Electronic Susceptibility Research Articles

Interplay between band crossing and charge density wave instabilities

Our measurements of the Hall coefficient in rare-earth tritelluride compounds reveal a strong hysteresis between cooling and warming in the low temperature range where a second unidirectional charge density wave (CDW) occurs. We show that this effect results from the interplay between two instabilities: band crossing of the Te $p_{x}$ and $p_{y}$ orbitals at the Fermi level and CDW, which have a close energy gain and compete. Calculation of the electron susceptibility at the CDW wave vector with and without band anticrossing reconstruction of the electron spectrum yields a satisfactory estimation of the temperature range of the hysteresis in Hall effect measurements.

Bayesian Inference for Susceptibility of Electronics to Transient Electromagnetic Disturbances With Failure Mechanism Consideration

It is a necessity to evaluate the susceptibility of electronics to transient electromagnetic disturbances, such as electromagnetic pulses, lightning, electro-static discharges, and switching pulses. One can conduct experiments on the system of interest and analyze the result through statistical inference for the relationship between electromagnetic excitations and effect phenomena. However, since conventional statistical models are driven by experimental data, it might result in inappropriate explanations of the effect mechanisms due to limited samples, leading to over- or under-estimations. To address this problem, we propose a hybrid model that combines the statistical estimation with the known failure mechanism obtained from either the theoretical analysis or the empirical evidence. The physical cause can be drawn from the mechanism analysis, and then a statistical classifier is introduced to build the relationship between the causes and the effects. Based on Bayesian assessment, all the parameters involved are estimated with the Markov chain Monte Carlo method. Numerical simulation results have verified that the model is capable of estimating the susceptibility of electronics with given failure mechanism assumptions and limited test samples. In the end, the breakdown characteristic of the gas discharge tube is investigated to demonstrate the applicability of the proposed model.

The Evolution of Electron Dispersion in the Series of Rare-Earth Tritelluride Compounds Obtained from Their Charge-Density-Wave Properties and Susceptibility Calculations.

We calculated the electron susceptibility of rare-earth tritelluride compounds RTe3 as a function of temperature, wave vector, and electron-dispersion parameters. Comparison of the results obtained with the available experimental data on the transition temperature and on the wave vector of a charge-density wave in these compounds allowed us to predict the values and evolution of electron-dispersion parameters with the variation of the atomic number of rare-earth elements (R).

Magnetovortical and thermoelectric transport in tilted Weyl metals

We investigate how tilting affects the off-diagonal, dissipationless response of a pair of chirally imbalanced Weyl cones to various external perturbations. The pair of chirally imbalanced Weyl cones can be described as a chiral electron fluid, that can flow with a velocity field that contains vorticity. Upon applying an external magnetic field, we obtain the so-called magnetovortical linear-response matrix that relates electric and heat currents to the magnetic field (chiral magnetic effect) and the vorticity (chiral vortical effect). We show how this reponse matrix becomes anisotropic upon tilting the cones and determine its non-analytic long-wavelength behavior, as well as the corresponding AC response. In addition, we discuss how the tilt dependence of the electronic (or density-density) susceptibility introduces anisotropy in the dispersion relation of the sound-like excitations in the fluid of chiral fermions, which are known as chiral magnetic waves. In the case of an externally applied electric field and a temperature gradient, we find a Hall-like response in the electric and heat current density that is perpendicular to both the tilting direction and the perturbations. As the tilting direction forms a time-reversal symmetry breaking vector, a non-zero (heat) orbital magnetization manifests itself. We calculate the magnetization currents microscopically and elucidate how to subtract these contributions to obtain the transport currents.

Study of the linear and nonlinear response properties of the zinc-blende AlP, GaP and their AlxGa1-xP ternary alloys using first principle calculations

The structural, electronic, thermodynamic, vibrational, elastic, linear and nonlinear optical properties of AlxGa1-xP ternary alloys are studied using plane-wave pseudopotential method based on the density functional theory. The alchemical mixing method is used to construct an alloy by mixing the pseudopotentials in an appropriate way. The local density approximation is used for the exchange and correlation potentials calculations using the ABINIT code. The Born effective charges, phonon frequencies, longitudinal-transvers optical splitting and thermal properties are calculated using density functional perturbation theory. By applying the many-body effects within the Bethe-Salpeter approach using the Tam-Dancoff approximation, the frequency-dependent macroscopic dielectric function is calculated. The nonlinear dielectric (electronic) susceptibility, the electro-optic tensor and the Raman tensor are investigated in the framework of density functional perturbation theory using the 2n+1 theorem. Moreover, due to density functional theory band gap problem, the band-gap correction is performed within the one-shot GW approximation of many-body perturbation theory. The calculated results of AlP and GaP compounds are in acceptable agreement with available theoretical and experimental results, so the present study on the AlxGa1-xP alloys would be helpful for future experimental and theoretical investigations.

Electronic Processing of Antimicrobial Susceptibilities to Enhance Communicable Disease Surveillance

ObjectiveIllustrate how the Utah Department of Health automatically processes antimicrobial susceptibility results that are received electronically.IntroductionThe emerging threat of antimicrobial resistant organisms is a pressing public health concern. Surveillance for antimicrobial resistance can prevent infections, protect patients in the healthcare setting and improve antimicrobial use. In 2018, the Utah Department of Health mandated the reporting of antimicrobial susceptibility panels performed on selected organisms. Utah utilizes the Electronic Message Staging Area (EMSA), a home-grown application to translate, process, and enter electronic laboratory results into UT-NEDSS, Utah’s integrated disease surveillance system. Processing these results electronically is challenging due to the need to interpret results based on the antimicrobial agent combined with the organism it was performed on. The receipt of antimicrobial susceptibility panels has required enhancements to EMSA for these results to be automatically processed.MethodsStand-alone antimicrobial susceptibility LOINCs are configured within EMSA to concatenate during the preprocessing stage. This tells EMSA that when this LOINC is sent within an HL7 message to find the organism name in the corresponding OBR 26.3 (the parent result field). EMSA then creates a new fabricated code that combines the antimicrobial agent with the organism identified from the culture (example: ‘18906-8 Pseudomonas aeruginosa’ is the fabricated code for Ciprofloxacin susceptibility to Pseudomonas aeruginosa).Once these new fabricated antimicrobial susceptibility codes are created, interpretation rules are programmed using current Clinical and Laboratory Standards Institute (CLSI) breakpoints for each unique organism/antimicrobial combination to determine if the result is Susceptible/Intermediate/Resistant. The interpreted test is then run through a set of condition-specific rules to determine how it should be included into UT-NEDSS.ResultsAntimicrobial susceptibility panels performed on Acinetobacter species, Escherichia coli, Klebsiella species, Pseudomonas aeruginosa, Enterobacter species, Candida auris/haemulonii, Mycobacterium tuberculosis, Neisseria gonorrhoeae, Salmonella species, Shigella species, Streptococcus pneumoniae and invasive Staphylococcus aureus are now included in Utah’s Communicable Disease Reporting Rule. Currently, there are 36 antimicrobial agents programmed into EMSA and there are a total of 217 antimicrobial susceptibility codes programmed into the system.ConclusionsProcessing electronic antimicrobial susceptibility results presents unique challenges for processing. Interpretation of results can vary based on test method, performing laboratory, and organism. Enhancing functionality within EMSA was necessary for combining the antimicrobial agent and organism it was performed on. Implementing systems capable of automatically processing complicated antimicrobial susceptibility results should be a priority for any health department interested in expanding their communicable disease rule to include antimicrobial susceptibility testing.

Polymer complexes. LXXVII. Synthesis, characterization, spectroscopic studies and immune response in cattle of quinoline polymer complexes

A series of novel polymeric metal complexes of Co(II), Ni(II), Cu(II), Zn(II) and Cr(III) with 5,5′‐{(1E,1E′)‐1,4‐phenylenebis(diazene‐2,1‐diyl)}bis(quinolin‐8‐ol) (H2L) ligand were synthesized and characterized using elemental analyses, 1H NMR, mass, infrared, UV–visible and electron spin resonance (ESR) spectroscopies, magnetic moment and conductivity measurements as well as thermal analyses. The spectral and analytical data revealed the ligand adopted a neutral bidentate fashion when binding to metal ions via the nitrogen of azomethine of pyridine ring and the deprotonated hydroxyl group. Electronic and magnetic susceptibility measurements of the polymer complexes indicated octahedral geometry for all polymer complexes. The ESR spectral data provided information about the structures on the basis of Hamiltonian parameters and the degree of covalency. Molecular docking was used to predict the binding between the H2L and the receptor of breast cancer (3hb5). The immune response of the synthesized polymer complexes with bovine respiratory syncytial (BRS) vaccine in cattle was studied using serum neutralizations test (SNT). It was found that the isolated polymer complexes with BRS vaccine caused a significant increase in the antibody titre against BRS virus in SNT compared to BRS vaccine alone.

Quantum oscillations in Stoner susceptibility: A theory

Oscillatory effects in magnetic susceptibility of free electrons in a strong magnetic field is well known phenomenon and is well captured by Lifshitz-Kosevich formula. In this paper we point out similar oscillatory effects in Stoner susceptibility which makes the system to oscillate between paramagnetic phase and ferromagnetic phase alternatively as a function of external magnetic field strength. This effect can happen in a material which is tuned near to its magnetic instability. We suggest an experimental set-up to observe this effect. We also suggest that our result can be exploited to control a quantum critical system around its quantum critical point to study its thermodynamical or transport properties.

Structural Transformations in the Thermal Dehydration of [Cu2(bpa)(btec)(H2O)4]n Coordination Polymer.

Reactions between pyridinic ligands such as 1,2-bis(4-pyridyl)ethane (bpa) and transition metal cations are a very widespread technique to produce extended coordination polymers such as Metal-Organic Frameworks. In combination with a second ligand these systems could present different topologies and behaviors. In this context, the use of 1,2,4,5-benzenetetracarboxylic acid (H4btec) gave us a novel 2D compound, [Cu2(bpa)(btec)(H2O)4]n (1), which was prepared by microwave-assisted synthesis and structurally characterized by means of single crystal X-ray diffraction. Its thermal behavior was analyzed through thermogravimetric analysis and variable temperature powder X-ray diffraction, concluding that thermal stability is influenced by the coordination water molecules, allowing two sequential thermochromic phase transformations to take place. These transformations were monitored by electronic paramagnetic resonance spectroscopy and magnetic susceptibility measurements. In addition, the crystal structure of the anhydrous compound [Cu2(bpa)(btec)]n (1.ah) was determined. Finally, a topological study was carried out for the bpa ligand considering all the structures deposited in the Cambridge Structural Databased. More than 1000 structures were analyzed and classified into 17 different topologies, according to the role of the ligand.

Concentration-dependence and luminescence studies of erbium doped barium lithium fluoroborate glasses

The present spectral investigations on erbium doped barium lithium fluoroborate glasses of the composition (70-x) H3BO3 − 10 Li2CO3 − 10 BaCO3 − 5 CaF2 − 5 ZnO − x Er2O3 (where x = 0.05, 0.1, 0.5, 1, 2 in wt %) were prepared by the conventional melt quenching technique. Dielectric constant, refractive index, electronic susceptibility, reflection loss and interionic distance were calculated for all the glass samples. The X-ray diffraction spectrum confirmed the amorphous nature of the prepared glasses. The optical properties of the prepared glasses were investigated by UV–Vis-NIR absorption and emission spectra. Nephelauxetic ratio and bonding parameters were determined from the absorption spectra and are found to be covalent in nature. Optical bandgap corresponding to the direct and indirect allowed transition were calculated to understand the electronic band structure and the Urbach energy values. Judd-Ofelt (JO) intensity parameters (Ωλ = 2, 4 and 6) were determined from the absorption spectrum. These JO parameters were used to analyse the transition probability (A), branching ratio (βR), and the stimulated emission cross section (σPE) parameter for different emission intensities. The emission of infrared at 1550 nm indicates that the glass material can act as a promising wave guide laser source and is suitable in optical fiber amplifier applications.

Synthesis, spectroscopic characterization and determination of the nonlinear optical properties of 2-(4-chlorobenzylidene) malononitrile using a computational method and Z-scan technique

A synthesis and theoretical study was carried out on UV-vis spectra of 2-(4-chlorobenzylidene) malononitrile. The structure, the geometry optimization, and the properties of non-linear optics were also investigated using the theory level M062X/6311 + +G (d, p). The Z-scan technique was used to establish the optical properties of 4ClD2MM as a function of the laser emission power; said compound was diluted in tetrahydrofuran to a fixed concentration of 0.1 M. By means of the same technique it was possible to establish non-linear parameters such as the non-linear refractive index, the non-linear absorption coefficient and the electronic third-order susceptibility. For these measurements, a Nd: YAG CW laser was used emitting at 532 nm, as well as a focus of a 10 cm lens, a 1 mm iris and a cell with a length of 1 mm.

Characterization by Potentiometric Procedures of the Stability Constants of the Binary and Ternary Complexes of Cu(II) and Duloxetine Drug with Amino Acids

Potentiometric titration method has been used to define stoichiometries and stability constants of ternary complexes of Cu(II) with duloxetine (D) and some selected amino acids (L). The protonation constants of the ligands and the stability constants of the binary and ternary complexes of Cu(II) with the ligands were calculated from the potentiometric data using the HYPERQUAD program. The formation constants of the complexes formed in aqueous solutions and their concentration distributions as a function of pH were evaluated at 25°C and ionic strength 0.10 mol·L−1NaNO3. Respective stabilities of ternary complexes have been determined compared with the corresponding binary complexes in terms ofΔlog Kand %R.S. values. A novel binary and ternary duloxetine (D) drug with glycine and its Cu(II) complexes has been synthesized and characterized by several spectroscopic methods. Electronic spectra and magnetic susceptibility measurements reveal square planar geometry for both complexes. The elemental analyses and mass spectral data have justified the [Cu(D)(Gly)] and [Cu(D)Cl(H2O)] composition of complexes, where D = duloxetine and Gly = glycine. The EPR spectra of Cu(II) complexes support the mononuclear structures. Thermal properties and decomposition kinetics of Cu(II) complexes are investigated.

Quantum criticality in the (Cr98.4Al1.6)100-yMoy alloy system

Indications of quantum critical behaviour (QCB), driven by electron-hole pair breaking effects through Mo doping of Cr98.4Al1.6 are reported. Previous studies on the electrical resistivity (ρ), Seebeck coefficient (S), Sommerfeld electronic specific heat coefficient (γ) and magnetic susceptibility (χ) as a function of temperature on the (Cr98.4Al1.6)100-yMoy alloy system point towards the existence of a quantum critical point (QCP) at yc ≈ 4.5. In the present study the Hall coefficient RH measurements and an analysis of the previous results are used to substantiate the presence of a QCP in the alloy system. The charge carrier density at 2 K, (qRH(2K))−1, of the alloy systems increases continuously with y from the antiferromagnetic (AFM) phase through yc ≈ 4.5 and into the paramagnetic (P) phase. Scaling relationships between the magnetic contribution to the electrical resistivity, Δρ2K, the magnetic contribution to the Sommerfeld electronic specific heat coefficient, Δγ, and (qRH(2K))−1, are furthermore used to support the presence of a QCP in the alloy system. dS/dT in the temperature limit T→ 2 K depicts an anomalous behaviour in the form of an upturn on decreasing y through the QCP, yc ≈ 4.5. The critical exponents in the vicinity of the QCP were found to be β = 0.5 ± 0.1 for the Δρ2K/ρ2K(y) curve and γ = 0.4 ± 0.1 for the TN(y) curve. The nature of the QCP in the present alloy system is classified as an incommensurate (I) spin-density-wave (SDW) type, driven mainly by electron-hole pair breaking effects.

New ternary aluminides RERh4Al15 (RE = La, Ce, Pr, Sm, Gd)

The aluminum-rich intermetallic rare earth compounds RERh4Al15 (RE = La, Ce Pr, Sm, Gd) were synthesized by arc melting of the elements under an argon atmosphere. The samples were characterized by powder X-ray diffraction which revealed a straight-forward agreement of the synthesized materials with tetragonal space group P42/nmc, NdRh4Al15.37 structure type. The structures of CeRh4Al15 and PrRh4Al15 were refined from single-crystal X-ray diffraction data. CeRh4Al15 is a new correlated electron compound with Kondo interaction. There is no magnetic ordering above 0.05 K despite the localized Ce3+ magnetic moment behaviour near room temperature. The electronic specific heat, magnetic susceptibility and electrical resistivity indicate that the compound may be accidently poised near a magnetic quantum critical point.

Synthesis, characterisation and molecular structure study of metal complexes of antipyrine based ligand

Three transition metal complexes [Co (II), Ni (II) and Fe (III)] of the ligand 5-[(1,5-dimethyl-3-oxo-2-phenyl-2,3-dihydro-1H-pyrazol-4-yl)diazenyl]-6-hydroxy-1,4-dimethyl-2-oxo-1,2-dihydropyridine-3-carbonitrile(L) which was found from the diazo-coupling reaction below 5 °C. The freshly synthesized metal chelates were characterized by both experimental and theoretical studies. Based on physico-chemical evidence, the azo dye acts as a tridentate ligand with nitrogen and oxygen atoms of the azo, carbonyl and phenyl groups are the coordinating sites. Non-electrolytic nature was observed for all the metal chelates because of their low molar conductivity. The electronic and magnetic susceptibility measurements suggested octahedral geometrical environment around all the metal ions. Quantum study of the synthesized moleculesby Zindo method to explaining about the electronic structure of the molecules.

Some new Ag(I), VO(II) and Pd(II) chelates incorporating tridentate imine ligand: Design, synthesis, structure elucidation, density functional theory calculations for DNA interaction, antimicrobial and anticancer activities and molecular docking studies

Some new complexes derived from VO(II), Ag(I) and Pd(II) metal ions and HNA imine ligand (L), i.e. (2‐((6‐allylidene‐2‐hydroxycyclohexa‐1,3‐dienylmethylene)amino)benzoic acid), have been prepared and their structures elucidated via molar conductance measurements, elemental analyses, infrared, NMR and electronic spectra and magnetic susceptibility estimations. Moreover, stability constants of the synthesized complexes were evaluated utilizing a spectrophotometric technique. On the basis of molar conductance and elemental analyses, the metal imine chelates have structure [M(L)], where M = Pd(II), VO(II) and Ag(I). The results indicate that the prepared HNA imine ligand acts as a tridentate moiety via nitrogen atom of azomethine group and two oxygen atoms of phenolic and carboxylic groups. All the complexes are found to be monomeric with 1:1 stoichiometry with square planar geometry for Pd(II), tetrahedral geometry for Ag(I) and distorted square pyramidal for VO(II). Theoretical density functional theory calculations were applied to verify the molecular geometry of the chelators and their metal chelates. The geometry optimization results are in agreement with experimental observations. The antimicrobial properties of the prepared HNA imine ligand and its metal chelates were evaluated against numerous plant pathogenic fungi and bacteria. The results of these studies indicate that the metal complexes exhibit a stronger antibacterial and antifungal effect compared to the imine ligand. In addition, the interaction of the metal imine chelates with calf thymus DNA was observed by way of viscosity, gel electrophoreses and spectral studies. Absorption titration studies reveal that each of the complexes is an avid binder to calf thymus DNA. Also, there are appreciable changes in the relative viscosity of DNA, which are consistent with enhanced hydrophobic interaction of the aromatic rings and intercalation mode of binding. Additionally, the cytotoxic activity of the investigated compounds against various cancer cell lines shows promising results which makes them prospective compounds for antibiotic and anticancer medicament studies. Furthermore, docking studies of the prepared compounds were conducted for confirming the biological results.

Relationship between the use of electronic devices and susceptibility to multiple sclerosis.

Multiple sclerosis (MS) is an autoimmune condition influenced by both genetic and environmental factors. Dirty electricity generated by electronic equipment is one of the environmental factors that may directly or indirectly impact MS susceptibility. The current Study aimed to evaluate the relationship between the usage time of electronic equipment and susceptibility to MS in North-West Iranian people. This approach was carried out upon 471 MS-diagnosed patients and 453 healthy participants as control group in East Province of Azerbaijan. By utilizing structured questionnaires, the information of all participants about usage status of some electronic devices was obtained. Data were analyzed by IBM SPSS Statistics version 18.0 and the quantitative variables were analyzed by Chi Square and Independent sample t tests. P values below or equal to 0.05 were considered as significant. Among the evaluated items in this approach, the utilization of cell phones and satellite television dishes were significantly higher in MS patients (p < 0.001, p = 0.07). Furthermore, a correlation was observed between sleeping with cell phone and/or laptop under the pillow (p = 0.011) and MS disease; however, there was no significant differences between MS patients and controls in computer using and television watching. Our study reinforces the concept that the utilization of some electronic devices and the continuous exposure to dirty electricity would increase the risk of MS disease thereupon by enhancing the cognizance of adverse effects of dirty electricity and reducing the time spent over electronic devices during adolescence and adulthood the occurrence probability of MS could be declined.

Enhanced Hybridization Sets the Stage for Electronic Nematicity in CeRhIn_{5}.

High magnetic fields induce a pronounced in-plane electronic anisotropy in the tetragonal antiferromagnetic metal CeRhIn_{5} at H^{*}≳30 T for fields ≃20° off the c axis. Here we investigate the response of the underlying crystal lattice in magnetic fields to 45T via high-resolution dilatometry. At low fields, a finite magnetic field component in the tetragonal ab plane explicitly breaks the tetragonal (C_{4}) symmetry of the lattice revealing a finite nematic susceptibility. A modest a-axis expansion at H^{*} hence marks the crossover to a fluctuating nematic phase with large nematic susceptibility. Magnetostriction quantum oscillations confirm a Fermi surface change at H^{*} with the emergence of new orbits. By analyzing the field-induced change in the crystal-field ground state, we conclude that the in-plane Ce 4f hybridization is enhanced at H^{*}, in agreement with the in-plane lattice expansion. We argue that the nematic behavior observed in this prototypical heavy-fermion material is of electronic origin, and is driven by the hybridization between 4f and conduction electrons which carries the f-electron anisotropy to the Fermi surface.

Preparation, Identification and Cancer Inhibitory Activity of a novel Pd (II) complex derived from E)-2-((4, 5-bis(4-methoxyphenyl)-1H-imidazol-2-yl)diazenyl)-5-iodobenzoic acid

The synthesis and spectral identification of metal complex for Pd(II) ion with newfangled heterocyclic azo dye as ligand (E)-2-((4, 5-bis(4-methoxyphenyl)-1H-imidazol-2-yl)diazenyl)-5-iodobenzoic acid (MPIAIBA) have been organized by reaction of diazonium chloride salt solution of 2-amino-5-iodobenzoic acid with imidazole derivatives in alkaline ethanolic solution. Azo dye ligand and its Pd (II) complex have been characterized by 1H-NMR, analytical data, Infrared, Mass spectrum, thermal analysis (TG-DTG), Electronic Spectral Data, molar conductance and magnetic susceptibility. The elemental investigation of the metal complexes validate the stoichiometry of the [Pd(L)Cl] type where L=azo dye ligand. Molar conductance measured results for organized Pd (II) complex showed 1: 1 electrolyte for Pd (II) ion. The azo dye ligand acts a tridentate and coordinates to the palladium ion via nitrogen atom of azo group of heterocyclic imidazole ring, nitrogen atom of azo group and oxygen of carboxyl group. Square planar geometry is suggested for Pd (II) complex. In this investigation, the cytotoxicity of the azo dye ligand and its Pd(II) complex has screened for in vitro, antitumor movement against human hepatocellular carcinoma HepG-2 utilizing MTT examine. The prepared ligand and its Pd(II) complex demonstrated anticancer movement with IC50 values indicated cytotoxicity against malignant growth cell line with IC50=172.3μg/ml, WRI-68 IC50=238.6μg/ml, while Pd(II)-complex demonstrated specific cytotoxicity in contradiction of disease cell line with IC50 =115.0μg/ml; WRI-68 IC50=192.1μg/ml. The outcomes demonstrated that this sort of compounds has a significant part in the hindrance rate of the development of cells of destructive and normal lines.

Third order nonlinear optical properties of DNA-based biopolymers thin films doped with selected natural chromophores

The results of linear and nonlinear optical (NLO) studies on thin films of DNA based biopolymers, doped with natural chromophores extracts of sweet paprika, turmeric as well as curry leaves are reported and discussed. The thin films were obtained by spin coating on glass substrates. The spectroscopy measurements show that the extracts absorb in visible, at different wavelengths, revealing an important π electron conjugation. The nonlinear optical measurements, done by the optical third harmonic generation technique at 1064.2 nm fundamental wavelength, show that the fast, electronic origin third order NLO susceptibility of natural extracts χ(3)(−3ω;ω,ω,ω), is large and comparable or higher than that measured for synthetic counterparts. The largest one in this study was found for the curry leaves extract: (396.9 ± 40) ×10−14 esu.