Potential Asymmetry Research Articles

The rating of Ukraine’s regional tourist systems according to their investment potential

The development and implementation of regional tourism development programs in Ukraine require the formation of the information environment for ranking the tourist systems of Ukraine’s regions according to the attractiveness of their investment potential, which determines the purpose of this study. The methods of economic analysis and rating modeling were used to rank regional tourism systems according to their investment potential by determining the integral indicator of the economic and tourist resources of each region. Accordingly, economic indicators are chosen to provide the regions with financial, labor, and production resources; tourism indicators include supply and demand for tourism services, availability of tourism resources, tourism efficiency, as well as tourism accommodation. According to the results of rating and grouping, three groups of regions were formed: the first (the priority in terms of investment potential of the tourist system has the value of the integrated indicator from 72.0 to 94.8); the second (values from 40.2 to 71.0, reflecting the average level of investment potential); and the third (values from 25.0 to 40.1 for regions with low investment potential). The rating of regional tourist systems reflects the development level of their potential; it is an indicator of the effectiveness of its management and information base necessary for management decisions of potential investors. The asymmetry of investment potential of regional tourism systems causes an imbalance in their competitiveness, so implementing regional and national programs will help intensifying their use and equalizing regions’ development. AcknowledgmentThe paper reflects the research results within the study carried out in 2021–2024 at the State University of Trade and Economics at the request of the Ministry of Education and Science of Ukraine “Digital Transformation of Trade, Economic and Tourist Systems of Ukraine,” state registration number 0117U000503, and “Forecasting the impact of the tourist system on the country’s economy,” state registration number 0122U001559.

The submarine Azores Plateau: Evidence for a waning mantle plume?

The submarine Azores Plateau in the Central Northern Atlantic has generally been considered to represent a large igneous plateau formed some 10 Ma by widespread volcanism, however a lack of age progression amongst the younger submarine and subaerial volcanism, an irregular distribution of platform-related magmas east and west of the Mid-Atlantic Ridge, a strong tectonic stress regime, and a lack of abundant tholeiitic compositions that reflect initial, high degrees of melting is not easily explainable in the framework of a classic, long-lived mantle plume model. Here, we present new bathymetric and seismic data from the submarine Azores Plateau obtained during cruises M113/1 and M128 with the German R/V Meteor. Our new data combined with prior geochemical and petrological studies indicate that the majority of the western Azores Plateau may indeed have formed during the arrival of a short-lived mantle melting anomaly at 10 Ma. However, our new data also indicate that volcanism <2 Ma is extremely localized and along structural features that result from plate reorganisation in the vicinity of the diffuse triple junction of the Eurasian, Nubian and North American plates, and that much of the easternmost Azores Plateau is magmatically inactive. Our model implies not only that the actual flood basalt province of the Azores is only some 30% of what has been previously estimated but may not have formed from a typical large-scale, long-lived mantle plume. Instead, excess melting as evident from the anomalously shallow water depth and the presence of islands in the Azores may be the result of a volumetrically small-scale melting anomaly in the upper mantle which is in its waning stages as evident from the localised distribution of magmatic activity at <1 Ma. Our model also solves the conundrum of a potential asymmetry of the recent submarine and subaerial volcanism both east and west of the Mid-Atlantic Ridge which instead is the result of an interacting upper mantle anomaly and the complex plate tectonic domain in the vicinity of the triple junction of the Eurasian, Nubian and North American plates.

Modeling and analysis of reluctance motion system with asymmetrical air gaps.

To achieve high throughput and efficiency, semiconductor photolithography machines need an actuation system that can meet high acceleration and precision demands on the nanoscale. One available solution is the reluctance actuator, which provides higher acceleration and force output than the standard Lorentz actuator. A floating stage with air-bearings is used to eliminate friction in the photolithography process; however, vibration transfer is not entirely eliminated, leading to potential misalignment and asymmetries between the actuator elements. With asymmetrical offsets between mover elements, the output force can be greatly affected. This paper shows a method for estimating the force of various asymmetrical cases for the C-core reluctance actuator. Analytical models are developed and further improved through polynomial curve fitting using precomputed finite element simulation results from Comsol Multiphysics (COMSOL) to achieve more optimal solutions. An experiment verified the results of the force estimation equations, which were within ∼11% for different cases of asymmetric air gaps. This contribution will lead to a design for a control system that will overcome the issue of asymmetries or other altered states.

Asymmetric Nanochannel Network-Based Bipolar Ionic Diode for Enhanced Heavy Metal Ion Detection

A higher rectification degree in ionic diodes is required to achieve better performance in applications. Nonetheless, the active geometrical change that is critical for inducing electrical potential asymmetry is difficult to realize in typical ionic diodes because of the intrinsic limitation of the fabrication method. Here, we propose a nanochannel-network-based bipolar diode with a high rectification degree of ∼1600─the highest value realized until now, to the best of our knowledge. Such a high rectification is obtained based on the synergetic effect of the bipolar surface charge and the optimization of the microchannel through experimental studies and multiphysics numerical simulations. It induces ion concentrations at the heterogeneous junction based on the accumulation effect under the forward potential bias. In particular, this proposed molecular concentration occurs in the ohmic region without vortex and instability that is inevitable at the conventional nano-electrokinetic concentration. Combining this accumulation with the horizontally aligned configuration of the nanochannel network membrane (NCNM), a highly sensitive and quantitative mercury ion (Hg2+) sensor based on a fluorescent signal is fabricated that allows direct measurement using a general fluorescent microscope. The detection limit of Hg2+ is 10 pM, which is ∼10 times lower than the best detection limit realized so far (∼100 pM) in fluorescent dye-based detection. This demonstrates the potential of asymmetric NCNM for high-performance ion transport in applications such as energy conversion, based on its design and material flexibility.

Fluctuating Asymmetry in Asteriscii Otoliths of Common Carp (Cyprinus carpio) Collected from Three Localities in Iraqi Rivers Linked to Environmental Factors

Otoliths, calcified structures in the inner ears, are used to estimate fish age, and their shape is an efficient fish stock identification tool. Otoliths are thus very important for the management and assessment of commercial stocks. However, most studies have used left or right otoliths, chosen arbitrarily without evaluation of the difference between these otoliths. In this study, the asteriscii otoliths from 263 common carp (Cyprinus carpio; Linnaeus, 1758) were sampled in three Iraqi rivers to test the potential asymmetry and the geographical effect on otolith growth from three measurements (length, width and weight), and on shape from two shape indices (ellipticity and form-factor). Among all asteriscii otolith features, there was significant fluctuating asymmetry between fish length and every otolith descriptor. At one fish length, the size and/or the shape of otoliths could be different between two individuals and/or between left and right asteriscii otoliths for the same individual. Moreover, the relationship between fish length and otolith shape/growth was significantly dependent on the studied geographical area and, more especially, the environmental effects as the water temperature and pH. Finally, the relationships between fish length and otolith shape indices showed that the otolith evolves into the elliptical shape during the life of the fish. To use the otolith shape, it is essential to take into account the developmental stage of individuals to integrate the ontogenetic effect. Our results highlight the importance of verifying potential otolith asymmetry, especially for the asteriscii otoliths (lagenar otoliths) before their use in fisheries research.

Asymmetric nexus between wages and productivity in the context of the global financial crisis

In the context of the breakdown of the wage-productivity nexus since the 2008–09 Global Financial Crisis, this study analyzes that nexus in the UK by accounting for potential asymmetries and nonlinearities. Employing a NARDL framework and data from 2000Q1 to 2018Q4, our key findings suggest that aggregate productivity and productivity within the retail sector have a significant and positive impact on aggregate wages and wages within the retail sector. However, there are important asymmetries and nonlinearities. The impact of productivity on wages in the retail sector is found to be many times smaller than that of aggregate productivity on aggregate wages across the economy as a whole. Economic growth, inflation and unemployment rates are found to have effects on wage growth over the short term. In the long run, it is productivity that is the sole statistically significant influence on wages. Our findings contribute to the debate on the productivity-wage nexus and have profound implications for the labour market and wage policies.

Overview of the TJ-II stellarator research programme towards model validation in fusion plasmas

TJ-II stellarator results on modelling and validation of plasma flow asymmetries due to on-surface potential variations, plasma fuelling physics, Alfvén eigenmodes (AEs) control and stability, the interplay between turbulence and neoclassical (NC) mechanisms and liquid metals are reported. Regarding the validation of the neoclassically predicted potential asymmetries, its impact on the radial electric field along the flux surface has been successfully validated against Doppler reflectometry measurements. Research on the physics and modelling of plasma core fuelling with pellets and tracer encapsulated solid pellet injection has shown that, although post-injection particle radial redistributions can be understood qualitatively from NC mechanisms, turbulence and fluctuations are strongly affected during the ablation process. Advanced analysis tools based on transfer entropy have shown that radial electric fields do not only affect the radial turbulence correlation length but are also capable of reducing the propagation of turbulence from the edge into the scrape-off layer. Direct experimental observation of long range correlated structures show that zonal flow structures are ubiquitous in the whole plasma cross-section in the TJ-II stellarator. Alfvénic activity control strategies using ECRH and ECCD as well as the relation between zonal structures and AEs are reported. Finally, the behaviour of liquid metals exposed to hot and cold plasmas in a capillary porous system container was investigated.

Transition Waves in One-Dimensional Periodic Bistable Mass-Spring Chains

The propagation of transition waves in multi-stable mechanical systems can be effectively harnessed in various fields, such as mechanical signal communication, mechanical diodes, and energy absorption. In this work, the propagation of transition waves in a one-dimensional (1D) bistable mass-spring chain is systematically studied. The underlying physical mechanism for the formation and propagation of transition waves is clarified, and the influences of some crucial factors, such as the pumped momentum, stiffness of the connecting springs, viscous damping, number of masses, and asymmetry of the double-well potential, on the propagation of transition waves are discussed in detail. As a result, the parameter space for achieving the robust propagation of transition waves through the whole chain is presented. This study is expected to be beneficial for the control of transition waves and design of novel devices used for mechanical signal transmission.

Is China’s green growth possible? The roles of green trade and green energy

In tandem with global initiatives to ‘go green’, China is undertaking a series of steps to achieve green economic growth. To investigate the dynamic nexus of green growth, green trade, and green energy (3 G) in China, an index is developed in this study to assess the level of provincial green growth by employing five types of indicators – economic growth, environmental pollution loss, carbon emissions loss, natural resource loss, and environmental and natural resource benefits. Then, this paper uses the SYS-GMM method to explore the influences of green trade and green energy on green growth by using data compiled from 30 provinces in China over the period 2007–2016. Furthermore, we check the potential heterogeneity, asymmetry, and internal mediating mechanism of the 3 G nexus. The main findings are highlighted as follows: (1) Green trade and green energy can accelerate China’s green growth; (2) enhancing medium- and high-technology green trade can contribute to improving local green growth; (3) this impact is heterogeneous in regions with different trade levels, and asymmetric at various quantiles for the full panel; (4) the positive investment effect, labour effect, and technical effect are effective mediators of the nexus between green trade and green growth.

Impact of insurance type on patient-reported outcome measures in patients with lumbar disc herniation

BACKGROUNDLumbar disc herniations (LDH) are among the most common spinal conditions. Despite increased appreciation for the importance of social determinants of health, the role that these factors play in patients with lumbar disc herniations is poorly defined. PURPOSETo elucidate the association between insurance status and baseline patient reported outcome measures (PROMs) in the setting of lumbar disc herniations. STUDY DESIGN/SETTINGRetrospective cohort study PATIENT SAMPLEBaseline patient-reported outcome measures (PROMS) were reviewed from 924 adult patients presenting for treatment of lumbar disc herniation within our institutional healthcare system (2015–2020). OUTCOME MEASURESThe Patient-Reported Outcomes Measurement Information System (PROMIS) Physical Function Short Form 10a (PF10a), PROMIS Global-Mental, PROMIS Global-Physical, and visual analogue scale (VAS) for back and leg pain were assessed. METHODSPROMIS scores at presentation were defined at the primary outcome and insurance status as the primary predictor. Differences in clinical and sociodemographic characteristics between our cohorts, stratified by insurance status, were evaluated using Wilcoxon rank-sum or chi-squared testing. We used multivariable negative binomial regression modeling to adjust for potential confounders including age, gender, race, language, ethnicity, comorbidity index, and median geospatial household income. RESULTSWe included 924 patients, with mean age of 58.4 +/- 15.2 years and 52.6% male prevalence. Patients insured through Medicaid were more likely to be Black, Hispanic, and non-English speaking patients compared with the commercially insured. The Charlson Comorbidity index was significantly higher in the Medicare group. Following adjusted analysis, patients with Medicaid insurance had significantly worse PF10a (IRR, 0.90, 95% CI 0.85–0.96), as well as PROMIS Global-Physical score (IRR 0.88, 95% CI 0.82–0.94), and VAS low back pain (IRR 1.20, 95% CI 1.04–1.40) when compared to the commercially insured. CONCLUSIONSWe encountered worse physical function, mental, and pain-related patient-reported outcomes for those with Medicaid insurance in a population of patients presenting for evaluation of lumbar disc herniation. These findings, including worse depression, anxiety, and higher axial back pain scores, merit further investigation into potential health system asymmetries, and should be accounted for by treating providers.

Ear Asymmetry and Contextual Influences on Speech Perception in Hearing-Impaired Patients

The left hemisphere preference for verbal stimuli is well known, with a right ear (RE) advantage obtained when competing verbal stimuli are presented simultaneously, at comfortable intensities, to both ears. Speech perception involves not only the processing of acoustic peripheral information but also top–down contextual influences, filling the gaps in the incoming information that is particularly degraded in hearing-impaired individuals. This study aimed to analyze the potential asymmetry of those contextual influences on a simple speech perception task in hearing-impaired patients in light of hemispheric asymmetry. Contextual influences on disyllabic word perception scores of 60 hearing-impaired patients were compared between left ear (LE) and RE, in a balanced design, involving two repetitions of the same task. Results showed a significantly greater contextual influence on the RE versus the LE and, for the second repetition versus the first one, without any interaction between the two. Furthermore, the difference in contextual influences between RE and LE increased significantly with the RE advantage measured by a dichotic listening test in the absence of any significant correlation with hearing threshold asymmetry. Lastly, the contextual influence asymmetry decreased significantly as age increased, which was mainly due to a greater increase, with age, of contextual influences on the LE versus the RE. Those results agree with the literature reporting a relative right-shift of hemispheric asymmetry observed with age in speech in noise perception tasks in normal hearing subjects and the clinical reports of generally better audiometric speech scores obtained in RE versus LE.

A Cross-Sectional Analysis of Growth and Profit Rate Distribution: The Spanish Case

We analyse the time evolution of the empirical cross-sectional distribution of firms’ profit and growth rates. In particular, we analyse the conditional properties of the empirical distributions depending on the size of the firms and the business cycle phase. In order to do so, we employ the Laplace distribution as a benchmark, further considering the Subbotin and Asymmetric Exponential Power (AEP hereafter) distributions, to capture the potential asymmetry and leptokurtosis of the empirical distribution. Our results show that the profit rates of large firms are characterised by an asymmetric Laplace distribution with parameters largely independent of the business cycle phase. Small firms, instead, are characterised by the AEP distribution, which accounts for the conditional dependence of distribution on the phase of the business cycle. We observe that the largest firms are more robust to downturns compared to the small firms, given their invariant distributional characteristics during crisis periods.

Testing for Long-Run Relationships between European Housing and Stock Markets: Evidence of the Wealth, Credit-price and Capital-switching Regime Effects

The purpose of this research is to study the asymmetric relationship between house prices and stock followed by the wealth effect/credit-price effect/capital-switching regime. Stock prices are more volatile in case of negative news, while real estate is rigid downwards. To depict this potential asymmetry, the TAR/M-TAR model is employed and the asymmetric ECM for causal inferences. For cases with no asymmetry are tested with the Johansen framework and VECM. Empirical results indicate asymmetric credit-price effect for Finland and symmetric cointegration for Ireland, Sweden, Switzerland. The VECM indicates that Sweden exhibits wealth effect and there is credit-price effect for Ireland. The European Union has implemented its policies that accounted for the unification of its member nations. It is the first to examine asymmetric linkages between the house and stock prices under the capital-switching behavior found in the European markets as well as their unification after the implementation of Maastricht Treaty.

Stress distribution and rockburst characteristics of roadway group under the influence of fault and fold structures: a case study

Dynamic disasters such as rockbursts have different characteristics with different geological structures. The rockburst mechanism and the influencing factors of a typical composite fault-fold structure were explored by theoretical analysis and numerical simulation. The results showed that: (1) the influence of the composite fault-fold structure on the roadway group rockburst was mainly caused by tectonic stress disturbance; (2) the stress peak value and the influence range of the hanging wall of the fault were larger than those in the footwall, and the stress of the syncline axis was larger than that of the anticline axis; (3) the tectonic stress of the composite fault-fold structure was the highest, the stress value reached to the peak when the fault dip angle was 65°, and the tectonic stress was directly proportional to the elastic modulus of coal and first increased and then decreased with the increase in coal seam thickness; and (4) before rockburst, seismic activities concentrated within 200 m from the footwall and 0–250 m in the hanging wall of the fault, mainly concentrated in 0–20 and 0–40 m, respectively. The spatial distribution coincided with the high static stress area. Highlights The asymmetry of stress and microseismic events of composite fault-fold structure reveals the asymmetry of rockburst potential. The rockburst potential of the hanging wall of the fault is greater than that of the footwall, and the rockburst potential of the syncline is greater than that of the anticline Based on the analysis of stress characteristics and fault activation, it is revealed that the rockburst of roadway group is mainly affected by the static tectonic stress of composite fault-fold structure. Four influencing factors: structure type, fault dip angle, coal seam thickness, and coal elastic modulus are analysed, and the causes of stress concentration of composite fault-fold structure are revealed.

Asymmetry of the C2 pars interarticularis: a clinical anatomical study with relevance to screw placement.

Potential asymmetries of the C2 posterior elements pose a problem for the spine surgeon seeking to make the best choice for spinal stabilization while reducing morbidity. A digital caliper was used to measure the pars interarticularis height and length on left and right sides of 25 adult C2 vertebrae. The pars interarticularis was defined as the bone between the posterior most aspect of the superior articular process and the anterior most aspect of the inferior articular process of C2. Also, the C2 vertebrae from 49 patients were scanned by CT. Parasagittal images were reviewed and using the same definitions as were used for the skeletal specimens, the length and the height of the C2 pars interarticularis from both the left and right sides were measured using CT. The image slices were acquired at 3mm intervals. The pars interarticularis height was determined on sagittal CT reconstruction, while the pars interarticularis length was calculated on the basis of the axial images. The lengths and the heights of the left and right pars interarticularis were compared using CTs of patients and skeletal specimens. No significant differences were found in the length and height measurements of the CT images on both sides. However, in the skeletal specimens, the left and right pars interarticularis did not differ significantly in length but differed significantly in height (p = 0.003). The mean height of the left pars interarticularis was approximately two times larger than the right in the skeletal specimens. Absolute differences were calculated between the side with the greater length and height and the side with the lesser length and height irrespective of their left-right orientations. For CT measurements, most differences in length and height between the greater pars interarticularis and lesser pars interarticularis occurred between 0 and 1mm with each successive disparity interval yielding lower numbers. Skeletal measurements revealed a similar length disparity distribution to the CT measurements. However, height measurements in the skeletal specimens varied widely. Eight pars interarticularis specimens demonstrated a height difference between 0 and 1mm. No dry bone pars interarticularis specimens demonstrated a height difference between 1 and 2mm. The pars interarticularis of nine specimens demonstrated a height difference between 2 and 3mm. Two demonstrated a height difference between 3 and 4mm. Four demonstrated a height difference between 4 and 5mm and two demonstrated a height difference greater than 5mm. The greater pars interarticularis lengths and heights were combined and compared to their lesser counterparts on CT and skeletal measurements. In all measurements of this type, significant differences were found in the pars interarticularis length and height, whether measured through CT or via digital calipers. Asymmetry between the left and right C2 pars interarticularis as shown in the present study can alter surgical planning. Therefore, knowledge of this anatomical finding might be useful to spine surgeons.

Urban natural gas demand and factors analysis in China: Perspectives of price and income elasticities

Urban natural gas is becoming the main sector driving China's natural gas consumption growth in recent years. This study explores the impacts of urban natural gas price, wage, socioeconomic determinants, and meteorological conditions on urban natural gas demand in China over 2006–2017. Furthermore, this study also analyzes the potential regional heterogeneity and asymmetry in the impacts of gas price and income on China's urban gas demand. Empirical results reveal that: (1) The increased gas price can significantly reduce the urban gas demand, and the average income level may effectively promote the gas demand, also, a strong switching effect exists between electricity and natural gas in urban China; (2) these impacts are heterogeneous in regions among China, urban natural gas demand is largely affected by the gas price in regions with high-gas-price and by income in regions with low-gas-price; and (3) the impact of gas price on urban gas consumption is consistent in regions with different urban natural gas consumption, while the impact of income is asymmetric. This study further provides several policy implications for improving the urban natural gas industry in China.

Electronic and Optical Properties of InAs QDs Grown by MBE on InGaAs Metamorphic Buffer.

We present the optical characterization of GaAs-based InAs quantum dots (QDs) grown by molecular beam epitaxy on a digitally alloyed InGaAs metamorphic buffer layer (MBL) with gradual composition ensuring a redshift of the QD emission up to the second telecom window. Based on the photoluminescence (PL) measurements and numerical calculations, we analyzed the factors influencing the energies of optical transitions in QDs, among which the QD height seems to be dominating. In addition, polarization anisotropy of the QD emission was observed, which is a fingerprint of significant valence states mixing enhanced by the QD confinement potential asymmetry, driven by the decreased strain with increasing In content in the MBL. The barrier-related transitions were probed by photoreflectance, which combined with photoluminescence data and the PL temperature dependence, allowed for the determination of the carrier activation energies and the main channels of carrier loss, identified as the carrier escape to the MBL barrier. Eventually, the zero-dimensional character of the emission was confirmed by detecting the photoluminescence from single QDs with identified features of the confined neutral exciton and biexciton complexes via the excitation power and polarization dependences.

Passive solute separation in AC electroosmosis including surface charge-coupled hydrodynamic slip effects.

Separation of electrically neutral, mutually noninteracting passive solutes via AC electroosmotic slit channel flows is investigated for general asymmetric wall surface zeta potentials and apparent hydrodynamic slip lengths. We consider the nontrivial coupling between the surface potentials (or charge densities) and the apparent slip lengths, and focus our attention on the occurrence of a so called "crossover phenomenon" for separating out the slow diffusers when both slow and fast diffusers are present. Results show that regardless of the potential-slip coupling, wider bandwidths become available for crossover phenomenon to occur when the electroosmotic velocity gradient (magnitude) is greater. Contrarily, plug-like velocity profiles inhibit crossover phenomenon, and the potential-slip parametric combinations leading to such profiles can be easily identified by the conditions for minimal transport enhancement reported in recent literature. When separating out the slow diffuser or crossover phenomenon is desired, we recommend incorporating significant asymmetry in the surface potential and apparent slip boundary conditions such that the operating frequency and flow oscillation amplitude may be lowered to more practical values. Our results also agree with and strengthen the physical picture for explaining crossover phenomenon in macroscopic pressure-driven oscillatory flows.

Europa wielu prędkości i kwestia Europy Wschodniej. Ujęcie centro-peryferyjne

This article examines the issue of insecurity in the European Union. The analysis is based on the centre-periphery approach with the starting hypothesis that the asymmetry of potentials in the states and regions within the European Union is a result of historical social and economic differences. Contemporary discourse on the concept called “Multi-speed Europe” is perceived as a creation of the concrete political and institutional framework for defined disparities. Therefore, this concept is criticized by the new members of the EU, which remain insecure and dependent on European cohesion policies. During my research, I have engaged several achievements of economic security and development studies.

Asymmetric one-dimensional slow electron holes.

Slow solitary positive-potential peaks sustained by trapped electron deficit in a plasma with asymmetric ion velocity distributions are in principle asymmetric, involving a potential change across the hole. It is shown theoretically how to construct such asymmetric electron holes, thus providing fully consistent solutions of the one-dimensional Vlasov-Poisson equation for a wide variety of prescribed background ion velocity distributions. Because of ion reflection forces experienced by the hole, there is generally only one discrete slow hole velocity that is in equilibrium. Moreover the equilibrium is unstable unless there is a local minimum in the ion velocity distribution, in which the hole velocity then resides. For stable equilibria with Maxwellian electrons, the potential drop across the hole is shown to be Δϕ≃2/9f^{'''}T_{e}/e(eψ/m_{i})^{2}, where ψ is the hole peak potential, f^{'''} is the third derivative of the background ion velocity distribution function at the hole velocity, and T_{e} is the electron temperature. Potential asymmetry is small for holes of the amplitudes usually observed, ψ≲0.5T_{e}/e.