scholarly journals Construction of C1 Rational Bi-Quartic Spline With Positivity-Preserving Interpolation: Numerical Results and Analysis

2021 ◽  
Vol 9 ◽  
Author(s):  
Samsul Ariffin Abdul Karim ◽  
Azizan Saaban ◽  
Van Thien Nguyen
Keyword(s):  
Boundary Curve ◽  
Coefficient Of Determination ◽  
Test Functions ◽  
Shape Modification ◽  
First Order ◽  
Surface Data ◽  
Four Corners ◽  
The Given ◽  
Curve Networks ◽  
Statistical Indicators

From the observed datasets, we should be able to produce curve surfaces that have the same characteristics as the original datasets. For instance, if the given data are positive, then the resulting curve or surface must be positive on entire given intervals, i.e., everywhere. In this study, a new partial blended rational bi-quartic spline with C1 continuity is constructed through the partially blended scheme. This rational spline is defined on four corners of the rectangular meshes. The sufficient condition for the positivity of rational bi-quartic spline is derived on four boundary curve networks. There are eight free parameters that can be used for shape modification. The first-order partial derivatives are estimated by using numerical techniques. We also show that the proposed scheme is local quadratic reproducing such that it can exactly reproduce the quadratic surface. We test the proposed scheme to interpolate various types of positive surface data. Based on statistical indicators such as the root mean square error (RMSE) and coefficient of determination (R2), we found that the proposed scheme is on par with some established schemes. In fact, it requires less CPU times (in seconds) to generate the interpolating surface on rectangular meshes. Furthermore, by combining the statistical indicators’ result and graphically visualizing the test functions, the proposed method has the capability to reconstruct very comparable smoothing interpolating positive surfaces compared to some existing schemes. This finding is significant in producing a better interpolating surface for computer graphics applications since the proposed scheme has a smaller error compared with existing schemes.

scholarly journals Positivity and Monotonicity Preserving Biquartic Rational Interpolation Spline Surface

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Xinru Liu ◽  
Yuanpeng Zhu ◽  
Shengjun Liu
Keyword(s):  
Sufficient Conditions ◽  
Rational Interpolation ◽  
Rectangular Domain ◽  
Interpolation Spline ◽  
Spline Surface ◽  
Surface Data ◽  
Shape Preserving Interpolation ◽  
The Given ◽  
Surface Construction ◽  
Special Case

A biquartic rational interpolation spline surface over rectangular domain is constructed in this paper, which includes the classical bicubic Coons surface as a special case. Sufficient conditions for generating shape preserving interpolation splines for positive or monotonic surface data are deduced. The given numeric experiments show our method can deal with surface construction from positive or monotonic data effectively.

scholarly journals Photostability study of amlodipine besylate tablets packed in primary packaging

2021 ◽  
Vol 10 (1) ◽  
pp. 20-28
Author(s):  
Ivana Savić-Gajić ◽  
Ivan Savić ◽  
Predrag Sibinović ◽  
Valentina Marinković
Keyword(s):  
Mobile Phase ◽  
Limit Of Detection ◽  
Degradation Products ◽  
Hplc Method ◽  
Coefficient Of Determination ◽  
Amlodipine Besylate ◽  
Limit Of Quantification ◽  
First Order Kinetics ◽  
The Given

In this study, the modified stability-indicating RP-HPLC method was validated for quantitative analysis of amlodipine besylate in the presence of its impurity D (3-ethyl 5-methyl 2-[(2-aminoethoxy)methyl]-4-(2-chlorophenyl)-6-methylpyridine-3,5-dicarboxylate). The method was applied for the determination of an analyte in the tablets and irradiated samples packed in the primary packaging (Alu/PVC/PVDC blister packaging). The efficient chromatographic separation was achieved using a ZORBAX Eclipse XDB-C18 column (4.6×250 mm, 5 mm) with isocratic elution of mobile phase which consisted of acetonitrile:methanol:triethylamine solution (15:35:50, v/v/v) (pH 3.0). The flow rate of the mobile phase was 1 mL min-1, while the detection of amlodipine besylate was carried out at 273 nm. Amlodipine besylate and its impurity D were identified at the retention times of 16.529 min and 2.575 min, respectively. The linearity of the method with the coefficient of determination of 0.999 was confirmed in the concentration range of 10 - 75 µg mL-1 for amlodipine besylate. The limit of detection was 0.2 µg mL-1, while the limit of quantification was 0.66 µg mL-1. After UV and Vis radiation of the tablets packed in the primary packaging, the content of amlodipine besylate was reduced by 22.38% and 19.89%, respectively. The presence of new degradation products was not detected under the given chromatographic conditions. The photodegradation of amlodipine besylate followed pseudo-first-order kinetics. Based on the half-life of amlodipine besylate (38.4 days for UV radiation and 43.3 days for Vis radiation), it was concluded that amlodipine besylate in the tablets has satisfactory photostability after its packing in the Alu/PVC/PVDC blister packaging.

scholarly journals Climatologia da Chuva em Maceió: Aspectos Climáticos e Ambientais

2021 ◽  
Vol 14 (4) ◽  
pp. 2253-2264
Author(s):  
José Francisco de Oliveira Júnior ◽  
Pedro Henrique de Almeida Souza ◽  
Edson de Oliveira Souza ◽  
Mário Henrique Guilherme dos santos Vanderlei ◽  
Washington Luiz Félix Correia Filho ◽  
...  
Keyword(s):  
Land Surface ◽  
Decadal Variability ◽  
Coefficient Of Determination ◽  
Rainfall Regime ◽  
Environmental Aspects ◽  
High Coefficient ◽  
Precipitation Product ◽  
Surface Areas ◽  
Period 2 ◽  
Statistical Indicators

The objectives of the study are: i) to evaluate the climatology of rain in Maceió based on observed data, with emphasis on climatic and environmental aspects and ii) to validate the precipitation product for the municipality. Data from 1979 to 2013 of the precipitation product CHELSA (Climatologies at High Resolution for the Earth's Land Surface Areas) were validated by rainfall data from the National Water Agency (NWA) from 1960 to 2016. Statistical indicators showed a high coefficient of determination and linear correlation between CHELSA and observed data (R2 = 0.80; r = 0.89) and the smallest errors (SEE = 6.58 mm and RMSE = 18.76 mm), therefore the CHELSA product can be applied in the region. The time series presented a period 1 (P1) - (1960 to 1989) with rainfall above the historical average and a period 2 (P2) - (1990 to 2016) with a significant reduction in rainfall. Observed data versus climatological normals showed a significant decrease in normal 1 (1961-1990) in the rainy season, while in relation to normal 2 (1981-2010) there was an increase in the months of February, March and April (between 10 to 20%) and October and December (between 5 to 15%). The spatial distribution of monthly rainfall via the CHELSA product showed the formation of a pluviometric gradient between the coast and the upper part of Maceió. The topography influences the rainfall regime in neighborhoods belonging to the administrative regions (AR) - (R4, R5 and R6) with the highest rainfall records. The ENOS phases are directly responsible for the variability of interannual rain, while the decadal variability corresponded to the PDO phase change and changes in land use and occupation in Maceió.

On two pursuit differential game problems with state and geometric constraints in a Hilbert space

2021 ◽  
Vol 65 (3) ◽  
pp. 5-16
Author(s):  
Abbas Ja’afaru Badakaya ◽  
Keyword(s):  
Differential Game ◽  
Convex Set ◽  
Sufficient Conditions ◽  
Nonempty Closed Convex Subset ◽  
Geometric Constraints ◽  
First Order ◽  
Control Functions ◽  
Closed Convex Set ◽  
The Given ◽  
First Order Differential Equations

This paper concerns with the study of two pursuit differential game problems of many pursuers and many evaders on a nonempty closed convex subset of R^n. Throughout the period of the games, players must stay within the given closed convex set. Players’ laws of motion are defined by certain first order differential equations. Control functions of the pursuers and evaders are subject to geometric constraints. Pursuit is said to be completed if the geometric position of each of the evader coincides with that of a pursuer. We proved two theorems each of which is solution to a problem. Sufficient conditions for the completion of pursuit are provided in each of the theorems. Moreover, we constructed strategies of the pursuers that ensure completion of pursuit.

scholarly journals Effect of inoculum to substrate ratio on biogas production of sheep paunch manure

2016 ◽  
Vol 62 (No. 1) ◽  
pp. 8-14 ◽  
Author(s):  
A.A. Lawal ◽  
A.U. Dzivama ◽  
M.K. Wasinda
Keyword(s):  
Biogas Production ◽  
Coefficient Of Determination ◽  
Order Kinetic ◽  
Production Rates ◽  
Exponential Equation ◽  
First Order ◽  
Gompertz Equation ◽  
Volatile Solids ◽  
Substrate Ratio ◽  
Order Kinetic Equation

Sheep paunch manure was anaerobically digested to study the effect of inoculum to substrate ratio on biogas production rates and accumulation. Inoculum to substrate ratios of 1.37, 2.05 and 4.1 were digested in biodigesters labelled R1, R2 and <br /> R3 respectively. Results showed that inoculum to substrate ratio had a significant effect on biogas production rates and accumulation. Biogas production rates increased to peak in the order of R3 (0.30526 Nm<sup>3</sup>/kg volatile solids (VS) days), R2 (0.15308 Nm<sup>3</sup>/kg VS d) and R1 (0.11009 Nm<sup>3</sup>/kg VS d) on the 5<sup>th</sup> day. The biogas production accumulation increased from 0.57195 to 1.46784 Nm<sup>3</sup>/kg VS as the inoculum to substrate ratio increased. The result of regression showed that coefficient of determination values for the linear equation ranged from 0.707 to 0.797, while the exponential equation had higher values that ranged from 0.7718 to 0.9929 showing better simulation. The modified Gompertz equation showed better simulation of the biogas production accumulation than the first order kinetic equation due to its higher coefficient of determination values.

scholarly journals Spectrum of a Differential Operator with Periodic Generalized Potential

2007 ◽  
Vol 2007 ◽  
pp. 1-8
Author(s):  
Mehmet Sahin ◽  
Manaf Dzh. Manafov
Keyword(s):  
Differential Operator ◽  
Infinite Number ◽  
Periodic Potential ◽  
Generalized Functions ◽  
Order Differential Operator ◽  
Nonzero Constant ◽  
Classic Case ◽  
First Order ◽  
Generalized Potential ◽  
The Given

We study some spectral problems for a second-order differential operator with periodic potential. Notice that the given potential is a sum of zero- and first-order generalized functions. It is shown that the spectrum of the investigated operator consists of infinite number of gaps whose length limit unlike the classic case tends to nonzero constant in some place and to infinity in other place.

Error bounds on multivariate Normal approximations for word count statistics

2002 ◽  
Vol 34 (03) ◽  
pp. 559-586 ◽  
Author(s):  
Haiyan Huang
Keyword(s):  
Covariance Matrix ◽  
Error Bounds ◽  
Multivariate Distribution ◽  
Finite Alphabet ◽  
Multivariate Normal ◽  
Word Count ◽  
First Order ◽  
Normal Approximations ◽  
Necessary And Sufficient ◽  
The Given

Given a sequence S and a collection Ω of d words, it is of interest in many applications to characterize the multivariate distribution of the vector of counts U = (N(S,w 1), …, N(S,w d )), where N(S,w) is the number of times a word w ∈ Ω appears in the sequence S. We obtain an explicit bound on the error made when approximating the multivariate distribution of U by the normal distribution, when the underlying sequence is i.i.d. or first-order stationary Markov over a finite alphabet. When the limiting covariance matrix of U is nonsingular, the error bounds decay at rate O ((log n) / √n) in the i.i.d. case and O ((log n)3 / √n) in the Markov case. In order for U to have a nondegenerate covariance matrix, it is necessary and sufficient that the counted word set Ω is not full, that is, that Ω is not the collection of all possible words of some length k over the given finite alphabet. To supply the bounds on the error, we use a version of Stein's method.

SURFACE-COVERED 1×3 GRATING WITH DIELECTRIC-METAL SLABS UNDER SECOND BRAGG INCIDENCE

2020 ◽  
Vol 27 (09) ◽  
pp. 1950201
Author(s):  
CHEN FU ◽  
BO WANG ◽  
WENHUA ZHU ◽  
KUNHUA WEN ◽  
ZIMING MENG ◽  
...  
Keyword(s):  
Incident Light ◽  
Polarized Light ◽  
Transverse Magnetic ◽  
Second Order ◽  
Bragg Angle ◽  
Efficiency Ratio ◽  
First Order ◽  
Rigorous Coupled Wave Analysis ◽  
Rigorous Coupled Wave ◽  
The Given

This paper designed a novel three-port reflective surface-covered grating with a connecting layer. The grating can be used as a splitter, and the polarized light can be divided into zero order, first order and second order. Through rigorous coupled-wave analysis, the efficiency of the three orders of diffraction light is close to 33% under the condition that the incident light at 1550 nm is incident at the second Bragg angle and the given duty cycle is 0.5. The efficiency and bandwidth of the surface-covered grating are improved compared with that of the surface-relief grating reported in the past. Especially for transverse magnetic polarized light, the beam splitting effect is more uniform, the efficiency ratio of the zeroth order to first order can reach 1.01, and the efficiency ratio of the first order to second order can reach 1.

Time Series Analysis of New Cars Sale in Bosnia and Herzegovina

2015 ◽  
Vol 806 ◽  
pp. 287-293
Author(s):  
Esad Jakupović ◽  
Vladimir Stojanović ◽  
Sanel Jakupović ◽  
Dragana Trnavac
Keyword(s):  
Time Series ◽  
Bosnia And Herzegovina ◽  
Polynomial Regression ◽  
Growth Index ◽  
Coefficient Of Determination ◽  
Chain Growth ◽  
Degree Polynomial ◽  
Car Sales ◽  
The Given ◽  
Polynomial Regression Model

The paper provides analysis of new car sales in Bosnia and Herzegovina for the period 2007-2014. For the examined period new car sales in B&H was reduced by 53.67%, from 12449 in 2007 to 6682 in 2014. The trend can be approximated using 3rd degree polynomial regression model with coefficient of determination R2=0,845. Most new cars sold were by Skoda and least was sold by Porsche. Total number of sold vehicles for this period was 73152. We also present annual growth, chain growth and cumulative growth index for the given period.

scholarly journals Uniqueness issues for evolution equations with density constraints

2016 ◽  
Vol 26 (09) ◽  
pp. 1761-1783 ◽  
Author(s):  
Simone Di Marino ◽  
Alpár Richárd Mészáros
Keyword(s):  
Velocity Field ◽  
Evolution Equations ◽  
Planck Equation ◽  
Wasserstein Distance ◽  
First Order ◽  
Uniqueness Results ◽  
Monotonicity Assumption ◽  
Crowd Motion ◽  
The Given ◽  
Uniqueness Of A Solution

In this paper, we present some basic uniqueness results for evolution equations under density constraints. First, we develop a rigorous proof of a well-known result (among specialists) in the case where the spontaneous velocity field satisfies a monotonicity assumption: we prove the uniqueness of a solution for first-order systems modeling crowd motion with hard congestion effects, introduced recently by Maury et al. The monotonicity of the velocity field implies that the [Formula: see text]-Wasserstein distance along two solutions is [Formula: see text]-contractive, which in particular implies uniqueness. In the case of diffusive models, we prove the uniqueness of a solution passing through the dual equation, where we use some well-known parabolic estimates to conclude an [Formula: see text]-contraction property. In this case, by the regularization effect of the nondegenerate diffusion, the result follows even if the given velocity field is only [Formula: see text] as in the standard Fokker–Planck equation.

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