Search Results (23)

In this short note, we focus on complete translating solitons with a bounded $L_f^n$-norm of the second fundamental form and obtain two results. First, based on a Sobolev-type inequality and a Simons-type inequality, we establish a rigidity theorem of complete translating solitons. Second, based on the same Sobolev-type inequality and a Bochner-type inequality, a vanishing theorem regarding $L_f^p$ weighted harmonic 1-forms is proved. Full article

Background and Objectives: Evidence regarding how dispositional traits, antenatal anxiety, substance use, and obstetric events converge to shape post-partum depression (PPD) in South-East Europe is limited. We analysed 102 third-trimester women and followed them to six weeks post-partum, and 102 age-matched community controls were used to (i) compare baseline psychological profiles, (ii) chart antenatal-to-post-partum symptom trajectories, and (iii) build an integrated model of clinically relevant PPD (Edinburgh Post-natal Depression Scale, EPDS ≥ 12). Materials and Methods: All 96 raw variables were forward–backward translated from Romanian, reconciled, and harmonized. The principal instruments used were EPDS, State–Trait Anxiety Inventory form Y (STAI-Y), Revised Obsessive–Compulsive Inventory (OCI-R), NEO Five-Factor Inventory (NEO-FFI-60), and the four-item Maternal Worry and Satisfaction Scale (MWSS). Results: Groups were age-matched (31.1 ± 5.4 vs. 30.3 ± 5.1 years, p = 0.268) but differed in urban residence (39% vs. 17%, p = 0.001) and current substance use (smoking 21% vs. 34%, p = 0.041; alcohol 6% vs. 22%, p = 0.002). Of five personality domains, only openness scored lower in peripartum women (26.1 ± 4.6 vs. 29.3 ± 5.2, p < 0.001). State anxiety rose significantly from pregnancy to puerperium (+5.1 ± 8.4 points, p < 0.001). Post-partum EPDS correlated most strongly with state anxiety (r = 0.62) and neuroticism (r = 0.50). A final model (pseudo-R² = 0.30) identified post-partum state anxiety (OR 1.10 per point, 95% CI 1.05–1.15, p < 0.001) as the independent predictor; neuroticism showed a trend (OR 1.08, p = 0.081). Obstetric factors (prematurity, birth weight, caesarean section) were not significant. Conclusions: In this Romanian cohort, heightened state anxiety—in synergy with high neuroticism and lower openness—dominated the risk landscape of early onset PPD, whereas delivery mode and neonatal status were neutral. Routine perinatal mental health screening should therefore incorporate anxiety metrics alongside depression scales and brief trait inventories to refine preventive targeting. Full article

Under the backdrop of urban renewal, harmonizing transit-oriented development (TOD) with urban renewal to maximize rail value has emerged as a critical focus in contemporary planning. Based on this, this paper proposes the node–place–revenue (NPR) model, which constructs evaluation indexes from the three dimensions of the node, place, and revenue. It determines the weights of each index by using expert scoring and the Analytic Hierarchy Process (AHP). Taking Shenyang Metro Line 1 as an example, the study first used the model to measure the node value, place value, and revenue value of each sample TOD station area. Secondly, K-means clustering analysis was used to form a spatial classification of five station areas. Finally, this paper proposes one differentiated urban renewal strategy for each type of station area. It is found that (1) the NPR model classifies stations into five categories: stress and high revenue, balanced, unbalanced node, unbalanced place, and dependence and low revenue and (2) the differentiated urban renewal strategies for each type of station area can be explored in terms of precise decongestion, node upgrading, function expansion, endogenous optimization, and infill quality improvement. This paper examines the economic driving effect of Shenyang Metro Line 1 stations on the renewal of the surrounding areas from the perspective of the economic balance of payments, providing a new reference for Shenyang-rail-transit-guided urban renewal work. Full article

In order to harmonize carcass grading, it was necessary to make sure that all methods used in the EU for assessing lean meat content give the same result when dissecting the same carcass. Research was conducted to establish the influence of the changes to the testing method introduced by the EU in 2018 on the meatiness value of pig carcasses. A question arose about whether this system would affect the results and, thus, change the lean meat content of domestic fattening pigs compared to the regression equations that are currently valid. In this study, the CGM-Sydel device was used. It was found that the form of the regression equation was not significantly affected by the new test procedure because the obtained SF (scaling factor), being equal to 0.89, was the same as the one used earlier by EU regulations. The change in the form of the regression equation was affected by the increase in the meatiness level of pig carcasses and their weight in the period from 2011 to 2023 in Poland. The implementation of the new equation for the CGM-device caused of the level of meatiness to be 0.58 pp. Full article

In this article, an attempt was made to model the body of a person moving in a passive manner (movement forced by another person) in a wheelchair. For this purpose, the Wan–Schimmels model was modified by 4 DOF, supplementing it with the weight of the wheelchair and a polyurethane cushion. The study was designed to test the effectiveness of utilizing a polyurethane cushion to reduce the whole-body vibration acting on a person while moving in a wheelchair. The study used a rheological model of polyurethane (PU) foam with concentrated parameters. Harmonic and random vibration analysis was carried out for this model. At the same time, the model with 5 DOF seems to be sufficient to describe vibrations transmitted to wheelchair users. The model presented in this paper can become a tool for future analysis of vibrations of people of different weights, moving passively on various types of wheelchairs on surfaces whose irregularities can be given by an appropriate form of kinematic excitation. The approach used in this study is likely to be useful in selecting a wheelchair and seat cushion so as to counteract and minimize vibrations perceived by humans. Full article

To solve the nonlinear vibration problems of second- and third-order nonlinear oscillators, a modified harmonic balance method (HBM) is developed in this paper. In the linearized technique, we decompose the nonlinear terms of the governing equation on two sides via a constant weight factor; then, they are linearized with respect to a fundamental periodic function satisfying the specified initial conditions. The periodicity of nonlinear oscillation is reflected in the Mathieu-type ordinary differential equation (ODE) with periodic forcing terms appeared on the right-hand side. In each iteration of the linearized harmonic balance method (LHBM), we simply solve a small-size linear system to determine the Fourier coefficients and the vibration frequency. Because the algebraic manipulations required for the LHBM are quite saving, it converges fast with a few iterations. For the Duffing oscillator, a frequency–amplitude formula is derived in closed form, which improves the accuracy of frequency by about three orders compared to that obtained by the Hamiltonian-based frequency–amplitude formula. To reduce the computational cost of analytically solving the third-order nonlinear jerk equations, the LHBM invoking a linearization technique results in the Mathieu-type ODE again, of which the harmonic balance equations are easily deduced and solved. The LHBM can achieve quite accurate periodic solutions, whose accuracy is assessed by using the fourth-order Runge–Kutta numerical integration method. The optimal value of weight factor is chosen such that the absolute error of the periodic solution is minimized. Full article

We investigate the linear arrangement of Euler harmonic sums that may be expressed in closed form in terms of special functions such as the classical Riemann zeta function and the Dirichlet eta function. Particular emphasis is given to Euler harmonic sums with even weight. New examples highlighting the theorems will be presented. Full article

We show that, as in the case of the principle of minimum action in classical and quantum mechanics, there exists an even more general principle in the very fundamental structure of quantum spacetime: this is the principle of minimal group representation, which allows us to consistently and simultaneously obtain a natural description of spacetime’s dynamics and the physical states admissible in it. The theoretical construction is based on the physical states that are average values of the generators of the metaplectic group $Mp\left(n\right)$, the double covering of $SL\left(2C\right)$ in a vector representation, with respect to the coherent states carrying the spin weight. Our main results here are: (i) There exists a connection between the dynamics given by the metaplectic-group symmetry generators and the physical states (the mappings of the generators through bilinear combinations of the basic states). (ii) The ground states are coherent states of the Perelomov–Klauder type defined by the action of the metaplectic group that divides the Hilbert space into even and odd states that are mutually orthogonal. They carry spin weight of 1/4 and 3/4, respectively, from which two other basic states can be formed. (iii) The physical states, mapped bilinearly with the basic 1/4- and 3/4-spin-weight states, plus their symmetric and antisymmetric combinations, have spin contents $s=0,1/2,1,3/2$ and 2. (iv) The generators realized with the bosonic variables of the harmonic oscillator introduce a natural supersymmetry and a superspace whose line element is the geometrical Lagrangian of our model. (v) From the line element as operator level, a coherent physical state of spin 2 can be obtained and naturally related to the metric tensor. (vi) The metric tensor is naturally discretized by taking the discrete series given by the basic states (coherent states) in the n number representation, reaching the classical (continuous) spacetime for n$\to \infty$. (vii) There emerges a relation between the eigenvalue $\alpha$ of our coherent-state metric solution and the black-hole area (entropy) as $A_{bh}/4l_p^2=\left|\alpha \right|$, relating the phase space of the metric found, $g_{ab}$, and the black hole area, $A_{bh}$, through the Planck length $l_p^2$ and the eigenvalue $\left|\alpha \right|$ of the coherent states. As a consequence of the lowest level of the quantum-discrete-spacetime spectrum—e.g., the ground state associated to $n=0$ and its characteristic length—there exists a minimum entropy related to the black-hole history. Full article

The article is an attempt to perform an ecological assessment of passenger cars with various types of engines in road emission tests. The main research problem and, at the same time, the goal was to develop a method for determining the exhaust emissions from motor vehicles in real traffic conditions based on results obtained in homologation tests. The tests were carried out on vehicles equipped with gasoline, diesel, and hybrid engines, and the obtained results were analyzed. All of the selected vehicles were of the same class—passenger cars, with a similar curb weight, similar maximum engine power, and in the same emission class (Euro 6d). The authors compared the dynamic parameters of vehicle motion in established emission tests: Worldwide harmonized Light vehicles Test Cycles and Real Driving Emissions. Four procedures were used to analyze and compare the operating conditions of the vehicles in the WLTC and RDE tests, differing in how the phases in the tests were divided as well as having a different methodology for determining the road emissions in the tests. The procedures were as follows: WLTC (where the test was divided and the determination of the road emission of exhaust gases was carried out according to the standard WLTP procedure), RDE (the road test was divided into sections and the exhaust emission was determined according to the standard RDE procedure), WLTC₁₊₂ (the test was divided into phases: 1 + 2, 3, and 4; a combination of phases 1 and 2 corresponding to the urban section of the RDE test), WLTC_RDE (where drive phases were divided and emissions determined in the same way as in the RDE procedure, which assumes the division of the test into sections based on vehicle speed). The implementation of the research task in the form of an algorithm procedure when comparing the dynamic parameters of the movement in the WLTC and RDE tests is the leading goal presented in this article. The division of the WLTC test into sections (urban, rural, and motorway) according to the RDE procedure and also the calculation of the total emissions in the test according to this procedure resulted in obtaining similar road emission values in the test. Full article

The free space solution to the wave equation in spherical coordinates is well known as a separable product of functions. Re-examination of these functions, particularly the sums of spherical Bessel and harmonic functions, reveals behaviors which can produce a range of useful beampatterns from radially symmetric sources. These functions can be modified by several key parameters which can be adjusted to produce a wide-ranging family of beampatterns, from the axicon Bessel beam to a variety of unique axial and lateral forms. We demonstrate that several special properties of the simple sum over integer orders of spherical Bessel functions, and then the sum of their product with spherical harmonic functions specifying the free space solution, lead to a family of useful beampatterns and a unique framework for designing them. Examples from a simulation of a pure tone 5 MHz ultrasound configuration demonstrate strong central axis concentration, and the ability to modulate or localize the axial intensity with simple adjustment of the integer orders and other key parameters related to the weights and arguments of the spherical Bessel functions. Full article

The Gravity Recovery and Climate Experiment (GRACE) gravity mission has become a leading platform for monitoring temporal changes in the Earth’s global gravity field. However, the usability of GRACE data is severely limited by 11 months of missing data between the GRACE and GRACE Follow-on (GRACE-FO) missions. To date, several approaches have been proposed to fill this data gap in the form of spherical harmonic coefficients (an expression of the Earth’s gravity field, SHCs). However, systematic analysis to reveal the characteristics and consistency of the datasets produced by these latest gap-filling techniques is yet to be carried out. Here, three SHC gap-filling products are systematically analyzed and compared: (1) Combining high–low satellite-to-satellite tracking with satellite laser ranging (SLR) observations (QuantumFrontiers, QF), (2) SLR-based recovery incorporating the GRACE empirical orthogonal function decomposition model proposed by the Institute of Geodesy and Geoinformation at the University of Bonn (hereafter, denoted as IGG), and (3) applying the singular spectrum analysis approach (SSA). The results show that (1) the SHCs of the QF, IGG, and SSA data are consistent up to degree 12; (2) the IGG and SSA data give similar results over the 11 gap months, but the IGG shows a faster increase in the mean ocean water mass and the SSA appears to better capture the interannual variation in the terrestrial water storage; and (3) the noise level increases significantly in the high-degree terms (l > 16) of the QF data, so these data are only applicable for large-scale mass migration research. These results provide a reference for users to select a gap-filling product. Finally, we propose a new scheme based on the triple collocation method to derive a weight matrix to fuse these three datasets into a more robust solution. Full article

The focus of this study is on the grid-forming operation of the Energy Router (ER) based on Model Predictive Control (MPC). ER is regarded as a key component of microgrids. It is a converter that interfaces the microgrid (s) with the utility grid. The ER has a multiport structure and bidirectional energy flow control. The ER concept can be implemented in Nearly Zero-Energy Buildings (NZEB) to provide flexible energy control. A concept is proposed where the ER works as a single grid-forming converter. The challenge is to keep the predefined reference voltage and frequency inside the NZEB in all possible modes, including the idle operation mode, current sources, and nonlinear load control. To gain stability and output voltage quality, the MPC is proposed. The design of the modified MPC algorithm with improved dynamics performance is explained. PLECS software is utilized to verify the proposed algorithm. The results demonstrate the suitable performance of the proposed control method in terms of total harmonic distortion of the output voltage. The influence of weighting coefficiencies is evaluated, showing the higher impact of the capacitor filter voltage on lowering the total harmonics distortion of the output voltage. Finally, the capability of the control system toward step change in the reference value is evaluated. Full article

Gravitational waves radiated during binary black hole coalescence are a perfect probe for studying the characteristics of strong gravity. Advanced techniques for creating numerical relativity substitute models for eccentric binary black hole systems are presumed to be crucial in existing and anticipated gravitational wave detectors. The imprint on the observation data of the gravitational wave emitted by the binary coalescence enhances two-body system studies. The aim of this study is to present an overview of the change in characteristic behaviors of hierarchical massive astrophysical objects merger, which are the databank of the early universe. We present results from numerical relativity simulations of an equal-mass and unequal mass nonspinning inspiral binary-black-hole system in the Post-Newtonian framework. We also consider the time evolution of eccentricity for an initial eccentric system. The eccentric Post-Newtonian equations are expanded in the form of the frequency related variable $x={\left(M\omega \right)}^{2/3}$. The model is restricted to the (2, 2) spin-weighted spherical harmonic modes. We conclude that for higher eccentricity as well as mass ratio, there is higher oscillation in orbital radius and in eccentricity. Full article

The theory of symmetry has a significant influence in many research areas of mathematics. The class of symmetric functions has wide connections with other classes of functions. Among these, one is the class of convex functions, which has deep relations with the concept of symmetry. In recent years, the Schur convexity, convex geometry, probability theory on convex sets, and Schur geometric and harmonic convexities of various symmetric functions have been extensively studied topics of research in inequalities. The present attempt provides novel portmanteauHermite–Hadamard–Jensen–Mercer-type inequalities for convex functions that unify continuous and discrete versions into single forms. They come as a result of using Riemann–Liouville fractional operators with the joint implementations of the notions of majorization theory and convex functions. The obtained inequalities are in compact forms, containing both weighted and unweighted results, where by fixing the parameters, new and old versions of the discrete and continuous inequalities are obtained. Moreover, some new identities are discovered, upon employing which, the bounds for the absolute difference of the two left-most and right-most sides of the main results are established. Full article

In this paper, we establish a new version of Hermite-Hadamard-Fejér type inequality for harmonically convex functions in the form of weighted fractional integral. Secondly, an integral identity and some weighted midpoint fractional Hermite-Hadamard-Fejér type integral inequalities for harmonically convex functions by involving a positive weighted symmetric functions have been obtained. As shown, all of the resulting inequalities generalize several well-known inequalities, including classical and Riemann–Liouville fractional integral inequalities. Full article