Convexity-preserving scattered data interpolation

This study deals with constructing a convexity-preserving bivariate C1 interpolants to scattered data whenever the original data are convex. Sufficient conditions on lower bound of Bezier points are derived in order to ensure that surfaces comprising cubic Bezier triangular patches are always convex and satisfy C1 continuity conditions. Initial gradients at the data sites are estimated and then modified if necessary to ensure that these conditions are satisfied. The construction is local and easy to be implemented. Graphical examples are presented using several test functions

Performance of the triangulation-based methods Of positivity-preserving scattered data interpolation

We present the result and accuracy comparison of generalized positivity-preserving schemes for triangular Bézier patches of 1C and 2C scattered data interpolants that have been c on structed. We compare three methods of 1C schemes using cubic triangular Bézier patches and one 2C scheme using quintic triangular Bézier patches.Our test case consists of four sets of node/test function pairs, with node-count ranging from 26 to 100 data points. The absolute maximum and mean errors are computed using 33×33 evaluation points on a uniform rectangular grid

Positivity-preserving scattered data interpolating surface using C1 piecewise cubic triangular patches

The construction of a bivariate C1 interpolant to scattered data is considered in which the interpolant is positive everywhere if the original data are positive. This study is motivated by earlier work in which sufficient conditions are derived on Bezier points in order to ensure that surfaces comprising cubic Bezier triangular patches are always positive and satisfy C1 continuity conditions. Initial gradients at the data sites are estimated and then modified if necessary to ensure that these conditions are satisfied. The construction is local and easy to implement. Graphical examples are presented using two test function

Range restricted positivity-preserving G1 scattered data interpolation

The construction of a range restricted bivariate G1 interpolant to scattered data is considered in which the interpolant is positive everywhere if the original data are positive. This study is motivated by earlier work in which sufficient conditions are derived on Bézier points in order to ensure that surfaces comprising quartic Bézier triangular patches are always positive and satisfy G1 continuity conditions. The gradients at the data sites are then calculated (and modified if necessary) to ensure that these conditions are satisfied. Its construction is local and easily extended to include as upper and lower constraints to the interpolating surfaces of the form z = C(x,y) where C is a polynomial of degree less or equal to 4. Moreover, G1 piecewise polynomial surfaces consisting of polynomial pieces of the form z = C(x,y) on the triangulation of the data sites are also admissible constraints. A number of examples are presented

Intraperitoneal drain placement and outcomes after elective colorectal surgery: international matched, prospective, cohort study

Despite current guidelines, intraperitoneal drain placement after elective colorectal surgery remains widespread. Drains were not associated with earlier detection of intraperitoneal collections, but were associated with prolonged hospital stay and increased risk of surgical-site infections.Background Many surgeons routinely place intraperitoneal drains after elective colorectal surgery. However, enhanced recovery after surgery guidelines recommend against their routine use owing to a lack of clear clinical benefit. This study aimed to describe international variation in intraperitoneal drain placement and the safety of this practice. Methods COMPASS (COMPlicAted intra-abdominal collectionS after colorectal Surgery) was a prospective, international, cohort study which enrolled consecutive adults undergoing elective colorectal surgery (February to March 2020). The primary outcome was the rate of intraperitoneal drain placement. Secondary outcomes included: rate and time to diagnosis of postoperative intraperitoneal collections; rate of surgical site infections (SSIs); time to discharge; and 30-day major postoperative complications (Clavien-Dindo grade at least III). After propensity score matching, multivariable logistic regression and Cox proportional hazards regression were used to estimate the independent association of the secondary outcomes with drain placement. Results Overall, 1805 patients from 22 countries were included (798 women, 44.2 per cent; median age 67.0 years). The drain insertion rate was 51.9 per cent (937 patients). After matching, drains were not associated with reduced rates (odds ratio (OR) 1.33, 95 per cent c.i. 0.79 to 2.23; P = 0.287) or earlier detection (hazard ratio (HR) 0.87, 0.33 to 2.31; P = 0.780) of collections. Although not associated with worse major postoperative complications (OR 1.09, 0.68 to 1.75; P = 0.709), drains were associated with delayed hospital discharge (HR 0.58, 0.52 to 0.66; P < 0.001) and an increased risk of SSIs (OR 2.47, 1.50 to 4.05; P < 0.001). Conclusion Intraperitoneal drain placement after elective colorectal surgery is not associated with earlier detection of postoperative collections, but prolongs hospital stay and increases SSI risk

Pre-treatment of Malaysian agricultural wastes toward biofuel production

Various renewable energy technologies are under considerable interest due to the projected depletion of our primary sources of energy and global warming associated with their utilizations. One of the alternatives under focus is renewable fuels produced from agricultural wastes. Malaysia, being one of the largest producers of palm oil, generates abundant agricultural wastes such as fibers, shells, fronds, and trunks with the potential to be converted to biofuels. However, prior to conversion of these materials to useful products, pre-treatment of biomass is essential as it influences the energy utilization in the conversion process and feedstock quality. This chapter focuses on pre-treatment technology of palm-based agriculture waste prior to conversion to solid, liquid, and gas fuel. Pre-treatment methods can be classified into physical, thermal, biological, and chemicals or any combination of these methods. Selecting the most suitable pre-treatment method could be very challenging due to complexities of biomass properties. Physical treatment involves grinding and sieving of biomass into various particle sizes whereas thermal treatment consists of pyrolysis and torrefaction processes. Additionally biological and chemical treatment using enzymes and chemicals to derive lignin from biomass are also discussed

PENGARUH ABU VULKANIK TERHADAP KUAT GESER DAN PERMEABILITAS TANAH LEMPUNG YANG DISTABILISASI KAPUR

Clay soil is a fine-grained soil types, which have the nature and development of high shrinkage, high consistency index, and strong support is low. In this study tried utilizing merapi ash (volcanic ash), combined with lime as an ingredient stability to resolve the issue. The research was carried out by mixing the original soil stabilization materials into six variations. Ash mixtures respectively variation of 5%, 10%, 15%, 20%, 25%, and 30%, of the dry weight of the soil. For all variations of the same limestone at 5%, of the dry weight of the soil. Tests were conducted that test the physical properties and mechanical properties test. Results of original research in soil that has been mixed with ash and lime merapi showed that the greater the ash content is given, the value of the plasticity index tends to be small, and the sliding angle increases however, the value of cohesion, and decreased permeability values. Based on these results, changes in the properties of the physical and mechanical properties after the original soil stabilized, then the optimal mixture that can be used for stability soil is mixed with a variety of merapi ash mixture of 15% + 5% lime or ash merapi variation of 20% + 5% lime. Dissolved heavy metal content is still safe for the environment, because the amount is very small and does not exceed the specified threshold standard in the indonesian government regulation no.. 20 of 1990

Visualization of rainfall data distribution using quintic triangular Bezier patches

This paper discusses the use of a C2 interpolant which is positive everywhere and the need to preserve positivity in the case of visualization of rainfall data distribution of Peninsular Malaysia. The results from our previous work, where sufficient conditions on Bezier points have been derived, will be used in order to ensure that surfaces comprising quintic Bezier triangular patches are always positive. The first and second derivatives at the data sites are calculated and modified (if necessary) to ensure that these conditions are satisfied. A number of examples are presented based on the average monthly rainfall data in a particular year at various locations in Peninsular Malaysia

Range restricted positivity-preserving scattered data interpolation

The construction of a range restricted bivariate C1( or G1) interpolant to scattered data is considered in which the interpolant is positive everywhere if the original data are positive. This study is motivated by earlier work in which sufficient conditions are derived on Bézier points in order to ensure that surfaces comprising cubic Bézier triangular patches are always positive and satisfy C1 continuity conditions. In the current work, simpler and more relaxed conditions are derived on the Bézier points. The gradients at the data sites are then calculated (and modified if necessary) to ensure that these conditions are satisfied. Each triangular patch of the interpolating surface is formed as a convex combination of three quartic Bézier triangular patches.Its construction is local and easily extended to include as upper and lower constraints to the interpolant surfaces of the form z = P(x,y) where P is a polynomial of degree less or equal to 4. Moreover, C1 ( or G1 ) piecewise polynomial surfaces consisting of polynomial pieces of the form z = P(x,y) on the triangulation of the data sites are also admissible constraints. A number of examples are presented