Zero Order Research Articles

Formulation development and evaluation of controlled release matrix tablets of glibenclamide

The present study aimed to formulate and evaluate the controlled-release matrix tablets of Glibenclamide which is an antidiabetic drug that belongs to the second-generation oral hypoglycemics. Matrix tablets were prepared by three different polymers as sustained-release agents, using Glibenclamide as a model drug. Three polymers were selected for this study- HPMC K 15, HPMC K 100, and EC in different drug: polymer ratios. The drug was identified by FTIR spectroscopic method. The pre-compression and post-compression parameters of all formulations were found to be within acceptable limits. The release rate of Glibenclamide from matrix tablets was studied using the USP Dissolution Testing Apparatus type-I (Basket method). The formulation F6 which contained EC 50mg showed a maximum release of 99.28% in 24 hrs and revealed that EC was more effective in sustaining the drug release therefore formulation F6 was selected as the optimized formulation. The in-vitro release data of optimized formulation was fit into various kinetic models, among the different model's data of in-vitro release of best fit into Zero order kinetic model. The formulation best fit the Higuchi model and showed that drug release from the prepared matrix tablets occurs via a diffusion process.

An Order Inventory Model for Delayed Deteriorating Items with Two-Storage Facilities, Time-Varying Demand and Partial Backlogging Rates Under Trade-Credit Policy

The retailer's ideal replenishment strategy for non-instantaneous decaying goods with two-phase demand rates, two storage facilities, and shortages under a permissible payment delay has been determined in this study. While the constant demand rate is considered once deterioration has begun, the demand rate up to that point is believed to be a time-dependent quadratic function. Backlogs and shortages are also taken into consideration. Whether or not the backlog will be accepted depends on how long it will be until the next replenishment. As a result, the backlogging rate fluctuates and depends on how long it takes for the next refill. The models identify the ideal cycle length, order amount, and period at which the inventory level in the owned warehouse reaches zero in order to reduce the overall variable cost per unit of time. For the solutions to exist and be unique, both the necessary and sufficient requirements must be met. The best trade credit period is identified for each model using numerical examples, and the best model among the created models is identified using the best trade credit periods. Sensitivity analysis can offer some managerial insights

Development and Validation of Derivative UV Spectrophotometric method for Simultaneous Determination of Amoxicillin and Clavulanic acid in Tablets (Augmentin 1000mg)

The simultaneous analysis of pharmaceutical mixtures by classical spectrophotometric methods without prior separation is a challenge owing to the strong overlapping of their zero order spectra (low selectivity). Hence, several techniques have been developed for solving this problem, such as derivative spectrophotometry. The aim of this study was to develop a simple, fast, accurate, precise, economical, and eco-friendly derivative spectrophotometric method for the quantitative determination of a binary mixture of amoxicillin (Amox) and clavulanic acid (Clav) without prior separation steps. The developed method is based on the use of first derivative spectra resulting from derivatisation of zero order, with using these parameters (d𝛌=4 and scaling factor=15). The measurements were achieved by using zero-crossing technique (𝛌= 278.5nm for Amox and 𝛌= 228.3nm for Clav), which eliminated the overlapping caused by two drugs and excipients of tablets. The method showed significant linearity in the range (5 45μg/ml with =0.9998) and (1 - 10μg/ml with =0.9986) for Amox and Clav, respectively. The developed technique was validated according to the ICH guidelines. The method was successfully utilized for the simultaneous determination of Amox and Clav in the formulation. The obtained results were statistically compared with the reported method (HPLC) by applying t-test and F-value at 95% confidence level. No significant difference was observed regarding accuracy and precision. Hence,the proposed procedure can be utilized for regular quality control studies as alternative to chromatographic techniques.

Exploring the mystery of soil carbon mineralization: Insights from incubation experiments and kinetic modeling

Soil carbon mineralization is vital for carbon sequestration but affected by factors like soil type and residue quality. Understanding the process and factors is still incomplete, including the interplay between soil properties and organic residues and the need for accurate kinetic models. Research faces significant challenges in describing carbon mineralization dynamics. The present study aimed to investigate carbon mineralization in three soils located in Tamil Nadu, India (S1, S2 and S3) that possess distinct textures. The study also focused on the effects of five different plant residues (Rice, maize, sugarcane, cotton and turmeric) on carbon mineralization in these soils. Incubation experiments were conducted for 150 days, and CO2 evolution was measured at different time intervals of 7, 10, 15, 30, 60, 90, 120 and 150 days. The performance of three kinetic models (Zero order model, exponential kinetic model and first order model) was also evaluated in predicting carbon mineralization using experimental data. The results showed that the rate and extent of carbon mineralization varied significantly among the different soils and residues. The highest carbon mineralization was observed in rice (989.02 µg C/g/day) and maize (966.53 µg C/g/day) residue, while the lowest was in sugarcane (752.09 µg C/g/day) residue. Among the kinetic models, the first-order kinetic model provided the best fit for all treatments (R2=0.98). The findings suggest that soil texture and residue quality play crucial roles in carbon mineralization. The first order kinetic model can be useful for predicting carbon mineralization in different soil-residue systems. These results have implications for managing soil carbon sequestration and mitigating climate change.

Masur–Veech volumes and intersection theory: The principal strata of quadratic differentials

We describe a conjectural formula via intersection numbers for the Masur–Veech volumes of strata of quadratic differentials with prescribed zero orders, and we prove the formula for the case when the zero orders are odd. For the principal strata of quadratic differentials with simple zeros, the formula reduces to computing the top Segre class of the quadratic Hodge bundle, which can be further simplified to certain linear Hodge integrals. An appendix proves that the intersection of this class with ψ-classes can be computed by Eynard–Orantin topological recursion. As applications, we analyze numerical properties of Masur–Veech volumes, area Siegel–Veech constants, and sums of Lyapunov exponents of the principal strata for fixed genus and varying number of zeros, which settles the corresponding conjectures due to Grivaux and Hubert, Fougeron, and elaborated in Andersen et al. We also describe conjectural formulas for area Siegel–Veech constants and sums of Lyapunov exponents for arbitrary affine invariant submanifolds, and verify them for the principal strata.

On the Time Frequency Compactness of the Slepian Basis of Order Zero for Engineering Applications

Time and frequency concentrations of waveforms are often of interest in engineering applications. The Slepian basis of order zero is an index-limited (finite) vector that is known to be optimally concentrated in the frequency domain. This paper proposes a method of mapping the index-limited Slepian basis to a discrete-time vector, hence obtaining a time-limited, discrete-time Slepian basis that is optimally concentrated in frequency. The main result of this note is to demonstrate that the (discrete-time) Slepian basis achieves minimum time-bandwidth compactness under certain conditions. We distinguish between the characteristic (effective) time/bandwidth of the Slepians and their defining time/bandwidth (the time and bandwidth parameters used to generate the Slepian basis). Using two different definitions of effective time and bandwidth of a signal, we show that when the defining time-bandwidth product of the Slepian basis increases, its effective time-bandwidth product tends to a minimum value. This implies that not only are the zeroth order Slepian bases known to be optimally time-limited and band-concentrated basis vectors, but also as their defining time-bandwidth products increase, their effective time-bandwidth properties approach the known minimum compactness allowed by the uncertainty principle. Conclusions are also drawn about the smallest defining time-bandwidth parameters to reach the minimum possible compactness. These conclusions give guidance for applications where the time-bandwidth product is free to be selected and hence may be selected to achieve minimum compactness.

On the rank-part of the Mazur–Tate refined conjecture for higher weight modular forms

Under some assumptions, we prove the rank-part of the Mazur–Tate refined conjecture of BSD type. More concretely, we prove that the rank of the Selmer group of an elliptic modular form is less than or equal to the order of zeros of Mazur–Tate elements, or modular elements, which are elements in certain group rings constructed from special values of the associated L-function. Our main result is regarded as a generalization of our previous work on elliptic curves.

A simple note on the number-theoretic function Omega (n) and Dirichlet L-functions

We give a relation between the orders of potential non-trivial zeros of Dirichlet L-functions and analytic properties of certain Dirichlet series first introduced by Selberg.

Development and in vitro assessment of Analgesic and Anti-inflammatory Mefenamic acid Nanosponge Loaded Topical Formulation

The present research work was done with the objective of topical formulation development of poorly water-soluble drug Mefenamic acid. The drug was firstly incorporated in nanosponge of ethyl cellulose. Then Mefenamic acid nanosponge-loaded topical gel formulations were developed by using Carbopol 934 as a gel-forming polymer. The Mefenamic acid-loaded nanosponges were tested for various quality parameters such as particle size distribution, polydispersity.index(PI),. Surface morphology and drug entrapment efficiency etc. Gel formulations were tested for viscosity, pH, in vitro diffusion and other parameters. The average size of developed nanosponge preparations was found between 250nm to 894nm. Scanning electron microscopy photographs of developed formulations clearly reveal the spongy and porous nature of particles along with spherical shape. The PI was. found in. the range. of 0.206 to 0.934. It was found that formulation N3 with a drug-to-polymer ratio of 1:4 has the highest drug loading. Further nanosponge were characterized for different parameters and results revealed acceptable characteristics of N3 formulation. These prepared nanosponges were loaded in topical Carbopol gel (Formulation G3) and evaluated for in vitro diffusion release. Obtained in vitro data was applied to numerous kinetic models which reveal typical zero order in vitro drug diffusion with prolonged release of Mefenamic acid and therefore it can be effectively used as analgesic and anti-inflammatory formulation.

Stability of natural convection in a vertical layer of Navier-Stokes-Voigt fluid

The stability of natural convection in a vertical layer of viscoelastic fluid confining between rigid-isothermal side walls held at different temperatures is investigated numerically using the Chebyshev collocation method. The viscoelastic behavior is modelled by means of a constitutive equation encompassing the Navier-Stokes-Voigt fluid or the Kelvin-Voigt fluid of order zero. The onset of convective instability is examined by linearizing the governing equations for the perturbations and an appropriate extension of Squire's theorem is given making a case to consider only two-dimensional perturbation stability equations. The numerical solution of the stability eigenvalue problem leads to the determination of the neutral stability condition. The dependence of the Kelvin-Voigt parameter on the critical stability parameters and also on the Prandtl number at which the point of transition from stationary to travelling-wave mode occurs is thoroughly analysed. The Kelvin-Voigt parameter shows an important role on the travelling-wave mode instability where it inducts both stabilizing and destabilizing effects on the base flow depending on the values of Prandtl number, while its impact on the stationary mode is found to be very weak. Furthermore, the streamlines and isotherms of the perturbation modes presented herein demonstrate the development of complex dynamics at the critical state. The results of a Newtonian fluid are obtained as a particular case.

Novel eco-friendly spectrophotometric approaches for resolution of fixed dose formulation of phenylbutazone with minor component of dexamethasone: Greenness assessment by AGREE tool

Spectrophotometric resolution of severely overlapped binary mixtures with minor component is challenging. Herein, coupling of mathematical manipulation steps with sample enrichment was conducted on the binary mixture spectrum of Phenylbutazone (PBZ) and Dexamethasone sodium phosphate (DEX) to resolve, for the first time each component separately. Simultaneous determination of both components in a mixture ratio of 1:0.002 was achieved in their zero or first order spectra by the recent factorized response method along with ratio subtraction and constant multiplication methods; all coupled with spectrum subtraction. In addition, a novel second derivative concentration value and second derivative constant value methods were developed for PBZ determination. The concentration of the minor component DEX was obtained, without preliminary separation steps by derivative ratio after sample enrichment by either spectrum addition or standard addition. Spectrum addition approach showed superior characteristics compared to standard addition technique. All proposed methods were placed through a comparative study. Linear correlation was found to be 1.5–18.0 µg/mL for PBZ, and 4.0–45.0 µg/mL for DEX. The proposed methods were validated in accordance with ICH guidelines. The greenness assessment of the proposed spectrophotometric methods was evaluated by AGREE software. Results obtained from the statistical data were evaluated by comparing to one another as well as the official USP methods. These methods offer a cost and time effective platform to analyze bulk materials and combined veterinary formulation.

FORMULATION DEVELOPMENT AND CHARACTERIZATION OF LAFUTIDINE RAFT SYSTEM

Objective: The present research work is focused to develop in situ raft gel of lafutidine. Sodium alginate is one of the critical components for the development in situ raft system. Methods: The formulation was prepared using hydrophilic polymers such as ethyl cellulose, HPMC K4M, and chitosan. The formulations were subjected to evaluation characteristics such as pH, in vitro gelling time, viscosity, density, gel strength, drug-polymer compatibility studies, drug content floating lag time, swelling index, and in vitro release studies. Results: The pH of all the prepared batches was found in the range of 5.7 to 7.6. All the prepared formulations showed viscosity in the range of 264 to 320 cps, with gelling time from 4-7 s. For F1-F15 batches Floating lag time was found to be in the range of 9-24 sec. Densities of all formulations stomach specific in situ gels were in the range of 0.4 to 0.8 gm/cm3. The highest swelling index was observed in F15 with 14.16% Highest gel strength is exhibited by F15; all the formulations were in the range of 95.46–99.95, indicating the uniform distribution of the drug. Formulation F15 containing chitosan in combination with ethyl cellulose gave the highest drug release of 99.78% and also showed sustained and controlled release for up to 24h. Conclusion: F15 shows an R2 value of 0.999. As its value is nearer to the ‘1’ it is confirmed as it follows the Zero order release with an ‘n’ value is 1.5021 for the optimized formulation (F15) i.e., the n value indicates super case II transport and is considered as optimized formulation.

Effective spectrophotometric methods for resolving the superimposed spectra of Diclofenac Potassium and Methocarbamol

The UV spectra of Diclofenac Potassium DIC and Methocarbamol MET are superimposed making their analysis using direct or derivative spectrophotometric methods quite complicated. This study presents four effective spectrophotometric methods that enable simultaneous determination of both drugs without interference. The first method is based on application of simultaneous equation method on their zero order spectra where DIC has shown absorbance maxima at 276 nm and MET displays two absorbances maxima at 273 nm and 222 nm in distilled water. The second method relies on dual wavelength method, the two wavelengths (232 and 285 nm) were chosen for determination of DIC where the absorbance differences at these wavelengths are proportional to DIC concentration while the absorbance differences of MET are equal to zero. For the determination of MET, the two wavelengths (212 and 228 nm) were selected. The third method of first-derivative ratio has been applied where the derivative ratio absorbances of DIC and MET were measured at 286.1 and 282.4 nm, respectively. The fourth method utilizing ratio difference spectrophotometric (RD) method was eventually performed on the binary mixture. The amplitude difference between the two wavelengths (291and 305 nm) was calculated for DIC estimation while the amplitude difference between the two wavelengths (227and 273 nm) for MET determination. All methods show linearity range from 2.0–25 μg. mL−1 and 6.0–40 μg. mL−1 for DIC and MET respectively. The developed methods have been statistically compared with a reported method based on first derivative method and the results of statistical comparison confirm the accuracy and precision of the proposed methods therefore they can be effectively applied for determination of MET and DIC in pharmaceutical dosage form.

Development and Validation of Novel Analytical Method for Estimation of Diltiazem HCL

A novel, simple, accurate and precise Zero order derivative spectroscopic method was developed and validated for the estimation of Diltiazem HCl in bulk and Pharmaceutical dosage forms and has an absorption maximum at 193 nm in 0.05N Sulphuric acid. The Linearity was found to be in the concentration range of 3-18 μg/ml and the correlation coefficient was found to be 0.998 and it has showed good linearity, reproducibility, precision in this concentration range. The regression equation was found to be Y = 0.0971x + 0.0268 .The % recovery values were found to be within 99.3 -102.06 % showed that the method was accurate. The LOD and LOQ were found to be 0.222 and 0.675μg/ml, respectively. The % RSD values were less than 2. The method has been validated according to ICH guidelines for linearity, accuracy, precision, ruggedness, Limit of detection and limit of quantitation. Proposed method was successfully applied for the quantitative estimation of Diltiazem HCl in bulk and pharmaceutical dosage form.

Orders of Zeros of Polynomials in Solutions to the Fuchsian Differential Equation

Orders of Zeros of Polynomials in Solutions to the Fuchsian Differential Equation

Biological Factors and Multiple Regression Analysis for Human Fertility among Four Different Endogamous Populations of Coastal Andhra Pradesh

Multiple regression analysis was done to examine the impact of the biological factors on fertility. This paper focuses on the biological factors on human fertility. Here fertility is used as the number of children ever born for a woman. This variable is easily measurable. The entire set of variables related to fertility are classified into the important biological factors influencing the fertility are age at marriage, age at menarche, age at first conception and age at last conception. To examine the impact of the factors on fertility by multiple regression analysis and the effect of each group on fertility is discussed separately and collectively. The resultant zero order correlation coefficients indicate that there is no serious problem of multicollinearity in estimated regression model. In all the four population groups, the R2 values are statistically significant which indicates that all the explanatory variables considered in the model together explain 63% of the variation in fertility among Kapu population, 55% among Settibalijas, 50% among Paki’s and 67% among Yerukala population.

Release kinetics modelling and in vivo-vitro, shelf-life study of resveratrol added composite transdermal scaffolds

In this article, the suitability of composite transdermal biomaterial for wound dressing applications is discussed. Bioactive, antioxidant Fucoidan and Chitosan biomaterials were doped into polyvinyl alcohol/β-tricalcium phosphate based polymeric hydrogels loaded with Resveratrol, which has theranostic properties, and biomembrane design with suitable cell regeneration properties was aimed. In accordance with this purpose, tissue profile analysis (TPA) was performed for the bioadhesion properties of composite polymeric biomembranes. Fourier Transform Infrared Spectrometry (FT-IR), Thermogravimetric Analysis (TGA) and Scanning Electron Microscopy (SEM-EDS) analyses were performed for morphological and structural analyses of biomembrane structures. In vitro Franz diffusion mathematical modelling of composite membrane structures, biocompatibility (MTT test) and in vivo rat tests were performed. TPA analysis of resveratrol loaded biomembrane scaffold design; compressibility; 13.4 ± 1.9(g.s), hardness; 16.8 ± 1(g), adhesiveness; −11 ± 2.0(g.s), elasticity; 0.61 ± 0.07, cohesiveness; 0.84 ± 0.04 were found. Proliferation of the membrane scaffold was 189.83 % at 24 h and 209.12 % at 72 h. In the in vivo rat test; at the end of 28th day, it was found that biomembrane_3 provided 98.75 ± 0.12 % wound shrinkage. The shelf-life of RES in the transdermal membrane scaffold, which was determined as Zero order according to Fick's law in in vitro Franz diffusion mathematical modelling, was found to be approximately 35 days by Minitab statistical analysis. The importance of this study is that the innovative and novel transdermal biomaterial supports tissue cell regeneration and cell proliferation in theranostic applications as a wound dressing.

Normal measures on large cardinals

The space of normal measures on a measurable cardinal is naturally ordered by the Mitchell ordering. In the first part of this paper we show that the Mitchell ordering can be linear on a strong cardinal where the Generalised Continuum Hypothesis fails. In the second part we show that a supercompact cardinal at which the Generalised Continuum Hypothesis fails may carry a very large number of normal measures of Mitchell order zero.

Advanced Control Algorithm for Three-Phase Shunt Active Power Filter Using Sliding DFT

This paper describes n digital control algorithm for a three-phase shunt active power filter (APF) using switching–sliding discrete Fourier transform (SSDFT). Traditionally, APF control algorithms use first harmonic detector circuits, which can be implemented using the SDFT algorithm. The classical SDFT algorithm is characterized by long-term stability issues, resulting from numerical errors. Many complex modifications to improve the stability of the SDFT algorithm have been proposed in the scientific literature. This article proposes a solution to the SDFT stability problem using the basic structure of the algorithm. The authors propose the use of the switching SDFT algorithm, where two original SDFT algorithms are implemented in parallel. Both algorithms are turned on alternately after a set period of time and reset to zero in order to reset numerical errors causing their unstable operation. Compared to the classical three-phase SDFT algorithm, the three-phase SSDFT requires only about 25% more arithmetic operations. The proposed approach has been validated using experimental tests and dramatically reduces the numerical errors. The control algorithm has been implemented using the TMS320F28379D microcontroller. The sampling method using only the internal A/D converter of a microcontroller is also presented. The article includes the experimental test results of the complete APF.

Efficacy of alginate and chickpea protein polymeric matrices in encapsulating curcumin for improved stability, sustained release and bioaccessibility

The present study compares the ubiquitously used alginate with seldom used chickpea protein as matrices for encapsulating curcumin, in terms of stability, in vitro release and bioaccessibility. Alginate and chickpea protein particles prepared via ionic gelation and isoelectric precipitation methods, respectively, were in the submicron range showing high encapsulation efficiencies of above 90%. Encapsulated particles stored in dark refrigerated conditions displayed greater stability of curcumin. In vitro release of curcumin from both encapsulated particles exhibited pH-dependent slow controlled release. However, alginate particles were more promising due to a protective role performed at gastric pH. The release profiles of curcumin from alginate and chickpea protein particles were best described by First order and Weibull models at pH 2 respectively, while those were well described by Higuchi and Zero order models at pH 6.8 respectively. Accordingly, release of curcumin from both encapsulated particles displayed diffusional controlled release at pH 2 while that from both particles showed diffusion-swelling controlled release at pH 6.8. Bioaccessibility of curcumin from both matrices after intestinal digestion was around 50% while that of free curcumin was approximately 18%. Overall, results point to alginate having an advantage over the chickpea protein matrix for safe efficacious oral delivery of curcumin. Thus, encapsulation of curcumin in alginate may be a promising method for the engineering of curcumin incorporated food with enhanced properties.