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Chirality-selective vibrational sum frequency generation (chiral SFG) spectroscopy has emerged as a powerful technique for the study of biomolecular hydration water due to its sensitivity to the induced chirality of the first hydration shell. Thus far, water O–H vibrational bands in phase-resolved heterodyne chiral SFG spectra have been fit using one Lorentzian function per vibrational band, and the resulting fit has been used to infer the underlying frequency distribution. Here, we show that this approach may not correctly reveal the structure and dynamics of hydration water. Our analysis illustrates that the chiral SFG responses of symmetric and asymmetric O–H stretch modes of water have opposite phase and equal magnitude and are separated in energy by intramolecular vibrational coupling and a heterogeneous environment. The sum of the symmetric and asymmetric responses implies that an O–H stretch in a heterodyne chiral SFG spectrum should appear as two peaks with opposite phase and equal amplitude. Using pairs of Lorentzian functions to fit water O–H stretch vibrational bands, we improve spectral fitting of previously acquired experimental spectra of model β-sheet proteins and reduce the number of free parameters. The fitting allows us to estimate the vibrational frequency distribution and thus reveals the molecular interactions of water in hydration shells of biomolecules directly from chiral SFG spectra. [ABSTRACT FROM AUTHOR]

Spontaneous emission and internal conversion rates are calculated within harmonic approximations and compared to the results obtained within the semi-classical extended thawed Gaussian approximation (ETGA). This is the first application of the ETGA in the calculation of internal conversion and emission rates for real molecular systems, namely, formaldehyde, fluorobenzene, azulene, and a dicyano-squaraine dye. The viability of the models as black-box tools for prediction of spontaneous emission and internal conversion rates is assessed. All calculations were done using a consistent protocol in order to investigate how different methods perform without previous experimental knowledge using density functional theory (DFT) and time-dependent DFT (TD-DFT) with B3LYP, PBE0, ωB97XD, and CAM-B3LYP functionals. Contrasting the results with experimental data shows that there are further improvements required before theoretical predictions of emission and internal conversion rates can be used as reliable indicators for the photo-luminescence properties of molecules. We find that the ETGA performs rather similar to the vertical harmonical model. Including anharmonicities in the calculation of internal conversion rates has a moderate effect on the quantitative results in the studied systems. The emission rates are fairly stable with respect to computational parameters, but the internal conversion rate reveals itself to be highly dependent on the choice of the spectral line shape function, particularly the width of the Lorentzian function, associated with homogeneous broadening. [ABSTRACT FROM AUTHOR]

Terahertz (THz) radiation sources based on two‐color femtosecond plasmas in air are becoming a mature technology for coherent spectroscopy and strong‐field physics across the extended THz range to several tens of THz. The field‐resolved detection of such THz transients relies on the third‐order nonlinearity of the detection medium. Here, a comparative measurement is demonstrated with air‐biased coherent detection (ABCD) and solid‐state biased detection (SSBCD) as a novel method to measure the dispersion of the magnitude and phase of the relevant third‐order nonlinearity χ(3)(2ω±Ω;ω,ω,±Ω)$\chi ^{(3)}(2\omega \pm \Omega;\omega,\omega,\pm \Omega)$ for fused silica (SiO2${\rm SiO}_2$) and silicon nitride (SiN). Based on the development of the ultrabroadband SSBCD device with a detection bandwidth exceeding 30 THz, χ(3)$\chi ^{(3)}$ measurements are obtained across the 1–28 THz frequency range, hence covering the THz and far‐infrared. It is shown that the vibrational modes in SiO2${\rm SiO}_2$ and SiN in the THz range lead to strong resonant enhancement and dispersion of the nonlinearity. The SSBCD devices operate down to nanojoule (nJ) probe energy, and their is demonstrated by measuring the dielectric function of the Lorentzian line profile of transverse‐optical (TO) phonon mode at 9 THz in single‐crystal gallium arsenide (GaAs) and observing the weak phonon combination bands near the TO phonon. [ABSTRACT FROM AUTHOR]

Aims. We study the importance of precise modelling of the photometric redshift error distributions when estimating parameters from cross-correlation measurements. We present a working example of the scattering matrix formalism to correct for the effects of galaxies ending in wrong redshift bins due to their photometric redshift errors. Methods. We measured the angular galaxy auto-power spectrum and cross-power spectrum in four tomographic bins with the redshift intervals z = [0.0, 0.3, 0.45, 0.6, 0.8] from the cross-correlation of the Planck cosmic microwave background lensing potential and the photometric galaxy catalogue from the Dark Energy Spectroscopic Instrument Legacy Imaging Survey Data Release 8. We estimated the galaxy linear bias and the amplitude of cross correlation using maximum likelihood estimation to put constraints on the σ8 parameter. Results. We show that the modified Lorentzian function used to fit the photometric redshift error distribution performs well only near the peaks of the distribution. We adopt a sum of Gaussians model to capture the broad tails of the error distribution. Our sum of Gaussians model yields values of the cross-correlation amplitude that are ∼2–5 σ smaller than those expected based on the Λ cold dark matter (ΛCDM) model. We compute the σ8 parameter after correcting for the redshift bin mismatch of objects following the scattering matrix approach. The σ8 parameter becomes consistent with ΛCDM model in the last tomographic bin but shows a tension of ∼1–3 σ in other redshift bins. [ABSTRACT FROM AUTHOR]

For a Lorentzian para-Kenmotsu manifold of dimension m (briefly, (LPK)m) admitting Bach almost soliton (g;z;l), we explored the characteristics of the norm of Ricci operator. Besides, we gave the necessary condition for (LPK)m (m≤4) admitting Bach almost soliton to be an h-Einstein manifold. Afterwards, we proved that Bach almost solitons are always steady when a Lorentzian para-Kenmotsu manifold of dimension three has Bach almost soliton. [ABSTRACT FROM AUTHOR]

Featured Application: Photoluminescence and resonant Raman scattering have the potential to characterize surface roughness. These optical spectroscopies can be complementary tools for monitoring and controlling semiconductor manufacturing processes. Surface roughness significantly affects light reflection and absorption, which is crucial for light–matter interaction studies and material characterization. This work examines how nanoscale surface roughness affects the electronic states and vibrational properties of cadmium telluride (CdTe) single crystals, using photoluminescence (PL) and resonant Raman scattering (RRS) spectroscopies. We have evaluated the surface roughness across various sample regions as the root-mean-square (RMS) value measured by atomic force microscopy (AFM). At room temperature, increasing RMS correlated with changes in PL intensity and peak width, as well as enhanced second-order longitudinal optical (2LO) phonon mode intensity. Fitting the PL and RRS spectra with Gaussian and Lorentzian functions, respectively, allowed us to explain the relationship between surface morphology and the observed spectral changes. Our findings demonstrate that surface roughness is a critical parameter influencing the surface states and vibrational properties of CdTe, with implications for the performance of CdTe-based devices. [ABSTRACT FROM AUTHOR]

We show that the natural bi-invariant cone structure on the linear symplectic group Sp (2 n) is globally hyperbolic in the positively elliptic region Sp ell + (2 n). This answers a question by Abbondandolo, Benedetti and Polterovich and implies a formula for a bi-invariant Lorentzian distance function defined by these authors for elements in this region. Moreover we give a characterization of the positively elliptic region and of − id ∈ Sp (2 n) in terms of the causality of this cone structure. [ABSTRACT FROM AUTHOR]

Many processes in chemistry, physics, and biology depend on thermally activated events in which the system changes its state by surmounting an activation barrier. Examples range from chemical reactions to protein folding and nucleation events. Parameterized forms of the mean field potential are often employed in the stochastic modeling of activated processes. In this contribution, we explore the alternative of employing parameterized forms of the equilibrium distribution by means of symmetric linear combination of two Gaussian functions. Such a procedure leads to flexible and convenient models for the landscape and the energy barrier whose features are controlled by the second moments of these Gaussian functions. The rate constants are examined through the solution of the corresponding diffusion problem, that is, the Fokker–Planck–Smoluchowski equation specified according to the parameterized equilibrium distribution. Numerical calculations clearly show that the asymptotic limit of large barriers does not agree with the results of the Kramers theory. The underlying reason is that the linear scaling of the potential, the procedure justifying the Kramers theory, cannot be applied when dealing with parameterized forms of the equilibrium distribution. A different kind of asymptotic analysis is then required and we introduce the appropriate theory when the equilibrium distribution is represented as a symmetric linear combination of two Gaussian functions: first in the one-dimensional case and afterward in the multidimensional diffusion model. [ABSTRACT FROM AUTHOR]

Field electron emission from nanometer-scale objects deviates from the predictions of the classical emission theory as both the electrostatic potential curves within the tunneling region and the image potential deviates from the planar one. This impels the inclusion of additional correction terms in the potential barrier. At the apex of a tip-like rotationally symmetric surface, these terms are proportional to the (single) local emitter curvature. The present paper generalizes this relation, showing that for any emitter geometry, the coefficient of the correction terms is given by the mean curvature, i.e., the average of the two principal curvatures. [ABSTRACT FROM AUTHOR]

Chromatic symmetric functions are well-studied symmetric functions in algebraic combinatorics that generalize the chromatic polynomial and are related to Hessenberg varieties and diagonal harmonics. Motivated by the Stanley–Stembridge conjecture, we show that the allowable coloring weights for indifference graphs of Dyck paths are the lattice points of a permutahedron P λ , and we give a formula for the dominant weight λ . Furthermore, we conjecture that such chromatic symmetric functions are Lorentzian, a property introduced by Brändén and Huh as a bridge between discrete convex analysis and concavity properties in combinatorics, and we prove this conjecture for abelian Dyck paths. We extend our results on the Newton polytope to incomparability graphs of (3 + 1) -free posets, and we give a number of conjectures and results stemming from our work, including results on the complexity of computing the coefficients and relations with the ζ map from diagonal harmonics. [ABSTRACT FROM AUTHOR]

Fast-Field-Cycling (FFC) Nuclear Magnetic Resonance (NMR) relaxometry is a powerful, non-destructive magnetic resonance technique that enables, among other things, the investigation of slow molecular dynamics at low magnetic field intensities. FFC-NMR relaxometry measurements provide insight into molecular motion across various timescales within a single experiment. This study focuses on a model-free approach, representing the NMRD profile R 1 as a linear combination of Lorentzian functions, thereby addressing the challenges of fitting data within an ill-conditioned linear least-squares framework. Tackling this problem, we present a comprehensive review and experimental validation of three regularization approaches to implement the model-free approach to analyzing NMRD profiles. These include (1) MF-UPen, utilizing locally adapted L 2 regularization; (2) MF-L1, based on L 1 penalties; and (3) a hybrid approach combining locally adapted L 2 and global L 1 penalties. Each method's regularization parameters are determined automatically according to the Balancing and Uniform Penalty principles. Our contributions include the implementation and experimental validation of the MF-UPen and MF-MUPen algorithms, and the development of a "dispersion analysis" technique to assess the existence range of the estimated parameters. The objective of this work is to delineate the variance in fit quality and correlation time distribution yielded by each algorithm, thus broadening the set of software tools for the analysis of sample structures in FFC-NMR studies. The findings underline the efficacy and applicability of these algorithms in the analysis of NMRD profiles from samples representing different potential scenarios. [ABSTRACT FROM AUTHOR]

An important tool to analyse the causal structure of a Lorentzian manifold is given by the Lorentzian distance function. We define a class of Lorentzian distance functions on the group of contactomorphisms of a closed contact manifold depending on the choice of a contact form. These distance functions are continuous with respect to the Hofer norm for contactomorphisms defined by Shelukhin [The Hofer norm of a contactomorphism, J. Symplectic Geom. 15 (2017) 1173–1208] and finite if and only if the group of contactomorphisms is orderable. To prove this, we show that intervals defined by the positivity relation are open with respect to the topology induced by the Hofer norm. For orderable Legendrian isotopy classes we show that the Chekanov-type metric defined in [D. Rosen and J. Zhang, Chekanov's dichotomy in contact topology, Math. Res. Lett. 27 (2020) 1165–1194] is nondegenerate. In this case, similar results hold for a Lorentzian distance functions on Legendrian isotopy classes. This leads to a natural class of metrics associated to a globally hyperbolic Lorentzian manifold such that its Cauchy hypersurface has a unit co-tangent bundle with orderable isotopy class of the fibres. [ABSTRACT FROM AUTHOR]

n this present paper, we classify and explore the geometrical significance of a class of Lorentzian almost paracontact metric manifolds namely Lorentzian para-Kenmotsu (briefly LP-Kenmotsu) mani- folds whenever the manifolds are either conformally flat or conformally symmetric. It was found that a conformally flat LP-Kenmotsu manifold is of constant curvature and a conformally symmetric LP-Kenmotsu manifold is locally isomorphic to a unit sphere. At the end, we obtain the scalar curvature of φ-conformally flat LP-Kenmotsu manifolds [ABSTRACT FROM AUTHOR]

In this work, we study a model in nonlinear electrodynamics in the presence of a CPT-even term that violates Lorentz symmetry. The Lorentz-breaking vector, in addition to the usual background magnetic field, produces interesting effects in the dispersion relations. The consequences on the vacuum refractive index and the group velocity are studied. Vacuum birefringence is discussed in the case the nonlinear electrodynamics is a Euler–Heisenberg model. [ABSTRACT FROM AUTHOR]

The manipulation and control of nanoscale magnetic spin textures are of rising interest as they are potential foundational units in next-generation computing paradigms. Achieving this requires a quantitative understanding of the spin texture behavior under external stimuli using in situ experiments. Lorentz transmission electron microscopy (LTEM) enables real-space imaging of spin textures at the nanoscale, but quantitative characterization of in situ data is extremely challenging. Here, we present an AI-enabled phase-retrieval method based on integrating a generative deep image prior with an image formation forward model for LTEM. Our approach uses a single out-of-focus image for phase retrieval and achieves significantly higher accuracy and robustness to noise compared to existing methods. Furthermore, our method is capable of isolating sample heterogeneities from magnetic contrast, as shown by application to simulated and experimental data. This approach allows quantitative phase reconstruction of in situ data and can also enable near real-time quantitative magnetic imaging. [ABSTRACT FROM AUTHOR]

We present a three-dimensional pseudo-Voigt function to analyze muon spin relaxation (μSR) in weakly magnetic materials. Our approach approximates the Voigt function by superimposing Gaussian and Lorentzian functions using a one-dimensional method proposed by Di Rocco and Cruzado [Acta Phys. Pol., A 122, 666 (2012)]. We derive the peak of the Voigt function analytically and express the Half Width at Half Maximum (HWHM) of the Voigt function as a function of the HWHMs of the Gaussian and Lorentzian functions. We compare the pseudo-Voigt function to the exact Voigt function and find a maximum normalized discrepancy of ∼20% at the tail of the distribution function, depending on the ratio of Lorentzian to Gaussian HWHMs and internal magnetic field. We apply the derived three-dimensional pseudo-Voigt function to calculate μSR functions for zero- and longitudinal-field experiments and use them to fit μSR time spectra of La2−xSrxCuO4 with 2.4% Sr, employing a strong collision model with the static-based pseudo-Voigt muon spin relaxation function as the initial condition. Our results show that the Gaussian- and Lorentzian-fitted parameters and fluctuation rate are in good agreement with results from the exact Voigt function for a temperature range of 30–200 K, with the deviation of Gaussian and Lorentzian width parameters reaching ∼0.15 G below 30 K. [ABSTRACT FROM AUTHOR]

Confocal Raman microspectroscopy provides the ability to diagnose cancer by quantitatively analyzing spectral features and identifying underlying biochemical changes. The differentiation of malignant skin neoplasms (basal cell carcinoma, squamous cell carcinoma), benign skin neoplasms (papilloma) and healthy skin was carried out by obtaining Raman spectra in vitro with excitation wavelengths of 532 and 785 nm. We present a new method for analyzing the parameters of spectral bands, based on the calculation of the second derivative and Lorentz approximation of the spectra. Using this method on a small selection of skin tumors, we have demonstrated that processes in skin tumors can cause deformation of the proteins' secondary structure, leading to degradation and shift of the corresponding bands (972, 1655 cm–1) to the lower frequency. Bands corresponding to lipids in skin neoplasms either broaden and increase or split into two peaks (bands 1061, 1127, 1297, 1439, 1745 cm–1). The disruption of lipid structure, also indicated in several bands as a shift to lower wavenumbers, is possibly due to increased cell membrane fluidity in tumors. The results of the study may be useful for the development of optical biopsy methods for early diagnosis of tumors. [ABSTRACT FROM AUTHOR]

A series of nanocrystalline iron oxide samples (M1–M5) which differ from each other in average crystallite size (from 26 to 37 nm) was studied. The raw material was nanocrystalline iron with an average crystallite size equal to 21 nm promoted with hardly reducible oxides: Al2O3, CaO, K2O (in total, max. 10 wt%). Nanocrystalline iron was subjected to oxidation with water vapor to achieve different oxidation degrees (α = 0.16–1.00). Metallic iron remaining in the samples after the oxidizing step was removed by etching. Magnetic resonance spectra of all samples were obtained at room temperature. All resonance lines were asymmetric and intense. These spectra were fitted by Lorentzian and Gaussian functions. All spectral parameters depend on the preparation method of the nanoparticles. We suppose that the Lorentz fit gives us a spectrum from larger agglomerated sizes whereas the Gaussian fit comes from much smaller magnetic centers. For the nanocrystalline samples with the largest size of iron oxide nanocrystallites, the highest value of total integrated intensity was obtained, indicating that at smaller sizes, they are more mobile in reorientation processes resulting in more settings of anti-parallel magnetic moments. The magnetic anisotropy should also increase with the increase in size of nanocrystallites. [ABSTRACT FROM AUTHOR]

The MIR reflectivity spectra ranging from 4000 to 900 cm−1 of the polarons in zinc oxide films doped with 0.24 at.% silver (AgZnO) as a function of temperature (190–360 K) in weakly concentrated gaseous methane environment were obtained. The decay rate, energy and intensity of polaron states at 1248 and 1484 cm–1 are analyzed using the Lorentzian line-shape function. The lines show the redshift (~ 3%) with an increase in temperature. The width and intensity of the line at 1248 cm–1 decrease by 23% and 38%, respectively, with an increase in temperature to 360 K. The one-phonon line at 1484 cm–1 broadens by ~ 50%, and the intensity decreases by 54% upon reaching a temperature of 330 K, and at T ≥ 350 K, the line 1484 cm–1 decays into many ultrafine weakly localized states due to the formation of a hydrocarbon adsorbate, which acts as a charge trapping center on the AgZnO surface. The calculated polaron scattering time τ = 2.2 fs decreases to 1.8 fs as the temperature rises from 250 to 360 K. The frequency dependences of the optical conductivity determined by Kramers–Kronig relations show a localization-delocalization crossover near 1900 cm–1. At frequencies below 1900 cm–1, the carriers are localized, and dc-conductivity satisfies the criterion of the Mott-VRH model with the hopping energy of 0.43 T3/4 meV. [ABSTRACT FROM AUTHOR]

To enhance the accuracy of the comprehensive evaluation of reservoir quality in shale oil fractured horizontal wells, the Pearson correlation analysis method was employed to study the correlations between geological parameters and their relationship with production. Through principal component analysis, the original factors were linearly combined into principal components with clear and specific physical meanings, aiming to eliminate correlations among factors. Furthermore, Gaussian membership functions were applied to delineate fuzzy levels, and the entropy weight method was used to determine the weights of principal components, establishing a fuzzy comprehensive evaluation model for reservoir quality. Without using principal component analysis, the correlation coefficient between production and evaluation results for the 40 wells in the Cangdong shale oil field was only 0.7609. However, after applying principal component analysis, the correlation coefficient increased to 0.9132. Field application demonstrated that the average prediction accuracy for the cumulative oil production per kilometer of fractured length over 12 months for the 10 applied wells was 91.8%. The proposed comprehensive evaluation method for reservoir quality can guide the assessment of reservoir quality in shale oil horizontal wells. [ABSTRACT FROM AUTHOR]

The present paper deals with a class of Lorentzian almost paracontact metric manifolds namely Lorentzian para-Kenmotsu (briefly LP-Kenmotsu) manifolds. We study and have shown that a quasi-conformally flat Lorentzian para-Kenmotsu manifold is locally isomorphic with a unit sphere Sn(1). Further it is shown that an LP-Kenmotsu manifold which is φ-conharmonically flat is an η-Einstein manifold with the zero scalar curvature. At the end, we have shown that a φ-projectively flat LP-Kenmotsu manifold is an Einstein manifold with the scalar curvature r = n(n - 1). [ABSTRACT FROM AUTHOR]

Semi-rational enzyme engineering is a powerful method to develop industrial biocatalysts. Profiting from advances in molecular biology and bioinformatics, semi-rational approaches can effectively accelerate enzyme engineering campaigns. Here, we present the optimization of a ketoreductase from Sporidiobolus salmonicolor for the chemo-enzymatic synthesis of ipatasertib, a potent protein kinase B inhibitor. Harnessing the power of mutational scanning and structure-guided rational design, we created a 10-amino acid substituted variant exhibiting a 64-fold higher apparent kcat and improved robustness under process conditions compared to the wild-type enzyme. In addition, the benefit of algorithm-aided enzyme engineering was studied to derive correlations in protein sequence-function data, and it was found that the applied Gaussian processes allowed us to reduce enzyme library size. The final scalable and high performing biocatalytic process yielded the alcohol intermediate with ≥ 98% conversion and a diastereomeric excess of 99.7% (R,R-trans) from 100 g L−1 ketone after 30 h. Modelling and kinetic studies shed light on the mechanistic factors governing the improved reaction outcome, with mutations T134V, A238K, M242W and Q245S exerting the most beneficial effect on reduction activity towards the target ketone. Ipatasertib is a potent Akt (protein kinase B) inhibitor synthesized via a chemoenzymatic process. Here, the authors use mutational scanning and algorithm-aided enzyme engineering to optimize a ketoreductase from Sporidiobolus salmonicolor and generate a 10-amino acid substituted variant exhibiting a 64-fold higher kcat and improved yield for the relevant alcohol intermediate, with ≥ 98% conversion and a diastereomeric excess of 99.7% (R,R-trans) from 100 g L−1 ketone after 30 h. [ABSTRACT FROM AUTHOR]

In the dense and cold atmosphere of Titan, the presence of C2H4 haze has been confirmed by the observations of spacecraft. In the present study, original cryogenic experimental equipment was developed to simulate the low-temperature solid formation of C2H4 in combination with in-situ infrared spectroscopic measurements. As a result, out-of-plane bending vibration ν7 of solid-phase C2H4 located at ~ 10.5 μm was successfully detected with high sensitivity, and two-dimensional spectrographs of C2H4 at low temperatures were obtained. The obtained spectra of C2H4 can be fitted to the double Lorentzian function with various heights, central wavelengths, and full widths at half the maximum (FWHM) of the two-component Lorentzian functions. They were classified into three types using the fitting parameters. However, their spectral shapes are different from the amorphous, metastable, and crystalline forms obtained by the previous laboratory experiment in terms of the distance of two peak wavelengths and FWHM. The results may link to understanding the spectral band properties of C2H4 condensation in the haze component of Titan. [ABSTRACT FROM AUTHOR]

We constructed phase diagrams of conformationally asymmetric diblock copolymer A-B melts using the polymer self-consistent field (SCF) calculations of both the dissipative particle dynamics chain (DPDC) model (i.e., compressible melts of discrete Gaussian chains with the DPD non-bonded potential) and the "standard" model (i.e., incompressible melts of continuous Gaussian chains with the Dirac δ-function non-bonded potential) in the χN-ε plane, where χN and ε characterize, respectively, the repulsion and conformational asymmetry between the A and B blocks, at the A-block volume fraction f = 0.2 and 0.3. Consistent with previous SCF calculations of the "standard" model, σ and A15 are the only stable Frank–Kasper (FK) phases among the five FK (i.e., σ, A15, C14, C15 and Z) phases considered. The stability of σ and A15 is due to their delicate balance between the energetic and entropic contributions to the Helmholtz free energy per chain of the system, which, within our parameter range, increases in the order of σ/A15, Z, and C14/C15. While in general the SCF phase diagrams of these two models are qualitatively consistent, A15 is not stable for the DPDC model at the copolymer chain length N = 10 and f = 0.3; any differences in the SCF phase diagrams are solely due to the differences between these two models. [ABSTRACT FROM AUTHOR]

We present a novel method for measuring the lags of (weak) variability components in neutron-star and black-hole low-mass X-ray binaries (LMXBs). For this we assume that the power and cross-spectra of these sources consists of a number of components that are coherent in different energy bands, but are incoherent with one another. The technique is based on fitting simultaneously the power spectrum (PS) and the Real and Imaginary parts of the cross-spectrum (CS) with a combination of Lorentzian functions. We show that, because the PS of LMXBs is insensitive to signals with a large Imaginary part and a small Real part in the CS, this approach allows us to uncover new variability components that are only detected in the CS. We also demonstrate that, contrary to earlier claims, the frequency of the type-C quasi-periodic oscillation (QPO) in the black-hole binary GRS 1915+105 does not depend on energy. Rather, the apparent energy dependence of the QPO frequency can be explained by the presence of a separate QPO component with a slightly higher frequency than that of the QPO, whose rms amplitude increases faster with energy than the rms amplitude of the QPO. From all the above we conclude that, as in the case of the PS, the CS of black-hole and neutron-star binaries can be fitted by a combination of Lorentzian components. Our findings provide evidence that the frequency-dependent part of the transfer function of these systems can be described by a combination of responses, each of them acting over relatively well-defined time-scales. This conclusion challenges models that assume that the main contribution to the lags comes from a global, broadband, transfer function of the accreting system. [ABSTRACT FROM AUTHOR]

In this manuscript, we consider an extended version of biconservativity condition (namely, C-biconservativity) on the Riemannian hypersurfaces of Lorentzian standard 4-space forms. This new condition is obtained by substituting the Cheng-Yau operator C instead of the Laplace operator ∆. We show that every C-biconservative Riemannian hypersurface of a Lorentzian 4-space form with constant mean curvature has constant scalar curvature. [ABSTRACT FROM AUTHOR]

The aim of this manuscript is to introduce and analyze a stochastic finite difference scheme for Itô stochastic partial differential equations. We also discuss the consistency, stability, and convergence for the stochastic finite difference scheme. The numerical simulations obtained from the proposed stochastic finite difference scheme show the efficiency of the suggested stochastic finite difference scheme. [ABSTRACT FROM AUTHOR]

Let R be a commutative ring with identity and R(RM ) denote the bounded lattice of radical submodules of an R-module M . We say that M is a radical distributive module, if R(RM ) is a distributive lattice. It is shown that the class of radical distributive modules contains the classes of multiplication modules and finitely generated distributive modules properly. Also, it is shown that if M is a radical distributive semisimple R-module and for any radical submodule N of M with direct sum complement Ñ, the complementary operation on R(RM ) is defined by N ′ := Ñ + rad{0}, then R(RM ) with this unary operation forms a Boolean algebra. In particular, if M is a multiplication module over a semisimple ring R, then R(RM ) is a Boolean algebra, which is also a homomorphic image of R(RR). [ABSTRACT FROM AUTHOR]

The prediction of dissolved gas change trends in power transformer oil is very important for the diagnosis of transformer faults and ensuring its safe operation. Considering the time series and nonlinear features of the gas change trend, this paper proposes a novel robust extreme learning machine (ELM) model combining an improved data decomposition method for gas content forecasting. Firstly, the original data with nonlinear and sudden change properties will make the forecasting model unstable, and thus an improved variational modal decomposition (IPVMD) method is developed to decompose the original data to obtain the multiple modal dataset, in which the marine predators algorithm (MPA) optimization method is utilized to optimize the free parameters of the VMD. Second, the ELM as an efficient and easily implemented tool is used as the basic model for dissolved gas forecasting. However, the traditional ELM with mean square error (MSE) criterion is sensitive to the non-Gaussian measurement noise (or outliers). In addition, considering the nonlinear non-Gaussian properties of the dissolved gas, a new learning criterion, called extended maximum correntropy criterion (ExMCC), is defined by using an extended kernel function in the correntropy framework, and the ExMCC as a learning criterion is introduced into the ELM to develop a novel robust regression model (called ExMCC-ELM) to improve the ability of ELM to process mutational data. Third, a gas-in-oil prediction scheme is proposed by using the ExMCC-ELM performed on each modal obtained by the proposed IPVMD. Finally, we conducted several simulation studies on the measured data, and the results show that the proposed method has good predictive performance. [ABSTRACT FROM AUTHOR]

We propose a statistical model for narrowing line shapes in spectroscopy that are well approximated as linear combinations of Lorentzian or Voigt functions. We introduce a log-Gaussian Cox process to represent the peak locations thereby providing uncertainty quantification for the line narrowing. Bayesian formulation of the method allows for robust and explicit inclusion of prior information as probability distributions for parameters of the model. Estimation of the signal and its parameters is performed using a sequential Monte Carlo algorithm followed by an optimization step to determine the peak locations. Our method is validated using a simulation study and applied to a mineralogical Raman spectrum. [ABSTRACT FROM AUTHOR]

In this present paper, a class of Lorentzian almost paracontact metric manifolds known as the LPKenmotsu (Lorentzian para-Kenmotsu) is considered that accepts a connection of quarter-symmetric. In this work, it was found that an LP-Kenmotsu manifold is either φ-symmetric or concircular φ-symmetric with respect to quarter-symmetric metric connection if and only if it is symmetric with respect to the Riemannian connection, provided the scalar curvature of Riemannian connection is constant. [ABSTRACT FROM AUTHOR]

The theory of Gaussian functions is reformulated using an umbral point of view. The symbolic method we adopt here allows an interpretation of the Gaussian in terms of a Lorentzian image function. The formalism also suggests the introduction of a new point of view of trigonometry, opening a new interpretation of the associated special functions. The Erfi (x) , is, for example, interpreted as the "sine" of the Gaussian trigonometry. The possibilities offered by the Umbral restyling proposed here are noticeable and offered by the formalism itself. We mention the link between higher-order Gaussian trigonometric functions, Hermite polynomials, and the possibility of introducing new forms of distributions with longer tails than the ordinary Gaussians. The possibility of framing the theoretical content of the present article within a redefinition of the hypergeometric function is eventually discussed. [ABSTRACT FROM AUTHOR]

Light–matter coupling strength and optical loss are two key physical quantities in cavity quantum electrodynamics (CQED), and their interplay determines whether light–matter hybrid states can be formed or not in chemical systems. In this study, by using macroscopic quantum electrodynamics (MQED) combined with a pseudomode approach, we present a simple but accurate method, which allows us to quickly estimate the light–matter coupling strength and optical loss without free parameters. Moreover, for a molecular emitter coupled with photonic modes (including cavity modes and plasmon polariton modes), we analytically and numerically prove that the dynamics derived from the MQED-based wavefunction approach is mathematically equivalent to the dynamics governed by the CQED-based Lindblad master equation when the Purcell factor behaves like Lorentzian functions. [ABSTRACT FROM AUTHOR]

Alzheimer's disease (AD) is considered one of the most spouting elderly diseases. In 2015, AD is reported the US's sixth cause of death. Substantially, non-invasive imaging is widely employed to provide biomarkers supporting AD screening, diagnosis, and progression. In this study, Gaussian descriptors-based features are proposed to be efficient new biomarkers using Magnetic Resonance Imaging (MRI) T1-weighted images to differentiate between Alzheimer's disease (AD), Mild Cognitive Impairment (MCI), and Normal controls (NC). Several Gaussian map-based features are extracted such as Gaussian shape operator, Gaussian curvature, and mean curvature. The aforementioned features are then introduced to the Support Vector Machine (SVM). They were, first, calculated separately for the Hippocampus and Amygdala. Followed by the fusion of the features. Moreover, Fusion of the regions before feature extraction was also employed. Alzheimer's disease Neuroimaging Initiative (ADNI) dataset, formed of 45, 55, and 65 cases for AD, MCI, and NC respectively, is appointed in this study. The shape operator feature outperformed the other features, with 74.6%, and 98.9% accuracy in the case of normal vs. abnormal, and AD vs. MCI classification respectively. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the beingness conditions for algebraic Schouten solitons associated with Yano connections in the background of three-dimensional Lorentzian Lie groups. By transforming equations of algebraic Schouten solitons into algebraic equations, the existence conditions of solitons are found. In particular, we deduce some formulations for Yano connections and related Ricci operators. Furthermore, we find the detailed categorization for those algebraic Schouten solitons on three-dimensional Lorentzian Lie groups. The major results demonstrate that algebraic Schouten solitons related to Yano connections are present in G1, G2, G3, G5, G6 and G7, while they are not identifiable in G4. [ABSTRACT FROM AUTHOR]

This project's goal was to mimic the Saharan silver ant's micro-hair arrays by creating a solar heat reflecting membrane with parallel-aligned Al-ZnO microrods using a Mayer rod coating method. The synthesis of Al-ZnO microrods was carried out using the hydrothermal method. The membrane was then produced by mixing the microrods with liquid silicone rubber and spreading the mixture into the shape of a membrane using a Mayer rod. The dragging of the Al-ZnO microrod, confined between the Mayer rod and the polypropylene film, induces the partial alignment of Al-ZnO microrods in the dragging direction. We note that the distribution of microrod alignment is well described by the Lorentzian function and that the full width at half maximum is measured to be 22.3°. Most Al-ZnO microrods are encased within silicone rubber. At wavelengths between 200 and 1100 nm, the membrane blocks light almost entirely. The solar heat gain coefficient of our solar heat reflecting membrane is 75% lower than the membrane containing commercial ZnO powder. [ABSTRACT FROM AUTHOR]

Faced with environmental issues and depleting oil reserves, engine research is venturing into novel paths, such as the dual-fuel engine. This has motivated the development of numerical models that provide highly accurate predictive tools. In this context, 0D/quasi-D modeling is necessary, with a compromise between control of computation time and acceptable prediction level, which will certainly enable the various studies on the dual fuel mode to be explored at reduced cost. The aim of the present study is to develop a combustion model adapted to the hydrogen-natural gas (HNG)/diesel dual fuel engine to ensure 0D/1D simulations over a wide load range and under different gas mixture compositions. This model is based on the separation of the different types of combustion in this mode, by first treating the combustion of the pilot fuel by jet modeling, then the combustion of the gas mixture (HNG) by a mathematical model based on the Gaussian function. This phase separation is carefully combined with a mathematical treatment of the heat release rate, in order to determine ignition delays for both phases and model each of them separately. The modeling approach unveiled in this work is based on a phenomenological aspect, where the distinction between pilot and primary fuel combustion is ensured with phase separation allowing precise monitoring of the combustion sequence with the detection of the start and end of each phase and the contribution of each to the overall heat release rate. The results confirm the predictive power of the model developed with a maximum error of around 2%. This accurate prediction is particularly evident at high loads with high hydrogen enrichment, where the combustion sequence becomes complicated. [ABSTRACT FROM AUTHOR]

Understanding the influence of dehydration on the membrane structure is crucial to control membrane functionality related to domain formation and cell fusion under anhydrobiosis conditions. To this end, we perform all-atom molecular dynamic simulations of 1,2-dimyristoyl-sn-glycero-3-phosphocholine dimyristoylphosphatidylcholine lipid membranes at different hydration levels at 308 K. As dehydration increases, the lipid area per head group decreases with an increase in bilayer thickness and lipid order parameters indicating bilayer ordering. Concurrently, translational and rotational dynamics of interfacial water (IW) molecules near membranes slow down. On the onset of bilayer ordering, the IW molecules exhibit prominent features of dynamical heterogeneity evident from non-Gaussian parameters and one-dimensional van Hove correlation functions. At a fully hydrated state, diffusion constants (D) of the IW follow a scaling relation, D ∼ τ α − 1 , where the α relaxation time (τα) is obtained from self-intermediate scattering functions. However, upon dehydration, the relation breaks and the D of the IW follows a power law behavior as D ∼ τ α − 0.57 , showing the signature of glass dynamics. τα and hydrogen bond lifetime calculated from intermittent hydrogen bond auto-correlation functions undergo a similar crossover in association with bilayer ordering on dehydration. The bilayer ordering is accompanied with an increase in fraction of caged lipids spanned over the bilayer surface and a decrease in fraction of mobile lipids due to the non-diffusive dynamics. Our analyses reveal that the microscopic mechanism of lipid ordering by dehydration is governed by dynamical heterogeneity. The fundamental understanding from this study can be applied to complex bio-membranes to trap functionally relevant gel-like domains at room temperature. [ABSTRACT FROM AUTHOR]

The evaluation of atomic polar tensors and Born Effective Charge (BEC) tensors from Density Functional Perturbation Theory (DFPT) has been implemented in the CP2K code package. This implementation is based on a combination of the Gaussian and plane wave approach for the description of basis functions and arising potentials. The presence of non-local pseudo-potentials has been considered, as well as contributions arising from the basis functions being centered on the atoms. Simulations of both periodic and non-periodic systems have been implemented and carried out. Dipole strengths and infrared absorption spectra have been calculated for two isomers of the tripeptide Ser–Pro–Ala using DFPT and are compared to the results of standard vibrational analyses using finite differences. The spectra are then decomposed into five subsets by employing localized molecular orbitals/maximally localized Wannier functions, and the results are discussed. Moreover, group coupling matrices are employed for visualization of results. Furthermore, the BECs and partial charges of the surface atoms of a periodic (101) anatase (TiO2) slab have been investigated in a periodic framework. [ABSTRACT FROM AUTHOR]

We present an analytic description of doubly resonant infrared-visible sum (SFG) and difference frequency generation (DFG) spectroscopies. Within the Born–Oppenheimer and Condon approximations for harmonic oscillators, we extend the usual theory, limited to linear electron–vibration coupling, and introduce the quadratic coupling phenomena (mode distortion and mode mixing) in the excited state. The excitation spectra of vibrations in SFG and DFG experiments are calculated in integral form for arbitrary mode distortions and small amplitude mode mixing between pairs of modes. Mode distortion modifies all orders of vibronic coupling including the fundamental process, whereas mode mixing appears as a perturbation added to the distorted mode case. For small quadratic coupling amplitudes, the results may be recast in simple analytic forms after the introduction of the overlap spectral function and developed in sums and products of Lorentzian functions. [ABSTRACT FROM AUTHOR]

Fundamental understanding of the subcritical/supercritical behavior of key hydrocarbon species inside nano-porous matrices at elevated pressure and temperature is less developed compared to bulk fluids, but this knowledge is of great importance for chemical and energy engineering industries. This study explores in detail the structure and dynamics of ethane (C2H6) fluid confined in silica nanopores, with a focus on the effects of pressure and different ratios of C2H6 and CO2 at non-ambient temperature. Quasi-elastic neutron scattering (QENS) experiments were carried out for the pure C2H6, C2H6:CO2 = 3:1, and 1:3 mixed fluids confined in 4-nm cylindrical silica pores at three different pressures (30 bars, 65 bars, and 100 bars) at 323 K. Two Lorentzian functions were required to fit the spectra, corresponding to fast and slow translational motions. No localized motions (rotations and vibrations) were detected. Higher pressures resulted in hindrances of the diffusivity of C2H6 molecules in all systems investigated. Pore size was found to be an important factor, i.e., the dynamics of confined C2H6 is more restricted in smaller pores compared to the larger pores used in previous studies. Molecular dynamics simulations were performed to complement the QENS experiment at 65 bars, providing supportive structure information and comparable dynamic information. The simulations indicate that CO2 molecules are more strongly attracted to the pore surface compared to C2H6. The C2H6 molecules interacting with or near the pore surface form a dense first layer (L1) close to the pore surface and a second less dense layer (L2) extending into the pore center. Both the experiments and simulations revealed the role that CO2 molecules play in enhancing C2H6 diffusion ("molecular lubrication") at high CO2:C2H6 ratios. The energy scales of the two dynamic components, fast and slow, quantified by both techniques, are in very good agreement. Herein, the simulations identified the fast component as the main contributor to the dynamics. Molecule motions in the L2 region are mostly responsible for the dynamics (fast and slow) that can be detected by the instrument. [ABSTRACT FROM AUTHOR]

Charge recombination in the photoinduced charge separated (CS) state of a rigidly linked donor/bridge/acceptor triad with a triarylamine (TAA) donor, a 1,3-diethynyl-2,5-dimethoxy benzene bridge (OMe), and a perylenediimide (PDI) unit as an acceptor, represents a spin chemical paradigm case of a rigid radical ion pair formed with singlet spin and recombining almost exclusively to the locally excited PDI triplet state (3PDI). The magnetic field dependence of the CS state decay and 3PDI formation kinetics are investigated from 0 to 1800 mT by nanosecond laser flash spectroscopy. The time-resolved magnetic field affected reaction yields spectra of the CS state population and 3PDI population exhibit a sharp and deep resonance at 18.9 mT, indicating level crossing of the S and T+ levels separated by an exchange interaction of J = 18.9/2 mT at zero field. The kinetics are biexponential around the resonance field and monoexponential outside that range. The monoexponential behavior can be simulated by a classical kinetic model assuming a single field dependent double Lorentzian function for the energy gap dependence of all spin conversion processes. The full field dependence of the kinetics has been simulated quantum theoretically. It has been shown that incoherent and coherent hyperfine coupling contribute to S/T+ spin conversion at all fields and that the biexponentiality of the kinetics at resonance is due to a partitioning of the overall kinetics into 2/3 of the singlet hyperfine states exhibiting strong isotropic coupling to T+ and 1/3 of the singlet hyperfine states that do not or only weakly couple isotropically to T+. [ABSTRACT FROM AUTHOR]

We study the dimer model on subgraphs of the square lattice in which vertices on a prescribed part of the boundary (the free boundary) are possibly unmatched. Each such unmatched vertex is called a monomer and contributes a fixed multiplicative weight z > 0 to the total weight of the configuration. A bijection described by Giuliani et al. (J Stat Phys 163(2):211–238, 2016) relates this model to a standard dimer model but on a non-bipartite graph. The Kasteleyn matrix of this dimer model describes a walk with transition weights that are negative along the free boundary. Yet under certain assumptions, which are in particular satisfied in the infinite volume limit in the upper half-plane, we prove an effective, true random walk representation for the inverse Kasteleyn matrix. In this case we further show that, independently of the value of z > 0 , the scaling limit of the centered height function is the Gaussian free field with Neumann (or free) boundary conditions. It is the first example of a discrete model where such boundary conditions arise in the continuum scaling limit. [ABSTRACT FROM AUTHOR]

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By applying suitable Liouville-type results, an appropriate parabolicity criterion, and a version of the Omori-Yau’s maximum principle for the drift Laplacian, we infer the uniqueness and nonexistence of complete spacelike translating solitons of the mean curvature flow in a Lorentzian product space ℝ1 × ℙnf endowed with a weight function ƒ and whose ℝiemannian base ℙn is supposed to be complete and with nonnegative Bakry-Émery-Ricci tensor. When the ambient space is either ℝ1 × Gn, where Gn stands for the so-called n-dimensional Gaussian space (which is the Euclidean space ℝn endowed with the Gaussian probability measure) or ℝ1 × ℍnf, where ℍn denotes the standard n-dimensional hyperbolic space and ƒ is the square of the distance function to a fixed point of ℍn, we derive some interesting consequences of our uniqueness and nonexistence results. In particular, we obtain nonexistence results concerning entire spacelike translating graphs constructed over ℙn. [ABSTRACT FROM AUTHOR]

This paper derives the expressions for spacelike ruled surfaces with stationary Disteli-axis by means of the E. Study map. This provides the ability to compute a set of Lorentzian curvature functions which define the local shape of spacelike ruled surfaces. Consequently, some well-known formulae of surface theory at Lorentzian line space and their geometrical explanations are obtained and examined. Lastly, a characterization for a spacelike line trajectory to be a constant Disteli-axis is derived and investigated in detail. [ABSTRACT FROM AUTHOR]

The goal of the paper is to give an optimal transport formulation of the full Einstein equations of general relativity, linking the (Ricci) curvature of a space-time with the cosmological constant and the energy-momentum tensor. Such an optimal transport formulation is in terms of convexity/concavity properties of the Boltzmann-Shannon entropy along curves of probability measures extremizing suitable optimal transport costs. The result gives a new connection between general relativity and optimal transport; moreover, it gives a mathematical reinforcement of the strong link between general relativity and thermodynamics/information theory that emerged in the physics literature of the last years. [ABSTRACT FROM AUTHOR]

Nowadays, electron spin resonance (ESR) systems are routinely used to measure the ferromagnetic resonance (FMR) in a wide range of experiments. However, the number of spins in ferromagnets far exceeds the small number of spins in paramagnetic systems that ESR systems were originally designed for. In this study, we show that high spin concentration and microwave input power—conditions routinely met in various FMR experiments—lead to the strong distortion of the FMR shape due to the sublinear operating regime of the microwave detector. We introduce the additional imbalance term in the FMR Lorentzian fitting function that allows extracting correct values of the Gilbert damping parameter under such conditions. Our results are crucial for the quantitative estimation of the Gilbert damping—the key parameter in many magnetic and spintronics measurements. [ABSTRACT FROM AUTHOR]