Zero Order Research Articles

PH-sensitive polymeric hydrogels coated with cobalt ferrite nanoparticles for combined drug delivery as controlled release carriers: fabrication and in-vitro estimation

In this investigation, we produced pH-responsive hydrogels for the controlled release of drugs by graft copolymerizing Gum ghatti and acrylic acid (AA) in an aqueous medium. N, N′-methylene-bis-acrylamide (MBA) and ammonium persulphate (APS) served as cross-linkers during the synthesis process. Our research explores the integration of cobalt ferrite (CoFe2O4) magnetic nanoparticles (CFMNPs) in delivering a combination drug comprising metformin hydrochloride and sodium diclofenac. The diverse applications of CoFe2O4 nanoparticles have driven the exploration of innovative and environmentally sustainable production methods. The development of novel materials for nanoparticle synthesis adheres to the principles of “Green Chemistry” through a co-precipitation technique. Characterization of the cross-linked hydrogels involved Fourier transform infrared spectroscopy (FT-IR) and X-ray diffraction (XRD) analyses. In vitro drug release kinetics were observed under physiological conditions using Ultraviolet–Visible Spectroscopy. The drug-loaded Gg-cl-poly(AA)/CoFe2O4 hydrogels exhibited a sustained drug release profile over 24 h, with significant release occurring at a pH of 4. To comprehend the drug release mechanism, we employed kinetic modeling, encompassing Zero order, First order, Higuchi model, Hixson-Crowell model, and Korsmeyer-Peppas model, for all developed hydrogels. The findings indicated that the drug release mechanism from the hydrogels followed the Korsmeyer-Peppas model. The study concludes that the developed hydrogel offers a promising solution for the controlled administration of metformin hydrochloride and diclofenac sodium.Graphical

Imaging of upper breakpoints of buried active faults through microtremor survey technology

Detecting buried active faults presents the challenge of precisely locating the upper breakpoint, the shallowest point in the Quaternary system where faults occur. Microtremor survey technology, unaffected by urban electromagnetic interference, offers an eco-friendly and efficient method for investigating buried faults and stratigraphic structures in urban areas. This research uses microtremor survey technology to identify the upper breakpoint of the buried Nankou-Sunhe Fault in Changping, Beijing. For data collection, 17 microtremor survey points were deployed across the northern section of the Nankou-Sunhe fault, employing a three-point nested circular array with a point spacing of approximately 200 m to form a profile spanning approximately 320 m. For data analysis, the spatial autocorrelation method was utilized. Each measurement point was divided into 9 sets of radii, ranging from a minimum of approximately 4 m to a maximum of 28 m. The correlation coefficients for each set were calculated, and the dispersion curve for each measurement point was generated by fitting the average coefficients with the Bessel function of the first kind of order zero. The apparent S-wave velocity was determined directly from the dispersion curve using empirical formulas and interpolated to generate the contour cross-section map. Integrating the section and inverted S-wave velocity data can significantly enhance interpretation accuracy, and based on these data, the spatial development characteristics and upper breakpoint locations of the Nankou-Sunhe fault zone were analyzed, and the strata shallower than 100 m were deduced. The results align well with known geological data, such as luminescence dating and 14C dating from boreholes at nearby locations.Graphical

Variational Iteration Method for Solving First Kind Bessel Differential Equation of Order Zero

The aim of this paper is to study the first kind Bessel differential equation of order zero. The variational iteration method (VIM) is used to obtain the approximate solutions of first kind Bessel differential equation (BDE) of order zero. The approximate solution of this equation is calculated in the form of a series which its components are computed, can be calculated rapidlyon computer systems and the convergence of this method is studied. Also two numerical examples are given . The findings, which illustrate the effectiveness and precision of the suggested strategy, are presented in tables and figures.

Planning, emphasis and proposal for implementation of gravimetric control network in Israel

AbstractThis study outlines the planning, emphases, and proposed implementation of a gravimetric control network for Israel. The establishment of a comprehensive and accurate gravimetric control network is crucial for various geodetic applications, including geoid determination, gravity field modelling, vertical datum establishment, and geophysical studies. This study aims to provide a framework for the development and implementation of such a network in Israel. The proposed network is divided into two orders. The first order, also known as the absolute order or zero order, comprises four stations situated in geologically stable and tranquil locations. The second order, referred to as the first order, is established through relative gravimetric measurements. This order will encompass 29 stations positioned in areas that are both stable and secure. The zero and first order stations will be evenly distributed throughout the country to ensure homogeneous coverage. The proposed gravimetric network is in conjunction with the requirements to improve the geoid undulation model of Israel. Through the establishment of a small gravimetric network and the implementation of relative gravimetric measurements, we were able to determine the optimal control point density and establish a well-structured methodology for measurement, analysis, and the adjustment process.

Adverse Childhood Experiences, maladaptive coping behaviours and protective factors in undergraduate students: A cross-sectional study

Objectives: The purpose is to examine the relationship between Adverse Childhood Experiences (ACEs), protective factors, and select maladaptive coping behaviors in postsecondary students. Participants: Undergraduate students attending Dalhousie University. Methods: An online anonymous survey was conducted. Zero order one-tailed correlations were computed to measure relationships between ACEs, levels of maladaptive coping behaviors and protective factors. A structural equation mediation model examined direct and indirect pathways between measures. Results: 42.5% of respondents (n = 327) reported ≥3ACEs. Higher ACEs were associated with higher expression of maladaptive coping behaviors. Respondents with high ACEs and low levels of protective factors reported lower levels of hope and forgiveness and higher levels of stress and rumination. Conclusion: Higher levels of protective factors were associated with lower levels of maladaptive coping behaviors in students with high ACEs.

Biomimetic Studies on the Antimicrobial Activity of Some Biocides Based on Garlic and Lavender in Surface Waters.

For a given aquatic ecosystem that will be used as a water source, it is necessary to establish the quality of the water from a microbiological point of view by identifying the pathogens present in the water. The aim of this study was to determine and analyze the antimicrobial activity of some biocides derived from garlic (garlic-methanol extract) and lavender (lavender-water extract). Their efficiency was evaluated at different concentrations and contact times. Initially, through specific laboratory analyses, the microbiological characteristics of the river were determined. Biomimetic studies on the antimicrobial activity of biocides based on garlic and lavender in surface waters involved detailed exploration of how the natural antimicrobial properties of these plants can be effectively utilized to treat water contaminated with harmful microorganisms. Both the contact time and the amount of biocide used have a significant effect on the microorganisms of interest. Thus, to describe the degradation rate of coliform bacteria, a pseudo-first-order and zero-order kinetic model was used, r=-(dN/dt)=kobs·t şi r0=kobs·N0=k0, where r is the rate of degradation of microorganisms (CFU/min), N0 is the initial number of microorganisms in the aqueous solution (colony-forming unit, CFU), N is the final number of microorganisms after a contact time t (CFU), kobs is the pseudo-first-order rate constant (min-1), t is the contact time (min), r0 is the initial rate of degradation of microorganisms (CFU/min), and k0 is the pseudo-rate constant zero order (min-1). Following 60 min of treatment with 1 mL of lavender-water biocide, the inhibition rate of pathogenic microorganisms in the water reached 59.09%, whereas, under the same conditions, the garlic-methanol biocide achieved an inhibition rate of 40.86%. This study confirms the antimicrobial activity of both lavender and garlic biocides, highlighting their potential in mitigating water pollution caused by pathogens.

Quantitative estimation of doxylamine succinate by zero-order derivative area under curve Spectrophotometric methods in bulk and in-tablet dosage form

The purpose of this study is to establish Zero-order UV-Spectrophotometric - absorbance and Zero Order- Area under curve (AUC) methods for estimation of Doxylamine succinate in bulk and in pharmaceutical dosage form . Doxylamine succinate is Histamine H1 antagonist with pronounced sedative properties. It is used in allergies and as an antitussive, antiemetic, and hypnotic. Doxylamine has also been administered in veterinary applications and was formerly used in parkinsonism, distilled water was used as solvent for solubilization of Doxylamine succinate. Maximum absorption for Doxylamine succinate was found to be at wavelength 260nm when dissolved in Distilled water. The methods are based upon measurement of absorbance at 260nm and integration of area under curve for analysis of Doxylamine succinate in the wavelength range of 251.20-267.20 nm. The drug followed linearity in the concentration range of 10 - 60µg/mL with correlation coefficient value r> 0.99 . The proposed methods were validated for accuracy (% recovery), precision, repeatability and ruggedness, as per ICH guidelines. The proposed methods were applied for qualitative and quantitative estimation of Doxylamine succinate in tablet and results were found in good agreement with the label claimed. Developed methods can be used for routine analysis of Doxylamine succinate in bulk and pharmaceutical tablet.

Preformulation of curcumin and eugenol nanoemulsion in-situ mucoadhesive gel

In situ mucoadhesive gel provides the drug release at a controlled rate for prolong period of time directly to the target site which reduces side effects, thus improving patient compliance. The main advantages of the implants of formation in situ are as follows: they can easily be injected into periodontal pockets, harden to form a solid implant with customized geometry, the time-controlled release of drugs and no need to remove the empty remnants. For the formulation of Curcumin and Eugenol Nanoemulsion in-situ Mucoadhesive gel poloxamer-407 was used as thermo reversible agent and surfactant for nanoemulsion while carbopol-934 was used as mucoadhesive and pH sensitive agent. Curcumin and Eugenol Nanoemulsion in-situ Mucoadhesive gel were prepared and evaluated for zeta potential, globule size, size distribution, viscosity, syringeability, gelation temperature, mucoadhesive strength, in-vitro release study. Batch F3 showed good in vitro drug release and also shown good result for all parameters when compared with all other formulations. Hence, Batch F3 was considered as the optimized formulations. Batch F3 was subjected for four different models viz. Zero order, First order, Higuchi matrix and Peppas model equations and the formulations best fit in to the Peppas model by giving the value of diffusion exponent (n) 1.596 for curcumin and 1.592 for Eugenol respectively, that indicate the formulation had release the drug by case II transport.

Independent concentration extraction as a novel green approach resolving overlapped UV–Vis binary spectra and HPTLC-densitometric methods for concurrent determination of levocloperastine and chlorpheniramine

BackgroundThe proposed research study introduces independent concentration extraction (ICE) as a novel UV–Vis spectrophotometric approach. The approach can be used for extracting the concentration of two analytes with severely overlapped spectra from their binary mixtures. ICE is based on spectral extraction platform involving simple smart successive methods that can directly extract the original zero order spectra of the analytes at their characteristic (λmax). Chlorpheniramine maleate (CPM) and Levocloperastine fendizoate (LCF) are two commonly co-formulated drugs in cough preparations. The combined mixture was used to confirm the validity of the developed ICE tool. Another less green HPTLC was developed for the first time to separate both drugs and help also in confirming the proposed tool.MethodsFor the simultaneous determination of CPM and LCF, two ecologically friendly techniques were employed. The first approach encompasses the use of the ICE spectrophotometric method that could be successively applied for extracting the concentration of two analytes with severely overlapped unresolved spectra in their binary mixtures. Other complementary methods aiming at original spectral extraction; including spectrum subtraction (SS) and unity subtraction (US) were also successfully employed to resolve the zero order spectra of the combined drugs with all their characteristic features and peaks. The second technique used, a high-performance TLC-densitometric one, was performed on silica plates with silica plates F254 and a mobile phase with a ratio of 3:3:3:1 by volume of toluene, ethanol, acetone, and ammonia as a developing system at 230 nm.ResultsThe presented extraction approach was executed without any optimization steps or sample pretreatment for the simultaneous determination of CPM and LCF. The method was found to be valid for their determination within concentration range of 3.0–30.0 μg mL−1 for both drugs. For HPTLC method, the resulting Rf values of CPM and LCF were 0.37 and 0.78, within concentration ranges of 0.3–4.0 μg/spot and 0.8–10.0 μg/spot, respectively. Greenness assessment of both developed methodologies showed that the HPTLC method is less green than the spectrophotometric method, yet with comparable sustainability when it comes to the used technique.ConclusionThe procedures were found to be selective, accurate, and precise for analysis of the studied binary mixture. Furthermore, the environmental impact of the introduced methods was assessed using novel greenness metrics, namely AGREE and Green Analytical Procedure Index (GAPI) to prove their ecological safety. In addition, white analytical chemistry (WAC) evaluation metric was employed to ensure the synergy and coherence of analytical, practical, and ecological attributes.

Microscopic instabilities in single crystal matrix composites

A finite strain micromechanical analysis is presented for the prediction of the loss of microscopic stability of a class of metal matrix composites that are subjected to axial compressive loading and undergoing large deformations. The metallic constituent behavior is modeled by the single crystal anisotropic plasticity theory in which, due to the resolved shear stresses, plastic deformations occur along certain pre-defined slip planes. Thus, this incremental plasticity theory is capable of providing the effect of the applied axial loading on the induced shear stresses which dominate the microbuckling. The composites are assumed to possess slight imperfections at the interfaces, and in order to satisfy the interfacial conditions, a perturbation expansion is employed which yields zero and first order micromechanical analysis problems. The zero order problem corresponds to the micromechanical modeling of the composite with no imperfections, whereas the solution of the first order problem is utilized to obtain the critical stresses and deformations at which bifurcation buckling occurs. Both problems are solved by employing the finite strain high-fidelity generalized method of cells (HFGMC) micromechanics. Applications are given for various types of single crystal matrix composites including layered, particulate, continuous and short fiber composites. Finally, a comparison between the compressive strengths of a standard metal matrix boron/aluminum and SiC/single crystal composites is presented and discussed.

Impact of Stock Market Integration on Industrial Corporate Investment in Nigeria: An Empirical Study (1986-2023)

Nigeria, a sub-Saharan African nation, is endowed with an abundance of natural resources, particularly those needed for industrial purposes. Despite this, the present level of output in the industrial sector in Nigeria is too low, particularly when it comes to investment undertaking by corporate investors. Therefore, the study examined the effect of stock market integration on industrial corporate investment in Nigeria from 1986-2023. Data used were sourced from the Central bank of Nigeria Statistical Bulletin. The study used Augmented Dickey-Fuller (ADF), bound test and Autoregressive Distributed Lag. The ADF estimate indicated that money supply and all share index were integrated of order one; while, corporate investment, stock market integration, real exchange rate, and lending interest rate were integrated of order zero. The F-value for the bound test estimate was much higher than upper bound of critical value at 5% conventional level; therefore, suggesting a long-run link between the use variables. The short-run estimates showed that stock market integration, real exchange rate and all share index were significant with direct effect on corporate investment; while, money supply and lending interest rate were significant also with indirect effects. Furthermore, long-run estimate showed that money supply and all share index were significant with direct effect on corporate investment; while, real exchange rate and lending interest rate were significant with indirect effects. This suggests that stock market integration currently witnessing in Nigeria is tentative. The study concluded that the current growth witnessing by industrial corporate investment in Nigeria due to stock market integration is not sustainable. Therefore, recommended that the Nigerian Exchange Group’s management should ensure that stock market price exhibit low volatility rate by making sure that its stocks management policies reflect best global stock exchange practice.

Amino-functionalised mesoporous silica nanoparticles for the delivery of isoniazid and its metal complexes

The effective delivery of poor water-soluble anti-tubercular drugs such as isoniazid to their target sites is a major factor that has made it difficult for tuberculosis to be eradicated. Isoniazid derivatives and nano-particulate drug delivery systems are explored as one way to address this limitation. This study investigated the use of amino-functionalised mesoporous silica nanoparticles (MCM-41) as nano-carriers for the delivery of isoniazid-based metal complexes, Cu–INH and Fe–INH. The Sol-gel method was used to synthesise the nano-carriers, which produced a series of well-ordered nano-carriers. Their physicochemical properties were modified through surface functionalisation with amino groups via post-grafting synthesis. The isoniazid-based metal complexes were incorporated into the nano-carriers using rotary evaporation. The nano-carriers were characterised using X-ray diffraction (XRD), Zeta potential, Fourier Transmission Infra-red (FT-IR), Brunaeur Emmett Teller (BET), Scanning Electron Microscopy (SEM), Transmission Electron Microscopy (TEM) and Thermogravimetric analysis (TGA). These characterisation techniques confirmed the successful surface functionalisation of the nano-carriers with amino groups and their encapsulation with INH, Cu–INH and Fe–INH. The amino-functionalised nano-carriers were observed to have the highest drug loading capacities and entrapment efficiencies within the range of 7.85%–19.31 % and 39.26%–96.53 %, respectively. The release rates of INH, Cu–INH, and Fe–INH from the nano-carriers were also studied in Phosphate Buffer Solution (PBS) with pH of 7.4 and 5.4 using ultraviolet–visible spectroscopy. The cumulative release rates of INH, Cu–INH, and Fe–INH from their nano-carriers depended on their release media's textural properties and environmental conditions. Amino functionalised nano-carriers had high release rates, with A-MCM-41+Cu–INH having the highest of 37.09 % in PBS at 5.4 after 24 h. The cumulative data obtained was fitted into Zero order, First order, Hixson Crowell, Higuchi, Korsmeyer-Peppas and Weibull models. The Hixson Crowell, Korsmeyer-Peppas, and Weibull models fitted well with correlation coefficients (R2) of 0.9813, 0.9769 and 0.9802, respectively, for MCM-41+INH in PBS of pH 5.4.

Optimal measurement-based cost gradient estimate for feedback real-time optimization

This work presents a simple and efficient way of estimating the steady-state cost gradient Ju based on available uncertain measurements y. The main motivation is to control Ju to zero in order to minimize the economic cost J. For this purpose, it is shown that the optimal cost gradient estimate for unconstrained operation is simply Jˆu=H(ym−y∗) where H is a constant matrix, ym is the vector of measurements and y∗ is their nominally unconstrained optimal value. The derivation of the optimal H-matrix is based on existing methods for self-optimizing control and therefore the result is exact for a convex quadratic economic cost J with linear constraints and measurements. The optimality holds locally in other cases. For the constrained case, the unconstrained gradient estimate Jˆu should be multiplied by the nullspace of the active constraints and the resulting “reduced gradient” controlled to zero.

Coupling several spectral manipulations with isosbestic approach to resolve overlapped spectra for concurrent analysis of lamivudine/tenofovir combination: Evaluating environmental sustainability

Acquired immunodeficiency syndrome (AIDS) is a chronic disease caused by the human immunodeficiency virus (HIV), which can severely damage the immune system. Recently, lamivudine (LAM) and tenofovir disoproxil fumarate (TDF) were co-formulated for the management of (AIDS). This work proposes three new UV spectrophotometric approaches based on the isosbestic point, namely: absorption subtraction method (AS), amplitude modulation method (AM) and amplitude summation method (A-Sum). The (AS) approach is based on the absorption factor method, and the two drugs can be determined at the isosbestic point in the range's zero order absorption spectra (224 nm). The (AM) method is utilizing normalized spectrum of LAM (1 μg/mL) as a divisor spectrum. After division, LAM and TDF can be determined at the isosbestic point that remained in the obtained ratio spectra at the same point even after division (224 nm). In (A-Sum) method, first order derivatization is done and the two drugs can be detected at the isosbestic point (276 nm) by using amplitude factor. The linear ranges for LAM and TDF were 5–30 μg/mL and 10–50 μg/mL, respectively. The limits of detection for LAM and TDF were 0.71–0.90 μg/mL and 0.56–1.09 μg/mL, respectively, indicating the sensitivity of these approaches. The two drugs were determined at the isospestic point without the requirement for a supplemental technique using the relevant unified regression equation. All methods were found to be accurate, repeatable, and selective based on ICH recommendations for linearity, accuracy, precision, and selectivity. The obtained results were statistically compared to the reported HPLC methods for LAM and TDF, which revealed no significant.

Quantitative estimation of fenticonazole nitrate by zero-order derivative area under curve spectrophotometric methods in bulk and in-capsule dosage form

The purpose of this study is to establish Zero-order UV-Spectrophotometric - absorbance and Zero Order- Area under curve (AUC) methods for estimation of Fenticonazole Nitrate in bulk and vaginal capsules. Fenticonazole Nitrate is an antifungal drug and it is completely insoluble in water. Methanol was used as solvent for solubilization of Fenticonazole Nitrate. Maximum absorption for Fenticonazole Nitrate was found to be at wavelength 253 nm when dissolved in Methanol. The methods are based upon measurement of absorbance at 253nm and integration of area under curve for analysis of Fenticonazole Nitrate in the wavelength range of 242-262 nm. The drug followed linearity in the concentration range of 5 - 30µg/mL with correlation coefficient value r> 0.99 for both methods. The proposed methods were validated for accuracy (% recovery), precision, repeatability and ruggedness, as per ICH guidelines. The proposed methods were applied for qualitative and quantitative estimation of Fenticonazole Nitrate in vaginal capsules and results were found in good agreement with the label claimed. Developed methods can be used for routine analysis of Fenticonazole Nitrate in bulk and Vaginal Capsules.

Domination of nonlinear semigroups generated by regular, local Dirichlet forms

AbstractIn this article we study perturbations of local, nonlinear Dirichlet forms on arbitrary topological measure spaces. As a main result, we show that the semigroup generated by a local, regular, nonlinear Dirichlet form $${\mathcal {E}}$$ E dominates the semigroup generated by another local functional $${\mathcal {F}}$$ F if, and only if, $${\mathcal {F}}$$ F is a specific zero order perturbation of $${\mathcal {E}}$$ E . On the way, we prove a nonlinear version of the Riesz–Markov representation theorem, we define an abstract boundary of a topological measure space, and apply the notion of nonlinear capacity. The main result helps to classify the perturbations that lie between Neumann and Dirichlet boundary conditions.

A Novel Uv Spectrophotometric Method Development and Validation of Dalfampridine in Bulk and Pharmaceutical Dosage Form

Simple, precise and accurate zero order derivative spectroscopic method has been developed and validated for the estimation of dalfampridine in bulk and pharmaceutical dosage form. The drug shows maximum absorption (λ max) at 262nm in 0.1M HCL and obeys Beer’s law in the concentration range of 0.5-3.0µg/ml. The linearity study was carried out and regression coefficient was found to be 0.9976 and it has showed good linearity, precision during this concentration range. The % recovery was found to be 98.66% -101.56%. The LOD and LOQ were found to be 0.0360 and 0.109µg/ml. The % relative standard deviation were found to be less than 2. According to ICH guidelines the technique has been validated for linearity, precision, accuracy, ruggedness, LOD and LOQ. The developed and validated method can be successfully applied for routine quantification of Dalfampridine in bulk and pharmaceutical dosage form.

Testing the Dynamic Affiliation among Financial inclusion, Energy Poverty, Environmental Degradation and Economic Development in the Selected African countries: Evidence of Panel Data Analysis

Energy is necessary for "cooking, lighting, and other business activities" and plays a vital part in daily living, in order to eradicate poverty in developing nations, affordable energy availability is a must. The study investigates the dynamic affiliation among financial inclusion, energy poverty, environmental degradation and economic development in the selected African countries using panel data analysis. The study used panel data for Nigeria, Ghana, Gabon and Niger from 2005 to 2021. The study employed fixed effect model. The panel unit root tests show that real gross domestic product, automated teller machine, depositors with commercial banks, and energy poverty are integrated of order one, while CO2 emission is integrated of order zero. The fixed effect model shows that automated teller machine, depositors with commercial banks and CO2 emission have positive and statistically significant effect on the real gross domestic product in Nigeria, Ghana, Gabon and Niger. While Energy poverty has a negative, but statistically significant effect on the real gross domestic product in Nigeria, Ghana and Gabon. The study recommends that in order to reduce energy poverty and environmental degradation in the region, African nation particularly Nigeria, Ghana, Gabon, and Niger should make sure that their citizens have access to affordable, readily available electricity. Policymakers and governments in Africa must create inclusive, well-directed financial policies that take into account the disparities in income, governance, and laws among their nations.

Universal Basic Mass Density inside Dark Matter Halos

Abstract In this work we propose a universal basic mass density and a universal basic metric inside dark matter halos in the framework of Einstein equations providing an analytical ground for learning about dark matter. In a previous work the authors have proposed a simplified model for galaxies: a Schwarzschild black hole (that contains all the baryonic matter of the galaxy) immersed inside a dark matter halo. The solution solved the Einstein equations perturbatively and successfully gave the flat rotation curve and the baryonic Tully-Fisher relation, the two signatures of spiral galaxies. In this work we take the black hole mass (the baryonic mass) of the solution to be zero in order to focus our study on the dark matter halo exclusively. Among the results (1) is the prediction of a universal basic mass density of dark matter, ρ = a_0/2πGr, where a_0 ≈ 2.8×10^{-11} m/s^2 is a universal constant whose value was deduced from observations, (2) we show that the mass and velocity curve of the dark halo agree excellently with observational data at intermediate distances where the baryonic matter contribution is negligible, (3) we show that the constant a0is the origin of the constant surface density of dark matter and the origin of the scale-radius/scale-density scaling relation of the Navarro-Frenk-White profile (4) we show how the inclusion of baryonic matter in our model solves the core-cusp problem.

Zero order meromorphic solutions of q-difference equations of Malmquist type

We consider the first order q-difference equation(†)f(qz)n=R(z,f), where q≠0,1 is a constant and R(z,f) is rational in both arguments. When |q|≠1, we show that, if (†) has a zero order transcendental meromorphic solution, then (†) reduces to a q-difference linear or Riccati equation, or to an equation that can be transformed to a q-difference Riccati equation. In the autonomous case, explicit meromorphic solutions of (†) are presented. Given that (†) can be transformed into a difference equation, we proceed to discuss the growth of the composite function f(ω(z)), where ω(z) is an entire function satisfying ω(z+1)=qω(z), and demonstrate how the proposed difference Painlevé property, as discussed in the literature, applies for q-difference equations.