Variational Technique Research Articles

Convergence of least energy sign-changing solutions for logarithmic Schrödinger equations on locally finite graphs

In this paper, we study the following logarithmic Schrödinger equation −Δu+λa(x)u=ulogu2inVon a connected locally finite graph G=(V,E), where Δ denotes the graph Laplacian, λ>0 is a constant, and a(x)≥0 represents the potential. Using variational techniques in combination with the Nehari manifold method based on directional derivative, we can prove that, there exists a constant λ0>0 such that for all λ≥λ0, the above problem admits a least energy sign-changing solution uλ. Moreover, as λ→+∞, we prove that the solution uλ converges to a least energy sign-changing solution of the following Dirichlet problem −Δu=ulogu2inΩ,u(x)=0on∂Ω,where Ω={x∈V:a(x)=0} is the potential well.

Water vapor thermal therapy: Technical variations among spanish hospitals and efficacy at 2-year follow-up

AimThe aim of this work is to evaluate the initial experience with water vapor thermal therapy (WVTT) for benign prostatic hyperplasia (BPH) in Spanish university hospitals, as well as to describe the differences in technique and follow-up between centers. Materials and MethodsThis retrospective observational multicenter study collected baseline characteristics, surgical, postoperative and follow-up data at 1, 3, 6, 12 and 24 months, including validated questionnaires, flowmetric variations, complications, and the need for pharmacological or surgical treatment following the procedure. Possible triggers for postoperative acute urinary retention (AUR) were also analyzed. ResultsA total of 105 patients were included. No differences were observed between the groups with and without AUR with respect to catheterization time (5 and 4.3 days respectively, P=.178), or prostate volume (47.9g and 41.4g respectively, P=.147). The mean improvement at 3, 6, 12 and 24 months in terms of peak flow was 5.3, 5.2, 4.2 and 3.8ml/s, respectively. As for ejaculation, an improvement was observed after 3 months of follow-up and was maintained over time. ConclusionsMinimally invasive treatment for BPH with WVTT shows good functional outcomes at 24 months follow-up, without significant impairment of sexual function and a low incidence of complications. There are minor inter-hospital variations, mainly in the immediate postoperative period.

Contactless Sensing-Aided Respiration Signal Acquisition Using Improved Empirical Wavelet Transform for Rhythm Detection.

Respiration is one of the most important vital signs indicating physical condition, while the signal detection is challenging due to the complex rhythm and effort in practical scenarios. In this paper, we propose a contactless sensing-aided respiration signal acquisition technique, which can adaptively extract the desired signal under time-varying respiration rhythms within a wide range. To be specific, respiration is perceived by piezoelectric ceramics sensors along with ballistocardiography and other interference in a contactless manner, and the proposed improved empirical wavelet transform (IEWT) performs spectrum division and recognition based on upper envelop and principal component criteria, respectively, to adaptively extract the respiration spectrum for signal reconstruction. For validations, we extracted respiration signals from 8 healthy individuals in lab breathing at specified rhythms from 0.2 Hz to 0.6 Hz as well as 38 in-patients suffering from sleep-disordered-breathing with reference of polysomnogram in practical clinic scenario. The results showed that the detected respiration rhythms perfectly fitted the ones in experimental lab dataset with a correlation coefficient of 0.98, which validated the effectiveness of the respiration spectrum extraction of the proposed IEWT method. Besides, in practical clinical dataset, the proposed IEWT method could yield mean absolute and relative errors of respiration intervals of 0.4 and 0.05 seconds, respectively, achieving significant improvement in comparison with conventional ones. Meanwhile, the performance of IEWT was robust to rhythm variation, individual difference and breathing cycle detection techniques, which demonstrated the feasibility and superiority of the proposed IEWT method for practical respiration monitoring.

A variational technique of mollification applied to backward heat conduction problems

A variational technique of mollification applied to backward heat conduction problems

POF Smart Pants: a fully portable optical fiber-integrated smart textile for remote monitoring of lower limb biomechanics.

This paper presents the development of an optical fiber-integrated smart textile used as an instrumented pants for biomechanical and activity recognition. The optical fiber sensor is based on the multiplexed intensity variation technique in which a side coupling between a polymer optical fiber (POF) and light sources with controlled modulation is developed. In addition, the sensor system is integrated into pants, where two POFs with 30 sensors each are placed on the left and right legs of the proposed POF Smart Pants. After the device's fabrication and assembly, the 60 optical fiber sensors are characterized as a function of the transverse displacement on the sensor's region. In this case, each sensor presented its sensitivities (108.03 ± 100 mV/mm), which are used on the sensor normalization prior to the data analysis. Then, the tests with volunteer performing different daily activities indicated the suitability of the proposed device on the assessment of biomechanics of human movement in different activities as well as the spatio-temporal parameters of the gait in different velocity conditions. For activity recognition, a neural network is applied and presented 100% accuracy on the activity recognition. Then, to provide an optimization of the number of sensors, the principal components analysis is applied and indicated a threefold reduction of the number of sensors with an accuracy of 99%. Thus, the proposed POF Smart Pants is a feasible alternative for a low-cost and highly reliable sensor system for remote monitoring of different patients, with the possibility of customizing the device for different users.

An elliptic problem of the Prandtl–Batchelor type with a singularity

We establish the existence of at least two solutions of the Prandtl–Batchelor like elliptic problem driven by a power nonlinearity and a singular term. The associated energy functional is nondifferentiable, and hence the usual variational techniques do not work. We shall use a novel approach in tackling the associated energy functional by a sequence of C^{1} functionals and a cutoff function. Our main tools are fundamental elliptic regularity theory and the mountain pass theorem.

Variational Problems Involving a Generalized Fractional Derivative with Dependence on the Mittag–Leffler Function

In this paper, we investigate the necessary conditions to optimize a given functional, involving a generalization of the tempered fractional derivative. The exponential function is replaced by the Mittag–Leffler function, and the kernel depends on an arbitrary increasing function. The Lagrangian depends on time, the state function, its fractional derivative, and we add a terminal cost function to the formulation of the problem. Since this new fractional derivative is presented in a general form, some previous works are our own particular cases. In addition, for different choices of the kernel, new results can be deduced. Using variational techniques, the fractional Euler–Lagrange equation is proved, as are its associated transversality conditions. The variational problem with additional constraints is also considered. Then, the question of minimizing functionals with an infinite interval of integration is addressed. To end, we study the case of the Herglotz variational problem, which generalizes the previous one. With this work, several optimization conditions are proven that can be useful for different optimization problems dealing with various fractional derivatives.

Breather solutions for a semilinear Klein-Gordon equation on a periodic metric graph

We consider the nonlinear Klein-Gordon equation∂t2u(x,t)−∂x2u(x,t)+αu(x,t)=±|u(x,t)|p−1u(x,t) on a periodic metric graph (necklace graph) for p>1 with Kirchhoff conditions at the vertices. Under suitable assumptions on the frequency we prove the existence and regularity of infinitely many spatially localized time-periodic solutions (breathers) by variational methods. Compared to previous results obtained via spatial dynamics and center manifold techniques our results provide existence for all values of α≥0 as well as multiplicity. Moreover, we deduce regularity properties of the solutions and show that they are weak solutions of the corresponding initial value problem. Our approach relies on the existence of critical points for indefinite functionals, the concentration compactness principle, and the proper set-up of a functional analytic framework. Compared to earlier work for breathers using variational techniques, a major improvement of embedding properties has been achieved. This allows in particular to avoid all restrictions on the exponent p>1 and to achieve higher regularity.

Plenty of accurate, explicit solitary unidirectional wave solutions of the nonlinear Gilson–Pickering model

This paper proposes abundant accurate wave solutions that represent the plasma wave propagation based on crystal lattice theory and physicochemical characterization. The Gilson–Pickering ([Formula: see text]) model is analytically and numerically solved by two recent techniques. This model is a basic unidirectional wave propagation model that describes the prorogation of waves in crystal lattice theory and plasma physics. The investigated model has a deep connection with some nonlinear evolution equations under specific values of its parameters, such as the Fuchssteiner–Fokas–Camassa–Holm ([Formula: see text]) equation, the Rosenau–Hyman ([Formula: see text]) equation, and the Fornberg–Whitham ([Formula: see text]) equation. The Sardar sub-equation and He’s variational iteration techniques are employed to construct novel and accurate solitary wave solutions of the handled model. The obtained solutions are explained through some distinct graphs in contour, three-, two-dimensional. The research value is explained by comparing our results with some recently published studies. The employed methods show their simple, direct, effectiveness and their ability for handling many nonlinear evolution equations.

Dynamical stability in presence of non-minimal derivative dependent coupling of k-essence field with a relativistic fluid

In this paper we investigate a non-minimal, space-time derivative dependent, coupling between the k-essence field and a relativistic fluid using a variational approach. The derivative coupling term couples the space-time derivative of the k-essence field with the fluid 4-velocity via an inner product. The inner product has a coefficient whose form specifies the various models of interaction. By introducing a coupling term at the Lagrangian level and using the variational technique we obtain the k-essence field equation and the Friedmann equations in the background of a spatially flat Friedmann–Lemaitre–Robertson–Walker (FLRW) metric. Explicitly using the dynamical analysis approach we analyze the dynamics of this coupled scenario in the context of two kinds of interaction models. The models are distinguished by the form of the coefficient multiplying the derivative coupling term. In the simplest approach we work with an inverse square law potential of the k-essence field. Both of the models are not only capable of producing a stable accelerating solution, they can also explain different phases of the evolutionary universe.

The rotational movement in solution of fumaramide- vs. succinamide [2]rotaxanes: The influence of intercomponent interactions

Due to their intrinsic topological features, most artificial molecular devices are based on rotaxane molecules. One of the most important characteristics of this class of compounds is the likelihood of performing molecular movements, which are directly correlated with the intercomponent interactions present in these molecules. The tetralactam macrocycle is quite versatile and used in numerous molecular threads, which have stations that work as fundamental parts in the formation, molecular stabilization, and molecular movements performed. Inspired by how these stations may influence molecular movements (e.g., rotational ones), we sought to study two diamides commonly used as rotaxane stations: fumaramide and succinamide. In this context, we explored the change of station in six pairs of [2]rotaxanes. Studies were carried out in solution through NMR experiments with temperature variation techniques. In the crystalline solid state, the quantum theory of atoms in molecules analysis was performed through quantum mechanics calculations using the density functional theory. The rotational movement found for fumaramide-based [2]rotaxanes is, on average, over 14.91 kcal mol−1. In comparison, succinamide-based [2]rotaxanes have values of 12.78 kcal mol−1 (a 14% difference). In solution, fumadamide-based rotaxanes better retain the macrocycle due to the rigidity of the double bond, making its rotation more difficult and consequently leading to higher rotational energy barriers. In the crystalline solid state, the succinamide station, which has greater structural freedom due to the simple carbon–carbon bond, promotes more interactions, having a greater “complementary adjustment” and a higher stabilization energy. Lastly, our findings demonstrated how intercomponent interactions present in the studied stations can be changed to be used as a “lubricant” in solution for these molecular machine prototypes.

Borderline scenarios of outranking classification based on α-cut variation in fuzzy intervals: Application in police investigations

This paper presents a new method for classifying actions called α-FlowSort, which uses sections of the fuzzy interval to allow vertical and horizontal decision strategies, which consider the decision-maker’s levels of certainty and optimism. α-FlowSort adds to the traditional MCDA FlowSort method the concepts of fuzzy sets with α-cut variation techniques and identification of outranking relations between fuzzy numbers, thus providing the decision-maker with scenarios for adjusting the decision, to add subjective elements at the time of assignment or to use a global recommendation. The decision maker is offered visual evaluation options that enable better identification and definition of the attribution of actions that in a single analysis would be positioned on the border between categories, in addition to which, by aggregating multiple simultaneous evaluations, a single recommendation is offered in a more robust way, even in a fuzzy environment. To demonstrate the results, an application of the new method is presented in the context of distributing resources to support criminal investigations, the results of which were compared with those obtained with the FlowSort and F-FlowSort methods. Simulations and comparisons between the methods were also carried out, using a thousand random alternatives.

On a nonhomogeneous, nonlinear Dirichlet eigenvalue problem

AbstractWe consider a nonlinear eigenvalue problem for the Dirichlet ‐Laplacian with a sign‐changing Carathodory reaction. Using variational tools, truncation and comparison techniques, and critical groups, we prove an existence and multiplicity result which is global in the parameter (bifurcation‐type theorem). Our work here complements the recent one by Papageorgiou–Qin–Rădulescu, Bull. Sci. Math. 172 (2021).

Optimization of Extraction Lannea coromandelica for Antioxidant Activity using Analytical Factorial Design Approach

Background: The yield of active compound in a plant can be affected by the extraction method, such as variety of solvent and extraction technique used. Objectives: This study aimed to optimize the yield of Lannea coromandelica leaf extract using several types of solvent and extraction techniques and evaluate the antioxidant activity of the extracts. Material and Methods: This study used a variety of solvent like distilled water, ethanol, n-hexane, and ethyl acetate with maceration, reflux, and sonication extraction techniques. The extract obtained was calculated for the percent yield and analyzed for their antioxidant activity using the DPPH method by UV -Vis Spectrophotometry with 523.5 nm maximum wavelength. The antioxidant activity was analyzed by factorial design analysis in Minitab 21 software. Results: The highest percentage yields was obtained from the extract with ethanol solvent, followed by distilled water, ethyl acetate and n-hexane. The highest extraction techniques was obtained from reflux and followed by maceration and sonication extracts. Analytical factorial design analysis showed that the linearity of solvent variation and extraction technique had a significant effect (P>0.05). From the analysis, it was found that there was a significant difference between the effect of the solvent on the antioxidant activities compared to the extraction technique. The extracts obtained have a very strong antioxidant activity against DPPH radicals. T Conclusions: L. coromandelica plant aquadest extract has potential to be developed in optimalization extraction method.

Detection of ADHD from EEG signals using new hybrid decomposition and deep learning techniques

Objective. Attention deficit hyperactivity disorder (ADHD) is considered one of the most common psychiatric disorders in childhood. The incidence of this disease in the community draws an increasing graph from the past to the present. While the ADHD diagnosis is basically made with the psychiatric tests, there is no active clinically used objective diagnostic tool. However, some studies in the literature has reported development of an objective diagnostic tool that facilitates the diagnosis of ADHD. Approach. In this study, it was aimed to develop an objective diagnostic tool for ADHD using electroencephalography (EEG) signals. In the proposed method, EEG signals were decomposed into subbands by robust local mode decomposition and variational mode decomposition techniques. These subbands and the EEG signals were fed as input data to the deep learning algorithm designed in the study. Main results. As a result, an algorithm has been put forward that distinguishes over 95% of ADHD and healthy individuals through using a 19-channel EEG signal. In addition, a classification accuracy of over 87% was obtained by the proposed approach of EEG signal decomposition followed by data processing in the designed deep learning algorithm. Significance. The findings of the current research enrich the literature based on originality and proposed method can be used as a clinical diagnostic tool in the near future.

The most probable distributions with finite number of particles and the applications on Bose–Einstein condensation

Motivated by the asynchronous finite differences method utilized for the calculation of the most probable distributions of finite particle number systems, this study employs numerical variation and central difference techniques to provide more precise estimations regarding these distributions. Specifically, three novel finite distributions are derived and applied to Bose–Einstein condensation, revealing that the critical condition (nλ3 = 2.612) may be relaxed in finite particle number scenarios. Moreover, maintaining density as a constant is anticipated to result in a higher critical temperature compared to infinite number systems. Notably, the obtained condensate number on the zero-energy level surpasses that of predictions generated by canonical distributions.

Optimal Amplitude–Density Synthesis of Linear Aperiodic Arrays

New deterministic procedures for the design of linear aperiodic arrays are described which permit exploiting, in a combined way, both the positions and the excitation amplitudes of the array elements obtaining a pattern which optimally fits, in terms of a weighted L2 norm, the pattern of a reference linear continuous aperture. A first numerical procedure is based on alternating optimization of positions and amplitudes by means of closed-form convex projectors. Sufficient conditions for the solution to be optimal are established. A second numerical procedure is based on a domino-like sequential determination of the unknowns which can be iterated to convergence. Additionally, analytical asymptotic expressions for the optimal inter-element spacing and amplitude are derived by means of variational techniques. The optimal asymptotic inter-element spacing is demonstrated to be proportional to the reference tapering to the power (-2/3) while the optimal asymptotic array amplitude is proportional to the reference tapering to the power (1/3). For aperiodic arrays with equiamplitude excitation it is proved that the optimal inter-element spacing is proportional to the reference tapering to the power (-1). Based on these asymptotic dependencies, closed-form analytical solutions are obtained for amplitudes and positions of the elements. Several numerical results confirm the effectiveness and accuracy of the new procedures.

Study of the performance of fault-tolerant multi-level inverter included in shunt active power filter

<p><span lang="EN-US">Nowadays, the large number of shunt active power filters (SAPF) is installed in many grid networks to eliminate the source currents harmonics and enhance power quality. These filters are installed in different places according to the filtration requirements. The connection between SAPF and grid network has a negative effect during the open-circuit fault of the insulated gate bipolar transistor (IGBT) switch of the SAPF. This paper proposes the application of the new diagnostic method based on the trigonometric circle and mean value variations techniques to the early detection and precise location of the open-circuit fault of the IGBT switches, and the inclusion of the modified reconfigurable inverter topology to allow the perfect continuity of the filter currents, and improve the diagnostic of the open-circuit fault. A single-sided amplitude spectrum technique (SSAS) is applied on the source currents to get the THDi% value. The obtained simulation results prove, the great success of the proposed diagnostic method, the ability of the modified reconfigurable inverter to be adapted to the grid network, the short response time between the diagnosis and the reconfiguration process is about 7 ms which is very sufficient to guarantee the rapid continuity of the shunt active power filter.</span></p>

Active Screening for Pulmonary Tuberculosis Among Jail Inmates: A Mixed Method Study From Puducherry, South India.

Sustainable Development Goal 3 (SDG) aims to end the epidemic of TB by 2030. To achieve this goal, active screening should be initiated in the target populations. These target populations are those without access to proper healthcare like jail inmates. With pulmonary tuberculosis (PTB) being cosmopolitan in India, passive case finding alone cannot suffice to achieve the above-mentioned goal. Thus, active case finding (ACF) becomes the need of the hour. So, we aimed to conduct a mixed methods study that has a quantitative component, i.e., to actively screen the prison inmates for PTB, and a qualitative component, i.e., to know the perceptions of jail inmates towards PTB and the stigmas associated with it. This was a mixed-method study conducted in the Central Jail, Puducherry. The quantitative component involved a facility-based cross-sectional study design and the qualitative component involved a focused group discussion (FGD). Participants were screened for PTB and diabetes mellitus (DM) and their anthropometry (weight, height, body mass index {BMI}, waist-to-hip ratio {WHR}) was noted. Presumptive cases were identified as those with symptoms of cough for more than two weeks with or without other concomitant symptoms. They were subjected to cartridge-based nucleic acid amplification test (CB-NAAT) assay. Data were entered in MS Excel 2017and analyzed using SPSS version 16 (Armonk, NY: IBM Corp). For the qualitative exercise, purposive sampling with maximum variation technique was done to enroll a diverse subset of population for the FGD. Iterative analysis of the content was performed by the team to generate codes and themes. Out of all the 187 inmates screened, 10.7% were symptomatic. On CB-NAAT examination of the symptomatic inmates, none turned positive. The inmates with presumptive TB were older by age and had a higher proportion of illiteracy and existing co-morbidity (p≤0.05). While random blood sugar (RBS) levels of >140 mg/dL were recorded in 19.7% of inmates, RBS levels of >200 mg/dLconsidered diagnostic were noted in 5.34% of inmates. A total of 2.67% of the inmates were newly diagnosed with diabetes mellitus. The further management of the newly diagnosed inmates was taken over by the medical supervision team of the Central Jail. From the FGD, thematic manual content analysis was performed. A total of 24 codes were generated. After merging similar codes and removing duplications, the remaining 16 codes were grouped into six broad themes. Conclusions were drawn by interpretation of these themes. ACF is important as it is associated with early detection and treatment. It must be done periodically. During the FGD, we came across negative ideologies and stigmas associated with PTB among jail inmates. We used the same platform to clear those ideologies and recommend frequent health education exercises even in socially ostracized communities like jail inmates.

Inverse Modeling of Formaldehyde Emissions and Assessment of Associated Cumulative Ambient Air Exposures at Fine Scale

Among air toxics, formaldehyde (HCHO) is an important contributor to urban cancer risk. Emissions of HCHO in the United States are systematically under-reported and may enhance atmospheric ozone and particulate matter, intensifying their impacts on human health. During the 2021 Michigan-Ontario Ozone Source Experiment (MOOSE), mobile real-time (~1 s frequency) measurements of ozone, nitrogen oxides, and organic compounds were conducted in an industrialized area in metropolitan Detroit. The measured concentrations were used to infer ground-level and elevated emissions of HCHO, CO, and NO from multiple sources at a fine scale (400 m horizontal resolution) based on the 4D variational data assimilation technique and the MicroFACT air quality model. Cumulative exposure to HCHO from multiple sources of both primary (directly emitted) and secondary (atmospherically formed) HCHO was then simulated assuming emissions inferred from inverse modeling. Model-inferred HCHO emissions from larger industrial facilities were greater than 1 US ton per year while corresponding emission ratios of HCHO to CO in combustion sources were roughly 2 to 5%. Moreover, simulated ambient HCHO concentrations depended significantly on wind direction relative to the largest sources. The model helped to explain the observed HCHO concentration gradient between monitoring stations at Dearborn and River Rouge in 2021.