This paper aims to introduce the notions of various types of Qc-contractions for which we establish some fixed circle and fixed disc theorems in the setting of metric spaces. Some illustrative examples are also provided to support our results. Moreover, we present some fixed circle and fixed disc results of integral type contractive self-mappings.

In this article, we introduce a relatively new concept of multi-valued (θ;R)-contractions and utilize the same to prove some xed point results for a new class of multi-valued mappings in metric spaces endowed with an amorphous binary relation. Illustrative examples are also provided to exhibit the utility of our results proved herein. Finally, we utilize some of our results to investigate the existence and uniqueness of a positive solution for the integral equation of Volterra type.

The purpose of this article is to characterize the Caristi type mapping by the absolute derivative. The equivalences of the Caristi mapping with contraction mapping is discussed too. In addition, it was shown that the contraction mapping can be characterized by its absolute derivative.

In this paper, the notion of θ∗-weak contraction is introduced, which is utilized to prove some fixed point results. These results are helpful to give a positive response to certain open question raised by Kannan [Amer. Math. Monthly 76:1969] and Rhoades [Contemp. Math. 72:1988] on the existence of contractive definition which does not force the mapping to be continuous at the fixed point. Some illustrative examples are also given to support our results. As applications of our result, we investigate the existence and uniqueness of a solution of non-linear matrix equations and integral equations of Volterra type as well.

Oncological patients need the proper doses of medications to facilitate their recovery. The two basic approaches used in dosing Monoclonal Antibodies (mAbs) are fixed-dose combination and variable dosing. In Fixed-Dose Combination Drugs (FDCs), two or more active components are combined in a single formulation at a predetermined dose. Variable dosage, which has long been the industry standard, is the polar opposite of this approach. The body changes over time; the Body Surface Area (BSA) in square meters is often used as a Measure (m2). This study uses a systematic review. Most mAbs used in oncology are predominantly given as cytotoxic anticancer drugs using body-size-based (variable) regimens. Despite the benefits of fixed-dose, variable dosing has become the industry standard, despite being criticized for ineffectiveness. While variable dosing has some advantages, the prevalent view is that continuous dosing has significant advantages based on the balance of probabilities. After assessing each alternative, including its benefits and drawbacks, history of use, and suitability in the current context, fixed dosing emerges as a viable option.

In this paper, it is proved that s-iteration with error and Picard-Mann iteration with error iterative processes converge strongly to the unique fixed point of Lipschitzian strongly pseudo-contractive map. This convergence is almost -stable and -stable. Applications of these results to the operator equations, where is a strongly accretive and accretive mappings of into itself.

We introduce the notion of generalized contraction on dualistic partial metric spaces. A fixed point theorem for mappings satisfying above mentioned contraction is obtained. Some consequences of our result are obtained. We construct an example to demonstrate the effectiveness of our result among the corresponding results in partial metric spaces. Our results provide substantial generalizations and improvements of several well known results existing in the comparable literature. We discuss an application of our fixed point results to show the existence of solution of functional equations.

Molecular diagnostics in healthcare relies increasingly on genomic and transcriptomic method-ologies and requires appropriate tissue specimens from which nucleic acids (NA) of sufficiently high quality can be obtained. Besides suration of ischemia and fixation type, NA quality depends on a variety of other pre-analytical parameters, like storage conditions and duration. It has been discussed that improper dehydration of tissue during processing influences quality of NAs and shelf-life of fixed tissue. Here we report on establishing a method to determine the amount of residual water in fixed, paraffin-embedded tissue (fixed by neutral buffered formalin, or a non-crosslinking fixative) and its correlation to the performance of NAs in qRT-PCR analyses. The amount of residual water depended primarily on the fixative type and the dehydration pro-tocol and, to a lesser extent on storage conditions and time. Moreover, we found that these pa-rameters were associated with the qRT-PCR performance of extracted NAs. Besides cross-linking of NAs and modification of nucleobases by formalin, hydrolysis of NAs by residual water was found to contribute to reduced qRT-PCR performance. The negative effects of residual water on NA stability are not only important for the design and interpretation of research, but must also be taken into account in clinical diagnostics where reanalysis of archived tissue from a primary tumour may be required, e.g., after disease recurrence. We conclude that improving shelf-life of fixed tissue requires meticulous dehydration and dry storage to minimize the degradative in-fluence of residual water on NAs.

In this paper, inspired by Jleli and Samet [journal of inequalities and applications 38 (2014) 2 1–8] we introduce two new classes of auxiliary functions and utilize the same to define (q, y)R-weak 3 contractions. Utilizing (q, y)R-weak contractions, we prove some fixed point theorems in the setting 4 of relational metric spaces. We employ some examples to substantiate the utility of our newly proved 5 results. Finally, we apply one of our newly proved results to ensure the existence and uniqueness of 6 solution of a Volterra-type integral equation.

A common reactor type in the chemical and process industry is the fixed-bed reactor. Accurate modeling can be achieved with particle-resolved Computational Fluid Dynamic (CFD) simulations. However, the underlying bed morphology plays a paramount role. Synthetic bed-generation methods are much more flexible and faster than image-based approaches. In this study, we look critically at the two different bed generation methods: Discrete Element Method (DEM) (in the commercial software STAR-CCM+) and the rigid-body model (in the open-source software Blender). The two approaches are compared in terms of synthetically generated beds with experimental data of overall and radial porosity, particle orientation, as well as radial velocities. Both models show accurate agreement for the porosity. However, only Blender shows similar particle orientation than the experimental results. The main drawback of the DEM is the long calculation time and the shape approximation with composite particles.

In this paper, we consider with a class of system of differential equations whose argument transforms are involution. In this an initial value problem for a differential equation with involution is reduced to an initial value problem for a higher order ordinary differential equation. Than either two initial conditions are necessary for a solution, the equation is then reduced to a boundary value problem for a higher order ODE.

The effects of the surface waves generated by the wind have a significant effect on the currents. A wave current coupled model plays an important role in the design of offshore structures. The interaction between fluids such as incompressible ocean waves and current and offshore structures is significant with many real-time applications in offshore engineering. These coupled models can be applied to Offshore Floating Production Operating and offloading (FPSO), Wind or current turbines and offshore pipelines. The complex issues related to the design are analyzed by using Computational Fluid Dynamics, which requires an investigation of the multiphase flow between wave and current and the structure which is considered restrictive due to the computational cost. If viscous effects are neglected then the single-phase flow models have been recommended, where wave-current interaction have been modelled successfully. Models have been developed where velocities and pressure are computed and the results can be verified with the experimental results available in the literature. In this study the existing numerical methods, mesh types are discussed along with their coupling methods. Here single-phase and multiphase models with small and medium movement are reviewed and their applications are highlighted.

In the present study, Electrocoagulated Metal Hydroxide Sludge (EMHS) was analyzed as adsorbent material to remove both fluoride ion (F-) and arsenic V (As(V)) from aqueous effluents. This material was generated during an electrocoagulation process using Aluminum anode. It was characterized by using specific surface areas and the surface morphology was studied by scanning electron microscopy (SEM). Adsorbent fixed-beds are generally studied to remove different class of contaminants. EMHS was evaluated using a continuous flow rate column test with an experimental design. The effect of initial concentration of F- (2.5–10 mg L⁻¹) and the Empty Bed Contact Time (EBCT (0.4–0.8 min)) was studied following a central composite design methodology. The experimented parameters had a significant influence on saturation time, breakthrough volume, and breakthrough time. A response surface analysis was a tool for analyzing the adsorption study, showing interactions that are complicated to identify by others methods. The results, here reported, revealed that EMHS is an efficient and promising adsorbent material in order to remove F- and As(V) from water contaminated by these pollutants.

The paper aims to investigate on the determinants of the capital structure of the Italian SMEs and it is based on a large panel of Italian manufacturing SMEs observed in the years 2001-2013. The analysis achieves a comparative investigation between the capital structure of the firms belonging in the Southern region, the so-called Italian Mezzogiorno that is the slow growing area of the country, and the firms of the Center-northern region of Italy, that is the more developed area of the country. Fixed effect panel techniques applied to the several standard leverage models allows to reaffirm some distinctive features showing differences of the financial behavior of regional firms.

In this paper, the fixed-time stabilization problem for a class of uncertain chained system is addressed by using a novel nonsingular recursive terminal sliding mode control approach. A fixed-time controller and an adaptive law are designed to guarantee the uncertain chained form system both Lyapunov stable and fixed-time convergent within the settling time. The advantage of the controller based on the sliding mode is that the settling time does not depend on the system initial state. Furthermore, we use RBF neural network to estimate the uncertainty of the system. Finally, the simulation results demonstrate the performance of the control laws.

In the framework of a multiplicative metric space. We have discuss some Properties of convex structures in pseudo multiplicative metric space and have applied these properties toiobtain alfixed point results in complete pseudo. It would be interesting to prove some further results in such metric spaces with completeness property.

Traffic congestion is one of the foremost problems confronted by the urban and suburban tenants of today. Traffic congestion increases vehicle emissions and degrades air quality. Urban planners and policy makers have consequently been always investigating choices to alleviate traffic congestion and to enhance air quality. Teleworking is one option that has received significant consideration and has been studied in the recent past. The aim of the study is to explore the relationship between teleworking, air quality and traffic in Switzerland. The analysis relies on panel individual and household level data over the period 2002-2013. We examine five main air pollutants; the sulphur dioxide (SO₂), the ground-level ozone (O₃) the nitrogen dioxide (NO₂), the carbon monoxide (CO) and the particulate matter less than 10 microns (PM₁₀). Based on the fixed effects estimates, teleworking reduces traffic volume by 1.9 per cent. Furthermore, the reduction observed on air pollution is higher for NO₂, CO and PM₁₀ ranging between 3.3-3.7 per cent, followed by O₃ at 2.3 per cent and SO₂ at 2.1 per cent. According to instrumental variable (IV) approach and the two stage least squares (2SLS) method, the effect is higher ranging between 2.6-4.1 per cent. The respective reduction on traffic becomes 2.7 per cent. Overall, the main concluding remark of the study is that teleworking can be a promising tool for urban planning and development, focusing at the traffic volume reduction, and the air quality improvement. Additional policy implications of teleworking and its beneficial effects for the society are further discussed.

Predicting the tidal wave is essential not only to better understand hydrological cycle at the boundary between land and ocean but also to improve energy production in the coastal area. As affected by various factors such as astronomical, meteorological, and hydrological effects, predicting the tidal wave at the estuary remains uncertain. In this study, we present a novel method to improve short-term tidal wave predictions using a fixed-lag smoother based on sequential data assimilation (DA). The proposed method is implemented for the tidal wave predictions at the estuary of Nakdong River. As a result, the prediction accuracy was improved by 63.9% with DA and the calibration using the regression. Although the accuracy of DA diminished for increasing forecast lead times, the 1-hr lead forecast by DA had still 44.4% improvement over the open loop without DA. Plus, the optimal conditions for the fixed-lag smoother were analyzed in terms of the order of a smoothing function and the length of assimilation window and forecast lead time. It was suggested that the optimal DA configuration could be obtained with the 8th order polynomial as a smoothing function assimilated under 6-hr or longer past and future DA windows.

Open-cell metallic foams used as catalyst supports exhibit excellent transport properties. In this work, a unique application of metallic foam, as pelletized catalyst in a packed bed reactor, is examined. By using a wall-segment Computational Fluid Dynamics (CFD) setup, parametric analyses are carried out to investigate the influence of foam morphologies (cell size ϕ=0.45-3 mm and porosity ε=0.55-0.95) and intrinsic conductivity on flow and heat transport characteristics in a slender packed bed (N=Ddp=6.78) made of cylindrical metallic foam pellets. The transport processes have been modeled using an extended version of conventional particle-resolved CFD, i.e., flow and energy in inter-particle spaces are fully resolved, whereas porous-media model is used for the effective transport processes inside highly-porous foam pellets. Simulation inputs include the processing parameters relevant to Steam Methane Reforming (SMR), analyzed for low (Rep~100) and high (Rep~5000) flow regimes. The effect of foam morphologies on packed beds has shown that the desired requirements contradict each other, i.e., increase in cell size and porosity favor the reduction in pressure drop, however lowering the heat transfer efficiency. A design study is also conducted to find the optimum foam morphology of a cylindrical foam pellet at higher Rep~5000, which yields ϕ = 0.45, ε = 0.8. Suitable correlations to predict the friction factor and the overall heat transfer coefficient in a foam packed bed have been presented, which considers the effect of different foam morphologies over a range of particle Reynolds number, 100≤Rep≤5000.

Although CAD/CAM ceramics present a promising alternative to metal-ceramic fixed dental prostheses, little is known about their mid- and long-term clinical performance. This systematic review aims to estimate the survival and success rates and describes the underlying complication characteristics for CAD/CAM tooth-supported fixed dental prostheses (FDPs). We systematically searched MEDLINE and Web of Science to find relevant prospective studies with a follow-up of at least one year. We estimated pooled 1-, 5- and 10-year survival and success rates by combining the collected data in a Poisson regression model. Descriptive statistics were conducted to evaluate the distribution of failures and complications in the included studies. Risk of bias for the included studies was assessed with an adapted checklist for single-arm trials. Pooled estimated 1-, 5-, and 10-year survival rates ranged from 93.80% to 94.66%, 89.67% to 91.1%, and 79.33% to 82.20%, respectively. The corresponding success rates, excluding failures but including any other types of intervention, were 94.53% to 96.77%, 90.89% to 94.62%, and 81.78% to 89.25%. Secondary caries was the most frequent cause of failure, followed by chipping of the veneering. The most common cause of complication, excluding failures but requiring intervention, was chipping of the veneering. Risk of bias was generally acceptable for the included studies, with 7 studies associated with low risk of bias, 8 studies with a moderate risk of bias, and 3 studies with serious risk of bias. The current meta-analysis on CAD/CAM supported FDPs revealed satisfying survival and success rates for up to 10 years of exposure. More prospective studies focusing on long-term performance are needed to strengthen the evidence currently available in the literature.

Since smoke usually occurs before a flame arises, fire smoke detection is especially significant for early warning systems. In this paper, a DSATA(Depthwise Separability And Target Awareness) algorithm based on depthwise separability and target awareness is proposed. Existing deep learning methods with convolutional neural networks pretrained by abundant and vast datasets are always used to realize generic object recognition tasks. In the area of smoke detection, collecting large quantities of smoke data is a challenging task for small sample smoke objects. The basis is that the objects of interest can be arbitrary object classes with arbitrary forms. Thus, deep feature maps acquired by target-aware pretrained networks are used in modelling these objects of arbitrary forms to distinguish them from unpredictable and complex environments. In this paper, this scheme is introduced to deal with smoke detection. The depthwise separable method with a fixed convolution kernel replacing the training iterations can improve the speed of the algorithm to meet the enhanced requirements of real-time fire spreading for detecting speed. The experimental results demonstrate that the proposed algorithm can detect early smoke, is superior to the state-of-the-art methods in accuracy and speed, and can also realize real-time smoke detection.

Purpose: To compare the therapeutic efficacy and safety of dorzolamide/timolol fixed-combination in newly diagnosed primary open angle glaucoma patients. Methods: In this prospective, interventional case series, newly diagnosed primary open angle glaucoma (POAG) patients that had not been treated for glaucoma were included. Patients were started on Cosopt twice a day (BID) for 1 month and then switched to three times a day (TDS) for additional 1 month. Patients underwent comprehensive ophthalmic examination, diurnal intraocular pressure (IOP), blood pressure (BP) and 24-hours heart rate (HR) measurements at baseline, month 1( BID), and month 2( TDS). IOP, systolic and diastolic pressures were measured at 8:00 AM,12:00 AM, 4:00 PM, 8:00 PM and 12:00 PM. Throughout the study, all adverse events were recorded and monitored by the investigators. Results: In 31 POAG patients that completed the study ,mean baseline IOP was 23.1±3.15 mmHg . IOP was decreased significantly 16.5 ± 2.21 at 1 month (P < 0.0001) and 13.9 ± 2.23 mmHg at 1 and 2 month follow up. (P < 0.0001) IOP was significantly lower in month 2 compared to month 1 (P = 0.0004). While Cosopt BID significantly reduced the mean 24-hour systolic BP and mean 24-hour HR from baseline (P < 0.0001), the mean 24-hour systolic BP and HR remained unchanged 2ith Cosopt TDS compared to BID (P = 0.62). Conclusions: Cosopt TDS has a superior IOP-lowering effect than Cosopt BID in POAG patients with comparable safety profile.

Free route airspace (FRA) is a new concept of European air transport. It has been designed to eliminate the negative impact of air traffic on the environment, minimize fuel consumption, simplify and expand flight planning. In our research, FRA is modelled by using graph theory, networks, and convex analysis. We also looked for answers to the question which are the basic mathematical properties of airspace? Basic mathematical properties are expressed using axioms. Therefore, in our work, we state the general, basic axiom of airspace based on our FRA research. The axiom is given using practical, significant entry points and geodetic coordinates.

In this article, we are interested in a new generic class of nonlocal fractional impulsive differential inclusions with linear sectorial operator and Lipschitz multivalued function in the setting of finite dimensional Banach spaces. By modifying the definition of PC-mild solutions initiated by Shu, we succeeded to determine new conditions that sufficiently guarantee the existence of the solutions. The results are obtained by combining techniques of fractional calculus and fixed point theorem for contraction maps. We also characterize the topological structure of the set of solutions. Finally, we provide a demonstration to address the applicability of the theoretical results.

This paper uses panel data to find the determinants of tracking errors in exchange traded funds (ETFs) in the Hong Kong stock market. A comparison of tracking errors between physical and synthetic ETFs also indicates that the synthetic ETFs have higher tracking errors. The magnitude of tracking errors is found to be negatively related to size but positively related to dividend yield, trading volumes of funds, and market risk. However, this study also finds that expense ratio has a negative impact on tracking error, which is not consistent with previous studies, and which this paper addresses.

In this paper, we established the existence of PC-mild solutions for non local fractional impulsive functional integro-differential equations with finite delay. The proofs are obtained by using the techniques of fixed point theorems, semi-group theory and generalized Bellman inequality. In this paper, we have used the distributed characteristic operators to define the mild solution of the system. Results obtained here improve and extend some known results.

This work aims to investigate the effect of catalyst content and reaction time by catalytic upgrading from pyrolysis vapors of residual fat at 450 °C and 1.0 atmosphere, on the yields of reaction products, physicochemical properties (density, kinematic viscosity, refractive index, and acid value) and chemical composition of organic liquid products (OLP), over a catalyst fixed bed reactor, in semi pilot scale. Pellets of Red Mud chemically activated with 1.0 M HCl were used as catalysts. The experiments were carried out at 450 °C and 1.0 atmosphere, using a process schema consisting of a thermal cracking reactor of 2.0 L coupled to a catalyst fixed bed reactor of 53 mL, without catalyst and using 5.0, 7.5, and 10.0% (wt.) Red Mud pellets activated with 1.0 M HCl, in batch mode. Samples of liquid phase products were withdrawn during the course of reaction at 40, 50, 60, 70 and 80 min in order to analyze the process kinetics. The physicochemical properties (density, kinematic viscosity, acid value, and refractive index) of OLP were determined by official methods. The chemical functions present in OLP determined by FT-IR and the chemical composition by GC-MS. The thermal catalytic cracking of residual fat show OLP yields from 54.4 to 84.88 (wt.%), aqueous phase yields between 2.21 and 2.80 (wt.%), solid phase yields (coke) between 1.30 and 8.60 (wt.%), and gas yields from 11.61 to 34.22 (wt.%). The yields of OLP increases with increasing catalyst content while those of aqueous, gaseous and solid phase decreases. For all the thermal and thermal catalytic cracking experiments, the density, kinematic viscosity, and acid value of OLP decreases with increasing reaction time. The GC-MS of liquid reaction products identified the presence of hydrocarbons (alkanes, alkenes, cycloalkanes, and aromatics) and oxygenates (carboxylic acids, ketones, esters, alcohols, and aldehydes). For all the thermal and thermal catalytic cracking experiments, the hydrocarbon content within OLP increases with reaction time, while those of oxygenates decrease, reaching concentrations of hydrocarbons up to 95.35% (area.). The best results for the physicochemical properties (density, kinematic viscosity, and acid value) and the maximum hydrocarbon content of OLP were obtained at 450 °C and 1.0 atmosphere, using a catalyst fixed bed reactor, with 5.0% (wt.) Red Mud pellets activated with 1.0 M HCl as catalyst.

In this paper, we consider the generalized sextic functional equation \begin{align*} \sum_{i=0}^{7}{}_7 C_{i} (-1)^{7-i}f(x+iy) = 0. \end{align*} And by applying the fixed point theory in the sense of L. C\u adariu and V. Radu, we will discuss the stability of the solutions for this functional equation.

This paper deals with the study of the existence and non existence of solutions of a three parameter's family of nonlinear fractional differential equation with mixed-integral boundary value conditions. We consider the $\alpha$-Riemann-Liouville fractional derivative, with $\alpha \in (1,2]$. In order to deduce the existence and non existence results, we first study the linear equation, by deducing the main properties of the related Green's functions. We obtain the optimal set of parameters where the Green's function has constant sign. After that, by means of the index theory, the nonlinear boundary value problem is studied. Some examples, at the end of the paper, are showed to illustrate the applicability of the obtained results.

In this article, we show the existence of fixed point for the derivative of interval-valued functions. Meanwhile, the fixed point inquiry will utilize the common fixed point methods under the condition of compatibility of the hybrid composite mappings in the sense of the Hausdorff metric. Some examples are given to support the usability of the result of this research .

With the increasing of copper consumption, the in-use stock of copper tends to increase. This paper used the “average use life method” to quantify the amount of copper in-use stock, and calculated the average age of in-use stock. It was indicated that the total in-use stock had an overall smooth trends, and reached its peak in 2007 was about 68.9 Mt (million tons), in addition, in-use stock per capita reached its peak ,234 kg/capita in 2001. The results demonstrated that during the period 1992-2002, the average age of copper in-use stock was continually decreased, but gradually increased since the year 2003. The fixed assets depreciation method used in this paper is applied to analyze depreciated copper in-use stock, and to analyze the relationship with economic indicator (GDP). It is demonstrated that it was inconsistent with the theory of Environmental Kuznets Curve (EKC) before 2000, this might be the demand for copper in the service sector is greater than the reduced strength of alternatives. Finally, scenario analysis of future copper in-use stock and depreciated copper in-use stock per capita in the U.S. were presented. The corresponding average age of the in-use stock will have a slight rise in the next decade.

This paper presents an extended Kalman filter derivation for loosely coupled GPS (Global Positioning System)/INS (Inertial Navigation System) integration based on quaternion attitude representation using the Earth-Centered Earth (ECEF) Frame. In this loosely coupling integration, both the position and velocity estimates from GPS receiver are used as the measurements to extended Kalman filter, and then they are integrated with inertial measurements from inertial measurement units (IMU) to estimate the attitude, position and velocity of an air vehicle. The velocity estimates which have centimeter level estimation error from the GPS receiver are used to improve the filter performance. For attitude estimation, the global attitude parameterization is given by a quaternion and a multiplicative quaternion-error approach is used to guarantee a normalization constraint of quaternion in the filter. Simulation results are shown to obtain the estimation of the attitude, position, velocity, biases and scale factors and to evaluate the performance of the EKF with the measurement combination composed of the two different t

Renewable energy sources will play a central role in the sustainable energy systems of the future. Scenario analyses of such hypothesized energy systems require sound knowledge of the techno-economic potential of renewable energy technologies. Although there have been various studies concerning the potential of offshore wind energy, higher spatial resolution, as well as the future design concepts of offshore wind turbines, has not yet been addressed in sufficient detail. Here, we aim to overcome this gap by applying a high spatial resolution to the three main aspects of offshore wind potential analysis, namely ocean suitability, the simulation of wind turbines and cost estimation. A set of constraints is determined that reveal the available areas for turbine placement across Europe’s maritime boundaries. Then, turbine designs specific to each location are selected by identifying turbines with the cheapest levelized cost of electricity (LCOE), restricted to capacities, hub heights and rotor diameters of between 3-20 MW, 80-200 m and 80-280 m, respectively. Ocean eligibility and turbine design are then combined to distribute turbines across the available areas. Finally, LCOE trends are calculated from the individual turbine costs, as well as the corresponding capacity factor obtained by hourly simulation with wind speeds from 1980 to 2017. The results of cost-optimal turbine design reveal that the overall potential for offshore wind energy across Europe will constitute nearly 8.6 TW and 40.0 PWh at roughly 7 €_ct kWh^-1 average LCOE by 2050. Averaged design parameters at national level are provided in an appendix.

In this paper, by means of the Banach fixed point theorem and the Krasnoselskii's fixed point theorem, we investigate the existence of solutions for some fractional neutral functional integro-differential equations involving infinite delay. This paper deals with the fractional equations in the sense of Caputo fractional derivative and in the Banach spaces. Our results generalize the previous works on this issue. Also, an analytical example is presented to illustrate our results.

The study uses annual time series data from the South Africa Reverse Bank (SARB) from 1980 to 2020 to examine the effectiveness of fiscal policy on economic growth in South Africa. The Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) unit root tests, as well as the Johansen Co-integration test, Granger causality test, and Vector Auto-Regression (VAR) method, were used in the study. Real GDP per capita (RGDP) is used as proxy of economic growth and gross fixed capital formation (GFCF), government expenditure (GEXP) and government deficit (GOVD) as the proxies of fiscal policy. The ADF test results show that all variables are stationary at the first difference, with the exception of GFCF and GEXP, which are stationary at I(0), whereas the PP test results show that all variables are stationary at I(1), with the exception of GEXP, which is stationary at I(0). At Maximum Eigenvalue, the four variables are not cointegrated. The findings of the Granger causality test demonstrated a unidirectional causation from GOVD to RGDP, as well as a bidirectional causality from RGDP to GFCF and GEXP. Error Correction Model Estimated using VAR shows that GFCF, GEXP have positive effect on RGDP whereas GOVD has a negative effect on RGDP in the short run. The findings also presented that the VAR's residuals are homoscedastic, which means they are normally distributed and have no serial correlation.

We analyze the modular geometry of the variable exponent Lebesgue space L^p(.). We show that L^p(.) possesses a modular uniform convexity property. Part of the novelty is that the property holds even in the case supp(x) = ∞ . We present specific applications to fixed point theory. xÆΩ

In this paper, we prove some random fixed point theorems for generalized random $\alpha-\psi-$contractive mappings in a Polish space and, as some applications, we show the existence of random solutions of second order random differential equation.

Acute low back pain (LBP) stands as a leading cause of activity limitation and work absenteeism, and its associated healthcare expenditures are expected to become substantial when acute LBP develops into a chronic and even refractory condition. Therefore, early intervention is crucial to prevent progression to chronic pain whose management is particularly challenging and for which the most effective pharmacological therapy is still controversial. Current guideline treatment recommendations vary and are mostly driven by expertise with opinion differing across different interventions. Thus, it is difficult to formulate evidence-based guidance when relatively few randomized clinical trials did explore the diagnosis and management of LBP while employing different selection criteria, statistical analyses, and outcome measurements. This narrative review aims to provide a critical appraisal of current acute LBP management by discussing the unmet needs and areas of improvement from bench-to-bedside and proposes multimodal analgesia as the way forward to attain an effective and prolonged pain relief and functional recovery in patients with acute LBP.

This study examines the spatial impact of FDI on the poverty of 44 African countries. In achieving this, the study uses the Driscoll-Kraay fixed effect instrumental variable regression, instrumental variable generalised method of moments estimator (IV-GMM), and the spatial durbin model. The empirical investigation of this study yielded four significant findings: (1) neighbouring countries’ FDI has a positive and significant impact on the incidence and intensity of host country’s poverty. (2) Improved institutional quality in neighbouring countries has a significant impact on FDI-poverty reduction nexus of the host country. (3) the empirical results lend support for a significant spatial spillover of poverty in the region. (4) the marginal effect results indicate that countries within the region are no longer in isolation or independent, i.e., the level of poverty in a particular country is influenced by its determinants in the neighbouring country. This result is robust to the alternative proximity matrix, which is the inverse distance. Since there is spatial interdependence among African countries, we recommend that African governments through the African Union (AU) should not only champion the institutional reform in the region, but also establish a binding mechanism to ensure reform implementation.

The purpose of this paper is to prove strong convergent theorems for Browder's type iterations and Halpern's type iterations of a family of nonexpansive mappings in a complete geodesic space with curvature bounded above by a positive number. Moudafi's viscosity type methods are also discussed without the nice projection property.

Causal relationships lie at the very core of our scientific description of biophysical phenomena. Nevertheless, observable facts such as chaotic dynamics, symmetry breaks, long-range collisionless neural interactions, zero-value energy singularities, particle/wave duality, ecological approaches to visual perception elude cause effect inductive explanations. We illustrate how simple topological claims, seemingly useless and far away from scientific inquiry (e.g., “given at least some wind on Earth, there must at all times be a cyclone or anticyclone somewhere”; “if one stirs to dissolve a lump of sugar in a cup of coffee, it appears there is always a point without motion”; “at any moment, there is always a pair of antipodal points on the Earth’s surface with equal temperatures and barometric pressures”) describe a real world, made of projections and mappings unsupplied with causality. Unavoidable, necessary, passive, spontaneous changes in systems’ shapes, dimensions and symmetries incarnate biophysical quantifiable counterparts of abstract mathematical concepts. Real features arising from topological mechanisms do not require causal powers to be produced, because are independent of exerted physical forces, energetic fields’ actions and thermodynamic constraints. Providing examples that shed novel interpretative light on phenomena such as double slit experiments, cellular mechanisms and brain function, we conclude as follows: countless scientific matters can be accessed through methodological weapons which not just break causality, replace temporal correlations and probabilistic a priori knowledge of previous cases, but also permit augments in available information devoid of entropy increases and energy losses.

The Doubly-Fed Induction Generator (DFIG) has significant features in comparison with Fixed Speed Wind Turbine (FSWT), which has popularized its application in power system. Due to partial rated back-to-back converters in the DFIG, Fault Ride-Through (FRT) capability improvement is one of the great subjects regarding new grid code requirements. To enhance the FRT capability of the DFIG, many studies have been carried out. Fault current limiting devices as one of the techniques are utilized to limit the current level and protect switches of the back-to-back converter from over-current damage. In this paper, a review is done based on fault current limiting characteristic of the proposed fault current limiting devices Therefore, Fault Current Limiters (FCLs) and Series Dynamic Braking Resistors (SDBRs) are mainly taken into account. Operation of all configurations including their advantages and disadvantages is explained. Impedance type and the fault current limiting devices’ location are two important factors, which significantly affect the DFIG behaviour in the fault condition. These two factors are basically studied by the simulation and their effects on the key parameters of the DFIG are investigated. Finally, future works in respect to the FCL application in the FRT improvement of the DFIG have also been discussed.

In the present work we study the existence of solutions for hybrid nonlinear fractional integrodifferential equations. We developed an algorithm by using the operator theoretical techniques in order to obtain the approximate solutions. The main results depend on the Dhage iteration method that were incorporated with the modern hybrid fixed point theorems. The approximate solutions were obtained by using Lipschitz conditions and weaker form of mixed partial continuity. Further, we provide some examples to explain the hypotheses and the related results.

In this paper, we study a three step iterative scheme to approximate fixed points of Suzuki's generalized non-expansive mappings. We establish some weak and strong convergence results for such mappings in uniformly convex Banach spaces. Further, we show numerically that iterative scheme (1.8) converges faster than some other known iterations for Suzuki's generalized non-expansive mappings. To support our claim, we give an illustrative example and approximate fixed points of such mappings using Matlab program. Our results are new and generalize several relevant results in the literature.

We prove a version of Ekeland Variational Principle (EkVP) in a weighted graph $G$ and its equivalence to Caristi fixed point theorem and to Takahashi minimization principle. The usual completeness and topological notions are replaced with some weaker versions expressed in terms of the graph $G$. The main tool used in the proof is the OSC property for sequences in a graph. Converse results, meaning the completeness of graphs for which one of these principles holds is also considered.

In this work, we extend the fundamental results of Schu to the class of monotone asymptotically nonexpansive mappings in modular function spaces. In particular, we study the behavior of the Fibonacci-Mann iteration process defined by $$x_{n+1} = t_n T^{\phi(n)}(x_n) + (1-t_n)x_n,$$ for $n \in \mathbb{N}$, when $T$ is a monotone asymptotically nonexpansive self-mapping.

It is known that the class of p-normed spaces (0 < p ≤ 1) is an important generalization of usual normed spaces with rich topological and geometrical structure, but the most of tools and general principles in nature with nonlinearity have not been developed yet, thus the main goal of this paper is to develop tools for nonlinear analysis under the framework of p-vector spaces. In particular, we first develop the general fixed point theorems which provide solutions to answer Schauder conjecture since 1930’s in the affirmative for p-vector spaces when p = 1 (which is just general topological vector spaces); then the one best approximation result for upper semi-continuous mappings is given, which is used as a powerful tool to establish fixed points for non-self set-valued mappings with either inward or outward set conditions; and finally we establish comprehensive existence results of solutions for Birkhoff-Kellogg Problems, and the general principle of nonlinear alternative by including Leray-Schauder alternative and related results. The results given in this paper not only include the corresponding results in the existing literature as special cases, but also expected to be useful tools for the study of nonlinear problems arising from theory to practice.