Positive Parameter Research Articles

Gumbel–Logistic Unit Distribution with Application in Telecommunications Data Modeling

The manuscript deals with a new unit distribution that depends on two positive parameters. The distribution itself was obtained from the Gumbel distribution, i.e., by its transformation, using generalized logistic mapping, into a unit interval. In this way, the so-called Gumbel-logistic unit (abbr. GLU) distribution is obtained, and its key properties, such as cumulative distribution function, modality, hazard and quantile function, moment-based characteristics, Bayesian inferences and entropy, have been investigated in detail. Among others, it is shown that the GLU distribution, unlike the Gumbel one which is always positively asymmetric, can take both asymmetric forms. An estimation of the parameters of the GLU distribution, based on its quantiles, is also performed, together with asymptotic properties of the estimates thus obtained and their numerical simulation. Finally, the GLU distribution has been applied in modeling the empirical distributions of some real-world data related to telecommunications.

On singular foliations tangent to a given hypersurface

We consider a class of singular foliations in the sense of Androulidakis and Skandalis that we call transverse order k foliations. These have a finite number of leaves: one hypersurface (the singular leaf) together with the components of its complement (open leaves). The positive integer parameter k encodes the “order of tangency” of the leafwise vector fields to L . We show that a loop in the singular leaf induces a well-defined holonomy transformation at the level of (k-1) -jets. The resulting holonomy invariant can be used to give a complete classification of these foliations and obtain concrete descriptions of their associated groupoids and algebras.

Phase transitions, critical behavior and microstructure of the FRW universe in the framework of higher order GUP

In this paper, we explore the phase transition, critical behavior and microstructure of the FRW in the framework of a new higher order generalized uncertainty principle (GUP). Our initial step involves deriving the equation of state by defining the work density W from GUP corrected Friedmann equations as the thermodynamic pressure P. Based on the modified equation of state, we conduct an analysis of the P−V phase transition in the FRW universe. Subsequently, we obtain the critical exponents and coexistence curves for the small and large phases of the FRW universe around the critical point. Finally, employing Ruppeiner geometry, we derive the thermodynamic curvature scalar RN, investigating its sign-changing curve and spinodal curve. The results reveal distinctive thermodynamic properties for FRW universes with positive and negative GUP parameters β. In the case of β>0, the phase transition, critical behavior and microstructure of FRW universe are like those of Van der Waals system and charged AdS. Conversely, for β<0, the results resemble those obtained through effective scalar field theory. These findings underscore the capacity of quantum gravity to induce phase transitions in the universe, warranting further in-depth exploration.

Poisson transform and unipotent complex geometry

Our concern is with Riemannian symmetric spaces Z=G/K of the non-compact type and more precisely with the Poisson transform Pλ which maps generalized functions on the boundary ∂Z to λ-eigenfunctions on Z. Special emphasis is given to a maximal unipotent group N<G which naturally acts on both Z and ∂Z. The N-orbits on Z are parametrized by a torus A=(R>0)r<G (Iwasawa) and letting the level a∈A tend to 0 on a ray we retrieve N via lima→0⁡Na as an open dense orbit in ∂Z (Bruhat). For positive parameters λ the Poisson transform Pλ is defined and injective for functions f∈L2(N) and we give a novel characterization of Pλ(L2(N)) in terms of complex analysis. For that we view eigenfunctions ϕ=Pλ(f) as families (ϕa)a∈A of functions on the N-orbits, i.e. ϕa(n)=ϕ(na) for n∈N. The general theory then tells us that there is a tube domain T=Nexp⁡(iΛ)⊂NC such that each ϕa extends to a holomorphic function on the scaled tube Ta=Nexp⁡(iAd(a)Λ). We define a class of N-invariant weight functions wλ on the tube T, rescale them for every a∈A to a weight wλ,a on Ta, and show that each ϕa lies in the L2-weighted Bergman space B(Ta,wλ,a):=O(Ta)∩L2(Ta,wλ,a). The main result of the article then describes Pλ(L2(N)) as those eigenfunctions ϕ for which ϕa∈B(Ta,wλ,a) and‖ϕ‖:=supa∈A⁡aReλ−2ρ‖ϕa‖Ba,λ<∞ holds.

Role of biquadratic exchange on thermodynamic quantities in anisotropic Heisenberg model

The magnetic and thermodynamic properties of the spin-1 anisotropic Heisenberg system are studied within Oguchi approximation. The system contains both the bilinear and biquadratic exchange interactions between the nearest neighboring spins located on a centered honeycomb lattice. For the positive biquadratic exchange interaction parameters, the phase transition in the Heisenberg case is of both second and first order where there is a discontinuity in the thermodynamic properties at this transition temperature. For some negative biquadratic exchange interaction parameters, in both the Heisenberg and Ising cases, the ferromagnetic state changes in favor of the antiferromagnetic state. The frustrated antiferromagnetic structure created by the biquadratic exchange parameter with negative sign was shown significantly influence the magnetization, quadrupolar moment, internal energy, heat capacity, entropy and free energy of the system, where the system has an oscillating chaotic phase regime. A double peak behavior was observed in the specific heat, with one at the critical temperature and another at a low temperature.

Branching random walks with regularly varying perturbations

We consider a modification of classical branching random walk, where we add i.i.d. perturbations to the positions of the particles in each generation. In this model, which was introduced and studied by Bandyopadhyay and Ghosh (2023), perturbations take the form 1/θ log X/E where θ is a positive parameter, X has an arbitrary distribution μ and E is exponential with parameter 1, independent of X. Working under finite mean assumption for μ, they proved almost sure convergence of the rightmost position to a constant limit, and identified the weak centered asymptotics when θ does not exceed certain critical parameter θ_0 . This paper complements their work by providing weak centered asymptotics for the case when θ &gt; θ_0 and presenting the results to μ with regularly varying tails. We prove almost sure convergence of the rightmost position and identify the appropriate centering for the weak convergence, which is of form αn + c log n, with constants α, c depending on the ratio of θ and θ_0. We describe the limiting distribution and provide explicitly the constants appearing in the centering.

Scalarization of Taub-NUT black holes in extended scalar-tensor-Gauss-Bonnet theory

Recently, the scalarization of the Schwarzschild black hole has been extensively studied. In this work, we explore the scalarization of the Taub-NUT black hole within the context of the extended scalar-tensor-Gauss-Bonnet theory, which admits a Ricci-flat Taub-NUT black hole as a solution. We carried out an analysis of the probe scalar field to identify the mass parameter and NUT parameter (m, n) where hairy black holes begin to emerge. Subsequently, we used the shooting method to construct the scalarized Taub-NUT black hole numerically. Unlike the Schwarzschild case, there are two branches of new hairy black holes that are smoothly connected. We calculated the entropy of the scalarized black holes and compared these entropies with those of scalar-free Taub-NUT black holes, finding that the entropies of the new hairy black holes are larger. A novel phenomenon emerges in this system: the entropy of the black holes at the bifurcation point is constant for a positive mass parameter. We then conjecture a maximal entropy bound for all scalarized black holes whose mass parameter at the bifurcation point is greater than zero.

Extending the blended generalized extreme value distribution

AbstractThe generalized extreme value (GEV) distribution is commonly employed to help estimate the likelihood of extreme events in many geophysical and other application areas. The recently proposed blended generalized extreme value (bGEV) distribution modifies the GEV with positive shape parameter to avoid a hard lower bound that complicates fitting and inference. Here, the bGEV is extended to the GEV with negative shape parameter, avoiding a hard upper bound that is unrealistic in many applications. This extended bGEV is shown to improve on the GEV for forecasting heat and sea level extremes based on past data. Software implementing this bGEV and applying it to the example temperature and sea level data is provided.

Microstructural abnormalities of the right hemisphere in preschool autism spectrum disorders

BackgroundThis study aims to investigate microstructural abnormalities within and between hemispheres in preschool children with autism spectrum disorders (ASD) using diffusion basis spectrum imaging (DBSI). MethodsA total of 35 ASD patients and 32 healthy controls (HC), matched for sex and age, underwent DBSI at 3T. We analyzed DBSI-derived indices of brain white matter using tract-based spatial statistics (TBSS) to compare ASD and HC groups. Support vector machine (SVM) classification was employed to evaluate the potential of positive DBSI parameters in distinguishing ASD patients. Additionally, correlation analyses were conducted to explore relationships between positive DBSI parameters and clinical scales. ResultsPatients in the ASD group exhibited significantly higher fiber ratios in the right brainstem tracts, increased radial diffusivity in the left superior longitudinal fasciculus, and reduced fractional anisotropy (FA) in various fiber tracts, including projection, commissural, and association fibers, compared to HC. Notably, the FA of the right cingulum correlated positively with the Gesell scale (r = 0.439, p = 0.008) and achieved a specificity of 90% in identifying ASD. ConclusionThe DBSI findings suggest asynchronous myelination in the right hemisphere and cerebellum in preschool ASD, with the FA value of the right cingulate gyrus appearing to be a reliable marker for ASD and may serve as a potential diagnostic parameter for preschool ASD.

A deterministic Analysis of an Age-Gender structured model for malaria transmission dynamics

Objectives: Children below five years and women especially pregnant women are at high risk of malaria infection and death due to their weak immunity and exposition to mosquitoes. Different studies have been undertaken considering only the age structured model and other factors but did not take into account the gender. The objective of this work is to develop and analyze the malaria transmission model including this structure, to contribute on the existing measures and mechanisms to eradicate malaria in Rwanda.Methods: The dynamic malaria transmission model considering age and gender structure was developed and analyzed. To study the dynamics of disease, the basic reproduction number was analytically computed and numerically estimated and the normalized forward sensitivity index was used to highlight its sensitive parameters.Results: The most positive sensitive parameters in the model are the force of infection and infection rate for vectors and Infection rate for female of 5 years and above. The most negative sensitive parameters are the per capita death rate for vectors and humans.Conclusion: To control the spread of malaria in Rwanda, the biting and infection rate should be decreased.Therefore, women must comply with government measures against malaria and educate children about it.

Value-Positivity for Matrix Games

Matrix games are the most basic model in game theory, and yet robustness with respect to small perturbations of the matrix entries is not fully understood. In this paper, we introduce value positivity and uniform value positivity, two properties that refine the notion of optimality in the context of polynomially perturbed matrix games. The first concept captures how the value depends on the perturbation parameter, and the second consists of the existence of a fixed strategy that guarantees the value of the unperturbed matrix game for every sufficiently small positive parameter. We provide polynomial-time algorithms to check whether a polynomially perturbed matrix game satisfies these properties. We further provide the functional form for a parameterized optimal strategy and the value function. Finally, we translate our results to linear programming and stochastic games, where value positivity is related to the existence of robust solutions. Funding: This research was supported by Fondation CFM pour la Recherche, the H2020 European Research Council [Grant ERC-CoG-863818 (ForM-SMArt)], the Austrian Science Fund [Grant 10.55776/COE12], ANID Chile [Grant ACT210005], and Agence Nationale de la Recherche [Grant ANR-21-CE40-0020].

Generalized boson and fermion operators with a maximal total occupation property

Abstract We propose a new generalization of the standard (anti-)commutation relations for creation and annihilation operators of bosons and fermions. These relations preserve the usual symmetry properties of bosons and fermions. Only the standard (anti-)commutator relation involving one creation and one annihilation operator is deformed by introducing fractional coefficients, containing a positive integer parameter p. The Fock space is determined by the classical definition. The new relations are chosen in such a way that the total occupation number in the system has the maximum value p. From the actions of creation and annihilation operators in the Fock space, a group theoretical framework is determined, and from here the correspondence with known particle statistics is established.

SS-DNN: A hybrid strang splitting deep neural network approach for solving the Allen–Cahn equation

The Allen–Cahn equation is a fundamental partial differential equation that describes phase separation and interface motion in materials science, physics, and various other scientific domains. The presence of interfacial width (ϵ) between two stable phases, associated with a nonlinear term, is a small positive parameter which makes the problem more challenging to solve as ϵ approaches zero. This paper proposes a novel hybrid deep splitting method to efficiently and accurately solve the Allen–Cahn equation in a convex polygonal domain in Rd(d=1,2,3). The method combines the benefits of deep learning and splitting strategies, leveraging the strengths of both approaches. Essentially, a second-order splitting method is employed to split the Allen–Cahn equation into two simpler linear and non-linear sub-problems. While the nonlinear sub-problem can be solved analytically, the deep neural network is utilized to approximate the linear sub-problem. By integrating deep learning into the splitting strategy, we achieve a more efficient and accurate solution for the Allen–Cahn equation, demonstrating promising results. We also derive an error estimate for the proposed hybrid method. Modified space adaptivity and transform learning techniques are employed to enhance the efficiency of the neural network.

Pengaruh Sistem Informasi Akuntansi dan Penerapan SAK EMKM terhadap Keberhasilan UMKM

The aim of this research is to determine the influence of the Accounting Information System and the Implementation of SAK EMKM on the Success of MSMEs in East Alok District. This research uses a quantitative approach with the nature of explanatory research. The sampling technique used saturated samples with a sample size of 30 people. The data collection technique used a questionnaire distributed to 30 respondents and the data analysis technique used multiple linear regression analysis using the Statistical Package for the Social Sciences (SPSS) version 23. From the research results it was found that the variables Accounting Information System (X1) and Implementation of SAK EMKM (X2) influences the success of MSMEs (Y) with positive parameters, which means that the better or higher the level of implementation of the Accounting Information System and EMKM SAK, the higher the level of success of MSMEs. The influence of the Accounting Information System (X1) and the Implementation of SAK EMKM (X2) is 72.9% on the Success of MSMEs (Y) of the Basic Food Kiosk Business in East Alok District, while 27.1% is influenced by other factors outside the research variables.

Nontrivial solutions for multiparameter k-Hessian systems

This paper is devoted to studying the coupled system of multiparameter k-Hessian equations where B = {x ∈ ℝ n : |x| < 1}, λ1, λ2 are positive parameters, ρi (i = 1, 2) is singular near the boundary ∂B, f i(i = 1, 2) satisfies a combined superlinear condition at ∞. Employing the fixed point theorem of Krasnosel’skii type in Banach space, the existence and multiplicity of nontrivial radial solutions are established. In particular, the dependence of the solutions on the parameters λ1, λ2 is also discussed. Finally, we study the nonexistence results of nontrivial radial solutions for the case λ1, λ2 ≫ 1.

A parameter-uniform hybrid method for singularly perturbed parabolic 2D convection-diffusion-reaction problems

The solution of the singular perturbation problems (SPP) of convection-diffusion-reaction type may exhibit regular and corner layers in a rectangular domain. In this work, we construct and analyze a parameter-uniform operator-splitting alternating direction implicit (ADI) scheme to efficiently solve a two-dimensional parabolic singularly perturbed problem with two positive parameters. The proposed model is a combination of the backward-Euler method defined on a uniform mesh in time and a hybrid method in space defined on a special Shishkin mesh. The analysis is presented on a layer adapted piecewise-uniform Shishkin mesh. The developed numerical method is proved to be first-order convergent in time and almost second-order convergent in space. The numerical experiments are performed to validate the theoretical convergence results and illustrate the efficiency of the current strategy.

Investigation of bi-directional relations between pre-sleep electronic media use and sleep: A seven-day dairy study

The current study aimed to examine the bi-directional relationships between pre-sleep electronic media use and sleep, and to assess the relative predictive strength of different types of electronic media use in the evening on subsequent sleep. Eighty-eight young adults (20.57 ± 0.99, 27 males) completed an online intake survey and received notifications to complete daily diaries for seven consecutive days. Results of dynamic structural equation models (DSEM) revealed that the total screen time, sleep onset time, sleep latency, sleep duration, and sleep quality showed significant positive autoregressive parameters. In contrast, the results revealed no statistically significant cross-lagged associations between the total screen time in the evening and sleep outcomes. Inspection of the predictive strength of various types of screen activities at the within-person level revealed that increased active social media use is linked to delayed sleep onset, while internet browsing is associated with shorter sleep latency. At the between-person level, screen time of T.V. watching, video streaming, social media use, and shopping correlated with delayed sleep onset. Shopping was also connected to longer sleep latency. Additionally, more time spent on T.V., video streaming, non-work internet browsing, and shopping was linked to reduced total sleep duration. These findings indicated a screen activity-dependent association between pre-sleep screen time and subsequent sleep. More objective assessments of electronic media use (e.g., app recording screen time) and sleep (e.g., actigraphy) and longitudinal monitoring over a relatively long period (i.e., several weeks or months) are warred to further elucidate (cross-lagged) relationships between electronic media use and sleep.

Existence, concentration and multiplicity of solutions for (p,N)-Laplacian equations with convolution term

In this paper, we concern some qualitative properties of the following [Formula: see text]-Laplacian equations with convolution term: [Formula: see text] where [Formula: see text] is a positive parameter, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] satisfies the critical exponential growth. By using the variational methods and the penalization method, we prove the existence of solutions for the above equations which concentrates at a local minimum of [Formula: see text] in the semi-classical limit as [Formula: see text]. Moreover, we obtain the multiplicity of solutions for the above equations by the Morse theory.

Analysis of clinical characteristics of terbinafine-induced subacute cutaneous lupus erythematosus

ABSTRACT Introduction Terbinafine may cause subacute cutaneous lupus erythematosus (SCLE), and we aimed to analyze its clinical characteristics. Methods We collected literature on terbinafine-induced SCLE from 1997 to 2023 for retrospective analysis. Thirty-seven patients (33 females and 4 males) were included. Results The patients have a median age of 49.5 years (range 18–79) and onset time of 5 weeks (range 1–12). SCLE is mainly manifested as annular erythematous (83.3%), scaly erythematous (44.4%), and maculopapular erythematous (13.9%). Mainly, histopathological manifestations are lymphocytic infiltrate (55.6%), hyperkeratosis (38.9%) and keratinocyte necrosis (38.9%). Positive immunological parameters mainly include antinuclear antibody (100.0%), anti-Ro/SSA antibody (94.1%), and anti-La/SSB antibody (72.2%). Past medical history usually includes photosensitivity (33.3%), inflammatory disease (33.33%), and lupus erythematosus (12.1%). Symptoms are completely resolved within a median time of 35 days (range 7–84) after discontinuation of terbinafine and treatment with topical corticosteroids, systemic corticosteroids, hydroxychloroquine, and immunosuppressant. No recurrence was observed within 12 months (range 1.5–48) of follow-up. Conclusion These results suggest that terbinafine-induced SCLE should be comprehensively diagnosed based on clinical symptoms, histopathological manifestations, immunological parameters, and past medical history. Terbinafine should be immediately discontinued when SCLE occurs, while systemic and topical corticosteroids combined with hydroxychloroquine may be an effective treatment.

Neimark–Sacker bifurcation of discrete Pielou model with delay

In this paper, we investigate the existence of the Neimark–Sacker bifurcation of discrete delay Pielou Model with positive parameters. It is shown that this model undergoes a Neimark–Sacker bifurcation when the parameter passes a critical value. Furthermore, based on the computational algorithm developed by Murakami in [The invariant curve caused by Neimark-Sacker bifurcation, Dyn. Contin. Discrete Impuls. Syst. Ser. A 9 (2002), pp. 121–132], the explicit algorithm for determining the direction and stability of the Neimark–Sacker bifurcations is derived. Also, an explicit approximate expression of the invariant curve caused by Neimark–Sacker bifurcation is given. Some numerical simulations are carried out to illustrate the analytical results found.