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Decomposition of a Video Pulse into Traveling and Evanescent Waves 视频脉冲分解为行波和倏逝波
IF 1.4 4区 物理与天体物理
JETP Letters Pub Date : 2025-04-21 DOI: 10.1134/S0021364024604950
I. V. Bubenshchikov, A. A. Tityapkin, V. V. Zalipaev, A. D. Kiselev, S. A. Kozlov
{"title":"Decomposition of a Video Pulse into Traveling and Evanescent Waves","authors":"I. V. Bubenshchikov,&nbsp;A. A. Tityapkin,&nbsp;V. V. Zalipaev,&nbsp;A. D. Kiselev,&nbsp;S. A. Kozlov","doi":"10.1134/S0021364024604950","DOIUrl":"10.1134/S0021364024604950","url":null,"abstract":"<p>Using the general solution of the wave equation for the empty space (vacuum), it has been shown that spatially limited video pulses may exist in it. However, video pulses in the empty space necessarily consist of two components: traveling and evanescent waves. It has been demonstrated that such structures can be created immediately beyond the interface between an optically dense medium and the empty space, as in near-field optics. In this work, the traveling and evanescent components are illustrated for a video pulse with Gaussian temporal and spatial profiles. It has been shown that the traveling wave is a one-and-half cycle pulse and its duration is determined by the ratio of the transverse and longitudinal dimensions of the video pulse. The same ratio also determines the distance at which the evanescent wave decays, and the video pulse becomes a few-cycle traveling wave. Using Gauss’s theorem, it has been demonstrated that transversely limited video pulses are not unipolar. The transverse and longitudinal components of their field perpendicular and parallel to the wave propagation axis, respectively, can be comparable in magnitude and differ in the character of their time evolution.</p>","PeriodicalId":604,"journal":{"name":"JETP Letters","volume":"121 5","pages":"332 - 337"},"PeriodicalIF":1.4,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143856607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Electronic Thermoelectric Properties of MgXY2Z2 Double Half-Heusler Alloys (X = Zr/Hf, Y = Pd/Pt, Z = Bi/Sb) MgXY2Z2双半heusler合金（X = Zr/Hf, Y = Pd/Pt, Z = Bi/Sb）的电子热电性能
IF 1.4 4区 物理与天体物理
JETP Letters Pub Date : 2025-04-01 DOI: 10.1134/S0021364025600016
A. N. Filanovich, A. V. Lukoyanov, A. A. Povzner
{"title":"Electronic Thermoelectric Properties of MgXY2Z2 Double Half-Heusler Alloys (X = Zr/Hf, Y = Pd/Pt, Z = Bi/Sb)","authors":"A. N. Filanovich,&nbsp;A. V. Lukoyanov,&nbsp;A. A. Povzner","doi":"10.1134/S0021364025600016","DOIUrl":"10.1134/S0021364025600016","url":null,"abstract":"<p>Double half-Heusler alloys represent a novel promising class of materials for applications, e.g., in thermoelectric energy converters. In this work, the electronic thermoelectric properties of five MgXY<sub>2</sub>Z<sub>2</sub> (X = Zr/Hf, Y = Pd/Pt, Z = Bi/Sb) compounds of this alloy class with the previously predicted low lattice thermal conductivity have been investigated for the first time. It has been shown that the Seebeck coefficients of MgHfPd<sub>2</sub>Sb<sub>2</sub> and MgTiPd<sub>2</sub>Sb<sub>2</sub> are among the highest in double half-Heusler alloys. The dependences of the Seebeck coefficient and power factor on the chemical potential at different temperatures and carrier densities have been analyzed, and the relationship between these dependences and the peculiarities of the electronic structure of the considered compounds has been revealed.</p>","PeriodicalId":604,"journal":{"name":"JETP Letters","volume":"121 4","pages":"301 - 305"},"PeriodicalIF":1.4,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143740758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Oscillations in Cross Sections for Single-Electron Charge Exchange in Collisions of Positive Ions with a Hydrogen Molecule 正离子与氢分子碰撞中单电子电荷交换的截面振荡
IF 1.4 4区 物理与天体物理
JETP Letters Pub Date : 2025-04-01 DOI: 10.1134/S0021364024604342
F. F. Goryaev
{"title":"Oscillations in Cross Sections for Single-Electron Charge Exchange in Collisions of Positive Ions with a Hydrogen Molecule","authors":"F. F. Goryaev","doi":"10.1134/S0021364024604342","DOIUrl":"10.1134/S0021364024604342","url":null,"abstract":"<p>Oscillations in the cross sections for single-electron charge-exchange of fast nonrelativistic positive ions on a hydrogen molecule are considered. The charge-exchange cross sections for the protons and alpha particles at fixed orientations of the hydrogen molecule are calculated as functions of the energy of the incident particles using the representation of the impact parameter in the Brinkman–Kramers approximation with normalized capture probabilities. The cross sections averaged over all orientations of the molecule are also presented. The results are compared with the available experimental data.</p>","PeriodicalId":604,"journal":{"name":"JETP Letters","volume":"121 4","pages":"236 - 242"},"PeriodicalIF":1.4,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143740680","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Magnetoelectric Effect in the Nd3Ga5SiO14 Paramagnet Nd3Ga5SiO14顺磁体中的磁电效应
IF 1.4 4区 物理与天体物理
JETP Letters Pub Date : 2025-04-01 DOI: 10.1134/S0021364024605244
A. A. Mukhin, V. Yu. Ivanov, A. M. Kuzmenko, A. Yu. Tikhanovskii, B. V. Mill
{"title":"Magnetoelectric Effect in the Nd3Ga5SiO14 Paramagnet","authors":"A. A. Mukhin,&nbsp;V. Yu. Ivanov,&nbsp;A. M. Kuzmenko,&nbsp;A. Yu. Tikhanovskii,&nbsp;B. V. Mill","doi":"10.1134/S0021364024605244","DOIUrl":"10.1134/S0021364024605244","url":null,"abstract":"<p>The electric polarization induced by a magnetic field <i>H</i> in Nd<sub>3</sub>Ga<sub>5</sub>SiO<sub>14</sub> noncentrosymmetric trigonal paramagnetic single crystals has been detected. In low fields, it is quadratic in <i>H</i> and its components in the basal <i>ab</i> plane are described by two magnetoelectric susceptibilities α<sub>1</sub> and α<sub>2</sub>. The polarization along the trigonal <i>c</i> axis is manifested only starting from the fourth-order terms ~<i>H</i><sup>4</sup>. In high magnetic fields at low temperatures, when the magnetic moments of Nd<sup>3+</sup> are saturated, the polarization qualitatively changes its field dependence to nearly quasilinear for all crystallographic directions and increases strongly (up to 250 μC/m<sup>2</sup> at 5 T along the <i>c</i> axis). The effects observed in Nd<sub>3</sub>Ga<sub>5</sub>SiO<sub>14</sub> have been quantitatively described using the spin Hamiltonian of the Nd<sup>3+</sup> ion in local low-symmetric (<i>C</i><sub>2</sub>) sites taking into account the magnetoelectric interaction allowed by symmetry. Magnetoelectric invariants nonlinear in <i>H</i> that make it possible to describe the observed the field, temperature, and angular dependences of the polarization using several magnetoelectric parameters have been constructed in terms of the local susceptibilities of Nd<sup>3+</sup> ions taking into account the nonequivalence of their magnetization.</p>","PeriodicalId":604,"journal":{"name":"JETP Letters","volume":"121 4","pages":"292 - 300"},"PeriodicalIF":1.4,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143740760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Topological Crossover in the Chiral Superconducting d + id Phase at Finite Temperatures 有限温度下手性超导d + id相的拓扑交叉
IF 1.4 4区 物理与天体物理
JETP Letters Pub Date : 2025-04-01 DOI: 10.1134/S0021364024604470
A. G. Groshev, A. K. Arzhnikov
{"title":"Topological Crossover in the Chiral Superconducting d + id Phase at Finite Temperatures","authors":"A. G. Groshev,&nbsp;A. K. Arzhnikov","doi":"10.1134/S0021364024604470","DOIUrl":"10.1134/S0021364024604470","url":null,"abstract":"<p>The temperature behavior of the topological index <i>C</i><sub>1</sub> of the chiral superconducting <i>d</i> + <i>id</i> phase of a two-dimensional single-band model on a triangular lattice has been studied. It has been found that the temperature dependence of the topological index fundamentally changes at carrier densities, at which the nodal points of the Brillouin zone approach the Fermi contour of the normal phase. It has been shown that the topological index <i>C</i><sub>1</sub> in a wide temperature range is close to <i>C</i><sub>1</sub> = 4 (–2) when the nodal points are located far inside (outside) the Fermi contour. However, when nodal points approach the Fermi contour, these values are maintained only at low temperatures, and values close to <i>C</i><sub>1</sub> = 1 in a wide temperature range. It has been assumed that such a topological crossover in the system under consideration can lead to significant changes in edge states in a similar open-boundary system.</p>","PeriodicalId":604,"journal":{"name":"JETP Letters","volume":"121 4","pages":"276 - 280"},"PeriodicalIF":1.4,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S0021364024604470.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143740761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Parametric Light–Dark Spatiotemporal Soliton 参数光-暗时空孤子
IF 1.4 4区 物理与天体物理
JETP Letters Pub Date : 2025-04-01 DOI: 10.1134/S0021364024605049
S. V. Sazonov
{"title":"Parametric Light–Dark Spatiotemporal Soliton","authors":"S. V. Sazonov","doi":"10.1134/S0021364024605049","DOIUrl":"10.1134/S0021364024605049","url":null,"abstract":"<p>The possibility of the appearance of a light–dark spatiotemporal soliton in the second-harmonic generation mode with the normal group velocity dispersion at the fundamental frequency in the absence of such a dispersion at the second harmonic frequency has been demonstrated theoretically. This object has the form of a dark two-color soliton with respect to time and coordinate in the direction of propagation and is light with respect to the transverse (spatial) coordinates.</p>","PeriodicalId":604,"journal":{"name":"JETP Letters","volume":"121 4","pages":"262 - 266"},"PeriodicalIF":1.4,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S0021364024605049.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143740689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Effect of Selenium, Copper and Silver Microparticles Obtained in Viscous Media on the Gram-Positive and Gram-Negative Bacteria Survival 粘性培养基中硒、铜和银微粒对革兰氏阳性和革兰氏阴性细菌存活的影响
IF 1.4 4区 物理与天体物理
JETP Letters Pub Date : 2025-04-01 DOI: 10.1134/S0021364024605190
I. N. Saraeva, E. R. Tolordava, R. A. Khmelnitsky, S. N. Shelygina, D. S. Pozdnyakova, A. A. Nastulyavichus, E. N. Rimskaya, A. E. Rupasov
{"title":"Effect of Selenium, Copper and Silver Microparticles Obtained in Viscous Media on the Gram-Positive and Gram-Negative Bacteria Survival","authors":"I. N. Saraeva,&nbsp;E. R. Tolordava,&nbsp;R. A. Khmelnitsky,&nbsp;S. N. Shelygina,&nbsp;D. S. Pozdnyakova,&nbsp;A. A. Nastulyavichus,&nbsp;E. N. Rimskaya,&nbsp;A. E. Rupasov","doi":"10.1134/S0021364024605190","DOIUrl":"10.1134/S0021364024605190","url":null,"abstract":"<p>The work presents a multiparametric analysis of the effect of antibacterial nanogels based on nano- and (sub)microparticles of silver, copper and selenium on single- and multicomponent biofilms of gram-positive bacteria <i>Staphylococcus</i> <i>aureus</i>, <i>Staphylococcus</i> <i>epidermidis</i>, as well as gram-negative bacteria <i>Escherichia</i> <i>coli</i>, <i>Klebsiella</i> <i>pneumoniae</i>, and <i>Pseudomonas</i> <i>aeruginosa</i>. Nanogels are based on glycerol, silicone oil and Vaseline, which are low-costing biocompatible materials, suitable for use in wound dressings. The active components are bactericidal Ag, Cu, and Se nanoparticles. Nanogels and their effect on the bacterial biofilms were studied by standard microbiological inoculations, as well as Fourier transform infrared spectroscopy methods, followed by principal component analysis. After the treatment of biofilms with nanogels, a decrease in the bacterial population up to 99% was observed. Principal component analysis demonstrated the ability to differentiate viable from nonviable bacteria.</p>","PeriodicalId":604,"journal":{"name":"JETP Letters","volume":"121 4","pages":"306 - 314"},"PeriodicalIF":1.4,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S0021364024605190.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143740801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Broadband X-Ray Diagnostics of a Relativistic Laser Plasma 相对论性激光等离子体的宽带x射线诊断
IF 1.4 4区 物理与天体物理
JETP Letters Pub Date : 2025-04-01 DOI: 10.1134/S0021364024604925
K. A. Ivanov, A. I. Sivko, I. N. Tsymbalov, G. Kh. Salakhutdinov, A. A. Kologrivov, A. A. Rupasov, E. A. Bolkhovitinov, R. V. Volkov, A. B. Savel’ev
{"title":"Broadband X-Ray Diagnostics of a Relativistic Laser Plasma","authors":"K. A. Ivanov,&nbsp;A. I. Sivko,&nbsp;I. N. Tsymbalov,&nbsp;G. Kh. Salakhutdinov,&nbsp;A. A. Kologrivov,&nbsp;A. A. Rupasov,&nbsp;E. A. Bolkhovitinov,&nbsp;R. V. Volkov,&nbsp;A. B. Savel’ev","doi":"10.1134/S0021364024604925","DOIUrl":"10.1134/S0021364024604925","url":null,"abstract":"<p>Absolute measurements of the X-ray spectrum of a plasma formed by intense femtosecond laser radiation on the surface of a solid target in a wide range of interaction parameters with varying the intensity and contrast of a laser pulse have been carried out. The energy distribution of the photon flux from the plasma created on the metal target in the range from 0.1 keV to 1 MeV and higher has been determined for the first time in a single experiment. Using the data obtained, physical processes in the interaction region have been analyzed. The temperatures of background and hot plasma electrons have been estimated. The role of these electron in the generation of the photon flux and the efficiency of laser radiation conversion into various ranges has been studied. A close relationship between the observed results and the contrast and peak intensity of laser radiation has been found.</p>","PeriodicalId":604,"journal":{"name":"JETP Letters","volume":"121 4","pages":"267 - 275"},"PeriodicalIF":1.4,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143740759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Features of the Conductivity of Nominally Undoped Single-Crystal CVD Diamond 名义上未掺杂的单晶 CVD 金刚石的电导率特征
IF 1.4 4区 物理与天体物理
JETP Letters Pub Date : 2025-03-25 DOI: 10.1134/S0021364024605293
M. S. Kagan, S. K. Paprotskiy, N. A. Khvalkovskiy, I. V. Altukhov, N. B. Rodionov, A. P. Bol’shakov, V. G. Ral’chenko, R. A. Khmel’nitskiy
{"title":"Features of the Conductivity of Nominally Undoped Single-Crystal CVD Diamond","authors":"M. S. Kagan,&nbsp;S. K. Paprotskiy,&nbsp;N. A. Khvalkovskiy,&nbsp;I. V. Altukhov,&nbsp;N. B. Rodionov,&nbsp;A. P. Bol’shakov,&nbsp;V. G. Ral’chenko,&nbsp;R. A. Khmel’nitskiy","doi":"10.1134/S0021364024605293","DOIUrl":"10.1134/S0021364024605293","url":null,"abstract":"<p>The conductivity of nominally undoped single-crystal diamond films grown epitaxially by chemical vapor deposition on a heavily boron-doped <i>p</i><sup>+</sup>-type diamond substrate has been studied. The conductivity of the films has been determined by the boron acceptor impurity. The temperature dependence of the conductivity in the temperature range of 300–500 K obeys the activation law, but the activation energy significantly exceeds the ionization energy of boron acceptors of ε<sub>i</sub> = 0.37 eV. It has been found that the acceptors are strongly compensated. This leads to the appearance of a random potential with a large amplitude of γ ≈ 0.2 eV, leading to a large increase in the activation energy ∼ε<sub>i</sub> + γ. The reason for the appearance of the strong random potential has been attributed to the self-compensation of boron impurities by nitrogen atoms during the chemical vapor deposition growth of diamond films on the heavily doped substrate.</p>","PeriodicalId":604,"journal":{"name":"JETP Letters","volume":"121 3","pages":"220 - 224"},"PeriodicalIF":1.4,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143698615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spectral Properties of Terahertz Radiation from Laterally Structured Spintronic Emitters 侧向结构自旋电子发射器太赫兹辐射的光谱特性
IF 1.4 4区 物理与天体物理
JETP Letters Pub Date : 2025-03-25 DOI: 10.1134/S0021364024604639
E. A. Karashtin, N. S. Gusev, M. V. Sapozhnikov, P. Yu. Avdeev, A. L. Alfer’ev, E. D. Lebedeva, A. M. Buryakov, E. D. Mishina
{"title":"Spectral Properties of Terahertz Radiation from Laterally Structured Spintronic Emitters","authors":"E. A. Karashtin,&nbsp;N. S. Gusev,&nbsp;M. V. Sapozhnikov,&nbsp;P. Yu. Avdeev,&nbsp;A. L. Alfer’ev,&nbsp;E. D. Lebedeva,&nbsp;A. M. Buryakov,&nbsp;E. D. Mishina","doi":"10.1134/S0021364024604639","DOIUrl":"10.1134/S0021364024604639","url":null,"abstract":"<p>In this work, the spectral properties of the terahertz radiation of a spintronic emitter based on the Co(2 nm)/Pt(2 nm) ferromagnet/heavy metal heterostructure and the periodic system of strips made of it (period from 4 μm to 1 mm) have been experimentally studied. Two main mechanisms that determine the terahertz spectrum of such emitters are demonstrated. The first of them is observed both in a continuous multilayer film and in a periodic lattice. In this mechanism, due to the interference of signals from different spatial regions of the emitter, the amplitude of the wave decreases with an increase in the angle between the normal to the film and the direction of radiation propagation, and the characteristic scale of this decrease depends on the wavelength. As a result, the increase in this angle is accompanied by the redshift of the spectral amplitude maximum of radiation. The second mechanism is possible only in the periodic system of strips. It occurs as the fact suppression of terahertz radiation due to the charge accumulation at the boundaries of the strips when periodic lattices with a short period are magnetized along the strips. This effect is more significant for longer wavelengths and is therefore accompanied by a blueshift of the spectral maximum. The mechanisms studied in this work will make it possible to create spintronic emitters of terahertz radiation with a given position of the spectral amplitude maximum of terahertz radiation.</p>","PeriodicalId":604,"journal":{"name":"JETP Letters","volume":"121 3","pages":"195 - 201"},"PeriodicalIF":1.4,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S0021364024604639.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143698602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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