Logarithmic Version Research Articles

A Hochschild-Kostant-Rosenberg theorem and residue sequences for logarithmic Hochschild homology

This paper incorporates the theory of Hochschild homology into our program on log motives. We discuss a geometric definition of logarithmic Hochschild homology of animated pre-log rings and construct an André-Quillen type spectral sequence. The latter degenerates for derived log smooth maps between discrete pre-log rings. We employ this to show a logarithmic version of the Hochschild-Kostant-Rosenberg theorem and that logarithmic Hochschild homology is representable in the category of log motives. Among the applications, we deduce a generalized residue sequence involving blow-ups of log schemes.

Quaternion linear canonicalS-transform and associated uncertainty principles

In this paper, we introduce the notion of quaternion linear canonical S-transform (Q-LCST) which is an extension of the linear canonical S-transform and study the uncertainty principles associated with the Q-LCST. First, we propose the definition of Q-LCST and then study the fundamental properties of [Formula: see text]-LCST including linearity, shift, modulation, orthogonality relation and reconstruction formula. Second, we derive the associated Heisenbergs uncertainty inequality and the corresponding logarithmic version for [Formula: see text]-LCST. Finally, some potential applications of the Q-LCST are introduced.

Modelling Trade Durations Using Dynamic Logarithmic Component ACD Model with Extended Generalised Inverse Gaussian Distribution

This paper proposes a logarithmic version of the two-component ACD (LogCACD) model with no restrictions on the sign of the model parameters while allowing the expected durations to be decomposed into the long- and short-run components to capture the dynamics of these durations. The extended generalised inverse Gaussian (EGIG) distribution is used for the error distribution as its hazard function consists of a roller-coaster shape for certain parameters’ values. An empirical application from the trade durations of International Business Machines stock index has been carried out to investigate this proposed model. Extensive comparisons are carried out to evaluate the modelling and forecasting performances of the proposed model with several benchmark models and different specifications of error distributions. The result reveals that the LogCACDEGIG(1,1) model gives the best in-sample fit based on the Akaike information criterion and other criteria. Furthermore, the estimated parameters obtained through the maximum likelihood estimation confirm the existence of the roller-coaster-shaped hazard function. The examination of LogCACDEGIG(1,1) model also provides the best out-of-sample forecasts evaluated based on the mean square forecast error using the Hansen’s model confidence set. Lastly, different levels of time-at-risk forecasts are provided and tested with Kupiec likelihood ratio test.

A facile method for Tauc exponent and corresponding electronic transitions determination in semiconductors directly from UV–Vis spectroscopy data

In this work, a facile method allowing for estimation of the exponent in the Tauc equation directly from the UV–vis spectra is presented. It is based on the Taylor expansion of the logarithmic version of the Tauc equation. The Tauc exponent is calculated from the tangent slope of the absorption data. Knowledge of this coefficient provides information about the optical transition types and is used as an input for the calculations of the band gap. As an exemplar material, TiO2 in form of thin film and nanotubes as well as their nanocomposites with other metal oxides are chosen. For the transparent thin 15 nm film of TiO2, two linear ranges with n = 2.0 and 1.2 are found. The first is assigned to the well-established indirect (allowed) transition. In the case of the second one, the n does not correspond to typically used values. Therefore, it is speculated that more than one transition is probable. This consideration is supported with ab-initio DFT calculations of the band structure of TiO2 with Hubbard U correction. Similar results are found for TiO2 nanotubes using diffuse reflectance spectroscopy indicating that the presented method applies both to transmission and reflection.

Hydrological modeling using remote sensing precipitation data in a Brazilian savanna basin

Precipitation is the main input for hydrological models. However, due to limitations of rain gauge stations, satellite precipitation estimates have become a good alternative to precipitation information. In this context, this study aimed to validate the precipitation data with Tropical Rainfall Measuring Mission Multisatellite Precipitation Analysis (TMPA) and Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (IMERG) data, in addition to assessing the uncertainty and performance of the Soil and Water Assessment Tool (SWAT) using observed precipitation (OP), TMPA, and IMERG data. Statistical coefficients were used to validate TMPA and IMERG precipitation data. P-factor and r-factor were considered for the uncertainty analysis, while the Nash-Sutcliffe efficiency (NSE), its logarithmic version (LNSE), and the percent bias (PBIAS) were analyzed to characterize the model performance analysis in monthly time steps. There was an overestimation by TMPA and IMERG in the precipitation estimation, especially in the dry period. OP, TMPA, and IMERG setups presented satisfactory results for uncertainty and performance analysis in hydrological modeling. The IMERG setup generally showed better results than the TMPA setup, being a good alternative for hydrological modeling, especially in regions with scarce precipitation datasets.

Assessment of Spatial and Temporal Soil Water Storage Using a Distributed Hydrological Model

Hydrological models are the main tools for water resources management. The Lavras Simulation of Hydrology (LASH) model was developed for watersheds with scarce data, and great results have been obtained in Brazil. This study aimed to incorporate hydrological response units (HRUs) in the LASH model to assess soil water storage (SWS) across space and time. The LASH model was calibrated and validated for the Grande River basin upstream of the Furnas Hydropower Plant, in southeastern Brazil. The Nash-Sutcliff coefficient (CNS) and its logarithmic version were analyzed in terms of both calibration and validation to appraise the model’s performance in a daily time step. The CNS for calibration and validation was 0.86 and 0.77, respectively, showing that LASH using the HRUs produced improvements in the simulations. The calibrated parameters showed a good relationship with hydrological processes in HRUs, and SWS estimates reflected the soils, topography, and land use of the watershed. LASH could describe the SWS behavior and identify the sub-watersheds with the highest and the lowest values. Therefore, the LASH model is a promising tool for SWS simulation in time and space.

A Critical Comparison of Three Notions of Fractional Stochastic Dominance

Two notions of fractional stochastic dominance are recently proposed by Muller et al. (2017) and Huang et al. (2020), respectively. Our main objective is to understand the comparative advantages of the two notions, as well as their suitability in different contexts, by establishing several new technical results. For a more comprehensive comparison, we further include a third natural notion of fractional stochastic dominance based on the coefficient of relative risk aversion. Among the three notions, it turns out that one can be seen as a logarithmic version of second-order stochastic dominance (SSD), another one can be seen as a power version of SSD, whereas there does not exist a transformation to associate the last one with SSD. We find that these notions of fractional stochastic dominance are naturally connected to five classes of risk measures, including Value-at-Risk, Expected Shortfall, expectiles, entropic risk measures, and loss certainty equivalents. The three notions are further characterized in the contexts of the rank-dependent utility model and the cumulative prospect theory. We make some recommendations on which notion to use in specific situations, as they all have their own merits.

Relative logarithmic cohomology and Nambu structures of maximal degree

We present local classification results for isolated singularities of functions with respect to a Nambu structure (multi-vector field) of maximal degree, in a neighbourhood of a smooth point of its degeneracy hypersurface. The results depend on a logarithmic version of the Brieskorn-Sebastiani theorem, which guarantees the finiteness and freeness of the corresponding deformation module. This relates the functional moduli of the classification problem with the integrals of logarithmic forms along the vanishing cycles of the complement of the Milnor fibres of the restriction of the function on the degeneracy hypersurface of the Nambu structure, inside the Milnor fibres of the function itself.

Hydrological modeling for the Piracicaba River basin to support water management and ecosystem services

The application of hydrological modeling is very important to support decision makers, providing technical basis for better management of water resources, correct use of soil and introduction of sectorial policies and programs, identifying potential areas for their implementation. In this study, the SWAT model was calibrated and validated and its performance was evaluated for the simulation of flow, total solids, total nitrogen and total phosphorus in the Piracicaba River basin. The performance of the model was evaluated based on the coefficient of determination, the Nash-Sutcliffe efficiency parameter (NS) and its logarithmic version, as well as on the percentage bias analysis (PBIAS). For simulation of the monthly flow, the NS values varied from 0.72 to 0.89 for the calibration period and from 0.50 to 0.75 for the validation period. Total solids showed NS greater than 0.48 and PBIAS less than 20.90%. For the nitrogen and total phosphorus data, the NS ranged from −1.53 to 0.78, with PBIAS below 42.62%. Based on the statistical parameters, after calibrating the SWAT model, it was able to properly reproduce the studied variables, providing a good fit between observed and simulated data, enabling the use of this tool to manage water resources, as well as supporting Payments for Ecosystem Services.

Nature of Higher-Dimensional Wormhole Mass Due to Accretion of Entropy Corrected Holographic and New Agegraphic Dark Energies

We study the accretion of dark matter and dark energy onto $$(n+2)$$ -dimensional Morris–Thorne wormholes. The wormhole mass and its rate of change have been written in the background of the $$(n+2)$$ -dimensional Friedmann-Robertson-Walker (FRW) model of the Universe. We have assumed the candidates of dark energy in the form of entropy-corrected holographic dark energy (ECHDE) and entropy-corrected new agegraphic dark energy (ECNADE) with its logarithmic and power-law versions. For these different dark energy models, the wormhole mass has been calculated in terms of the redshift when dark matter and the above types of dark energies accrete onto the wormhole. For this purpose, we have taken two classes of scale factors, where in class I the scale factor describes a future singularity while class II follows from an initial singularity. We graphically present the nature of the wormhole mass in different dimensions (4D, 5D, 6D) for ECHDE and ECNADE accretion. In the class I scale factor, we observe that the wormhole mass increases during the evolution of the Universe in both ECHDE and ECNADE models in both the power-law and logarithmic versions. Also, with the class II scale factor, we see that the wormhole mass decreases during the evolution of the Universe for ECHDE in both power-law and logarithmic versions, and for ECNADE with power law models, while the wormhole mass increases during the evolution of the Universe for ECNADE in its logarithmic version.

Symplectic cohomology rings of affine varieties in the topological limit

We construct a multiplicative spectral sequence converging to the symplectic cohomology ring of any affine variety X, with first page built out of topological invariants associated to strata of any fixed normal crossings compactification $$(M,{\mathbf {D}})$$ of X. We exhibit a broad class of pairs $$(M,{\mathbf {D}})$$ (characterized by the absence of relative holomorphic spheres or vanishing of certain relative GW invariants) for which the spectral sequence degenerates, and a broad subclass of pairs (similarly characterized) for which the ring structure on symplectic cohomology can also be described topologically. Sample applications include: (a) a complete topological description of the symplectic cohomology ring of the complement, in any projective M, of the union of sufficiently many generic ample divisors whose homology classes span a rank one subspace, (b) complete additive and partial multiplicative computations of degree zero symplectic cohomology rings of many log Calabi-Yau varieties, and (c) a proof in many cases that symplectic cohomology is finitely generated as a ring. A key technical ingredient in our results is a logarithmic version of the PSS morphism, introduced in our earlier work Ganatra and Pomerleano, arXiv:1611.06849.

The Neural Network Analysis of Normality of Small Samples of Biometric Data through Using the Chi-Square Test and Anderson–Darling Criteria

Introduction. The aim of the work is to reduce the requirements to test sample size when testing the hypothesis of normality. Materials and Methods. A neural network generalization of three well-known statistical criteria is used: the chi-square criterion, the Anderson–Darling criterion in ordinary form, and the Anderson–Darling criterion in logarithmic form. Results. The neural network combining of the chi-square criterion and the Anderson–Darling criterion reduces the sample size requirements by about 40 %. Adding a third neuron that reproduces the logarithmic version of the Andersоn–Darling test leads to a small decrease in the probability of errors by 2 %. The article deals with single-layer and multilayer neural networks, summarizing many currently known statistical criteria. Discussion and Conclusion. An assumption has been made that an artificial neuron can be assigned to each of the known statistical criteria. It is necessary to change the attitude to the synthesis of new statistical criteria that previously prevailed in the 20th century. There is no current need for striving to create statistical criteria for high power. It is much more advantageous trying to ensure that the data of newly synthesized statistical criteria are low correlated with many of the criteria already created.

On a logarithmic version of the derived McKay correspondence

We globalize the derived version of the McKay correspondence of Bridgeland, King and Reid, proven by Kawamata in the case of abelian quotient singularities, to certain logarithmic algebraic stacks with locally free log structure. The two sides of the correspondence are given respectively by the infinite root stack and by a certain version of the valuativization (the projective limit of every possible logarithmic blow-up). Our results imply, in particular, that in good cases the category of coherent parabolic sheaves with rational weights is invariant under logarithmic blow-up, up to Morita equivalence.

Quaternionic shearlet transform

The shearlet transform has been shown to be a valuable and powerful time–frequency analyzing tool for optics and non-stationary signal processing. In this article, we propose a novel transform called quaternionic shearlet transform which is designed to represent quaternion-valued signals at different scales, locations and orientations. We investigate the fundamental properties of quaternionic shearlet transform including Parseval's formula, Moyal's principle, inversion formula, and characterization of its range using the machinery of quaternion Fourier transform and quaternion convolution. We conclude our investigation by deriving an analogue of the classical Heisenberg–Pauli–Weyl uncertainty inequality and the associated logarithmic version for the quaternionic shearlet transform.

𝔸¹-equivalence of zero cycles on surfaces

In this paper, we study A 1 \mathbb {A}^1 -equivalence classes of zero cycles on open algebraic surfaces. We prove the logarithmic version of Mumford’s theorem on zero cycles. We also prove that the log Bloch conjecture holds for surfaces with log Kodaira dimension − ∞ -\infty .

Polar Wavelet Transform and the Associated Uncertainty Principles

The polar wavelet transform– a generalized form of the classical wavelet transform has been extensively used in science and engineering for finding directional representations of signals in higher dimensions. The aim of this paper is to establish new uncertainty principles associated with the polar wavelet transforms in $L^{2}(\mathbb R^{2})$ . Firstly, we study some basic properties of the polar wavelet transform and then derive the associated generalized version of Heisenberg–Pauli–Weyl inequality. Finally, following the idea of Beckner (Proc. Amer. Math. Soc. 123, 1897–1905 1995), we drive the logarithmic version of uncertainty principle for the polar wavelet transforms in $L^{2}(\mathbb R^{2})$ .

ON BINARY CORRELATIONS OF MULTIPLICATIVE FUNCTIONS

We study logarithmically averaged binary correlations of bounded multiplicative functions $g_{1}$ and $g_{2}$. A breakthrough on these correlations was made by Tao, who showed that the correlation average is negligibly small whenever $g_{1}$ or $g_{2}$ does not pretend to be any twisted Dirichlet character, in the sense of the pretentious distance for multiplicative functions. We consider a wider class of real-valued multiplicative functions $g_{j}$, namely those that are uniformly distributed in arithmetic progressions to fixed moduli. Under this assumption, we obtain a discorrelation estimate, showing that the correlation of $g_{1}$ and $g_{2}$ is asymptotic to the product of their mean values. We derive several applications, first showing that the numbers of large prime factors of $n$ and $n+1$ are independent of each other with respect to logarithmic density. Secondly, we prove a logarithmic version of the conjecture of Erdős and Pomerance on two consecutive smooth numbers. Thirdly, we show that if $Q$ is cube-free and belongs to the Burgess regime $Q\leqslant x^{4-\unicode[STIX]{x1D700}}$, the logarithmic average around $x$ of the real character $\unicode[STIX]{x1D712}\hspace{0.6em}({\rm mod}\hspace{0.2em}Q)$ over the values of a reducible quadratic polynomial is small.

Logarithmic Ramifications of Étale Sheaves by Restricting to Curves

Abstract In this article, we prove that the Swan conductor of an étale sheaf on a smooth variety defined by Abbes and Saito’s logarithmic ramification theory can be computed by its classical Swan conductors after restricting it to curves. It extends the main result of Barrientos [7] for rank $1$ sheaves. As an application, we give a logarithmic ramification version of generalizations of Deligne and Laumon’s lower semi-continuity property for Swan conductors of étale sheaves on relative curves to higher relative dimensions in a geometric situation.

𝔸-curves on log smooth varieties

Abstract In this paper, we study 𝔸 1 {\mathbb{A}^{1}} -connected varieties from log geometry point of view, and prove a criterion for 𝔸 1 {\mathbb{A}^{1}} -connectedness. As applications, we provide many interesting examples of 𝔸 1 {\mathbb{A}^{1}} -connected varieties in the case of complements of ample divisors, and the case of homogeneous spaces. We also obtain a logarithmic version of Hartshorne conjecture characterizing projective spaces and affine spaces.

Sum rules and the role of pressure on the excitation spectrum of a confined hydrogen atom by a spherical cavity

Sum rule relations over the excitation spectrum of a quantum system contain information about both the energy spectrum and eigenfunctions of the system in a compact form, particularly regarding closure relations. In this work, the effects of pressure induced by a spherical cavity on an atomic hydrogen impurity on the dipole oscillator strength (DOS) sum rule, Sk, and its logarithmic version, Lk, are studied by means of a numerical approach based on a finite-difference solution to the Schrödinger equation. Pressure effects are accounted for by means of a spherical cavity of radius R0 immersed in a medium characterized by a penetrable potential height V0. The DOS sum rules Sk and Lk are investigated as a function of these cavity parameters and thus directly related to the impurity static pressure and surrounding material. One finds that the sum rules are fulfilled within the numerical precision for low pressure conditions. However, when the barrier height is large or infinite (a non-penetrable cavity), the sum rule, for positive k, differs from its closure relation. One finds that this occurs for a cavity radius au, corresponding to a pressure such that the first p-state that contributes to the sum rule has positive energy and it is due to the fact that the spherical confinement cavity potential dominates over the Coulombic interaction for the hydrogenic impurity. Thus, as pressure increases, the excitation spectrum approaches that of a particle confined by a spherical cavity while the ground state is slightly affected by the cavity and more closely resembles a hydrogenic atom. Therefore, the sum rule over the excitation spectrum tends to a particle confined by a spherical cavity, while the closure relation gives that of a confined hydrogen atom in the ground state. For negative k, low excitations are the most important and this behavior is not presented. As the sum rule is the static dipole polarizability, the results are compared to available data in the literature, showing excellent agreement. This behavior in the sum rule and oscillator strength in electron–impurity excitations affects optical transitions of importance in semiconductor nanostructures.