Uniqueness Results Research Articles

A generalized Gronwall inequality via $ \psi $-Hilfer proportional fractional operators and its applications to nonlocal Cauchy-type system

<p>This paper establishes a novel generalized Gronwall inequality concerning the $ \psi $-Hilfer proportional fractional operators. Before proving the main results, the solution of the linear nonlocal coupled $ \psi $-Hilfer proportional Cauchy-type system with constant coefficients under the Mittag-Leffler kernel is created. The uniqueness result for the proposed coupled system is established using Banach's contraction mapping principle. Furthermore, a variety of the Mittag-Leffler-Ulam-Hyers stability of the solutions for the proposed coupled system is investigated. Finally, a numerical example is given to show the effectiveness and applicability of the obtained results, and graphical simulations in the case of linear systems are shown.</p>

Some convergence results in modular spaces with application to a system of integral equations

<p>The paper aimed to achieve three primary objectives. First, it introduced significant common fixed point results in the context of newly proposed partial modular $ b- $metric spaces, thus contributing to the advancement of this field. Second, it presented unique results using a direct approach that did not depend on the strong continuity of the mapping, thereby offering a valuable perspective. Finally, it applied previously established convergence techniques to determine a common solution for a system of Fredholm integral equations, demonstrating the practical implications of the theoretical findings.</p>

Stability and Uniqueness Results for the Nonseparated Boundary Conditions of Nonlinear Coupled System of Fractional Differential Equations

In this article, the focus is on investigating the uniqueness, existence, and stability of a coupled system of fractional differential equations with non‐separated coupled boundary conditions. The uniqueness of solutions for the presented problem is discussed by employing the fixed‐point theorem. The Leray–Schauder’s alternative is used to investigate the existence of solutions for the presented equation. A formulation of certain conditions for the Hyers–Ulam type stability of solutions pertaining to the boundary value problem (BVP) is discussed. Finally, two numerical examples are presented to examine and illustrate our results.

Modeling Rift Valley fever transmission: insights from fractal-fractional dynamics with the Caputo derivative

<abstract><p>The infection caused by Rift Valley fever (RVF) virus is a dangerous vector-borne disease found in humans, domestic, and wild animals. It is transferred through insect vectors to ruminant host and then spread through direct contact of infected animals with their body fluid or organs. In this paper, a fractal-fractional model for the transmission of RVF in the Caputo's sense was presented. We analyzed the model and determined the basic reproduction number through the next-generation matrix technique, indicated by $ \mathcal{R}_0 $. The global sensitivity technique is used for the sensitivity test of $ \mathcal{R}_0 $ to find out the most sensitive input-factors to the reproduction parameter $ \mathcal{R}_0 $. The existence and uniqueness results of the proposed fractal-fractional model were established. Then, we presented the fractal-fractional dynamics of the proposed RVF model through a novel numerical scheme under the fractal-fractional Caputo operator. In the end, the recommended model of RVF was highlighted numerically with the variation of different input parameters of the system. The key factors of the system were highlighted to the policymakers for the control and prevention of the infection.</p></abstract>

TOPOLOGICAL DEGREE METHOD FOR A CLASS OF Ψ-CAPUTO FRACTIONAL DIFFERENTIAL LANGEVIN EQUATION

This paper deals with the existence and uniqueness of solution for a new class of Ψ-Caputo fractional differential Langevin equation. The suggested study is based on some basic definitions of topological degree theory and fractional calculus. We established the existence result by using the topological degree method for condensing maps, and by means of Banach’s fixed point theorem we obtained the uniqueness result. As application, we give an illustrative example to demonstrate our theoretical result.

Impact of social media usage on academic performance of university students: Mediating role of mental health under a cross-sectional study in Bangladesh.

Social media is undeniably more accessible and more appreciated today. It is undoubtedly one of the most crucial instruments for student communication. Mental health status can also meaningfully influence the students at the higher levels of the educational institutions. This study aims to evaluate the social media usage of university students and its impact on academic performance and mental health. To examine under confirmatory factor analysis (CFA) several scale measurements were confirmed by justifying the validity and reliability of several necessary indices and structural equation model. The mediation analysis was also estimated to evaluate the students' Social media addiction (employed Bergen Social Media Addiction Scale) under maximum likelihood estimation with 2000 bootstrapping and 95% bias-corrected bootstrap confidence intervals. This study shows that the usage of social media significantly improves academic performance on psychological well-being, with a Comparative Fit Index of 0.921 and an RMSEA of 0.06 indicating a good fit of the CFA model. Finally, we exhibit a strong statistically significant positive impact of social media usage on academic success, and as supporting the hypothesis, the study observed a positive mediating role of mental health between social media addiction and academic performance. The present research investigations produced unique results, that is, online social media enhances mental health and mediates the link between social media addiction and academic performance in Bangladeshi students. This finding also add to the empirical database on social media usage and have significant theoretical and practical ramifications.

Shinrin-Yoku (Forest Bathing): A Scoping Review of the Global Research on the Effects of Spending Time in Nature.

This Scoping review (ScR) builds upon the 2017 review conducted by Hansen et al which contributed to evidence base shinrin-yoku (SY), also known as forest bathing (FB), has many positive health effects and is becoming a prescribed dose (specific time spent in nature) by health care providers. Practice and research regarding SY, has been historically based in Asian countries with a recent increase in Europe. The need and call for more research worldwide continues to further the evidence of SY as a health promotion modality. Through this ScR the authors identified programmatic components, health information monitored and screened, time spent in nature, geographical regions, trends, and themes in SY research worldwide. Following PRISMA-ScR guidelines we searched across 7 electronic databases for SY or FB research articles from 2017 through 2022. PubMed, CINAHL, PsycInfo, ScienceDirect, SCOPUS, Embase, JSTOR were included due to the interdisciplinary nature of SY or FB research. Each database provided unique strengths ensuring a capture of a wide range of articles. The resulting articles were screened and extracted through Covidence. Database searches returned 241 results, with 110 references removed during the deduplication process, 131 were initially screened in the title and abstract review stage. Resulting in 82 unique results deemed relevant and screened in full text. During the final stage of the review, 63 articles met all inclusion criteria and were extracted for data. The practice of SY has physiological (PHYS) and psychological (PSYCH) benefits across age groups. Research findings indicate either the natural or the virtual environment (VW) has significant health benefits. Continued research is encouraged globally for short- and long-term health outcomes for all individuals. The connection with nature benefits the mind, body and soul and is supported by Henry David Thoreau's philosophy: "Our livesneed the relief of where the pine flourishes and the jay still scream."

Chemometrically assisted differential pulse voltammetry for simultaneous and interference-free quantification of gallic and caffeic acids.

This article explores the application of chemometric tools including multivariate curve resolution with alternating least squares for the simultaneous determination of gallic and caffeic acids on the surface of a glassy carbon electrode without additional modification. Gallic and caffeic acids are primary polyphenols, the most abundant in red wines produced in Argentina, and are often used as quality markers for them. These polyphenols significantly contribute to the organoleptic properties of wines from this origin, but their electrochemical signals overlap significantly, making simultaneous quantification challenging without additional experiments such as electrode modification or alternative analytical techniques beyond differential pulse voltammetry. This study successfully quantified these compounds in complex mixtures by generating second-order data from differential pulse voltammetry experiments conducted at various potential steps and subsequently applying multivariate curve resolution with alternating least squares. The use of constraints during optimization prevented rotational ambiguities common in this modeling, leading to unique results in validation samples. The limits of detection (LOD) found for gallic and caffeic acids were 1.6 and 7.6 mg L-1, which are in excellent agreement with the expected concentrations of these compounds in red wines. The concentration ranges analyzed showed a linear dependency (between the LOD and 300 mg L-1) with the signals estimated by the model for both analytes. Advantages such as simplicity, low cost, and high speed, as well as not requiring electrode modification, combined with excellent results obtained for real samples, make it a promising alternative for polyphenol analysis in the wine industry.

Effectiveness of conservation measures to support biodiversity in boreal timber-production forests

Large parts of the boreal forest ecosystems have been greatly affected by human use, and the current timber-oriented forest management practice that dominates boreal forests is proven to cause biodiversity and ecosystem services declines. These negative effects are mitigated in various ways, including in-situ measures implemented upon harvest. The measures comprise trade-offs between economic and ecological aims; thus, requiring solid knowledge of their effectiveness. However, comprehensive literature review of the effectiveness of such measures is scarce. We aim to fill part of this void by reviewing the scientific literature that have gauged effects of four in-situ conservation measures: green tree retention (GTR), patch retention (PR), dead wood retention (DW) and riparian buffer zones (RB). Two outcomes were considered, species richness and species abundance across taxa. From a total of 3012 initial papers, 48 met our inclusion criteria that generated 238 unique results. Results were grouped according to control. 178 studies used mature, unlogged forest as control. Out of those, 68% of the findings were not significant, i.e., suggesting no significant impact of harvest with biodiversity measures on species richness and species abundance compared to no harvest. Eighteen percent of the observations showed negative effects and 14% of the observations showed positive effects compared to no harvest. Sixty studies used harvest with no measures as control, of which 45% showed significant positive effects, meaning that compared to harvest with no measures, harvest with conservation measures has positively effects on species richness and abundance. However, 43% of the studies found no significant effect of the implemented conservation measures compared to harvest with no measures taken. The relatively few significant results reported restrain distinct conclusions on the effectiveness of the assessed conservation measures, but some degree of conservation measure is likely to have positive effects on biodiversity in timber-production forest. However, the scientific basis does not allow for pointing to threshold levels. Higher transparency of study design and statistical results would allow us to include more studies. There is a clear need for more research of effectiveness of common conservation measures in timber-production forests in order to strengthen the knowledge basis. In particular, there are few studies that employ harvest without any conservation measure as control. This is pivotal knowledge for forest managers as well as for policymakers for preserving biodiversity and the ecosystems in forest.

Response of Non-local and Heat Source in Moore-Gibson-Thompson Theory of Thermoelasticity with Hyperbolic Two Temperature

A new mathematical model of the Moore–Gibson–Thompson (MGT) theory of thermoelasticity under non-local and hyperbolic two-temperature (HTT) has been developed. The preliminary equations are put in two-dimensional form and are converted into dimensionless form. The obtained equations are simplified by applying potential functions. The Laplace transform w.r.t time variable and Fourier transforms w.r.t space variable are employed in the resulting equations. The assumed model has been used to explore the outcome of heat source in the form of a laser pulse decaying with time and moving with constant velocity in one direction. The problem is further examined with normal distributed force and ramp type thermal source. In the transformed domain, the physical field quantities like displacements, stresses, conductive temperature, and thermodynamic temperature are obtained. The resulting expressions are obtained numerically with the numerical inversion technique of the transforms. In simulation, various impacts such as non-local, heat source velocity-time, and HTT are examined and presented in the form of figures. Unique results are also deduced.

Co-doping of Fe2O3 nanoparticles with Y and Zr by green synthesis

The study aims to co-dope nanoparticles of iron oxide with yttrium and zirconium by one-pot green synthesis method using freshly plucked Simarouba Glauca (Paradise tree) leaf extract. The focus is on the effect of co-doping and also the effect of different annealing durations such as 2–4 h at a constant temperature of 600 °C. The nanoparticles were characterized using various techniques, such as Scanning Electron Microscopy (SEM), Transmission Electron Microscopy (TEM), X-ray Diffraction (XRD), Ultraviolet-visible Spectroscopy (UV–vis), Raman Spectroscopy, and Fourier Transform Infrared Spectroscopy (FT-IR). Antibacterial tests on Gram-positive and Gram-negative bacteria were performed to determine the bactericidal activity of the samples. The particle size was calculated to be around 55.95 nm through Bright Field-TEM (BF-TEM) images. XRD data confirms doping and indicates the formation of haematite phase with crystallite size increasing from 1.94 to 41.17 nm on increasing annealing duration and the phase was confirmed through HR-TEM data. Bandgap calculated through UV–vis data shows a decrease from 2.13 to 2.09 eV. Annealing duration had a notable effect on the crystallinity of the samples and their bandgap, but had no impact on their antibacterial properties. A unique result was observed in the degradation of methylene blue, where the reduced form of methylene blue undergoes a reversible change to reproduce methylene blue after a certain period. Liquid Chromatography Mass Spectrometry (LC-MS) was used to identify the intermediates and the products formed on catalysis. The result was a simultaneous reduction, oxidation and demethylation, as all three corresponding intermediates were formed.

Inverse coefficient problem for a time‐fractional wave equation with initial‐boundary and integral type overdetermination conditions

This paper considers the inverse problem of determining the time‐dependent coefficient in the time‐fractional diffusion‐wave equation. In this case, an initial boundary value problem was set for the fractional diffusion‐wave equation, and an additional condition was given for the inverse problem of determining the coefficient from this equation. First of all, it was considered the initial boundary value problem. By the Fourier method, this problem is reduced to equivalent integral equations. Then, using the Mittag‐Leffler function and the generalized singular Gronwall inequality, we get a priori estimate for solution via unknown coefficient which we will need to study of the inverse problem. The inverse problem is reduced to the equivalent integral of equation of Volterra type. The principle of contracted mapping is used to solve this equation. Local existence and global uniqueness results are proved. The stability estimate is also obtained.

A kinetic model with time‐dependent proliferative/destructive rates

This paper presents a new kinetic model with time‐dependent proliferative/destructive parameters, where the activity variable of the system attains its values in a discrete real subset. Therefore, a system of nonautonomous nonlinear ordinary differential equations is gained, with the related Cauchy problem. A first result of local existence and uniqueness of positive and bounded solution is proved. Then, the possibility of extend this result globally in time is discussed, with respect to the shape of nonconservative time‐dependent parameters. Numerical simulations are performed for some scenarios, corresponding to different shapes of time‐dependent parameters themselves. Furthermore, the pattern and long‐time behavior of solutions are numerically analyzed. Finally, these results show that equilibria and oscillations may occur.

Multi-Scale Analysis of Lithium-Sulfur Pouch Cells Using Imaging Methods

Lithium-sulfur batteries (Li-S) are promising energy storage technologies. Its high gravimetric energy density, the abundance of sulfur and low costs at high production volume, this battery type is especially applicable for automotive and aerospace applications. In recent years, the number of reported prototype cells has increased, as well as their accessible energy density. This underlines the progress of technology readiness of the Li-S system. However, despite this important breakthrough density and cycling stability have to be overcome in the Li-S research. Additionally, the influence of the cathode porosity as well as the surface of the carbon material and the electrolyte composition play an important role on the conversion of sulfur and the performance of prototype cells.Hard X-ray beamlines, as BAMline at the electron storage ring BESSY II in Berlin, Germany, have now been in service for over two decades. Several improvements have been implemented, allowing for operando tomography and fast radiographic measurements on the micrometer scale by using well-shaped synchrotron X-ray beam. In this study, operando X-ray imaging measurements on Li-S pouch cells are complemented by scanning and transmission electron microscopy and focused-ion-beam measurements on the nanometer scale delivering unique and multi-scale results about the morphology of sulfur inside the porous cathode material. Therefore, tiny pouch cells designs have been developed, allowing for operando tomography of stacked cells. Figure 1

Existence Result for Coupled Random First-Order Impulsive Differential Equations with Infinite Delay

In this paper, we consider a system of random impulsive differential equations with infinite delay. When utilizing the nonlinear variation of Leray–Schauder’s fixed-point principles together with a technique based on separable vector-valued metrics to establish sufficient conditions for the existence of solutions, under suitable assumptions on Y1, Y2 and ϖ1, ϖ2, which greatly enriched the existence literature on this system, there is, however, no hope to discuss the uniqueness result in a convex case. In the present study, we analyzed the influence of the impulsive and infinite delay on the solutions to our system. In addition, to the best of our acknowledge, there is no result concerning coupled random system in the presence of impulsive and infinite delay.

Unique laboratory “Currents in the ground”

A brief description of the scientific laboratory is given, which has become a flagship in the field of electrical energy, which made it possible to obtain unique results on grounding and electrical safety, which were included in state regulatory documents. It is shown that a well-known scientific school has been created in the laboratory for the study of processes in grounding devices of electrical installations. The laboratory was founded in 1971 and has not been described previously. The article shows the main building in the form of a two-story building and a nearby stack-type pulse voltage generator for a voltage of 1,250,000 V. The circuit allows for reconnecting capacitors on floors to obtain different capacitances in the discharge. To connect to the grounding device under study, a portable overhead line with split wires is used. A map of grounding fields on the laboratory territory is provided. This allows you to design almost any design of a grounding device. Fields of vertical and horizontal grounding conductors of various lengths are used; fields of complex mesh grounding conductors; groups of single vertical electrodes of different lengths. The laboratory has several sets of self-powered electronic high-speed oscilloscopes, shielded and isolated from ground to avoid interference. The range of research questions can be significantly expanded by using already installed objects: an experimental overhead line with a voltage of 220 kV on nine reinforced concrete supports; cable line 600m long; a dynamic and thermal test stand, equipped with a circuit for obtaining industrial frequency currents of up to 4 kA at a voltage of 0.4 kV; 120 linear meters of reinforced concrete trays were laid on the field of a complex mesh grounding device for laying communication and control cables in them; two additional pulse voltage generators 1,600,000 V and 1,000,000 V (the latter allows transportation to full-scale test sites outside the laboratory); test transformers IOM-100/100.

Physical activity following discharge from inpatient adult mental health settings

BackgroundPeople with severe mental illness are considerably less physically active than the general population and experience a premature mortality of 10–20 years, often attributed to modifiable behaviours, including physical activity. Inpatient environments provide opportunities for people with SMI to become more physically active, however evidence is limited on its sustainability following discharge to community settings. ObjectiveThis review aimed to summarise the published evidence relating to physical activity interventions following discharge from inpatient adult mental health settings. DesignMEDLINE, CINAHL, PsycINFO and AMED databases were searched to identify articles considering physical activity interventions taking place following discharge from an adult (>18) inpatient mental health setting, published after 2007. ResultsOf 3412 unique results, 5 studies were eligible for inclusion. Despite all included studies involving some transition between inpatient and community mental health settings, to-date no study has focused exclusively on physical activity interventions delivered following discharge from inpatient mental health settings. ConclusionsThis review has found insufficient evidence to guide the delivery of physical activity following discharge from inpatient mental health services. Future research is required to improve our knowledge of the optimal forms and delivery of physical activity interventions during this time, alongside quantifying the impact on readmission rates and clinical presentation.

Uniqueness of Meromorphic Functions With Nonlinear Differential Polynomials Sharing a Small Function IM

In the paper, we discuss the distribution of uniqueness and its elements over the extended complex plane from different polynomials of view. We obtain some new results regarding the structure and position of uniqueness. These new results have immense applications like classifying different expressions to be or not to be unique. The principal objective of the paper is to study the uniqueness of meromorphic functions when sharing a small function $a(z)$ IM with restricted finite order and its nonlinear differential polynomials. The lemma on the logarithmic derivative by Halburb and Korhonen (Journal of Mathematical Analysis and Applications, \textbf{314} (2006), 477--87) is the starting point of this kind of research. In this direction, the current focus in this field involves exploring unique results for the differential-difference polynomials of meromorphic functions, covering both derivatives and differences. Liu et al. (Applied Mathematics A Journal of Chinese Universities, \textbf{27} (2012), 94--104) have notably contributed to this research. Their research establishes that when $n \leq k + 2$ for a finite-order transcendental entire function $f$ the differential-difference polynomial$[f^{n}f(z+c)]^{(k)} - \alpha(z)$ has infinitely many zeros. Here, $\alpha(z)$ is characterized by its smallness relatively to $f$. Additionally, for two distinct meromorphic functions $f$ and $g$, both of finite order, if the differential-difference polynomials $[f^{n}f(z+c)]^{(k)}$\ and\ $[g^{n}g(z+c)]^{(k)}$ share the value $1$ in the same set, then $f(z)=c_1e^{dz},$ $g(z)=c_2e^{-dz}.$ We prove two results, which significantly generalize the results of Dyavanal and Mathai (Ukrainian Math. J., \textbf{71} (2019), 1032--1042), and Zhang and Xu (Comput. Math. Appl., \textbf{61} (2011), 722-730) and citing a proper example we have shown that the result is true only for a particular case. Finally, we present the compact version of the same result as an improvement.

Investment project management paradigm: budgeting challenges

Introduction. The paper discusses methods of investment capital budget management, which adapts budget management practices and increases synergy with project management, adjusting the allocation of resources in accordance with the constraints and operational risks of business processes. Businesses regularly use project management to achieve unique results with limited resources under critical time constraints. In the service sector of the economy (in particular, trade), the use of project management to achieve organizational goals is even more common. The purpose of the paper is the application of the budgeting system in the management of the investment project. Results. As a result, it encourages flexibility in dealing with contingencies, focus on a strategic perspective, speed of budget management, cost-effective budgeting, added value to the enterprise and encouragement of collaboration. Thus, constraints can be operational or managerial, related to organizational politics and culture. To identify constraints in an organization, you must understand how the organization works as a system. In the business sphere, the functioning of the company is a vision of business processes. Business processes are sets of activities that create results (products and services) whose value is perceived by interest groups (stakeholders). The impact of deterministic decisions in the short term on the overall result of the organization decreases. However, budget management methods do not represent a probabilistic approach, as seen in the proposal of the critical path method as a means of improving project management in a volatile business environment. Conclusion. It is recommended that each capital investment of the organization be structured in the form of projects, and the method of rewarding managers should also reward those who achieve goals with minimal use of investment resources. If possible, the manager should strive to evenly return resources to investment capital. Finally, it is suggested for future research to identify other business practices that can benefit from this paradigm shift.

Bounded solutions in incompressible hydrodynamics

In this article, we study bounded solutions of Euler-type equations on Rd which have no integrability at |x|→+∞. As has been previously noted, such solutions fail to achieve uniqueness in an initial value problem, even under strong smoothness conditions. This contrasts with well-posedness results that have been obtained by using the Leray projection operator in these equations. This apparent paradox is solved by noting that using the Leray projector requires an extra condition the solutions must fulfill at |x|→+∞. Our goal is to find one such condition which is sharp. We then apply the methods we develop to prove a full uniqueness result for Besov-Lipschitz solutions, as to the theory of Serfati solutions. In the last Section, we see how these techniques also apply to the Elsässer variables used in ideal MHD.