Logarithmic Form Research Articles

Gravitational baryogenesis in f(Q,C) gravity

The matter–anti-matter asymmetry in the early Universe’s history is explained theoretically by the baryogenesis. It is well known that modified gravity theories are highly effective in explaining the Universe’s current accelerated state. In this paper, we examine the gravitational baryogenesis for [Formula: see text] gravity, where [Formula: see text] is the non-metricity scalar and [Formula: see text] is the boundary term. To perform the baryogenesis, we assume linear, nonlinear and logarithmic forms of [Formula: see text]. We evaluate the baryon-to-entropy ratio for our models by assuming the power law form of the scale factor [Formula: see text]. We also investigate the generalized baryogenesis for our model by assuming the interaction term [Formula: see text]. We constrain the model parameters by comparing with the observational value [Formula: see text]. Our derived models are physically viable.

Fibonacci numbers as mixed concatenations of Fibonacci and Lucas numbers

Abstract Let (Fn ) n≥0 and (Ln ) n≥0 be the Fibonacci and Lucas sequences, respectively. In this paper we determine all Fibonacci numbers which are mixed concatenations of a Fibonacci and a Lucas numbers. By mixed concatenations of a and b, we mean the both concatenations ab and ba together, where a and b are any two nonnegative integers. So, the mathematical formulation of this problem leads us searching the solutions of two Diophantine equations Fn = 10 d Fm + Lk and Fn = 10 d Lm + Fk in nonnegative integers (n, m, k), where d denotes the number of digits of Lk and Fk , respectively. We use lower bounds for linear forms in logarithms and reduction method in Diophantine approximation to get the results.

A Bridge between Trace Anomalies and Deconfinement Phase Transitions

Inspired by the fact that both the dilaton potential encoding the trace anomalies of QCD and the Polyakov loop potential measuring the deconfinement phase transition can be expressed in the logarithmic forms, as well as the fact that the scale symmetry is expected to be restoring and colors are deconfined in extreme conditions such as high temperatures and/or densities, we conjecture a relation between the dilaton potential and the Polyakov loop potential. Explicitly, we start from the Coleman–Weinberg type potential of a real scalar field—a dilaton or conformal compensator—and make an ansatz of the relation between this scalar field and the Polyakov loop to obtain the Polyakov loop potential, which can be parameterized in Lattice QCD (LQCD) in the pure glue sector. We find that the coefficients of Polyakov potential fitted from Lattice data are automatically satisfied in this ansatz, the locations of deconfinement and scale restoration are locked to each other, and the first-order phase transition can be realized. Extensions to the low-energy effective quark models are also discussed. The conjectured relation may deepen our understanding of the evolution of the universe, the mechanism of electroweak symmetry breaking, the phase diagram of QCD matter, and the properties of neutron stars.

Predictor‐based collision‐free and connectivity‐preserving resilient formation control for multi‐agent systems under sensor deception attacks

AbstractMalicious attack is a potential threat to collision‐free and connectivity‐preserving formation. In this article, a predictor‐based collision‐free and connectivity‐preserving resilient formation control strategy is proposed for a class of multi‐agent systems under sensor deception attacks. The predictor states are constructed to replace original states in the control strategy, and a novel attack compensator is constructed to suppress sensor deception attacks. Prediction errors, instead of compromised errors, are introduced to update weights of radial basis function neural networks (RBFNNs). To achieve collision avoidance and connectivity preservation, a transformation function in logarithmic form is introduced. To avoid static and dynamic obstacles, an improved artificial potential function (APF) combined with their velocity information is constructed. Furthermore, to solve the local minimum problem in the combining of transformation function and APF, a virtual force is added. Based on the Lyapunov function, all closed‐loop signals are bounded and collision‐free and connectivity‐preserving formation is achieved. The simulation related to a group of quadrotors verifies the effectiveness of the proposed resilient control strategy.

Can the late dark energy parameterization reconcile the Hubble tension?* *Ming-Jian Zhang is Supported by the Natural Science Foundation of Shandong Province, China (ZR2021MA075), and the Talent Research Project of Qilu University of Technology (2023RCKY029). Li Chen is Supported by the Natural Science Foundation of Shandong Province, China (ZR2019MA033)

In this study, we constructed ten dark energy models to test whether they can reconcile the Hubble tension and how much it is affected by parameterization. To establish a fair test, the models are diverse, encompassing fractional, logarithmic, exponential, and inverse exponential forms as well as several non-parameterized models. The dataset we used includes the NPIPE pipeline of cosmic microwave background (CMB) power-spectrum data from Planck2020, Pantheon+ samples from Supernovae Type Ia, and baryon acoustic oscillations. The MCMC calculations imply dark energy transferring from to for the four parameterized dark energy models. However, these models cannot adequately reconcile the Hubble tension. Notably, we found that phantom-like dark energy with can achieve the greatest reduction in the Hubble tension to . However, AIC analysis indicates that this alleviation is at the cost of high AIC. We also investigated the effect of constructions on the derivative of the equation of state , cosmic density parameter, CMB power spectrum , and matter spectra . We also found that the Hubble tension may be related to the reionization process.

Improving a hydrological model by coupling it with an LSTM water use forecasting model

Long short-term memory (LSTM) networks have demonstrated excellent capabilities in identifying nonlinear relationships between variables and have proven to be effective in water use forecast modeling. However, current LSTM water use forecasting models do not consider the influence of regional water resources, which limits their ability to make full use of hydrological data. To address this issue, a distributed hydrological model (WetSpa-WW) was integrated in this study with a deep learning model (LSTM) based on water use activities. The water resources results simulated by WetSpa-WW were considered as an additional training input in the LSTM for water use forecasting. The coupled WetSpa-LSTM model was tested on the upper-middle of the Weihe River Basin, and the simulations were compared with those obtained from an experiment that did not consider water resources factors. The results indicated that the WetSpa-LSTM model performed better than the original model in simulating the streamflow. During calibration, logarithmic form of Nash-Sutcliffe efficiency (NSEln) increased from 0.33 to 0.54 and the relative error (RE) decreased from 28 % to 13 %. Moreover, we observed that water resources factors can improve the accuracy of agricultural water use forecasting (NSE increases by 0.10) more than that of non-agricultural water use forecasting (NSE increases by 0.04). Overall, this study demonstrates the value of considering regional water resources in water use forecasting, and provides a perspective for integrating a distributed hydrological model (WetSpa-WW) and a deep learning model (LSTM) based on water use activities.

An improved simple model for α decay half-lives*

Abstract In this paper, using the α particle preformation probabilities from Xu et al. [Xu and Ren, Nucl. Phys. A 760, 303 (2005)], which were extracted by fitting experimental half-lives of α decay, based on a phenomenological harmonic oscillator potential model (HOPM) [Bayrak, J Phys G 47, 025102 (2020)], refitting 178 α decay half-lives of even-even nuclei obtained from the latest nuclear property table NUBASE2020, we obtain the only one adjustable parameter MeV in the HOPM, i.e., the depth of nuclear potential. The corresponding root-mean-square (rms) deviation is . Furthermore, to consider the contribution of centrifugal potential to unfavored α decay half-lives, adding a new term (d and l are the adjustable parameter and orbital angular momentum carried away by emitted α particle) to the logarithmic form of favored α decay half-lives under the HOPM framework, we propose an improved simple model (ISM) for calculating favored and unfavored α decay half-lives. Fitting the experimental half-lives of 205 unfavored α decay, we obtain . The ISM is used to calculate the unfavored α decay half-lives of 128 odd-A and 77 odd-odd nuclei. The results improve by 54.2% and 53.6%, respectively, compared with HOPM. In addition, we extend the ISM to predict the α decay half-lives of 144 nuclei with , and 120. For comparison, the improved model with eight parameters (DUR) proposed by Deng et al. [Deng, Phys. Rev. C 101, 034307 (2020)] and the modified universal decay law (MUDL) proposed by Soylu et al. [Soylu, Nucl. Phys. A 1013, 122221 (2021)] are also used. The predictions of these models and/or formulas are generally consistent with each other.

Generalized ghost dark energy model in Brans–Dicke theory with logarithmic scalar field

We study generalized ghost dark energy model in Brans–Dicke theory within the framework of flat Friedmann–Lemaitre–Robertson–Walker Universe. We assume the well-motivated logarithmic form of Brans–Dicke scalar field in terms of the scale factor to find the observational parameters such as equation of state parameter [Formula: see text] and deceleration parameter q. It is observed that the equation of state parameter crosses the phantom divide line [Formula: see text] for a suitable range of model parameters. We observe that the deceleration parameter is time-dependent which shows the recent phase transition from decelerated to accelerated expansion of the Universe. Moreover, the model shows that the Universe will go through two future phase transitions, recent accelerated expansion to decelerated expansion and again decelerated expansion to accelerated expansion. We have also plotted the trajectories of the model in the [Formula: see text] plane for different values of parameters and explored the freezing and thawing regions. Further, we apply the sound squared speed method to check the stability of the model and found that the model is stable for suitable range of parameters.

Nexus between digital financial inclusion and economic growth: a panel data investigation of Asian economies

PurposeThis study aims to investigate the relationship between digital financial inclusion and economic growth in specific Asian countries, emphasizing the exploration of how digital financial inclusion dynamics impact gross domestic per capita income.Design/methodology/approachThe study creates a digital financial inclusion composite index (DFII) by incorporating essential metrics from the Global Findex report. Economic growth is measured using Gross Domestic Product per capita income in its natural logarithmic form (LnPCI), with three control variables– employment-to-population ratio; population growth and inflation. The analysis utilizes a fixed-effect dummy variable model to examine the relationship, considering unobserved country-specific heterogeneity. 30 Asian countries have been selected for the study for the periods 2014, 2017 and 2021 based on their availability, as outlined in Table 4.FindingsThe research revealed a robust positive correlation between the Digital Financial Inclusion Index (DFII) and logarithmic GDP per capita income (LnPCI), indicating higher per capita income with enhanced digital financial inclusion. Employment and population exhibited minimal influence, whereas inflation had a notable negative effect on per capita income. Population growth showed a limited impact. The model demonstrated a high explanatory power for the dependent variable (high R-squared), and the residuals displayed low autocorrelation (Durbin–Watson of 1.96).Originality/valueThis study adds to the existing literature by examining the intricate connection between digital financial inclusion (DFI) and economic growth in 30 Asian countries, employing a comprehensive composite index for analysis.

Research on p order nonlinear half wave Schrödinger equations

The objective of our research is to scrutinize the presence and singularity of the comprehensive potent solution for the half-wave Schrödinger equation characterized by order. Take into account the nonlinear half-wave Schrödinger equations represented by order: . We apply the Brezis-Gallouet style inequality to attain a logarithmic form of regulation. These rationales will be pivotal in validating our primary theorem within Global Well-Posedness. When discussing global Solutions, we infer the solutions for Schrödinger equations within the realm when . Specifically, when , we leverage the Strichartz estimations alongside inequalities following the Brezis-Gallouët pattern to ascertain the well-posedness of Schrödinger equations within the framework. To elucidate the global well-posedness of Schrödinger equations in the energy subspace , we undertake a traditional tactic to craft the frail solution within the realm, succeeded by the application of a rationale found in existing academic literature to verify the singularity of the frail solution. The coherent progression of the frail solution is derived from the sustained conservation of both mass and energy elements. An analogous strategy is likewise harnessed to affirm the global well-posedness of Schrödinger equations in the sphere when .

Attractor behavior of [formula omitted] modified gravity and the cosmic acceleration

In this paper, we have performed the dynamical system analysis of f(T) gravity cosmological models at both background and perturbation levels. We have presented three models pertaining to three distinct functional forms of f(T). The first form is that of the logarithmic form of the torsion scalar T, the second one is in the power law form, and the third one is the combination of the first two forms. For all these three forms of f(T), we have derived the corresponding cosmological parameters in terms of the dynamical variables. Subsequently, the critical points are obtained and the condition(s) of its existence has been derived. Critical points of each model have been analyzed individually and the corresponding cosmology are derived. The stability behavior of these critical points are discussed from the behavior of the eigenvalues and the phase portraits. At least one stable node has been obtained in each of these models. Further from the evolution plots of the cosmological parameters, the accelerating behavior of the cosmological models are also verified.

Higgs fields, non-abelian Cauchy kernels and the Goldman symplectic structure

We consider the moduli space of vector bundles of rank n and degree ng over a fixed Riemann surface of genus g⩾2 with the explicit parametrization in terms of the Tyurin data. The ‘non-abelian’ theta divisor consists of bundles such that h1⩾1 . On the complement of this divisor we construct a non-abelian (i.e. matrix) Cauchy kernel explicitly in terms of the Tyurin data. With the additional datum of a non-special divisor, we can construct a reference flat holomorphic connection which also depends holomorphically on the moduli of the bundle. This allows us to identify the bundle of Higgs fields, i.e. the cotangent bundle of the moduli space, with the affine bundle of holomorphic connections and provide a monodromy map into the GLn character variety. We show that the Goldman symplectic structure on the character variety pulls back along this map to the complex canonical symplectic structure on the cotangent bundle and hence also on the space of connections. The pull-back of the Liouville one-form to the affine bundle of connections is then shown to be a logarithmic form with poles along the non-abelian theta divisor and residue given by h 1.

An improved change detection method for high-resolution soil moisture mapping in permafrost regions

ABSTRACT Soil moisture plays a crucial role in understanding the hydrological cycle and the ecological environment. This research presents an improved change detection method that leverages time series data from Sentinel-1 radar and Sentinel-2 optical sensors (2019–2021) to estimate surface soil moisture. The response of backscatter to soil moisture in bare soil was expressed in a logarithmic form, and the influence function of the normalized difference vegetation index (NDVI) on the backscatter difference was established for various vegetation-covered surfaces. Therefore, the impact of vegetation on backscatter is effectively mitigated, and the resulting change in backscatter relative to bare soil conditions can be obtained. An empirical function is subsequently formulated to ascertain the reference values of soil moisture in each pixel. The retrieval of soil moisture is demonstrated in the Wudaoliang permafrost region of the Qinghai-Tibet Plateau and validated against ground measurements. The retrieval results of the improved change detection method exhibit correlation coefficients ranging from 0.672 to 0.941, with root mean squared errors (RMSE) ranging from 0.031 m 3 / m 3 to 0.073 m 3 / m 3 . Compared to the Soil Moisture Active Passive (SMAP) 9-km product, our new method demonstrates higher correlation (0.898 vs. 0.867) and lower RMSE (0.037 m 3 / m 3 vs. 0.044 m 3 / m 3 ). The soil moisture retrieved from Sentinel shows a strong correlation with the SMAP 9-km soil moisture in the time series, thereby providing a better representation of the region’s soil moisture heterogeneity. Our method demonstrates the feasibility of combining Sentinel-1 and 2 for high-resolution (100 m) soil moisture mapping in permafrost regions.

Technical Efficiency Analysis Of Home Industry Kamang Crackers In Kenagarian Kamang Hilir Kamang Magek District, Agam Regency West Sumatra Province

Technical efficiency is the ability of an industry to use minimum total input to produce maximum output. This research aims to 1) Analyze the level of technical efficiency in the Kamang cracker home industry in Kamang Hilir Kenagarian, and 2) Analyze what factors influencing the level of technical efficiency in the Kamang cracker home industry in Kamang Hilir Kenagarian. This research was carried out deliberately in Kenagarian Kamang Hilir, Kamang Magek District, Agam Regency. Respondents in this study using the Slovin formula, totaling 51 Kamang cracker home industry entrepreneurs using a simple random sampling technique. Using primary and secondary data, while the data analysis used is qualitative descriptive analysis and the Cobb-Douglass production function method which is converted into logarithmic form, then data analysis uses Stochastic Frontier. The analysis results showed that the average level of technical efficiency was 0.5792, proving that the hypothesis in this research was proven correct. Can be concluded that the Kamang cracker home industry is technically efficient and the factors that influence technical efficiency are raw materials, salt, hours people work, age, number of family members while green onions, pertalite and gas fuel, education, business experience are not significant in the Kamang cracker home industry

Common Terms of k-Pell and Tribonacci Numbers

Let Tm be a Tribonacci sequence, and let the k-Pell sequence be a generalization of the Pell sequence for k ≥ 2 . The first k terms are 0, 0, ..., 0, 1, and each term after the forewords is defined by linear recurrence P (k) n = 2P (k) n−1 + P (k) n−2 + ... + P (k) n−k . We study the solution of the Diophantine equation P (k) n = Tm for the positive integer (n, k, m) with k ≥ 2. We use the lower bound for linear forms in logarithms of algebraic numbers with the theory of the continued fraction.

Dynamic interaction of gravity currents in a confined porous layer

We study the dynamic interaction of two gravity currents in a confined porous layer, one heavier and one lighter, partly inspired by the practice of geological $\mathrm {CO}_2$ sequestration in oil fields. Two coupled nonlinear advective-diffusive equations are derived to describe the time evolution of the profile shape of both the upper (lighter) and lower (heavier) currents. At early times, the upper and lower currents remain separated and propagate independently. As time progresses, the currents approach each other and start to interact. We have identified eight different regimes of gravity current interaction at late times, impacted by four dimensionless parameters, representing the flow rate partition, ratio of buoyancy over the injection force, and the viscosity contrasts between the two injecting and displaced fluids. By defining appropriate similarity variables at either the early or late times, the governing partial differential equations (PDEs) reduce to different ordinary differential equations (ODEs), corresponding to the classic nonlinear diffusion solutions at early times and eight different self-similar solutions at late times when the currents attach to each other. It is of interest to note that in four of the eight regimes of late-time interaction (regimes 2, 6–8), self-similar solutions can be constructed by combining appropriately the three basic solutions (i.e. shock, rarefaction and travelling wave solutions) identified during single fluid injection in confined porous layers. In the four other regimes (regimes 1, 3–5), implicit solutions in the form of logarithm or error functions are obtained due to the influence of flow confinement and interaction of gravity currents. Potential implications of the model and solutions are also briefly discussed in the context of ${\rm CO}_2$ -water co-flooding for simultaneous ${\rm CO}_2$ sequestration and oil recovery.

A case study on finding efficient monetary policy to solve Shenzhen's excessive-priced housing

Background The real estate market has developed rapidly since 1980s in Shenzhen, China. This study aims to find and investigate an efficient monetary policy to solve the excessive-priced housing problem in Shenzhen. Methods By regulating the contractionary monetary policy which are open market operation, the discount rate and legal reserve deposit can decrease the accelerating rate of excessive housing price in Shenzhen. Firstly, the relationship between housing prices and the other three tools of monetary policy has been analyzed. Then, from collecting the secondary data online, models were established by using the ordinary least square to find the correlation between housing price and money supply from 2011 to 2017. Results This model shows the relationship with the change of the logarithmic form of the amount of M2 and housing index is significantly positive. With the decrease in change of the logarithmic form of the amount of M2, the increase in housing index can be controlled in a relative decelerated rate. Conclusions In the reduced monetary supply, the housing price can be managed to an ideal condition and then it can help the government to achieve the goal of maintaining Shenzhen’s healthy real estate market development.

Repdigits base $ \eta $ as sum or product of Perrin and Padovan numbers

<abstract><p>Let $ \left\{E_{n}\right\}_{n\geq0} $ and $ \left\{P_{n}\right\}_{n\geq0} $ be sequences of Perrin and Padovan numbers, respectively. We have found all repdigits that can be written as the sum or product of $ E_{n} $ and $ P_{m} $ in the base $ \eta $, where $ 2\leq\eta\leq10 $ and $ m\leq n $. In addition, we have applied the theory of linear forms in logarithms of algebraic numbers and Baker-Davenport reduction method in Diophantine approximation approaches.</p></abstract>

Measuring Technical Efficiency of Small-Scale Farms of Beef Cattle Farming in Selected Areas of Bangladesh

The stochastic production frontier was employed to estimate the technical efficiency of small-scale beef cattle farmers. Two Upazilas from the Rajbari district of Bangladesh were purposively selected as the study area. The snowball technique was adopted to select seventy (70) beef cattle farmers for data collection with structured questionnaires in collecting data for the study. The Ordinary Least Square (OLS) technique was used in estimating the coefficients of the logarithmic form of the Cobb-Douglass Production function by SPSS 25 and their determinants in the study area. Linear Programming (LP) was used to estimate technical efficiency by using Microsoft Excel 2013. The mean technical efficiency of the beef cattle farmers was 87%. The results confirm that in some cases, the beef cattle farmers were technically inefficient, implying that there is room to improve 13% technical efficiency with the farmers' current resources and available technology. Age (Table 4) of the farmers had negative but significant effects on their technical efficiency, while education, farming experience, and farm size had significant and positive influences on farmer's technical efficiency. Among the dummy variables, the coefficient of training facilities is negative which reveals that there is a scope of increasing the production of beef cattle by improving the quality and regularity of training. For that, policies that would encourage experienced and educated farmers, to continue beef cattle farming are recommended.

SMRF'nin Sinir Ağı ve Artımlı Dinamik Analizin Birleşimine Dayanan Güvenilirlik Tahmini

This paper conducts a comprehensive vulnerability analysis of steel structures, taking into account the stringent HAZUS restrictions. The demand distribution for each mode of failure takes the form of a normal logarithm after extracting the fragility chart. Thus, the two parameters of mean and standard deviation can be used to construct the fragility chart. A total of five modes of failure were used in this paper. Therefore, 10 unknown values were used to derive the fragility curves. Afterward, Incremental Dynamic Analysis (IDA) was used under 40 natural records to obtain the fragility curve. To save time in the analysis and prediction of structural responses, a neural network method was used to select records more efficiently. It was observed that this method is better than the analytical method in considering random uncertainty in steel structures when several acceleration values are used.