Zero Order Research Articles

Product of Pseudo-Differential Operators Associated with Zero Order Mehler-Fock Transform

Product of Pseudo-Differential Operators Associated with Zero Order Mehler-Fock Transform

On nonlocal Ginzburg-Landau superconductivity and Abrikosov vortex

In this study, the basic concepts of superconductivity based on nonlocal momentum operator have been addressed. The theory is characterized by the presence of higher-order moments and a symmetric kernel which give rise to a higher-derivative superconductivity theory. We have derived the Ginzburg-Landau equations and we have analyzed their properties. The solution has been found to be periodic comparable to the one obtained in chaotic regimes. The magnitude of the coherence length was found to depend on the first moment of order zero. Both decrease of increase in magnitude occurs in semiconductors engineering including hybrid superconductors. It was observed the emergence of bound states in the continuum holding two-degree degenerate energy and the presence of non-periodic vortex arrangement occurring in nano-superconductors. Furthermore, type-III superconductor arises which is characterized by a negative flux, although a weird property, it has been detected thin films superconductor and in type-II superconductors characterize by flux-antiflux interface.

Encapsulation of Milk Protein with Inulin for Improved Digestibility

Encapsulation is the packaging of bioactive compounds to isolate and control their release upon applying specific conditions. By using inulin as the wall material for milk protein encapsulation, it can improve the stability and reduce the rate of protein release which can be related to better digestibility. This study aims to find the best encapsulation parameters for milk protein encapsulation using inulin based on the encapsulation efficiency and evaluate the protein release by simulation of intestinal fluid in vitro. Protein encapsulation was prepared under various parameters including inulin concentration, stirring temperature and stirring speed. The encapsulation parameters were analysed by Response Surface Methodology to obtain the highest encapsulation efficiency, which was subsequently used for the analysis of particle size, zeta potential and protein release kinetics. The results showed that inulin concentration was the most significant in determining encapsulation efficiency, and the highest encapsulation efficiency (75.90%) was achieved at 0.47 % w/v of inulin concentration, stirring temperature of 35.17°C and stirring speed of 510.79 rpm. The inulin-encapsulated milk protein produced under the best encapsulation parameters had an average particle size value of 485.8 nm and zeta potential of -10.5 mV. Zero order kinetics model was most suited to describe the encapsulated milk protein release, indicating slow release of protein that may be associated with better digestibility.

Formulation and optimization of Paliperidone palmitate biodegradable injectable microspheres using Box-Behnken design

The objective of study was to formulate and optimize poly lactic-co-glycolic acid based long-acting injectable microspheres of Paliperidone palmitate (PP) using Box- Behnken design for treatment of schizophrenia. The oral bioavailability of PP is 28%, it necessitates the formulation of PP in injectable dosage form. In this study, PP microspheres were manufactured using oil in water (O/W) emulsion solvent evaporation technique. Box-Behnken design was selected to study effect of independent variables (X) on dependent variables (Y). Independent variables in this study were drug: polymer ratio (X1), homogenization speed (X2), rate of addition (X3). While mean particle size (Y1), drug loading (Y2), entrapment efficiency (Y3), burst release (Y4) and drug release on day 21 (Y5) were considered as dependent variables. The statistical evaluation of data was performed by using Design Expert software. Size of formulated microspheres was studied using laser diffraction technique. The shape of particles was determined using digital microscope and scanning electron microscopy (SEM). Drug release was studied using controlled temperature shaking water bath apparatus. Fourier transforms infrared spectroscopy (FTIR) and differential scanning calorimetric (DSC) study was carried out to detect any incompatibility. Nuclear magnetic resonance (NMR) techniques were used to characterize end cap and monomer ratio in developed microspheres. The prepared PP microspheres exhibited smooth surface and spherical shape. Box-Behnken design was employed for optimization of microspheres. Mean particle size of prepared PP microspheres was found to be in between 12 ± 3.7 μm and 152 ± 3.4 μm. Drug loading in prepared microspheres was found in between 19.4 ± 0.2% to 46.5 ± 0.7%. Entrapment efficiency of prepared microspheres was obtained between 58.6 ± 0.8% and 96.8 ± 1.4%. Drug release from PP microspheres was observed as near zero order. The observed and predicted values of all responses were in close agreement with each other. End cap analysis and molar ratio of Lactic acid: Glycolic acid for formulated microspheres was found to be ester end cap and ∼75:25 respectively. The optimized PP microspheres were capable of releasing drug in vitro up to 28 days. The optimized novel PP injectable microspheres are having profound advantages over conventional oral drug delivery systems in treatment of schizophrenia.

Development of hydrogel based on Carboxymethyl cellulose/poly(4-vinylpyridine) for controlled releasing of fertilizers

A novel Carboxymethyl cellulose (CMC) and poly (4-vinylpyridine) (P4VP) hydrogel system is synthesized with different ratios, in the presence of cross-linker N, N,- methylene bis-acrylamide (MBA). The hydrogel is characterized via FTIR spectroscopy, thermal gravimetric analysis (TGA), X-ray diffraction (XRD), and scanning electron microscope (SEM). The FTIR results showed a strong interaction between both CMC, P4VP and the loaded fertilizer. The water uptake of the hydrogel was evaluated by swelling tests under variations in pH, biodegradability was investigated in soil to simulate real-world conditions. To determine the best release behavior of urea and calcium nitrate from the hydrogel, fertilizers were loaded with different ratios onto the hydrogel during its formation. Fertilizers release was followed by Atomic absorption spectroscopy to study the release of calcium nitrate and urea. Release kinetic parameters were obtained based on different mathematical models as Zero order, First order, Korsmeyer–Peppas and Higuchi models. The suitable proportionality between the mathematical models used and the fertilizers release was determined based on the correlation coefficients (R2). According to Zero order model urea release showed independent concentration. Based on Korsmeyer-Pappas and Higuchi models with high n value and R2 equals to 0.97. Compared to urea, Ca2+, Zero order and Higuchi have been ignored due to their poor correlation coefficients values as proportion with Ca2+ fertilizer release.

DEVELOPMENT AND CHARACTERIZATION OF SUSTAINED RELEASE GASTRO-RETENTIVE FLOATING TABLETS OF AMBROXOL HYDROCHLORIDE

Introduction: The objective of this study was to formulate floating tablets of Ambroxyl hydrochloride (AMB HCl) using the dry granulation technique to increase its bioavailability and the gastric residence time (GRT) of the dosage form. Materials and Methods: The gastro-retentive floating tablets of Ambroxol hydrochloride (AMB HCl) were prepared by direct compression method using different concentrations of polymers such as HPMC K4, HPMC K15 and PVP K30, gas releasing agents (Sodium bicarbonate and citric acid) and diluents (Microcrystalline cellulose). Citric acid was also used as an antioxidant. The final mixing was done by adding talc and magnesium stearate to the granules. Results and Discussion: The prepared formulation of AMB HCl was evaluated by some evaluation parameters such as hardness, friability, weight variation, buoyancy lag time, drug contents, total floating time, in vitro dissolution study, drug release study etc. The result from the FT-IR data study of formulation it was disclosed that there is no interaction between the drug and excipients. In the FT-IR study, it was revealed that there is no interaction between the drug and excipients. The formulation containing the combination of HPMC K 15M polymer and Sodium bicarbonate shows a good drug release pattern with less floating lag time and good floating duration. In vitro drug release study of the prepared formulation (gastro retentive floating tablets of AMB HCl) was shown that the formulation F5 was the best formulation which was found to be 99.87% drug release. The release mechanism and its kinetics were evaluated by plotting various mathematical models of release data such as the Higuchi model, Korsmeyer model, First order and Zero order drug release. The optimized formulation showed no significant change at various evaluation parameters such as hardness, friability, weight variation and % drug release for accelerated stability condition at 40±2oC temperature and 75±5% (RH) relative humidity for 3 months. The floating tablets of AMB HCl showed their potential over a prolonged period as a gastro retentive drug delivery system (GRDDS).

Order of zeros of Dedekind zeta functions

Answering a question of Browkin, we provide a new unconditional proof that the Dedekind zeta function of a number field L L has infinitely many nontrivial zeros of multiplicity at least 2 if L L has a subfield K K for which L / K L/K is a nonabelian Galois extension. We also extend this to zeros of order 3 when G a l ( L / K ) Gal(L/K) has an irreducible representation of degree at least 3, as predicted by the Artin holomorphy conjecture.

Development and Evaluation of Losartan Potassium Floating Matrix Tablet

The present study was aimed towards the development of controlled release formulations of Losartan Potassium based on designed to enhance the bioavailability by prolonging its duration in the stomach via the floating dosage forms with controlled release. This study was intended to evaluate the influence of formulation variables like levels of polymer, amount of mannitol concentrations, and coating solution ratios of semi permeable membrane on the drug release from the developed formulations. Thus, there is a strong clinical need and market potential for a dosage form that will deliver Losartan Potassium in a controlled manner to a patient needing this therapy, thereby resulting in a better patient compliance. This study was designed to enhance the bioavailability of drug by prolonging its duration in the stomach via the floating dosage forms with controlled release. Floating matrix tablets of Losartan Potassium were prepared by the direct compression method, using locust bean gum and HPMC K 15M as polymers and Sodium bicarbonate as floating agent. The effect of the nature of polymers was studied by preparing various formulations of tablets. In all these formulations, a constant amount of drug (100 mg) was maintained. The blend was initially characterized for pre-compression and post- compression parameters. Pre-compression characterization was done for angle of repose, bulk density, tapped density, Carr’s index, and Hausner’s ratio. The results of pre-compression characterization were indicated good to excellent flow characteristics. Post-compression characterization includes thickness, hardness, friability, weight variation, drug content, buoyancy lag time, floating time and in-vitro drug release. All the results were satisfactory as per the guideline of pharmacopoeia. The in vitro drug release studies found that formulations LPFT4 showed best sustained release profile in 24 hrs. Among the nine formulations (LPFT1 to LPFT9) prepared formulations LPFT4 was found to be the best formulations in terms of sustained drug release. Drug release kinetics was performed by using various kinetic models such as Zero order, First order, Korsmeyer- Peppas and Higuchi’s equation and followed supercase II transport diffusion kinetic models.
 Keywords: Oral drug delivery system, Gastroretentive technology, losartan potassium, floating tablet, matrix tablet

Spectral Analysis for Preconditioning of Multi-Dimensional Riesz Fractional Diffusion Equations

In this paper, we analyze the spectra of the preconditioned matrices arising from discretized multi-dimensional Riesz spatial fractional diffusion equations. The finite difference method is employed to approximate the multi-dimensional Riesz fractional derivatives, which will generate symmetric positive definite ill-conditioned multi-level Toeplitz matrices. The preconditioned conjugate gradient method with a preconditioner based on the sine transform is employed to solve the resulting linear system. Theoretically, we prove that the spectra of the preconditioned matrices are uniformly bounded in the open interval (1/2,3/2) and thus the preconditioned conjugate gradient method converges linearly. The proposed method can be extended to multi-level Toeplitz matrices generated by functions with zeros of fractional order. Our theoretical results fill in a vacancy in the literature. Numerical examples are presented to demonstrate our new theoretical results in the literature and show the convergence performance of the proposed preconditioner that is better than other existing preconditioners.

Green’s Functions for First-Order Systems of Ordinary Differential Equations without the Unique Continuation Property

This paper is a contribution to the spectral theory associated with the differential equation $Ju'+qu=wf$ on the real interval $(a,b)$ when $J$ is a constant, invertible skew-Hermitian matrix and $q$ and $w$ are matrices whose entries are distributions of order zero with $q$ Hermitian and $w$ non-negative. Under these hypotheses it may not be possible to uniquely continue a solution from one point to another, thus blunting the standard tools of spectral theory. Despite this fact we are able to describe symmetric restrictions of the maximal relation associated with $Ju'+qu=wf$ and show the existence of Green's functions for self-adjoint relations even if unique continuation of solutions fails.

Characterization and in vitro release kinetics of chitosan based biocomposites from ScotchBonnets

The main aim of this study is to formulate the combination of the bioactive composite containing chitosan/β -tricalcium phosphate (CH/β-TCP) as potential drug delivery platforms for the sustained release of antibiotics. Herein the mode of amoxicillin (AMX) maintained in the β-TCP/chitosan composite was characterized using XRD, FT-IR to confirm the phase purity and functional groups. SEM was used to examine the size and shape of particles. The SEM images of the biocomposites after drug release confirmed that they are biodegradable. In vitro drug release experiments in PBS (pH 7.4) revealed a sustained release profile in a neutral medium. Drug release profiles were evaluated according to five different kinetic models including Zero Order, First Order, Higuchi, Hixon Crowel, and Korsmeyer-Peppas. The release profile was best expressed by the Korsmeyer Peppas model because the results showed high linearity. Overall, the positive effect of chitosan coating on the drug elution profile of β-TCP as carriers for the controlled delivery of antibiotics was regarded as biocompatible for the controlled drug delivery system.

Theoretical Study on Non-Improvement of the Multi-Frequency Direct Sampling Method in Inverse Scattering Problems

Generally, it has been confirmed that applying multiple frequencies guarantees a successful imaging result for various non-iterative imaging algorithms in inverse scattering problems. However, the application of multiple frequencies does not yield good results for direct sampling methods (DSMs), which has been confirmed through simulation but not theoretically. This study proves this premise theoretically by showing that the indicator function with multi-frequency can be expressed by the Bessel and Struve functions and the propagation direction of the incident field. This is based on the fact that the indicator function with single frequency can be expressed by the exponential and Bessel function of order zero of the first kind. Various simulation outcomes are shown to support the theoretical result.

Threshold estimation for continuous three‐phase polynomial regression models with constant mean in the middle regime

AbstractThis paper considers a continuous three‐phase polynomial regression model with two threshold points for dependent data with heteroscedasticity. We assume the model is polynomial of order zero in the middle regime, and is polynomial of higher orders elsewhere. We denote this model by , which includes models with one or no threshold points, denoted by and , respectively, as special cases. We provide an ordered iterative least squares (OiLS) method when estimating and establish the consistency of the OiLS estimators under mild conditions. When the underlying model is and is th‐order differentiable but not th‐order differentiable at the threshold point, we further show the convergence rate of the OiLS estimators, which can be faster than the convergence rate given in Feder when . We also apply a model‐selection procedure for selecting ; . When the underlying model exists, we establish the selection consistency under the aforementioned conditions. Finally, we conduct simulation experiments to demonstrate the finite‐sample performance of our asymptotic results.

Aggregating Composite Indicators through the Geometric Mean: A Penalization Approach

In this paper, we introduce a penalized version of the geometric mean. In analogy with the Mazziotta Pareto Index, this composite indicator is derived as a product between the geometric mean and a penalization term to account for the unbalance among indicators. The unbalance is measured in terms of the (horizontal) variability of the normalized indicators opportunely scaled and transformed via the Box–Cox function of order zero. The penalized geometric mean is used to compute the penalized Human Development Index (HDI), and a comparison with the geometric mean approach is presented. Data come from the Human Development Data Center for 2019 and refer to the classical three dimensions of HDI. The results show that the new method does not upset the original ranking produced by the HDI but it impacts more on countries with poor performances. The paper has the merit of proposing a new reading of the Mazziotta Pareto Index in terms of the reliability of the arithmetic mean as well as of generalizing this reading to the geometric mean approach.

Quantitative estimation of molnupiravir by UV- Spectrophotometric method

A simple, rapid, accurate and economical UV-spectrophotometric method has been developed for estimation of Molnupiravir from bulk and pharmaceutical formulation. The λ of Molnupiravir in Distilled water was found to be 235 nm. The is for zero order of drug and for Zero order AUC. The AUC of the drug was found to be in the range of 228.00 – 243.40 nm. The drug follows linearity in the concentration range 5-30 µg/ml with correlation coefficient value 0.999. The proposed method was applied to pharmaceutical formulation and % amount of drug estimated 99.99was found in good agreement with the label claim. The accuracy of the method was checked by recovery experiment performed at three different levels i.e., 80%, 100% and 120 % w/w. The % recovery was found to be in the range 98.15%– 99.97% for method A and 98.85% — 99.56% for method B. The low values of % R.S.D. are indicative of the accuracy and reproducibility of the method. The precision of the method was studied as an intra-day, inter-day variations and repeatability. The % R.S.D. value less than 2 indicate that the method is precise. Ruggedness of the proposed method was studied with the help of two analysts. The above method was a rapid and cost-effective quality-control tool for routine analysis of Molnupiravir in bulk and in pharmaceutical dosage form.

Formulation, Development and Characterization of Sustained Release Formulation of Herbal Extracts

Aim: The aim of the present investigation is to design of sustained release dosage form of different extracts that will help in releasing only small quantities of drug over a prolonged period of time. Material and Methods: The different ingredients for formulations are given as in Table 1 below. The measured quantities of drug, HPMC, MCC and NaHCO3 were mixed thoroughly using a mortar and pistil. The granules were punched into tablets using direct compression technique. The blank formulation (or) placebo (HPMC+ MCC+NaHCO3) and polyherbal formulation were also tested using FTIR Spectrometer. The release rate kinetics of the formulations was analyzed and the data obtained were fitted into Zero order, First order, Higuchi model and Kozmeyer Peppas model. Results: The pre-formulation study results obtained on various parameters on granules were found satisfactory. The granules obtained for the batches (F1-F12) were satisfactory. No rat holing, capping or sticking was observed during the flow of granules from the hopper. The maximum weight variation of the tablets was±1.8%, which falls within the acceptable range of±5%, hence the tablets passed the weight variation test. Hardness for tablets of all batches was in the range of 4.92 to 5.35 kg/cm², which falls above the limit of not less than 3.0 kg/cm². The floating lag time ranged from 35 s to 50 s. From the Table 5, it was found that the formulation F11 has the minimum floating lag time of 35 s and maximum total floating time of 15 h with 100.12% drug content. Conclusion: The effect of ingredients in the polyherbal tablet was analyzed, where HPMC contributed as the floating matrix, MCC to increase the bulk density of the tablet and sodium bicarbonate to initiate the dissolution process.

Application of Mathematical Models in Drug Release Kinetics of Lagerstroemia Speciosa Extract-Phospholipid Complex

The aim of present work is to govern and scrutinize the kinetics of drug release from the complex by employing various mathematical models. A study was done with Lagerstroemia speciosa extract-phospholipid complex, 50 mg/200mg by employing anticipation precipitation technique using soya lecithin and cholesterol as complex forming polymer. In-vitro drug release profile was carried out in phosphate buffer saline, pH 7.4 (900mL) using USP dissolution apparatus II (Paddle) at 50 RPM at an extended time period of 0.5, 0.75, 1, 1.5, 2, 2.5, 3 and 4 hours. The drug release data was obtained, quantitatively correlated and interpreted with various mathematical models viz. Zero order model, first order model, Higuchi model and Korsmeyer-Peppas model and evaluated to understand the kinetics of drug release. The criterion for the most suitable model was based on the high degree of coefficient of correlation of drug release profile was best fitted with Korsmeyer-Peppas model and follows drug release kinetics which is diffusion controlled.

Preparation and evaluation of matrix type of transdermal patches containing anti –diabetic drug

The current research aims to formulate and evaluated medicated transdermal patches containing an anti-diabetic drug. A good penetration enhancer would improve drug delivery from various polymer-based transdermal patches. Transdermal patches of the matrix type are made. Using various PVP K30, MC ratios and solvent evaporation techniques. All prepared formulations were tested for weight variation, thickness, drug content, moisture content, moisture uptake, flatness, and in vitro drug release. Bath F3 was optimised formula from all formulation baths shows linear zero order release for 24 hours, with a cumulative percentage of drug diffusion of 87.35% from 4cm2 patches. It has been determined that polymer concentration. When the concentration of PVP K30 increases in the primary layer, the in – vitro diffusion rate increases, and when the concentration of PVP K30 decreases, the drug diffusion decreases. It allows for more controlled drug release from the patch.

Cost Function Analysis Applied to Different Kinetic Release Models of Arrabidaea chica Verlot Extract from Chitosan/Alginate Membranes.

This work focuses on the mathematical analysis of the controlled release of a standardized extract of A. chica from chitosan/alginate (C/A) membranes, which can be used for the treatment of skin lesions. Four different types of C/A membranes were tested: a dense membrane (CA), a dense and flexible membrane (CAS), a porous membrane (CAP) and a porous and flexible membrane (CAPS). The Arrabidae chica extract release profiles were obtained experimentally in vitro using PBS at 37 °C and pH 7. Experimental data of release kinetics were analyzed using five classical models from the literature: Zero Order, First Order, Higuchi, Korsmeyer–Peppas and Weibull functions. Results for the Korsmeyer–Peppas model showed that the release of A. chica extract from four membrane formulations was by a diffusion through a partially swollen matrix and through a water filled network mesh; however, the Weibull model suggested that non-porous membranes (CA and CAS) had fractal geometry and that porous membranes (CAP and CAPS) have highly disorganized structures. Nevertheless, by applying an explicit optimization method that employs a cost function to determine the model parameters that best fit to experimental data, the results indicated that the Weibull model showed the best simulation for the release profiles from the four membranes: CA, CAS and CAP presented Fickian diffusion through a polymeric matrix of fractal geometry, and only the CAPS membrane showed a highly disordered matrix. The use of this cost function optimization had the significant advantage of higher fitting sensitivity.

Testing for Co‐explosive Behaviour in Financial Time Series

AbstractThis article proposes a test to determine if two price series that each contain an explosive autoregressive regime consistent with the presence of a bubble are related in the sense that a linear combination of them is integrated of order zero. We refer to such a phenomenon as ‘co‐explosive behaviour’, and propose a test based on a stationarity testing framework. The test allows the explosive episode in one series to lead (or lag) that in the other by a number of time periods. We establish the asymptotic properties of the test statistic and propose a wild bootstrap procedure for obtaining critical values that are robust to heteroskedasticity. Simulations show that the proposed test has good finite sample size and power performance. An empirical application to detect whether co‐explosive behaviour exists among a set of precious and non‐ferrous metals is presented.