Logarithmic Order Research Articles

Protection capacity of Lactiplantibacillus plantarum 83114 against contamination of dry pet food with Aspergillus flavus

A wide range of pet food types are available on the market and one of the most common ingredients of dry food are cereals, vectors of harmful mycotoxins. Mycotoxins are toxic secondary fungal metabolites that contaminate dry pet food and their levels remain stable during food processing. This has a direct effect on the quality of the product and on animal health. Lactiplantibacillus plantarum 83114 is a probiotic strain isolated from traditional fermented milk with proven antifungal activity in different matrix. This study investigated the antifungal activities of this strain against contamination of dry pet food with a mycotoxigenic Aspergillus flavus strain. The antifungal activity was assessed using a complete culture of viable L. plantarum 83114, cell free supernatants (CFS), and non-viable cells (postbiotics). The CFS of L. plantarum CIDCA 83114 (pH 4.04) exhibited a high germination reduction rate (GR 94.7 %). However, the neutralized CFS (pH 7.0) lost approximately 60 % of its inhibitory capacity. L. plantarum CIDCA 83114 CFS and postbiotic treatments at 50 % exerted a total fungal growth inhibition, observed in a growth rate (KD) of zero. The viability of L. plantarum 83114 inoculated in dry pet food decreased by one logarithmic order after the first week of storage and, by the second week, no viable cells were detected. The DNA concentration of A. flavus in dry pet food supplemented with the probiotic strain remained consistently low and stable throughout the storage period. Lactiplantibacillus plantarum 83114 played a crucial role in inhibiting fungal growth and could act as a biopreservative agent in pet food.

N3LO power corrections for 0-jettiness subtractions with fiducial cuts

We compute the leading logarithmic power corrections at next-to-next-to-next-to-leading order for 0-jettiness subtractions for Drell-Yan and Higgs production in gluon fusion differential in both the invariant mass and rapidity of the color singlet. We review how to disentangle these power corrections from those arising from the presence of fiducial and isolation cuts by using Projection-to-Born improved slicing. Our results include all the channels contributing at leading logarithmic order for these processes, including the off-diagonal channels that receive contributions from soft quark emission. We study the numerical impact of the power corrections for Drell-Yan and Higgs production and find it to become negligible compared to the size of the N3LO corrections only below τcut ~ 10−5. We estimate that in a fully differential calculation at N3LO combining the Projection-to-Born improved slicing method and our results for the leading logarithmic power corrections may allow for keeping the slicing uncertainties under control already with τcut ≲ 10−3, marking a significant improvement in efficiency for these methods. These results constitute a crucial ingredient for fully differential N3LO calculations based on the N-jettiness subtraction scheme.

Finite logarithmic order meromorphic solutions of linear difference/differential-difference equations

Finite logarithmic order meromorphic solutions of linear difference/differential-difference equations

N3LL resummation of one-jettiness for Z -boson plus jet production at hadron colliders

We present the resummation of one-jettiness for the color-singlet plus jet production process pp→(γ*/Z→ℓ+ℓ−)+jet at hadron colliders up to the fourth logarithmic order (N3LL). This is the first resummation at this order for processes involving three colored partons at the Born level. We match our resummation formula to the corresponding fixed-order predictions, extending the validity of our results to regions of the phase space where further hard emissions are present. This result paves the way for the construction of next-to-next-to-leading order simulations for color-singlet plus jet production matched to parton showers in the framework. Published by the American Physical Society 2024

The Hilbert problem in a half-plane for generalized analytic functions with a singular point on the real axis

This article analyzes the inhomogeneous Hilbert boundary value problem for an upper half-plane with the finite index and boundary condition on the real axis for one generalized Cauchy–Riemann equation with a singular point on the real axis. A structural formula was obtained for the general solution of this equation under restrictions leading to an infinite index of the logarithmic order of the accompanying Hilbert boundary value problem for analytic functions. This formula and the solvability results of the Hilbert problem in the theory of analytic functions were applied to solve the set boundary value problem.

Diophantine conditions in the law of the iterated logarithm for lacunary systems

AbstractIt is a classical observation that lacunary function systems exhibit many properties which are typical for systems of independent random variables. However, it had already been observed by Erdős and Fortet in the 1950s that probability theory’s limit theorems may fail for lacunary sums $$\sum f(n_k x)$$ ∑ f ( n k x ) if the sequence $$(n_k)_{k \ge 1}$$ ( n k ) k ≥ 1 has a strong arithmetic “structure”. The presence of such structure can be assessed in terms of the number of solutions $$k,\ell $$ k , ℓ of two-term linear Diophantine equations $$a n_k - b n_\ell = c$$ a n k - b n ℓ = c . As the first author proved with Berkes in 2010, saving an (arbitrarily small) unbounded factor for the number of solutions of such equations compared to the trivial upper bound, rules out pathological situations as in the Erdős–Fortet example, and guarantees that $$\sum f(n_k x)$$ ∑ f ( n k x ) satisfies the central limit theorem (CLT) in a form which is in accordance with true independence. In contrast, as shown by the first author, for the law of the iterated logarithm (LIL) the Diophantine condition which suffices to ensure “truly independent” behavior requires saving this factor of logarithmic order. In the present paper we show that, rather surprisingly, saving such a logarithmic factor is actually the optimal condition in the LIL case. This result reveals the remarkable fact that the arithmetic condition required of $$(n_k)_{k \ge 1}$$ ( n k ) k ≥ 1 to ensure that $$\sum f(n_k x)$$ ∑ f ( n k x ) shows “truly random” behavior is a different one at the level of the CLT than it is at the level of the LIL: the LIL requires a stronger arithmetic condition than the CLT does.

Growth of Solutions to Complex Linear Differential Equations with Analytic or Meromorphic Coefficients in ℂ̅ − {z0} of Finite Logarithmic Order

Growth of Solutions to Complex Linear Differential Equations with Analytic or Meromorphic Coefficients in ℂ̅ − {z0} of Finite Logarithmic Order

The shelf life of cooked sausages with reduced salt content

The aim of this study was to compare the microbiological quality of cooked sausages produced with a traditional salt content (2.1%) and reformulated batches with a salt content reduced to 1.7%. The reformulation was tested on two types of comminuted meat products – Špekáčky sausage with a diameter of up to 46 mm or Bologna-type sausages in diameter of 85 mm (Gothaj sausage) or 75 mm (Junior sausage). The total viable count (TVC) increased only slightly during the four-week storage (4 ± 1 °C) of all batches of Špekáčky sausage. Comparing batches 1.7 and 2.1, there is an evident difference in the number of CFU/g, with samples of Špekáčky 1.7 showing numbers of bacteria higher by approximately 1 logarithmic order throughout practically the entire storage period (P = 0.001). The population of lactic acid bacteria (LAB) remained well beneath a value of 5.0 log CFU/g even at the end of the experiment. For Bologna-type sausages, the TVC was either beneath the limit of detection or at its boundary in all samples. LAB were not detected during storage of Bologna-type sausages. The results confirmed that the proportion of salt in cooked sausages can be reduced to 1.7% without negatively affecting the shelf life or safety of the final products.

Fast Convergence on Perfect Classification for Functional Data

We investigate the availability of approaching perfect classification on functional data with finite samples. The seminal work (Delaigle and Hall (2012)) showed that perfect classification for functional data is easier to achieve than for finite-dimensional data. This result is based on their finding that a sufficient condition for the existence of a perfect classifier, named a Delaigle--Hall condition, is only available for functional data. However, there is a danger that a large sample size is required to achieve the perfect classification even though the Delaigle--Hall condition holds, because a minimax convergence rate of errors with functional data has a logarithm order in sample size. This study solves this complication by proving that the Delaigle--Hall condition also achieves fast convergence of the misclassification error in sample size, under the bounded entropy condition on functional data. We study a reproducing kernel Hilbert space-based classifier under the Delaigle--Hall condition, and show that a convergence rate of its misclassification error has an exponential order in sample size. Technically, our proof is based on (i) connecting the Delaigle--Hall condition and a margin of classifiers, and (ii) handling metric entropy of functional data. Our experiments support our result, and also illustrate that some other classifiers for functional data have a similar property.

Bounds for the sum of the first k-eigenvalues of Dirichlet problem with logarithmic order of Klein-Gordon operators

Bounds for the sum of the first <i>k</i>-eigenvalues of Dirichlet problem with logarithmic order of Klein-Gordon operators

Propagation of logarithmic regularity and inviscid limit for the 2D Euler equations

&lt;p&gt;The aim of this note is to study the Cauchy problem for the 2D Euler equations under very low regularity assumptions on the initial datum. We prove propagation of regularity of logarithmic order in the class of weak solutions with $ L^p $ initial vorticity, provided that $ p\geq 4 $. We also study the inviscid limit from the 2D Navier-Stokes equations for vorticity with logarithmic regularity in the Yudovich class, showing a rate of convergence of order $ |\log\nu|^{-\alpha/2} $ with $ \alpha &amp;gt; 0 $.&lt;/p&gt;

Finite Logarithmic Order Meromorphic Solutions of Complex Linear Delay-Differential Equations

Finite Logarithmic Order Meromorphic Solutions of Complex Linear Delay-Differential Equations

NNLL resummation of Sudakov shoulder logarithms in the heavy jet mass distribution

The heavy jet mass event shape has large perturbative logarithms near the leading order kinematic threshold at ρ=13\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\rho =\\frac{1}{3} $$\\end{document}. Catani and Webber named these logarithms Sudakov shoulders and resummed them at double-logarithmic level. A resummation to next-to-leading logarithmic level was achieved recently. Here, we extend the resummation using an effective field theory framework to next-to-next-to-leading logarithmic order and show how to combine it with the resummation of dijet logarithms. We also solve the open problem of an unphysical singularity in the resummed momentum space distribution, in a way similar to how it is resolved in the Drell-Yan qT spectrum: through a careful analysis of the kinematics and scale-setting in position space. The heavy jet mass Sudakov shoulder is the first observable that does not involve transverse momentum for which position space resummation is critical. These advances may lead to a more precise extraction of the strong coupling constant from e+e− data.

An influence of molecular weight, deacetylation degree of chitosan xerogels on their antimicrobial activity and cytotoxicity. Comparison of chitosan materials obtained using lactic acid and CO2 saturation

This paper presents a comparison of the antimicrobial activity and cytotoxicity against L929 cells of chitosan xerogels prepared by dissolving the polymer in a solution of lactic acid (LA) or carbonic acid (CO2) and then freeze-drying. There was no simple relationship between the antimicrobial activity and cytotoxicity of the samples obtained using both techniques (LA and CO2). Chitosan materials obtained by the LA method in a 1:1 dilution were characterized by the highest cytotoxicity against L929 cells (∼20%). For the same diluted samples prepared using the CO2 saturation method, the viability of L929 cells was approximately 2.5 times greater. Some of the tested chitosan materials obtained by the innovative method were characterized by significantly lower antimicrobial activity, for example, reduction of E. coli bacteria for MMW-LA and MMW-CO2 samples by 6.00 and 0.75 logarithmic order, respectively. This clearly indicates that in many applications, the presence of the acid necessary to dissolve chitosan is responsible for the antimicrobial activity of the polymer solution and its products.

On the growth of solutions of complex linear differential equations with analytic coefficients in $\overline{\mathbb{C}}\backslash\{z_{0}\}$ of finite logarithmic order

In this article, we study the growth of solutions of homogeneous and non-homogeneous complex linear differential equations where the coefficients are analytic functions in the extended complex plane except a finite singular point with finite logarithmic order. We extend some previous results obtained very recently by Fettouch and Hamouda.

Remembrance of things past

Nonlinear sigma models on de Sitter background have proved a useful prototype for quantum gravity in summing the large logarithms which arise from loop corrections. We consider a model whose evolution is described, at leading logarithm order, by the trace of the coincident, doubly differentiated scalar propagator. An analytic approximation for this quantity on an arbitrary expansion history is applied to generalize the resummed de Sitter result to any cosmological background which has experienced primordial inflation. In addition to analytic expressions, we present explicit numerical results for the evolution in a plausible expansion history. The large scales of primordial inflation are transmitted to late times.

The modified model for hyperspectral estimation of soil organic matter using positive and inverse grey relational degree

PurposeIn order to improve the estimation accuracy of soil organic matter, this paper aims to establish a modified model for hyperspectral estimation of soil organic matter content based on the positive and inverse grey relational degrees.Design/methodology/approachBased on 82 soil sample data collected in Daiyue District, Tai'an City, Shandong Province, firstly, the spectral data of soil samples are transformed by the first order differential and logarithmic reciprocal first order differential and so on, the correlation coefficients between the transformed spectral data and soil organic matter content are calculated, and the estimation factors are selected according to the principle of maximum correlation. Secondly, the positive and inverse grey relational degree model is used to identify the samples to be identified, and the initial estimated values of the organic matter content are obtained. Finally, based on the difference information between the samples to be identified and their corresponding known patterns, a modified model for the initial estimation of soil organic matter content is established, and the estimation accuracy of the model is evaluated using the mean relative error and the determination coefficient.FindingsThe results show that the methods of logarithmic reciprocal first order differential and the first-order differential of the square root for transforming the original spectral data are more effective, which could significantly improve the correlation between soil organic matter content and spectral data. The modified model for hyperspectral estimation of soil organic matter has high estimation accuracy, the average relative error (MRE) of 11 test samples is 4.091%, and the determination coefficient (R2) is 0.936. The estimation precision is higher than that of linear regression model, BP neural network and support vector machine model. The application examples show that the modified model for hyperspectral estimation of soil organic matter content based on positive and inverse grey relational degree proposed in this article is feasible and effective.Social implicationsThe model in this paper has clear mathematical and physics meaning, simple calculation and easy programming. The model not only fully excavates and utilizes the internal information of known pattern samples with “insufficient and incomplete information”, but also effectively overcomes the randomness and grey uncertainty in the spectral estimation of soil organic matter. The research results not only enrich the grey system theory and methods, but also provide a new approach for hyperspectral estimation of soil properties such as soil organic matter content, water content and so on.Originality/valueThe paper succeeds in realizing both a modified model for hyperspectral estimation of soil organic matter based on the positive and inverse grey relational degrees and effectively dealing with the randomness and grey uncertainty in spectral estimation.

Thrust distribution in Higgs decays up to the fifth logarithmic order

Thrust distribution in Higgs decays up to the fifth logarithmic order

Quark and gluon two-loop beam functions for leading-jet pT and slicing at NNLO

We compute the complete set of two-loop beam functions for the transverse momentum distribution of the leading jet produced in association with an arbitrary colour-singlet system. Our results constitute the last missing ingredient for the calculation of the jet-vetoed cross section at small veto scales at the next-to-next-to-leading order, as well as an important ingredient for its resummation to next-to-next-to-next-to-leading logarithmic order. Our calculation is performed in the soft-collinear effective theory framework with a suitable regularisation of the rapidity divergences occurring in the phase-space integrals. We discuss the occurrence of soft-collinear mixing terms that might violate the factorisation theorem, and demonstrate that they are naturally absorbed into the beam functions at two loops in the exponential rapidity regularisation scheme when performing a multipole expansion of the measurement function. As in our recent computation of the two-loop soft function, we present the results as a Laurent expansion in the jet radius R. We provide analytic expressions for all flavour channels in x space with the exception of a set of R-independent non-logarithmic terms that are given as numerical grids. We also perform a fully numerical calculation with exact R dependence, and find that it agrees with our analytic expansion at the permyriad level or better. Our calculation allows us to define a next-to-next-to-leading order slicing method using the leading-jet pT as a slicing variable. As a check of our results, we carry out a calculation of the Higgs and Z boson total production cross sections at the next-to-next-to-leading order in QCD.

Isogeometric approach for thermal buckling analysis of FG graphene platelet reinforced composite trapezoidally corrugated laminated panels

In this research, thermal buckling of trapezoidally corrugated functionally graded graphene platelet reinforced composite (FG-GPLRC) laminated panels are considered and analyzed. Each layer of trapezoidally corrugated panels (TCPs) are reinforced with different value of graphene platelets (GPLs) leading to a piecewise functionally graded (FG) media. The elastic properties of the laminated TCP are evaluated using the Halpin-Tsai scheme. The TCP is modeled by multiple patches. The stability equation of each patch is established using a logarithmic higher order shear deformation theory (HSDT) and then incorporating the isogeometric method. The associated matrices are then transformed appropriately to the global coordinates. Also, the continuity requirements between the boundaries of the patches are satisfied by the bending strip method (BSM). The reliability and accuracy of the proposed method are ascertained through comparison of the computed results with those exist in the open literature as well as those generated by ABAQUS. Afterwards comprehensive parametric studies are provided to show the effects of all influencing factors on the thermal buckling behavior of trapezoidally corrugated FG-GPLRC laminated panels. It is found that with constant corrugation angle and amplitude, when more corrugation units are added to the original panel, the critical buckling temperature difference remains almost constant.