Fractal Sobolev systems of functions associated with orthonormal systems of functions

This paper introduces the α-fractal Sobolev system of functions corresponding to Sobolev orthonormal system of functions. An approximation-related result similar to Weierstrass theorem is derived. It is shown that the set of α-fractal versions of Sobolev sums is dense and complete in the weighted Sobolev space Wr,2ρ(I). A Schauder basis and a Riesz basis of fractal type for the space Wr,2ρ(I) are found. The Fourier–Sobolev expansion of an α-fractal function fα corresponding to a certain set of interpolation points is presented. Moreover, some results on convergence of Fourier–Sobolev expansion of fα with respect to uniform norm and Sobolev norm are established

Fractal functions on the real projective plane

Formerly the geometry was based on shapes, but since the last centuries this founding mathematical science deals with transformations, projections and mappings. Projective geometry identifies a line with a single point, like the perspective on the horizon line and, due to this fact, it requires a restructuring of the real mathematical and numerical analysis. In particular, the problem of interpolating data must be refocused. In this paper we define a linear structure along with a metric on a projective space, and prove that the space thus constructed is complete. Then we consider an iterated function system giving rise to a fractal interpolation function of a set of data.Comment: 25 pages, 18 figure

Seizure during hyperbaric oxygen therapy for carbon monoxide toxicity: a case series and five-year experience.

BACKGROUND: Hyperbaric oxygen (HBO) therapy is recommended to reduce the delayed neurologic sequelae resulting from carbon monoxide (CO) toxicity. Although HBO is generally well tolerated, there exists a risk of seizure in all patients that may be increased in patients with predisposing factors including: fever, hypothermia, prior seizure, or brain injury. CASE REPORT: We present two cases of patients without known risk factors who experienced seizures associated with HBO therapy during treatment for CO toxicity. CONCLUSION: This facility\u27s 5-year experience and a review of the germane literature are also presented to elucidate the risk factors and incidence of seizures in patients treated with HBO for CO toxicity

OPTIMIZATION OF INJECTION MOLDING PARAMETERS: IMPROVING MECHANICAL PROPERTIES OF KENAF REINFORCED POLYPROPYLENE COMPOSITES

Natural fiber composites offer significant benefits as alternative material composites in terms of renewable materials. Therefore, natural fibers are commonly used in automotive industries primarily as interior and exterior parts. The manufacturing process of the automotive parts is essential to minimize the defects such as residual stress with better mechanical properties. Hence, this study focused on the employment of rational design of experiment (DOE) to determine the optimized injection molding parameters by improving the mechanical properties of kenaf fibers reinforced polypropylene composites. Taguchi method with L27 (34)orthogonal array applied to optimize the injection molding process parameters, based on the highest response of the strength properties generated by S/N ratio using the larger the better. Moreover, ANOVA analysis was employed to evaluate the most significant parameter including injection temperature, injection pressure, holding pressure and injection rate which affected the mechanical properties. The confirmation test was conducted to verify the predicted range of optimum mechanical properties. Results indicated that the optimum injection molding parameter obtained with the injection temperature at 190 °C, injection pressure at 1300 bar, holding pressure at 1900 bar, and the injection rate at 20 cm³/s. Implementing the optimum parameters is able to fabricate better mechanical properties of kenaf/PP composites where most of the confirmation mechanical strength values are evaluated within the predicted range or lie near the acceptable limits

Amino Acid Compositions of 27 Food Fishes and Their Importance in Clinical Nutrition

Proteins and amino acids are important biomolecules which regulate key metabolic pathways and serve as precursors for synthesis of biologically important substances; moreover, amino acids are building blocks of proteins. Fish is an important dietary source of quality animal proteins and amino acids and play important role in human nutrition. In the present investigation, crude protein content and amino acid compositions of important food fishes from different habitats have been studied. Crude protein content was determined by Kjeldahl method and amino acid composition was analyzed by high performance liquid chromatography and information on 27 food fishes was generated. The analysis showed that the cold water species are rich in lysine and aspartic acid, marine fishes in leucine, small indigenous fishes in histidine, and the carps and catfishes in glutamic acid and glycine. The enriched nutrition knowledge base would enhance the utility of fish as a source of quality animal proteins and amino acids and aid in their inclusion in dietary counseling and patient guidance for specific nutritional needs

Non-intrusive polynomial chaos method applied to full-order and reduced problems in computational fluid dynamics: A comparison and perspectives

In this work, Uncertainty Quantification (UQ) based on non-intrusive Polynomial Chaos Expansion (PCE) is applied to the CFD problem of the flow past an airfoil with parameterized angle of attack and inflow velocity. To limit the computational cost associated with each of the simulations required by the non-intrusive UQ algorithm used, we resort to a Reduced Order Model (ROM) based on Proper Orthogonal Decomposition (POD)-Galerkin approach. A first set of results is presented to characterize the accuracy of the POD-Galerkin ROM developed approach with respect to the Full Order Model (FOM) solver (OpenFOAM). A further analysis is then presented to assess how the UQ results are affected by substituting the FOM predictions with the surrogate ROM ones

Soy protein–gum karaya conjugate: emulsifying activity and rheological behavior in aqueous system and oil in water emulsion

The main objective of this study is to investigate the effects of mixing and conjugation of soy protein isolate (SPI) with gum karaya on the characteristics of the hybrid polymer (protein–gum) in both aqueous systems and oil-in-water (O/W) emulsions. It was hypothesized that the covalent linkage of gum karaya with SPI would improve the emulsifying activity and rheological properties of both polymers. Conjugation occurred under controlled conditions (i.e., 60 °C and 75 % relative humidity, 3 days). The conjugated hybrid polymer produced smaller droplet with better uniformity, higher viscosity and stronger emulsifying activity than native gum karaya, suggesting the conjugated polymer provided a bulkier secondary layer with more efficient coverage around oil droplets, thereby inducing stronger resistance against droplet aggregation and flocculation. Emulsions containing the native gum karaya produced the largest droplet size among all prepared emulsions (D 3,2 = 8.6 μm; D 4,3 = 22.4 μm); while the emulsion containing protein–gum conjugate (1:1 g/g) had the smallest droplet size (D 3,2 = 0.2 μm; D 4,3 = 0.7 μm) with lower polydispersity. The protein–gum conjugate (1:1 g/g) also showed the highest elastic and viscous modulus, the lowest polydispersity (span) and the highest emulsifying activity among all native, mixed and conjugated polymers. Therefore, the percentage of gum karaya used for production of O/W emulsion can be decreased by partially replacing it with the conjugated gum

Utilisation of an operative difficulty grading scale for laparoscopic cholecystectomy

Background A reliable system for grading operative difficulty of laparoscopic cholecystectomy would standardise description of findings and reporting of outcomes. The aim of this study was to validate a difficulty grading system (Nassar scale), testing its applicability and consistency in two large prospective datasets. Methods Patient and disease-related variables and 30-day outcomes were identified in two prospective cholecystectomy databases: the multi-centre prospective cohort of 8820 patients from the recent CholeS Study and the single-surgeon series containing 4089 patients. Operative data and patient outcomes were correlated with Nassar operative difficultly scale, using Kendall’s tau for dichotomous variables, or Jonckheere–Terpstra tests for continuous variables. A ROC curve analysis was performed, to quantify the predictive accuracy of the scale for each outcome, with continuous outcomes dichotomised, prior to analysis. Results A higher operative difficulty grade was consistently associated with worse outcomes for the patients in both the reference and CholeS cohorts. The median length of stay increased from 0 to 4 days, and the 30-day complication rate from 7.6 to 24.4% as the difficulty grade increased from 1 to 4/5 (both p < 0.001). In the CholeS cohort, a higher difficulty grade was found to be most strongly associated with conversion to open and 30-day mortality (AUROC = 0.903, 0.822, respectively). On multivariable analysis, the Nassar operative difficultly scale was found to be a significant independent predictor of operative duration, conversion to open surgery, 30-day complications and 30-day reintervention (all p < 0.001). Conclusion We have shown that an operative difficulty scale can standardise the description of operative findings by multiple grades of surgeons to facilitate audit, training assessment and research. It provides a tool for reporting operative findings, disease severity and technical difficulty and can be utilised in future research to reliably compare outcomes according to case mix and intra-operative difficulty