear Lattices

Nearness and quasi-uniform structures

The concept of a locally right symmetric quasi-uniform space is introduced. Every symmetric topological space admits a locally right symmetric quasi-uniform structure. It is shown that this property characterizes those quasi-uniform spaces for which the collection of quasi-uniform covers forms a nearness structure with the same closure operator. With this link, various concepts and results in these two areas are compared.

On Precompact (Quasi-) Uniform Structures

The following are shown: (1) The subbasis theorem on precompactness does not hold even in uniform spaces. (2) The supremum of (even finitely many) precompact quasi-uniform structures is not necessarily precompact. (3) A compact quasi-uniform space is not necessarily totally bounded. These results contradict corresponding assertions in the literature.

On precompact (quasi-) uniform structures

The following are shown: (1) The subbasis theorem on precompactness does not hold even in uniform spaces. (2) The supremum of (even finitely many) precompact quasi-uniform structures is not necessarily precompact. (3) A compact quasi-uniform space is not necessarily totally bounded. These results contradict corresponding assertions in the literature.

Some Results on Quasi-Uniform Spaces

Constructions are made of a T1 space which does not have a T1 completion and of a quasi-uniform space which is complete, but not strongly complete. An example relating to a completion due to Popa is given. An alternate definition for Cauchy filter, called C-filter, is examined and a construction of a C-completion is given. We discuss quasi-pseudometrics over a Tikhonov semifield RΔ. Every topological space is quasi-pseudometrizable over a suitable RΔ. It is shown that if a quasi-pseudometric space over RΔ is complete, the corresponding quasi-uniform structure is C-complete. A general method for constructing compatible quasiuniform structures is given.

Some properties of quasi-uniform structures

Some properties of quasi-uniform structures