Real Functions Research Articles

No periodic geodesics in jet space

The $J^k$ space of $k$-jets of a real function of one real variable $x$ admits the structure of a sub-Riemannian manifold, which then has an associated Hamiltonian geodesic flow, and it is integrable. As in any Hamiltonian flow, a natural question is the existence of periodic solutions. Does $J^k$ have periodic geodesics? This study will find the action-angle coordinates in $T^*J^k$ for the geodesic flow and demonstrate that geodesics in $J^k$ are never periodic.

Finding and improving bounds of real functions by thermodynamic arguments

The possibility of stating the second law of thermodynamics in terms of the increasing behaviour of a physical property establishes a connection between that branch of physics and the theory of algebraic inequalities. We use this connection to show how some well-known inequalities, such as the standard bounds for the logarithmic function or generalizations of Bernoulli's inequality, can be derived by thermodynamic methods. Additionally, we show that by comparing the global entropy production in processes implemented with decreasing levels of irreversibility but subject to the same change of state of one particular system, we can find progressively better bounds for the real function that represents the entropy variation of the system. As an application, some new families of bounds for the function log (1+x) are obtained by this method.

A modified version of the ABC algorithm and evaluation of its performance

The artificial bee colony (ABC) optimization algorithm has been widely used to solve the global optimization problems. Many versions of ABC algorithm exist in the literature intending to achieve optimum solution for problems in different domains. Some modifications of the ABC algorithm are general and can be applied to any problem domain, while some are application dependent. This paper proposes a modified version of the ABC algorithm named as, MABC-SS (modified artificial bee colony algorithm with selection strategy), that can be applied to any problem domain. The algorithm is modified in terms of population initialization and update of a bee position using the old and a new food source equation based on the algorithm's performance in the previous iteration. The selection strategy is measured based on a novel approach called the rate of change. The population initialization in any optimization algorithm plays an important role in achieving the global optimum. The algorithm proposed in the paper uses random and an opposition-based learning technique to initialize the population and updates a bee's position after exceeding a certain number of trial limits. The rate of change is based on the average cost and is calculated for the past two iterations and compared for a method to be used in the current iteration to achieve the best result. The proposed algorithm is experimented with 35 benchmark test functions and 10 real world test functions. The findings indicate that the proposed algorithm is able to achieve the optimal result in most cases. The proposed algorithm is compared with the original ABC algorithm, modified versions of the ABC algorithm, and other algorithms in the literature using the test mentioned above. The parameters such as population size, number of iterations and runs were kept same for comparison with non-variants of ABC. In case of ABC variants, ABC specific parameters such as abandonment limit factor (0.6) and acceleration coefficient (1) were kept same. Results indicate that in 40% of the traditional benchmark test functions, the suggested algorithm works better than other variants of ABC (ABC, GABC, MABC, MEABC, BABC, and KFABC), while 30% of the traditional benchmark test functions are comparable. The proposed algorithm was compared to non-variants of ABC as well. The results show that the proposed algorithm achieved the best mean result in 50% of the CEC2019 benchmark test functions and in 94% of the classical benchmark test functions. The result is confirmed by Wilcoxon sum ranked test which shows that MABC-SS achieved statistically significant result in 48% of the classical and 70% of the CEC2019 benchmark test functions when compared with the original ABC. Overall, based on assessment and comparison in benchmark test functions used in this paper, the suggested algorithm is superior to others.

Influence of the Ignition Method on the Characteristics of Propellant Burning in the Context of the Geometric Burning Model

Mathematical models for the simulation of the operation of various projectile-throwing systems are continuously modified, simultaneously with the development of propellants. For these models, properly determined values of energetic ballistic characteristics of propellants are very important. This paper presents an original test and the results of closed vessel comparative investigations. The study analyses specific combustion characteristics of single-base propellants using conventional black powder ignition, plasma ignition, and gas ignition. The results of the study indicate the need to take into account—in the calculation of the burning rate—not only the dynamics of gas pressure changes but also the real (experimental) form function, which differs from the theoretical one resulting from the assumed geometric burning model. The obtained results allow for a critical analysis of the existing methods used for the determination of values of ballistic characteristics of propellants. Further, it will allow for creating pyrostatic test conditions that would reflect the condition of instantaneous ignition of propellant grains over their entire surface in the most realistic way.

Schwarz lemma for real harmonic functions onto surfaces with non-negative Gaussian curvature

AbstractAssume that f is a real ρ-harmonic function of the unit disk $\mathbb{D}$ onto the interval $(-1,1)$, where $\rho(u,v)=R(u)$ is a metric defined in the infinite strip $(-1,1)\times \mathbb{R}$. Then we prove that $|\nabla f(z)|(1-|z|^2)\le \frac{4}{\pi}(1-f(z)^2)$ for all $z\in\mathbb{D}$, provided that ρ has a non-negative Gaussian curvature. This extends several results in the field and answers to a conjecture proposed by the first author in 2014. Such an inequality is not true for negatively curved metrics.

Models of VTC0$\mathsf {VTC^0}$ as exponential integer parts

AbstractWe prove that (additive) ordered group reducts of nonstandard models of the bounded arithmetical theory are recursively saturated in a rich language with predicates expressing the integers, rationals, and logarithmically bounded numbers. Combined with our previous results on the construction of the real exponential function on completions of models of , we show that every countable model of is an exponential integer part of a real‐closed exponential field.

News Media, Inflation, and Sentiment

We study the relationship between media portrayals of inflation and consumer sentiment. Using tools from natural language processing, we uncover two competing narratives in US news coverage of inflation: the first relates inflation to financial variables, while the second relates inflation to real variables. As inflation rose in 2021, media increasingly emphasized the real economy. Linking inflation news to social network data from Twitter, we find that exposure to articles emphasizing the connection between inflation and the real economy significantly reduces sentiment, particularly in periods of high inflation. Shifting media narratives may therefore have contributed to declining consumer sentiment in 2021.

Parlementarne platformy oddziaływania na realziację zadań rządu związkowego w Republice Federalnej Niemiec

The paper provides an analysis of the influence of the parliamentary institutions on the working and activity of the government in the Federal Republic of Germany. The author does not aim at presenting the parliamentary institutions as such: in their constitutional position, authority exercised in the political system of the state, and the mechanism of their working. He concentrates on particular aspects of their formal and real functions: on their role as platforms of legally organised political influence on the activity of the federal government. In the first part of his paper, he presents the competence and activity of the federal council — Bundesrat — in legislation, and supervision of regulations issued by federal government, to direct the execution of federal. tasks. In the second part, he tries to analyse the mechanism of political parliamentary influence exercised by federal house of representatives Bundestag — on the exercise of its functions by the federal government.According to the author federal council is a second chamber of federal parliament, although organised in a very particular form. It assures the governing strata of several partial states — Länder — a functional platform of influence on activity of federal administration. The legal basis of this influence is provided by the authority of the federal council to give necessary assent to ca 50% of federal legislation and ca 75% of administrative regulations issued by federal government to state authorities. As practical effect of its authority a system of informal cooperation between federal and state administration was created. It provides not only channels of communication, but a structure of influencing the government in its activity on behalf of power-elites centred in the government of several states. The author tries to treat the subject of relations between the representative chamber and the parliamentary government in GFR in most realistic way. He accepts as dominant the position of federal government in the political system of the GFR. This does not contradict the legally superior authority of the representative chamber, and its real capacity, to exercise a controlling activity, in respect of legislation and in allowance of funds necessary to effect the state tasks. The author presents the structure of activities of the representative chamber and of the parliamentary parties providing formal and informal means to assure the possibilities to take i consideration, supervise and influence the activity of federal government.

Bayesian evolutionary optimization for crafting high-quality adversarial examples with limited query budget

Due to the importance of security, the adversarial attack has become an increasingly popular area for deep learning, especially the black-box adversarial attack, which can only obtain the input and output of the target model, resulting in closer to the real world. Query-based methods are a common strategy for performing black-box attacks, and they can find a slight perturbation to make target model misclassify by continuously querying the target model to obtain the output of the target model. However, query-based methods usually suffer from a serious flaw that needs massive queries, which is unaccepted in the real world. Although some query-efficient methods have been proposed to alleviate the above problems, they greatly sacrifice the quality of adversarial examples due to their problem formulations. To generate high-quality adversarial examples with a limited query budget, we propose a Bayesian evolutionary optimization (BEO) based black-box attack method using differential evolution, where a Gaussian processes model is employed to approximate the real objective function. As a key component of the BEO, we use seven acquisition functions to sample the new solution to update the Gaussian processes model, and an information entropy based selection strategy is proposed to adaptively choose the acquisition function. Finally, an effectiveness validation study is carried out comparing the proposed method with five other black-box attack methods and one Bayesian optimization (BO) method using the CIFAR-10 and ImageNet datasets. Experimental results demonstrate that the proposed method can effectively generate adversarial examples using only 200 queries.

Generalized Criteria for Admissibility of Singular Fractional Order Systems

Unified frameworks for fractional order systems with fractional order 0<α<2 are worth investigating. The aim of this paper is to provide a unified framework for stability and admissibility for fractional order systems and singular fractional order systems with 0<α<2, respectively. By virtue of the LMI region and GLMI region, five stability theorems are presented. Two admissibility theorems for singular fractional order systems are extended from Theorem 5, and, in particular, a strict LMI stability criterion involving the least real decision variables without equality constraint by isomorphic mapping and congruent transform. The equivalence between the admissibility Theorems 6 and 7 is derived. The proposed framework contains some other existing results in the case of 1≤α<2 or 0<α<1. Compared with published unified frameworks, the proposed framework is truly unified and does not require additional conditional assignment. Finally, without loss of generality, a unified control law is designed to make the singular feedback system admissible based on the criterion in a strict LMI framework and demonstrated by two numerical examples.

Species distribution models affected by positional uncertainty in species occurrences can still be ecologically interpretable

Species distribution models (SDMs) have become a common tool in studies of species–environment relationships but can be negatively affected by positional uncertainty of underlying species occurrence data. Previous work has documented the effect of positional uncertainty on model predictive performance, but its consequences for inference about species–environment relationships remain largely unknown. Here we use over 12 000 combinations of virtual and real environmental variables and virtual species, as well as a real case study, to investigate how accurately SDMs can recover species–environment relationships after applying known positional errors to species occurrence data. We explored a range of environmental predictors with various spatial heterogeneity, species' niche widths, sample sizes and magnitudes of positional error. Positional uncertainty decreased predictive model performance for all modeled scenarios. The absolute and relative importance of environmental predictors and the shape of species–environmental relationships co‐varied with a level of positional uncertainty. These differences were much weaker than those observed for overall model performance, especially for homogenous predictor variables. This suggests that, at least for the example species and conditions analyzed, the negative consequences of positional uncertainty on model performance did not extend as strongly to the ecological interpretability of the models. Although the findings are encouraging for practitioners using SDMs to reveal generative mechanisms based on spatially uncertain data, they suggest greater consequences for applications utilizing distributions predicted from SDMs using positionally uncertain data, such as conservation prioritization and biodiversity monitoring.

The impact of world oil price shocks on macroeconomic variables in Vietnam: the transmission through domestic oil price

This study examines the impact of world oil price shocks on macroeconomic variables in Vietnam with a focus on the transmission channel of domestic oil prices. The Structural Vector Autoregression model with two blocks of real economy variables and monetary variables is employed. The world oil price follows an autoregressive process to reflect the exogenous nature of world oil price shocks to the domestic economy. The retail domestic oil price is determined simultaneously by only the world oil price due to the government's control of the domestic oil market. Using monthly data in the period between 2009 and 2021, the study indicates that a positive shock to world oil prices will increase the domestic oil prices significantly, industrial production (slightly and only statistically significant in the third month after), and inflation (significantly in 8 months). Besides, the domestic oil price is not the only transmission channel of world oil price shocks to the economy. This result implies forecasting, assessing, and controlling the impact of the world oil price shock on the economy should focus on both domestic oil prices and other indirect channels.

Large deviations of multichordal $\operatorname{SLE}_{0+}$, real rational functions, and zeta-regularized determinants of Laplacians

We prove a strong large deviation principle (LDP) for multiple chordal \operatorname{SLE}_{0+} curves with respect to the Hausdorff metric. In the single-chord case, this result strengthens an earlier partial result by the second author. We also introduce a Loewner potential, which in the smooth case has a simple expression in terms of zeta-regularized determinants of Laplacians. This potential differs from the LDP rate function by an additive constant depending only on the boundary data, which satisfies PDEs arising as a semiclassical limit of the Belavin–Polyakov–Zamolodchikov equations of level 2 in conformal field theory with central charge c \to -\infty . Furthermore, we show that every multichord minimizing the potential in the upper half-plane for given boundary data is the real locus of a rational function and is unique, thus coinciding with the \kappa \to 0+ limit of the multiple \operatorname{SLE}_\kappa . As a by-product, we provide an analytic proof of the Shapiro conjecture in real enumerative geometry, first proved by Eremenko and Gabrielov: if all critical points of a rational function are real, then the function is real up to post-composition with a Möbius transformation.

On the Solution of Equations with Linear-Fractional Shifts

This work represents a continuation of the studies relating to nonlinear equations, carried out by the authors. Special attention is paid to the operators with linear-fractional shifts that act on the argument of the unknown function, but also on the unknown function itself. In this work, we study homogeneous equations with such operators. The main classes of functions for which non-linear equations are considered are Hölder class real functions. Solutions of the equations have the form of infinite products or the form of infinite continued fractions; an abstract description of the solutions is also offered. The developed mathematical methods can be applied to finding the conditions of invertibility of certain operators found in modelling, as well as for the construction of their inverse operators. Subsequently, we suggest using these results for the modelling of renewable systems with elements that can be in different states: sick, healthy, immune, or vaccinated. These results can also be applied to the analysis of balance equations of the model and for finding equilibrium states of the system.

Research on Path Planning Problem of Smart Car Considering Kinematic Constraints

With the development of artificial intelligence, intelligent cars have gradually appeared in people's lives and brought many conveniences to people's lives and work. On the street, we can see many busy figures of unmanned delivery cars; In some factories, smart cars shuttle back and forth between product production processes for material distribution; In some hospitals, we can also find that some smart cars replace medical staff to undertake the task of sending medicines and tests. For intelligent cars, autonomous collision-free path planning and trajectory tracking of the planned path are the most basic and core tasks of intelligent vehicles. The existing path planning algorithms are mainly divided into search-based algorithms (Dijkstra, A*, etc.) and sample-based algorithms (PRM, RRT, etc.), and different types of algorithms have good performance in their respective applicable scenarios. However, these path planning algorithms all use the same simplification assumption, that is, the intelligent car is regarded as a freely moving point or sphere in the path planning task, and the driving experience in life tells us that the movement of the wheel-driven intelligent car is constrained by the turning radius of the vehicle, so the path planned by the simplified intelligent car for a point is often not suitable for the driving of the intelligent car in reality. Considering this constraint, this project models the kinematics of the intelligent trolley with four-wheel steering, and adds kinematic constraints to the path planning, so as to plan the path that conforms to the kinematics model of the intelligent trolley. The path planning algorithm proposed in this topic will be tested in ROS and Gazebo simulation environments, and compared with the traditional search-based A* algorithm, the results of multiple scenarios verify the effectiveness of the algorithm. Finally, this project summarizes and looks forward to this research, which has completed the construction of low-cost physical intelligent vehicles, and plans to complete the verification of the real vehicle function by combining the designed path planning algorithm with the real-time mapping and positioning system of the car in the future.

Latent signal models: Learning compact representations of signal evolution for improved time‐resolved, multi‐contrast MRI

To improve time-resolved reconstructions by training auto-encoders to learn compact representations of Bloch-simulated signal evolution and inserting the decoder into the forward model. Building on model-based nonlinear and linear subspace techniques, we train auto-encoders on dictionaries of simulated signal evolution to learn compact, nonlinear, latent representations. The proposed latent signal model framework inserts the decoder portion of the auto-encoder into the forward model and directly reconstructs the latent representation. Latent signal models essentially serve as a proxy for fast and feasible differentiation through the Bloch equations used to simulate signal. This work performs experiments in the context of T2 -shuffling, gradient echo EPTI, and MPRAGE-shuffling. We compare how efficiently auto-encoders represent signal evolution in comparison to linear subspaces. Simulation and in vivo experiments then evaluate if reducing degrees of freedom by incorporating our proxy for the Bloch equations, the decoder portion of the auto-encoder, into the forward model improves reconstructions in comparison to subspace constraints. An auto-encoder with 1 real latent variable represents single-tissue fast spin echo, EPTI, and MPRAGE signal evolution to within 0.15% normalized RMS error, enabling reconstruction problems with 3 degrees of freedom per voxel (real latent variable + complex scaling) in comparison to linear models with 4-8 degrees of freedom per voxel. In simulated/in vivo T2 -shuffling and in vivo EPTI experiments, the proposed framework achieves consistent quantitative normalized RMS error improvement over linear approaches. From qualitative evaluation, the proposed approach yields images with reduced blurring and noise amplification in MPRAGE-shuffling experiments. Directly solving for nonlinear latent representations of signal evolution improves time-resolved MRI reconstructions.

A q-Analog of the Class of Completely Convex Functions and Lidstone Series

This paper introduces a q-analog of the class of completely convex functions. We prove specific properties, including that q-completely convex functions have convergent q-Lidstone series expansions. We also provide a sufficient and necessary condition for a real function to have an absolutely convergent q-Lidstone series expansion.

The Effectiveness of Smartphone App-Based Interventions for Assisting Smoking Cessation: Systematic Review and Meta-analysis.

Smoking is a leading cause of premature death globally. Quitting smoking reduces the risk of all-cause mortality by 11%-34%. Smartphone app-based smoking cessation (SASC) interventions have been developed and are widely used. However, the evidence for the effectiveness of smartphone-based interventions for smoking cessation is currently equivocal. The purpose of this study was to synthesize the evidence for the effectiveness of smartphone app-based interventions for smoking cessation. We conducted a systematic review and meta-analysis of the effectiveness of smartphone interventions for smoking cessation based on the Cochrane methodology. An electronic literature search was performed using the Cochrane Library, Web of Science, PubMed, Embase, PsycINFO, China National Knowledge Infrastructure, and Wanfang databases to identify published papers in English or Chinese (there was no time limit regarding the publication date). The outcome was the smoking abstinence rate, which was either a 7-day point prevalence abstinence rate or a continuous abstinence rate. A total of 9 randomized controlled trials involving 12,967 adults were selected for the final analysis. The selected studies from 6 countries (the United States, Spain, France, Switzerland, Canada, and Japan) were included in the meta-analysis between 2018 and 2022. Pooled effect sizes (across all follow-up time points) revealed no difference between the smartphone app group and the comparators (standard care, SMS text messaging intervention, web-based intervention, smoking cessation counseling, or apps as placebos without real function; odds ratio [OR] 1.25, 95% CI 0.99-1.56, P=.06, I2=73.6%). Based on the subanalyses, 6 trials comparing smartphone app interventions to comparator interventions reported no significant differences in effectiveness (OR 1.03, 95% CI 0.85-1.26, P=.74, I2=57.1%). However, the 3 trials that evaluated the combination of smartphone interventions combined with pharmacotherapy compared to pharmacotherapy alone found higher smoking abstinence rates in the combined intervention (OR 1.79, 95% CI 1.38-2.33, P=.74, I2=7.4%). All SASC interventions with higher levels of adherence were significantly more effective (OR 1.48, 95% CI 1.20-1.84, P<.001, I2=24.5%). This systematic review and meta-analysis did not support the effectiveness of delivering smartphone-based interventions alone to achieve higher smoking abstinence rates. However, the efficacy of smartphone-based interventions increased when combined with pharmacotherapy-based smoking cessation approaches. PROSPERO CRD42021267615; https://www.crd.york.ac.uk/prospero/display_record.php?RecordID=267615.

Combining x-ray real and reciprocal space mapping techniques to explore the epitaxial growth of semiconductors

In the present work, the importance of determining the strain states of semiconductor compounds with high accuracy is demonstrated. For the matter in question, new software titled LAPAs, the acronym for LAttice PArameters is presented. The lattice parameters as well as the chemical composition of Al1−x In x N and Ge1−x Sn x compounds grown on top of GaN- and Ge- buffered c-Al2O3 and (001) oriented Si substrates, respectively, are calculated via the real space Bond’s method. The uncertainties in the lattice parameters and composition are derived, compared and discussed with the ones found via x-ray diffraction reciprocal space mapping. Broad peaks lead to increased centroid uncertainty and are found to constitute up to 99% of the total uncertainty in the lattice parameters. Refraction correction is included in the calculations and found to have an impact of 0.001 Å in the lattice parameters of both hexagonal and cubic crystallographic systems and below 0.01% in the quantification of the InN and Sn contents. Although the relaxation degrees of the nitride and tin compounds agree perfectly between the real and reciprocal-spaces methods, the uncertainty in the latter is found to be ten times higher. The impact of the findings may be substantial for the development of applications and devices as the intervals found for the lattice match the condition of Al1−x In x N grown on GaN templates vary between ∼1.8% (0.1675–0.1859) and 0.04% (0.1708–0.1712) if derived via the real- and reciprocal spaces methods.

Measure-Based Extension of Continuous Functions and p-Average-Slope-Minimizing Regression

This work is inspired by some recent developments on the extension of Lipschitz real functions based on the minimization of the maximum value of the slopes of a reference set for this function. We propose a new method in which an integral p–average is optimized instead of its maximum value. We show that this is a particular case of a more general theoretical approach studied here, provided by measure-valued representations of the metric spaces involved, and a duality formula. For p=2, explicit formulas are proved, which are also shown to be a particular case of a more general class of measure-based extensions, which we call ellipsoidal measure extensions. The Lipschitz-type boundedness properties of such extensions are shown. Examples and concrete applications are also given.