Local Representation is Not Enough: Soft Point-Wise Transformer for Descriptor and Detector of Local Features

Significant progress has been witnessed for the descriptor and detector of local features, but there still exist several challenging and intractable limitations, such as insufficient localization accuracy and non-discriminative description, especially in repetitive- or blank-texture regions, which haven't be well addressed. The coarse feature representation and limited receptive field are considered as the main issues for these limitations. To address these issues, we propose a novel Soft Point-Wise Transformer for Descriptor and Detector, simultaneously mining long-range intrinsic and cross-scale dependencies of local features. Furthermore, our model leverages the distinct transformers based on the soft point-wise attention, substantially decreasing the memory and computation complexity, especially for high-resolution feature maps. In addition, multi-level decoder is constructed to guarantee the high detection accuracy and discriminative description. Extensive experiments demonstrate that our model outperforms the existing state-of-the-art methods on the image matching and visual localization benchmarks.

Connectedness and Local Connectedness on Infra Soft Topological Spaces

This year, we introduced the concept of infra soft topology as a new generalization of soft topology. To complete our analysis of this space, we devote this paper to presenting the concepts of infra soft connected and infra soft locally connected spaces. We provide some descriptions for infra soft connectedness and elucidate that there is no relationship between an infra soft topological space and its parametric infra topological spaces with respect to the property of infra soft connectedness. We discuss the behaviors of infra soft connected and infra soft locally connected spaces under infra soft homeomorphism maps and a finite product of soft spaces. We complete this manuscript by defining a component of a soft point and establishing its main properties. We determine the conditions under which the number of components is finite or countable, and we discuss under what conditions the infra soft connected subsets are components.

Some New Concepts on int-soft Ideals in Ordered Semigroups

In the present paper, we introduce some new notions on ordered semigroup. In fact, notion of a convex soft set in an ordered semigroup is introduced, and its basic properties are investigated. Moreover, we consider a characterization of a convex soft set. Furthermore, relations between a convex soft set and an int-soft [Formula: see text]-ideal (or, int-soft [Formula: see text]-ideal) are studied. Finally, int-soft [Formula: see text]-ideals (or, int-soft [Formula: see text]-ideals) generated by an ordered soft point are established.

SEQUENCE OF SOFT POINTS IN SOFT Δ-METRIC SPACES

In this paper, we have constructed a sequence of soft points in one soft set with respect to a fixed soft point of another soft set. The convergence and boundedness of these sequences in soft Δ-metric spaces are defined and their properties are established. Further, the complete soft Δ-metric spaces are introduced by defining soft Δ-Cauchy sequences.

Generalized Ideals of BCK/BCI-Algebras Based on Fuzzy Soft Set Theory

In the present paper, using Lukaswize triple-valued logic, we introduce the notion of α , β -intuitionistic fuzzy soft ideal of BCK / BCI -algebras, where α and β are the membership values between an intuitionistic fuzzy soft point and intuitionistic fuzzy set. Moreover, intuitionistic fuzzy soft ideals with thresholds are introduced, and their related properties are investigated.

Impact of PVC mixtures of the Electrical Conduit on the Physical Properties

The use of PVC mixtures in the manufacturing of electrical conduit has been employed for a long time along with other materials. In this study, the impact of changing the ratio of the components of the PVC mixtures on the physical properties of the electrical conduit was investigated. The emphasis was placed on three properties: Density, Tensile Strength and Soft Point. The application of the electrical conduit controls the types of materials and their percentages. Physical properties of the PVC products are the most important factors that help to choose compared with other materials. These properties change with the change of the chemical components of the PVC mixture. The study discussed how to enhance and improve these properties by controlling the proportions of some substances in the PVC mixtures. This article aims to demonstrate the strong relationship between PVC polymer, calcium and stabilizers and the physical properties of the electrical conduit. The focus concentrated on three components in the mixture and three physical properties. Random samples were taken to calculate the average percentages of the components in the mixtures. Various tools and several statistical methods were used such as correlation coefficients and scatter charts to prove the relationship between the ratios of the materials and the respective properties. The correlation coefficients between the PVC polymer, stabilizers, calcium, and the density, tensile strength, vicat soft points were (0.92, 0.83, 0.82) respectively. Decreasing the PVC polymer by (17.1%) has caused an increase in the density of the conduit by (2%). Finally, the physical properties of PVC mixtures could be improved by changing component ratios to reach the optimized mixture for the specific application, taking into account other competitive issues such as the final price of the product, environmental impact, and other issues.

New soft separation axioms and fixed soft points with respect to total belong and total non-belong relations

In this article, we exploit the relations of total belong and total non-belong to introduce new soft separation axioms with respect to ordinary points, namely t t tt -soft pre T i ( i = 0 , 1 , 2 , 3 , 4 ) {T}_{i}\hspace{0.33em}\left(i=0,1,2,3,4) and t t tt -soft pre-regular spaces. The motivations to use these relations are, first, cancel the constant shape of soft pre-open and pre-closed subsets of soft pre-regular spaces, and second, generalization of existing comparable properties on classical topology. With the help of examples, we show the relationships between them as well as with soft pre T i ( i = 0 , 1 , 2 , 3 , 4 ) {T}_{i}\hspace{0.33em}\left(i=0,1,2,3,4) and soft pre-regular spaces. Also, we explain the role of soft hyperconnected and extended soft topological spaces in obtaining some interesting results. We characterize a t t tt -soft pre-regular space and demonstrate that it guarantees the equivalence of t t tt -soft pre T i ( i = 0 , 1 , 2 ) {T}_{i}\hspace{0.33em}\left(i=0,1,2) . Furthermore, we investigate the behaviors of these soft separation axioms with the concepts of product and sum of soft spaces. Finally, we introduce a concept of pre-fixed soft point and study its main properties.

Soft Separation Axioms and Fixed Soft Points Using Soft Semiopen Sets

The importance of soft separation axioms comes from their vital role in classifications of soft spaces, and their interesting properties are studied. This article is devoted to introducing the concepts of t t -soft semi- T i i = 0 , 1 , 2 , 3 , 4 and t t -soft semiregular spaces with respect to ordinary points. We formulate them by utilizing the relations of total belong and total nonbelong. The advantages behind using these relations are, first, generalization of existing comparable properties on general topology and, second, eliminating the stability shape of soft open and closed subsets of soft semiregular spaces. By some examples, we show the relationships between them as well as with soft semi- T i i = 0 , 1 , 2 , 3 , 4 and soft semiregular spaces. Also, we explore under what conditions they are kept between soft topology and its parametric topologies. We characterize a t t -soft semiregular space and demonstrate that it guarantees the equivalence of t t -soft semi- T i i = 0 , 1 , 2 . Further, we investigate some interrelations of them and some soft topological notions such as soft compactness, product soft spaces, and sum of soft topological spaces. Finally, we define a concept of semifixed soft point and study its main properties.

On Fuzzy Soft Linear Operators in Fuzzy Soft Hilbert Spaces

Due to the difficulty of representing problem parameters fuzziness using the soft set theory, the fuzzy soft set is regarded to be more general and flexible than using the soft set. In this paper, we define the fuzzy soft linear operator T~ in the fuzzy soft Hilbert space H~ based on the definition of the fuzzy soft inner product space U~,·,·~ in terms of the fuzzy soft vector v~fGe modified in our work. Moreover, it is shown that ℂnA, ℝnA and ℓ2A are suitable examples of fuzzy soft Hilbert spaces and also some related examples, properties and results of fuzzy soft linear operators are introduced with proofs. In addition, we present the definition of the fuzzy soft orthogonal family and the fuzzy soft orthonormal family and introduce examples satisfying them. Furthermore, the fuzzy soft resolvent set, the fuzzy soft spectral radius, the fuzzy soft spectrum with its different types of fuzzy soft linear operators and the relations between those types are introduced. Moreover, the fuzzy soft right shift operator and the fuzzy soft left shift operator are defined with an example of each type on ℓ2A. In addition, it is proved, on ℓ2A, that the fuzzy soft point spectrum of fuzzy soft right shift operator has no fuzzy soft eigenvalues, the fuzzy soft residual spectrum of fuzzy soft right shift operator is equal to the fuzzy soft comparison spectrum of it and the fuzzy soft point spectrum of fuzzy soft left shift operator is the fuzzy soft open disk λ~<~1~. Finally, it is shown that the fuzzy soft Hilbert space is fuzzy soft self-dual in this generalized setting.