Rough Topology Research Articles

Employing a Generalization of Open Sets Defined by Ideals to Initiate Novel Rough Approximation Spaces with a Chemical Application

A close similarity and analogy between rough set theory and topology is attributed to the corresponding behavior of lower and upper rough approximations with interior and closure topological operators, respectively. This relation motivates joint studies between topology and this theory. We endeavor by rough set theory to enlarge the knowledge we obtain from the information systems, for this reason, we apply the abstract concept of ideal structures to build new generalized approximation spaces with less vagueness. In the present work, we employ a novel type of nearly open sets in topology so-called ``${\mathcal{L}}$-${\theta\beta}_{\lambda}$-open" with an ideal structure to introduce novel approximation spaces satisfying the desired properties concerning shrinking the boundary region of uncertainty and expanding the domain of confirmed information. We set up the fundamentals of the proposed rough paradigms and demonstrate their superiority over the preceding paradigms induced by some nearly open sets. Two algorithms are furnished to illustrate the way of specifying the family of ${\mathcal{L}}$-${\theta\beta}_{\lambda}$-open sets and exploring whether a subset is ${\mathcal{L}}$-${\theta\beta}_{\lambda}$-definable or ${\mathcal{L}}$-${\theta\beta}_{\lambda}$-rough. Then, we put forward the concepts of rough membership relations and functions and uncover their core characterizations. Finally, we examine the proposed models to model a real situation in the Chemistry field and clarify how our models improve the outcomes of generalized approximation spaces over the previous models.

Effect of surface roughness on methane adsorption in shale organic nanopores from the perspective of molecular simulations

Understanding the shale gas adsorption behavior within organic nanopores is crucial for its development. The pore surfaces commonly exhibit random inherent roughness, which can significantly impact gas adsorption, while it’s still in debate about whether the roughness could enhance the gas adsorption or not. To clarify the underlying mechanisms of the effect of surface roughness, in this study, the Grand Canonical Monte Carlo and Molecular Dynamic simulations are used to investigate the methane adsorption in wrinkled graphene nanochannels with various roughness. The heterogeneity of the adsorption layer along the rough topology is described in detail. The adsorption is enhanced near the concave region and weakened near the convex region. Additionally, increased surface roughness shifts the gas molecules’ aggregation modes in the concave region from a gradual gradient to oscillatory “adsorption points”. We observe that wall roughness due to the wrinkle can enhance the adsorption amount overall, attributed to the increased surface area and the increased unit adsorption capacity due to potential energy overlap. However, the contributions of both factors differ under various pressure and roughness conditions. Then a new mathematical method to estimate the gas adsorption amounts is provided and aligns well with molecular simulation results for a wide range of pressure and roughness conditions. And a potential answer the current debate about the positive or negative impact of adsorption due to roughness is promoted. The key may lie in the dominant role of the co-existed roughness caused by the fragment basal or edge surface. Our work could shed light on the underlying effect of surface roughness on the gas adsorption in shale, and have significant implications for the reserve estimation of shale gas formations.

Numerical Simulations of Scalar Transport on Rough Surfaces

Numerical simulations provide unfettered access to details of the flow where experimental measurements are difficult to obtain. This paper summarises the progress achieved in the study of passive scalars in flows over rough surfaces thanks to recent numerical simulations. Townsend’s similarity applies to various scalar statistics, implying the differences due to roughness are limited to the roughness sublayer (RSL). The scalar field exhibits a diffusive sublayer that increasingly conforms to the roughness surface as ks+ or Pr increase. The scalar wall flux is enhanced on the windward slopes of the roughness, where the analogy between momentum and scalar holds well; the momentum and scalar fields, however, have very different behaviours downwind of the roughness elements, due to recirculation, which reduces the scalar wall flux. Roughness causes breakdown of the Reynolds analogy: any increase in St is accompanied by a larger increase in cf. A flattening trend for the scalar roughness function, ΔΘ+, is observed as ks+ increases, suggesting the possibility of a scalar fully rough regime, different from the velocity one. The form-induced (FI) production of scalar fluctuations becomes dominant inside the RSL and is significantly different from the FI production of turbulent kinetic energy, resulting in notable differences between the scalar and velocity fluctuations. Several key questions remain open, in particular regarding the existence of a fully rough scalar regime and its characteristics. With the increase in Re and Pr, various quantities such as scalar roughness function, the dispersive fluxes, FI wall flux, etc., appear to trend towards saturation. However, the limited range of Re and Pr achieved by numerical simulations only allows us to speculate regarding such asymptotic behaviour. Beyond extending the range of Re and Pr, systematic coverage of different roughness types and topologies is needed, as the scalar appears to remain sensitive to the geometrical details.

Valorization of Eichhornia crassipes for the production of cellulose nanocrystals further investigation of plethoric biobased resource

Chemical processing is among the significant keys to tackle agro-residues utilization field, aiming to obtain value-added materials. Extraction of cellulose nanocrystals (CNCs) is an emerging route to valorize lignocellulosic wastes into high value particles. In this investigation, effect of acidic hydrolysis duration was monitored on size and morphology of obtained crystals; namely: CNCs from Nile roses fibers (NRFs) (Eichhornia crassipes). Different acidic hydrolysis duration range or different characterization techniques set this article apart from relevant literature, including our group research articles. The grinded NRFs were firstly subjected to alkaline and bleaching pretreatments, then acid hydrolysis process was carried out with varied durations ranging from 5 to 30 min. Microcrystalline cellulose (MCC) was used as reference for comparison with NRFs based samples. The extracted CNCs samples were investigated using various techniques such as scanning electron microscopy (SEM), Atomic force microscopy (AFM), Raman spectroscopy, and thermogravimetric (TGA) analysis. The figures gotten from SEM and AFM depicted that NRFs based CNCs appeared as fibril-like shapes, with reduced average size when the NRFs underwent pulping and bleaching processes. This was indicated that the elimination of hemicellulose and lignin components got achieved successfully. This outcome was proven by chemical composition measurements and TGA/DTG curves. On the other hand, AFM-3D images indicated that CNCs topology and surface roughness were mostly affected by increasing hydrolysis durations, besides smooth and homogeneous surfaces were noticed. Moreover, Raman spectra demonstrated that the particle size and crystallinity degree of NRFs based CNCs can be affected by acidic hydrolysis durations and optimum extraction time was found to be 10 min. Thermal stability of extracted CNCs-NRFs and CNCs-MCC was measured by TGA/DTG and the kinetic models were suggested to identify the kinetic parameters of the thermal decomposition of CNCs for each acid hydrolysis duration. Increasing hydrolysis duration promoted thermal stability, particularly for NRFs based CNCs. Results showcased in this article add new perspective to Nile rose nanocellulose and pave down the way to fabricate NRFs based humidity nano-sensors.

Osteoimmune-modulating and BMP-2-eluting anodised 3D printed titanium for accelerated bone regeneration.

3D printing of titanium (Ti) metal has potential to transform the field of personalised orthopaedics and dental implants. However, the impacts of controlled surface topographical features of 3D printed Ti implants on their interactions with the cellular microenvironment and incorporation of biological growth factors, which are critical in guiding the integration of implants with bone, are not well studied. In the present study, we explore the role of surface topological features of 3D printed Ti implants using an anodised titania nanotube (TiNT) surface layer in guiding their immune cell interaction and ability to deliver bioactive form of growth factors. TiNT layers with precisely controlled pore diameter (between 21and 130 nm) were anodically grown on 3D printed Ti surfaces to impart a nano-micro rough topology. Immune biomarker profiles at gene and protein levels show that anodised 3D Ti surfaces with smaller pores resulted in classical activation of macrophages (M1-like), while larger pores (i.e., >100 nm) promoted alternate activation of macrophages (M2-like). The in vitro bone mineralisation studies using the conditioned media from the immunomodulatory studies elucidate a clear impact of pore diameter on bone mineralisation. The tubular structure of TiNTs was utilised as a container to incorporate recombinant human bone morphogenetic protein-2 (BMP-2) in the presence of various sugar and polymeric cryoprotectants. Sucrose offered the most sustainable release of preserved BMP-2 from TiNTs. Downstream effects of released BMP-2 on macrophages as well as bone mineralisation were assessed showing bioactivity retention of the released rhBMP-2. Overall, the TiNT surface topography in combination with controlled, sustained, and local release of bioactive growth factors can potentially enhance the osseointegration outcomes of custom 3D printed Ti implants in the clinic.

Roughness Effect on Thermal-Hydraulic Performances of Additively Manufactured Meandering Mini-Channels

Additive manufacturing has made possible new geometry’s design. The promise of these technologies is of prime importance in the heat exchanger’s performance. Nevertheless, this fabrication process creates new more or less rough topologies, thus, different thermal-hydraulic behaviors, which are not fully known, controlled and predictable in the case of mini-channels (2 mm diameter in this study). The aim of this work is to test and compare the experimental thermal-hydraulic performances of different meandering mini–channels. They are obtained by a Laser-Powder Bed Fusion process with a circular or square cross-section. The geometry and the roughness of the channels are also characterized. Tests were conducted over a Reynolds number range of 200–6000. These experimental data are then used to build and validate a numerical model of the mockup. The experimental and numerical results are consistent without requiring the use of tuning parameters.

Superhydrophobic silicone/graphene oxide-silver-titania nanocomposites as eco-friendly and durable maritime antifouling coatings

In this work, a novel ecofriendly series of polydimethylsiloxane-polymethylmethacrylate (PDMS-PMMA) blend filled with silver nanospheres and titanium dioxide nanorods grafted on the graphene oxide surface (Ag–TiO2@GO) were produced by the catalytic hydrosilation method as outstanding marine antifouling coatings. Innovative Ag–TiO2@GO hybrid nanofillers, that would release fouling and confer surface robustness, were developed by a single-phase procedure. Ag nanospheres with 20 nm mean diameter were prepared by a controlled solvothermal method, while anatase TiO2 nanorods with 10 nm average diameter were grown by a hydrothermal technique. The solution casting method was used to distribute various Ag–TiO2@GO filler percentages throughout the silicone matrix. Atomic force microscopy, surface free energy, and water contact angle (WCA) were employed to examine the superhydrophobicity and roughness of the coatings. The mechanical durability and antifouling characteristics of the PDMS-PMMA nanocomposites filled with Ag–TiO2@GO composites were also investigated. Several microorganisms were employed to examine the fouling resistance of the coated specimens for 30 days. Trichogaster lalius fish and the bivalve Brachidontes variabilis species were used to examine the nanocomposites’ toxicity. Well-dispersion of Ag–TiO2@GO nanofillers in the PDMS-PMMA resin until 2.5 wt% exhibited the highest WCA (160° ± 2°), the lowest surface free energy (22.9 mN/m), rough topology, and improved bulk mechanical properties. Furthermore, the well-dispersed PDMSPMMA/Ag–TiO2@GO (2.5 wt%) nanocomposite presented the lowest biodegradability percentages and optical density against various gram-positive and gram-negative bacterial strains. Furthermore, it displayed non-toxicity against the tested species of fish and bivalve. The developed non-toxic and non-stick nanocoating exhibited various merits, including superhydrophobicity, mechanical robustness, and fouling retardancy, for using as maritime ship hull coatings.

Modeling Unsteady Surface Pressure Autospectra for Turbulent Boundary-Layer Flow over Small Dense Roughness

This work concentrates on analyzing and modeling the unsteady surface pressure autospectra beneath zero-pressure gradient, turbulent boundary-layer flowfields with variably rough flow surfaces. These surface conditions are qualitatively described as being for small, dense, rigid, spatially homogeneous roughness topologies, along with corresponding quantitative parameters. Turbulent boundary-layer velocity and unsteady surface pressure data from a new wind tunnel test with multiple surface conditions are analyzed in conjunction with the compiled results from five, distinct, additional references. These compiled results are utilized to develop and propose a new empirical model for the unsteady surface pressure autospectra for a range of variably rough surfaces. This new modeling framework is approached as an extension of the Goody model, which pertains to smooth-wall flows. The variable character of the newly proposed model is controlled by parameters based on viscous scaling of the effective roughness height and friction velocity such that the surface pressure model inputs are based on readily available mean properties of the turbulent boundary-layer flowfield. For the data utilized in this analysis the approximate values of viscous scaled effective roughness height range between approximately 100 and 2000. Finally, this newly proposed model is used to compare to the unsteady surface pressure data of two additional and separate experimental references for rough-wall flows, yielding further positive comparisons as well as isolated examples of the sensitivity of analysis and modeling to the determined friction velocity for a flow configuration.

Tuning electrical properties of BaTiO3 with iron modification

BaTiO3 plays an important role in advanced functional devices owing to its fascinating properties. Though it is an excellent ferroelectric material, its magnetism can be switchable via suitable modification. In this report, we have studied iron-modified BaTiO3, which has been prepared using cost-effective high-temperature solid-state reaction techniques. The Fe-modified BaTiO3 maintains its crystallinity in the tetragonal phase with P4mm space group with a slight variation of tetragonality ratio to 1.002 from 1.008 of BaTiO3 of the identical synthesis method. This is confirmed by Rietveld refinement. Field emission scanning electron microscopy (FESEM) and EDX (energy dispersive X-rays) spectrum along with an elemental mapping analysis has provided the feature of the Fe-modifed BaTiO3. Atomic force microscope (AFM) has been employed to get the detailed surface topology (2D and 3D) and surface roughness of the developed systems. This deformation caused by the incorporation of Fe significantly modifies the electrical properties of barium titanate. The ferroelectric-paraelectric phase transition temperature (Tc) of Fe-modified BaTiO3 has been diffused and shifted to 300 °C from 120 °C of pure BaTiO3, suggesting the materials for the high-temperature capacitive application. The room temperature M-H hysteresis of Fe-modified BaTiO3 indicates the ferromagnetism developed in the BaTiO3 with the introduction of Fe. The ac conductivity is in the order of 10−4 Ω−1cm−1, and its frequency response obeys Jonscher's power law. Different charge carriers are responsible for diverse conduction processes in different temperature ranges confirmed by the Arrhenius plot. Impedance spectroscopy studies reveal the existence of NTCR characteristics of the developed system. Well defined ferroelectric hysteresis loop indicates the existence of ferroelectricity in the developed system. The analysis of various electrical parameters has provided information on the material's dielectric relaxation and conduction mechanisms for possible application in functional devices.

Developing 3D-network gels from polysaccharide gums for biomedical applications

Keeping in view the recent advancements in polysaccharide materials, gum acacia (GA) - tragacanth gum (TG) was investigated for designing polymeric network structures impregnated with cephalexin antibiotics for drug delivery (DD). Grafted product of polyvinylimidazole [poly(VIm)] and GA-TG was characterized by field emission scanning electron microscopy (FESEM), atomic force microscopy (AFM), X-ray photoelectron spectroscopy (XPS), X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), thermo-gravimetric analysis (TGA) and differential scanning calorimetry (DSC). Change in mesh size (from 17.73 to 32.98 nm) and crosslinking density (between 1.64 × 10−5 to 5.06 × 10−5 mol cm−3) was found with change in poly(VIm), gum and crosslinker NNMBA content which revealed that these parameters can be tailored made as per requirement and applications. Swelling properties illustrated pH sensitivity in copolymers because of composition which is useful for colon or site-specific DD of cephalexin. FESEM and AFM demonstrated heterogeneous morphology with the rough surface topology of grafted product. XPS and FTIR confirmed the grafting of poly(VIm) onto polysaccharide chains. Drug diffusion was non-Fickian and release was fitted in Higuchi kinetic model from copolymers. The release was slow and prolonged due to drug-polymer interactions. Copolymers exhibited 31.29% scavenging ability in DPPH assay and haemolysis was less than 2% that inferred biocompatible nature. Bio-surface interactions with intestinal membrane indicated the muco-adhesive nature of copolymers. Antimicrobial properties of hydrogel were evaluated against E. coli, P. aeruginosa and S. aureus. All observations revealed that GA-TG crosslinked copolymers could be explored for colon DD of antibiotic drugs with tailored crosslinking density.

Modeling of COVID-19 in View of Rough Topology

Rough-based topology has become an important technique for decision making in numerous real-life problems. The main purpose of this research paper is to use some topological notions in the approximation space of a rough set. Firstly, some concepts of topological near open sets and rough concepts are presented. A new approximation structure based on the topological near open sets is introduced. We debate the properties of the new approximation structure. We included an algorithm for detecting COVID-19 infection by its side effects. We believe that our approach will be helpful for any future detection.

Development of a novel triple perovskite barium bismuth molybdate material for thermistor-based applications

In this communication, development (synthesis and characterization) of a novel triple perovskite sample Ba3Bi2MoO9 (BBMO) is reported. The material has monoclinic crystal symmetry. A detailed study of microstructure and compositional analysis of the sample by using scanning electron microscopy (SEM) and EDX (energy dispersive X-rays) spectrum has provided the quality of the BBMO ceramic. The topological and surface roughness of the novel material has been analyzed to clarify the surface texture and compactness of the sample surface. The variation of conductivity under the alternating current of the material varies according to the Jonscher's universal power law. The high dielectric constant and low tangent loss are applicable for fabrication of various electrical instruments. The resistance decreases with an increase in temperature supports the NTCR (negative temperature coefficient of resistance) behavior, which is clarified by using TCR and β (thermistor constant) for NTC thermistor application.

Synthesis of nanostructured novel ion-imprinted polymer for selective removal of Cu2+ and Sr2+ ions from reverse osmosis concentrated brine

This study aims to prepare an ion-imprinted polymer (IIP) using copper sulfate as a template and potassium persulfate as an initiator to selectively adsorb copper ions (Cu2+) from aqueous solutions and in an attempt to also test its applicability for removing strontium ions (Sr2+). The prepared polymer was denoted by IIP-Cu. Various physical and chemical characterizations were performed for the prepared IIP-Cu. The scanning electron microscopy and transmission electron microscopy analyses confirmed the cavities formed after the removal of the template. It also indicated that the IIP-Cu had a rough and porous topology. The X-ray photoelectron spectroscopy confirmed the successful removal of the Cu template from IIP-Cu. The Brunauer-Emmet-Teller revealed that the surface area of IIP-Cu is as high as 152.3 m2/g while the pore radius is 8.51 nm. The effect of pH indicated that the maximum adsorption of Cu2+ was achieved at pH 8 with 98.7%. Isotherm studies revealed that the adsorption of Cu2+ was best explained using Langmuir models with a maximum adsorption capacity of 159 mg/g. The effect of temperature revealed that an increase in temperature had an adverse impact on Cu2+ removal from the aqueous solution, which was further confirmed by thermodynamic studies. The negative value of standard enthalpy change (−4.641 kJ/mol) revealed that the adsorption of Cu2+ onto IIP-Cu was exothermic. While the continuous increase in Gibbs free energy from −6776 kJ/mol to −8385 kJ/mol with the increase in temperature indicated that the adsorption process was spontaneous and feasible. Lastly, the positive value of the standard entropy change (0.023 J/mol.K) suggested that the Cu2+ adsorption onto IIP-Cu had a good affinity at the solid-liquid surface. The efficiency of the prepared IIP-Cu was also tested by studying the adsorption capacity using Sr2+ and real brine water. The results revealed that IIP-Cu was able to remove 63.57% of Sr2+ at pH 8. While the adsorption studies revealed that the experiment was best described using the Langmuir model with a maximum adsorption capacity of 76.92 mg/g. Additionally, IIP-Cu was applied in a real brine sample, which consisted of various metal ions. The highest percentage of Cu2+ removal was 90.6% and the lowest was 65.63% in 1:4 and 1:1 brine ratios, respectively. However, this study indicates the successful application of IIP-Cu in a real sample when it comes to the effective and efficient removal of Cu2+ in a solution consisting of various competing ions.

Brief review of the development of theories of robustness, roughness and bifurcations of dynamic systems

The development issues of theories of robustness, roughness and bifurcations of dynamic systems are considered. In the modern theory of dynamic systems and automatic control systems, researches of the properties of roughness and robustness of systems are becoming more and more important. The work considers methods of research and ensuring robust stability of interval dynamic systems of both algebraic and frequency directions of robust stability. The main results of the original algebraic method of robust stability for continuous and discrete time are given. In the frequency direction of robust stability, the issues of a frequency-robust method to the analysis and synthesis of robust multidimensional control systems based on the use of the frequency condition number of the transfer matrix of the “input-output” ratio are considered. The main provisions of the theory and method of topological roughness of dynamic systems based on the concept of roughness according to Andronov-Pontryagin are presented with the introduction of a measure of roughness of systems in the form of a condition number of matrices of reduction to a diagonal (quasi-diagonal) basis at special points of phase space. Criteria for dynamic systems bifurcations are formulated. Applications of the topological roughness method to synergetic systems and chaos have been used to investigate many systems, such as Lorenz and Rössler attractors, Belousov-Jabotinsky, Chua systems, “predator-prey” and “predator-prey-food”, Hopf bifurcation, Schumpeter and Caldor economic systems, Henon mapping, and others. For research of weakly formalized and non-formalized systems, the use of the approach of analogies of theoretical-multiple topology and the abstract method to such systems is proposed. Further research suggests the development of roughness and bifurcation theories for complex nonlinear dynamical systems.

Biomimetic virus-like mesoporous silica nanoparticles improved cellular internalization for co-delivery of antigen and agonist to enhance Tumor immunotherapy

Nanocarrier antigen-drug delivery system interacts specifically with immune cells and provides intelligent delivery modes to improve antigen delivery efficiency and facilitate immune progression. However, these nanoparticles often have weak adhesion to cells, followed by insufficient cell absorption, leading to a failed immune response. Inspired by the structure and function of viruses, virus-like mesoporous silica nanoparticles (VMSNs) were prepared by simulating the surface structure, centripetal-radialized spike structure and rough surface topology of the virus and co-acted with the toll-like receptor 7/8 agonist imiquimod (IMQ) and antigens oocyte albumin (OVA). Compared to the conventional spherical mesoporous silica nanoparticles (MSNs), VMSNs which was proven to be biocompatible in both cellular and in vivo level, had higher cell invasion ability and unique endocytosis pathway that was released from lysosomes and promoted antigen cross-expression. Furthermore, VMSNs effectively inhibited B16-OVA tumor growth by activating DCs maturation and increasing the proportion of CD8+ T cells. This work demonstrated that virus-like mesoporous silica nanoparticles co-supply OVA and IMQ, could induce potent tumor immune responses and inhibit tumor growth as a consequence of the surface spike structure induces a robust cellular immune response, and undoubtedly provided a good basis for further optimizing the nanovaccine delivery system.

Bioinspired Graphene Oxide-Magnetite Nanocomposite Coatings as Protective Superhydrophobic Antifouling Surfaces.

Antifouling (AF) nanocoatings made of polydimethylsiloxane (PDMS) are more cost-efficient and eco-friendly substitutes for the already outlawed tributyltin-based coatings. Here, a catalytic hydrosilation approach was used to construct a design inspired by composite mosquito eyes from non-toxic PDMS nanocomposites filled with graphene oxide (GO) nanosheets decorated with magnetite nanospheres (GO-Fe3O4 nanospheres). Various GO-Fe3O4 hybrid nanofillers were dispersed into the PDMS resin through a solution casting method to evaluate the structure-property relationship. A simple coprecipitation procedure was used to fabricate magnetite nanospheres with an average diameter of 30-50 nm, a single crystal structure, and a predominant (311) lattice plane. The uniform bioinspired superhydrophobic PDMS/GO-Fe3O4 nanocomposite surface produced had a micro-/nano-roughness, low surface-free energy (SFE), and high fouling release (FR) efficiency. It exhibited several advantages including simplicity, ease of large-area fabrication, and a simultaneous offering of dual micro-/nano-scale structures simply via a one-step solution casting process for a wide variety of materials. The superhydrophobicity, SFE, and rough topology have been studied as surface properties of the unfilled silicone and the bioinspired PDMS/GO-Fe3O4 nanocomposites. The coatings' physical, mechanical, and anticorrosive features were also taken into account. Several microorganisms were employed to examine the fouling resistance of the coated specimens for 1 month. Good dispersion of GO-Fe3O4 hybrid fillers in the PDMS coating until 1 wt % achieved the highest water contact angle (158° ± 2°), the lowest SFE (12.06 mN/m), micro-/nano-roughness, and improved bulk mechanical and anticorrosion properties. The well-distributed PDMS/GO-Fe3O4 (1 wt % nanofillers) bioinspired nanocoating showed the least biodegradability against all the tested microorganisms [Kocuria rhizophila (2.047%), Pseudomonas aeruginosa (1.961%), and Candida albicans (1.924%)]. We successfully developed non-toxic, low-cost, and economical nanostructured superhydrophobic FR composite coatings for long-term ship hull coatings. This study may expand the applications of bio-inspired functional materials because for multiple AF, durability and hydrophobicity are both important features in several industrial applications.

Bipolar soft ideal rough set with applications in COVID-19

Bipolar soft rough set represents an important mathematical model to deal with uncertainty. This theory represents a link between bipolar soft set and rough set theories. This study introduced the concept of topological bipolar soft set by combining a bipolar soft set with topologies. Also, the topological structure of bipolar soft rough set has been discussed by defining the bipolar soft rough topology. The main objective of this paper is to present some solutions to develop and modify the approach of the bipolar soft rough sets. Two kinds of bipolar soft ideal approximation operators which represent extensions of bipolar soft rough approximation operator have been presented. Moreover, a new kind of bipolar approximation space via two ideals, called bipolar soft biideal approximation space, was introduced and studied by two different methods. Their properties are discussed and the relationships between these methods and the previous ones are proposed. The importance of these methods is reducing the vagueness of uncertainty areas by increasing the bipolar lower approximations and decreasing the bipolar upper approximations. Also, the bipolar soft biideal rough sets represent two opinions instead of one opinion. Finally, an application in multicriteria group decision making (MCGDM) in COVID-19 by using bipolar soft ideal rough sets is suggested by using two methods.

New extensions of fuzzy sets with applications to rough topology and medical diagnosis

New extensions of fuzzy sets with applications to rough topology and medical diagnosis

Topology on Rough Pentapartitioned Neutrosophic Set

The main focus of this article is to introduce the notion of rough pentapartitioned neutrosophic set and rough pentapartitioned neutrosophic topology by using rough pentapartitioned neutrosophic lower approximation, rough pentapartitioned neutrosophic upper approximation, and rough pentapartitioned neutrosophic boundary region. Then, we provide some basic properties, namely operations on rough pentapartitioned neutrosophic set and rough pentapartitioned neutrosophic topology. By defining rough pentapartitioned neutrosophic set and topology, we formulate some results in the form of theorems, propositions, etc. Further, we give some examples to justify the definitions introduced in this article.

Characterizing Streamwise Development of Surface Roughness Effects on a Supersonic Boundary Layer

Two-component particle image velocimetry was employed to measure the influence of surface roughness on a Mach 2 boundary layer. Three surface conditions were examined: a smooth wall, patterned diamond-shaped roughness, and an approximately random realistic roughness. The response of the boundary layer was characterized in ensemble-averaged measurements of the mean velocity and Reynolds stresses. The streamwise development of the mechanical distortions introduced by the diamond-shaped roughness was also explored through observation of roughness-generated shock waves and changes in the boundary-layer profile. Measurements acquired at three streamwise locations are consistent with the trends observed in other studies when scaled by the roughness friction velocity. Ensemble-averaged outer-scaled streamwise velocity profiles showed a velocity deficit in the near-wall region. Inner-scaled boundary-layer profiles showed a downward vertical shift in the scaled velocities of 4.5 and 3 for the diamond roughness and nonuniform/realistic roughness topologies, respectively. These values show similar responses to the results seen in the literature for similar test conditions. The roughness effects were shown to increase in magnitude along the streamwise distance.