Transcendental Function Research Articles

Transcendental Julia sets of positive finite Lebesgue measure

We show that there exists a transcendental entire function whose Julia set has positive finite Lebesgue measure.

A compromise solution approach for efficiency measurement with shared input: The case of tourist hotels in Taiwan

Shared input occurs often when a production system performs two or more functions and some of the functions share the same input. To determine the proportion of the shared input devoted to each function, the conventional data envelopment analysis (DEA) models that allow each decision making unit (DMU) to select the most favorable value to attain the highest efficiency score is usually used. The result is that many DMUs assign proportions of different bound values to the same function, which is not reasonable. This paper proposes a compromise solution approach that aggregates the viewpoints of all DMUs to obtain a consensus regarding the proportion of the shared input used by each function. The approach is actually a parametric DEA approach for constructing the production function. To increase the explanation power, transcendental functions are considered. The tourist hotel, where the accommodation and catering functions share the input of management employees is used for illustration. The results show that a transcendental function has stronger explanation power, and reasonable compromised values for the proportions of the effort of the management employees devoted to the two functions are obtained.

QUANTIFYING THE SPATIAL AND TEMPORAL VARIABILITY OF CARBON-BIASED TECHNOLOGICAL PROGRESS AND ITS DRIVING FACTORS IN CHINA

The carbon resource’s role in guiding energy conservation and emission reduction through technological progress has become a focal point in theoretical research and policy discussions. By introducing carbon resource as a production factor into the transcendental logarithmic function, this study comprehensively employs statistical methods and GeoDetector to investigate carbon-biased technological progress in China from 2010 to 2020. The findings reveal an overall U-shaped trend in carbon-biased technological progress. As technology advances, the high-level areas of DLC and DKC shift toward the inland northwest, and each region’s carbon-biased technological progress is demarcated by the Heihe–Tengchong Line, exhibiting higher levels in the northwest and lower levels in the southeast. The spatial variation of carbon-biased technological progress is influenced by multiple factors, with the level of economic development playing a dominant role in the earlier period and the role of R&D investment becoming more significant in the later stage. In-depth research on carbon-biased technological progress is of great significance for optimizing carbon factor market allocation and achieving sustainable green economic development in China.

Research on carbon sink prices in China’s marine fisheries: an analysis based on transcendental logarithmic production function model from 1979 to 2022

Research on carbon sink prices in China’s marine fisheries: an analysis based on transcendental logarithmic production function model from 1979 to 2022

Current-Mode Control of a Distributed Buck Converter with a Lossy Transmission Line

This article presents a buck converter in which the inductor has been replaced by a transmission line. This approach would be practically conceivable if the power supply and load had a greater spatial distance. Alternatively, the model derived in this way could also be regarded as an intermediate model in order to replace a power coil via discretization with a larger number of smaller coils and capacitors. In the time domain, this new converter can be described by a system of coupled partial and ordinary differential equations. In the frequency domain, a transcendental transfer function is obtained. For comparison with an equivalently parameterized conventional converter, Padé approximants are derived. A linear controller is designed for the converter topology under consideration.

Measurement and Influencing Factors of Total Factor Water Resources Utilization Efficiency in the Yellow River Basin

This paper focuses on the total factor water resources utilization efficiency (WRUE) as the research object, employing the Stochastic Frontier Analysis (SFA) model based on the transcendental logarithmic production function to measure the WRUE of nine provinces in the Yellow River Basin of China from 2012 to 2021, obtains WRUE values for each province. And then, we perform a regression analysis of influencing factors using the Tobit model. The results indicate that: (1) The average value of WRUE of nine provinces in the Yellow River Basin is 0.541, which deviates greatly from the fully effective frontier of SFA, with an overall downward trend during the study period. (2) There is a significant polarization of WRUE among the provinces. Inner Mongolia exhibits the highest WRUE at 0.978, close to the SFA efficient frontier, while Ningxia has the lowest WRUE at only 0.314; the remaining provinces display efficiency values between 0.4 and 0.6. (3) Among the influencing factors affecting the WRUE, the value added of the primary industry, per capita disposable income, and the number of reservoirs have a significant positive impact on the WRUE. In contrast, the value added of the secondary industry, local financial environmental protection expenditures, comprehensive water supply production capacity, and per capita daily water consumption negatively affect the WRUE.

On the Love Numbers of an Andrade Planet

AbstractThe Andrade rheological model is often employed to describe the response of solar system or extra‐solar planets to tidal perturbations, especially when their properties are still poorly constrained. While for uniform planets with steady‐state Maxwell rheology the analytical form of the Love numbers was established long ago, for the transient Andrade rheology no closed‐form solutions have been yet determined, and the planetary response is usually studied either semi‐analitically in the frequency domain or numerically in the time domain. Closed‐form expressions are potentially important since they could provide insight into the dependence of Love numbers upon the model parameters and the time‐scales of the isostatic readjustment of the planet. First, we focus on the Andrade rheological law in 1‐D and we obtain a previously unknown explicit form, in the time domain, for the relaxation modulus in terms of the higher Mittag‐Leffler transcendental function Eα,β(z) that generalizes the exponential function. Second, we consider the general response of an incompressible planetary model — often referred to as the “Kelvin sphere” — studying the Laplace domain, the frequency domain and the time domain Love numbers by analytical methods. Through a numerical approach, we assess the effect of compressibility on the Love numbers in the Laplace and frequency domains. Furthermore, exploiting the results obtained in the 1‐D case, we establish closed‐form — although not elementary — expressions of the time domain Love numbers and we discuss the frequency domain response of the Kelvin sphere with Andrade rheology analytically.

Dimensional analysis and logarithmic functions

Students are often confused by units when dealing with a logarithmic function. This is frequently dealt with by stating that the function gives a unitless result. Though correct, it does not address the deeper question of why the logarithm is unitless and how a graphical analysis involving logarithms can lead to unitless results that depend on the original data’s units. This paper explains this by considering the logarithm as a transcendental function and how that relates to the determination of units.

A Transcendental LASSO Function for Combining Machine Learning and Statistical Model Forecasts

The aim of the study is the development of methodology for accurate estimation of electric vehicle demand; which is paramount regarding various aspects of the firms decision-making such as optimal price, production level, and corresponding amounts of capital and labor; as well as supply chain, inventory control, capital financing, and operational expenses management. The forecasting methods utilized include statistical techniques (autoregressive integrated moving average [ARIMA], and polynomial regression), machine learning (nonlinear autoregressive neural network [NAR]), deep learning (long short-term memory [LSTM]), hybrid and combination forecasting. With regard to the latter method, our study experiments with four different combining model approaches, including the introduction of an original, novel combining method with the employment of a transcendental LASSO function, which is used to form combinations of forecasts generated by the NAR, ARIMA, and polynomial regression models. The LASSO-based combining model proved superior to all other models, for the majority of forecast error statistics; where the root mean square error (RMSE) and mean absolute percentage error (MAPE) values are 4.5% and 8% respectively lower than the average level of the component model forecasts. The major implications of our empirical findings are that greater accuracy in demand forecasting can be achieved with a combining model approach, rather than reliance on any particular, singular model. Furthermore, given its superior performance, the employment of the studys LASSO-based combining model to forecast electric vehicle demand may lead to optimal firm decision-making over a range of organizational facets, which is predicated on accurate demand function estimation.

Productivity and technical inefficiency: A case study of small dryland mungbean farming in East Nusa Tenggara, Indonesia

Mungbeans are one of the important agricultural products for food security in East Nusa Tenggara (NTT) Province, which is one of the driest regions in Indonesia. The low productivity and profitability of mungbean farming in this region are caused by factors that influence agricultural inefficiency. This study was conducted to measure the productivity and technical efficiency levels, as well as investigate the factors affecting farm inefficiency, using the Technical Efficiency Effect Model (TEEM) applied to the frontier logarithmic transcendental production function. The method applied in this research is descriptive qualitative based on survey and interview results through primary and secondary data. Firstly, the results showed that mungbean farming was in the increasing return to scale stage of production and productivity only reached 57% of its production potential, with a technical efficiency level of 66%. Secondly, the factors that positively influence the low productivity and technical efficiency level of mungbean farming are land, seeds, labor, and the interaction between land and labor. Meanwhile, farmer experience and farm training significantly reduce the inefficiency of mungbean farming. It is suggested that increasing land productivity with appropriate and intensive modern technology and improving labor skills are the main strategies for reducing inefficiencies and increasing the income of smallholder farmers in drylands.

Three-point energy correlators in hadronic Higgs boson decays

We present the analytic calculation of the leading-order three-point energy correlator (EEEC) in hadronic Higgs decays, including both the gluon-initiated channel H→gg+X and quark-initiated channel H→qq¯+X. The phase-space integration is evaluated directly using Mandelstam variables sij=(pi+pj)2, and the appearing square roots can be rationalized by either conformal ratios or celestial coordinate variables. Throughout the calculation, we observe the same transcendental function space as in N=4 super–Yang-Mills theory and e+e−→hadrons. Different infrared limits are also explored using the full analytic result, offering the fixed-order data for EEEC factorization and resummation. Given its nontrivial shape dependence, the EEEC presents an excellent opportunity to explore the dynamics of gluon jets originating from the H→gg decay channel at future lepton colliders. Published by the American Physical Society 2024

LIMITING DIRECTIONS FOR ENTIRE SOLUTIONS OF A

Let us consider f as being an entire solution of the differential-difference equation G(z, f)+h(z)fm(z) = 0, (m ∈ N), where h(z) is a transcendental entire function and G(z, f) is a differential-difference polynomial in f with entire coefficients. By considering the order and deficiency of h(z) and such coefficients, we mainly study the radial distribution of f, and establish a lower bound of measure for the set of common limiting directions of the Julia sets of derivatives and primitives of its shifts.

Path to clean and sustainable energy from nuclear and renewable sources: Evidence from France

France is one of the countries that have made commendable progress towards accomplishing sustainable development goals but still struggles with combating environmental challenges. Decarbonizing the energy sector by deploying clean energy and reducing fossil fuels in the energy mix are essential steps. The study uses annual time series data from 1980 to 2021 and employs the ridge regression estimation technique to estimate a twice-differentiable transcendental production function, which approximates the second-order Taylor series to explore the potential for such decarbonization for France. The study finds that substitution possibilities exist between clean energy and fossil fuels, with substantial substitution possibilities coming from nuclear energy. Nuclear energy and renewables are found to be complements that can be deployed concurrently, but since nuclear energy already constitutes a significant proportion of clean energy for France, the study recommends increasing the proportion of renewable energy in the overall energy mix as the most plausible path to decarbonization. Other complementary sustainable energy policies are recommended in the body of the paper.

Will advancement in technologies bring fear and damage human employment? Evidence from China's manufacturing industry.

Advancement in technologies such as robotic industries and artificial intelligence bring fear among human being that jobs will be substituted by robots. Base on the panel data of 28 China's manufacturing industries, this research analyzed the impact of technical progress bias on employment. First, we calculate the technical progress bias index of 28 industries base on the stochastic frontier model with transcendental logarithm function found 16 industries were toward the skilled labor while the remaining 12 industries were toward the unskilled labor. Second, the empirical results show that technical progress bias has a positive impact on the total manufacturing employment and significant positive effect on the unskilled labor, while no significant impact on skilled labor employment. Third, the threshold effect test proves that if taking industry value-added per capita or R&D capital stock as threshold variable, the threshold about the impact exist, making the impact on skilled labor was insignificant.

On a version of the Problem B of Mahler involving derivatives

In 1902, Paul St\"ackel constructed an analytic function $f(z)$ in a neighborhood of the origin, which was transcendental, and with the property that both $f(z)$ and its inverse, as well as its derivatives, assumed algebraic values at all algebraic points in this neighborhood. Inspired by this result, Mahler in 1976 questioned the existence of an transcendental entire function $f(z)$ such that $f(\overline{\mathbb{Q}})$ and $f^{-1}(\overline{\mathbb{Q}})$ are subsets of $\overline{\mathbb{Q}}.$ This problem was solved by Marques and Moreira in 2017. As St\"acklel's result involved derivatives, it is natural to question whether we have an analogous result for transcendental entire functions involving derivatives. In this article, we show that there are an uncountable amount of such functions.

Psychology of dreams: justification and development of a synthetic approach

The object of the study is the mental reality of a personality, and the subject is its dream activity, which is considered in the context of a multilevel and multidimensional structure of personality as a system. Thus, the function of dream activity is considered through the prism of a dialogic (transcendental) function that allows consciousness to perceive mental facts beyond its boundaries, that is, to acquire the ability to metareflexion, combining the ontological and epistemological paradigms. It follows from this that the study touches on the "multi-dimensionality" of the personal structure, both on the surface and in the deep planes, combined in the space of a dream through conscious perception of symbols. It is proposed to combine the idea of the structure of the psyche according to S. Groff and an understanding of the specifics of the material manifested in specific dreams of a particular person. The research methodology is based on the idea of mental reality as a self-regulating system, within which dreams serve the inherent desire for integrity of the personality. The author uses the following methods: case studies, interpretation, analysis and synthesis, introspection and self-report. The article attempts to develop an integrative-synthetic theory of dreams based on the works of V.V. Kozlov, S.A. Parfentiev, V.V. Maikov and other modern authors working in the field of practical depth psychology. Based on the author's vision and generalization of many years of experience, the concept of seven "dimensions" (levels) is proposed for working with dream material for the purposes of psychological psychotherapy and personal development. The results of an experiment are presented, proving both the effectiveness of this algorithm and the scientific validity of understanding dreams as a multidimensional natural psychotherapeutic space, process and mechanism at the same time. In general, the work is very relevant from the point of view of both theory and practice, while being characterized by a certain scientific novelty.

Feedback enhanced Dyakonov–Shur instability in graphene field-effect transistors

Graphene devices are known to have the potential to operate THz signals. In particular, graphene field-effect transistors (gFETs) have been proposed as devices to host plasmonic instabilities in the THz realm; for instance, Dyakonov–Shur (DS) instability which relies upon dc excitation. In this work, starting from a hydrodynamical description of the charge carriers, we extend the transmission line description of gFETs to a scheme with a positive feedback loop, also considering the effects of delay, which leads to the transcendental Laplace-transform transfer function, with complex frequency s, with terms of the form e−assechk(s)/s , for a given a∈R0+ arising from the delay time and with k∈N . Applying the conditions for the excitation of DS instability, we report an enhanced voltage gain in the linear regime that is corroborated by our simulations of the nonlinear hydrodynamic model for the charge carriers. This translates to both greater saturation amplitude—often up to 50% increase—and faster growth rate of the self-oscillations. Thus, we bring forth a prospective concept for the realization of a THz oscillator suitable for future plasmonic circuitry.

Modification of Intertwining Logistic Map and a Novel Pseudo Random Number Generator

Chaotic maps have been widely studied in the field of cryptography for their complex dynamics. However, chaos-based cryptosystems have not been widely used in practice. One important reason is that the following requirements of practical engineering applications are not taken into account: computational complexity and difficulty of hardware implementation. In this paper, based on the demand for information security applications, we modify the local structure of the three-dimensional Intertwining Logistic chaotic map to improve the efficiency of software calculation and reduce the cost of hardware implementation while maintaining the complex dynamic behavior of the original map. To achieve the goal by reducing the number of floating point operations, we design a mechanism that can be decomposed into two processes. One process is that the input parameters value of the original system is fixed to 2k by Scale index analysis. The other process is that the transcendental function of the original system is replaced by a nonlinear polynomial. We named the new map as “Simple intertwining logistic”. The basic chaotic dynamic behavior of the new system for controlling parameter is qualitatively analyzed by bifurcation diagram and Lyapunov exponent; the non-periodicity of the sequence generated by the new system is quantitatively evaluated by using Scale index technique based on continuous wavelet change. Fuzzy entropy (FuzzyEn) is used to evaluate the randomness of the new system in different finite precision digital systems. The analysis and evaluation results show that the optimized map could achieve the designed target. Then, a novel scheme for generating pseudo-random numbers is proposed based on new map. To ensure its usability in cryptographic applications, a series of analysis are carried out. They mainly include key space analysis, recurrence plots analysis, correlation analysis, information entropy, statistical complexity measure, and performance speed. The statistical properties of the proposed pseudo random number generator (PRNG) are tested with NIST SP800-22 and DIEHARD. The obtained results of analyzing and statistical software testing shows that, the proposed PRNG passed all these tests and have good randomness. In particular, the speed of generating random numbers is extremely rapid compared with existing chaotic PRNGs. Compared to the original chaotic map (using the same scheme of random number generation), the speed is increased by 1.5 times. Thus, the proposed PRNG can be used in the information security.

Real Branches and Stability of a New Transcendental Function Arising in Pharmacokinetic Modeling

Real Branches and Stability of a New Transcendental Function Arising in Pharmacokinetic Modeling

Analytical modeling of novel equivalent circuits of double diode solar cell circuits using a special transcendental function approach.

Solar photovoltaic (PV) cell modeling is crucial to understanding and optimizing solar energy systems. While the single-diode model (PVSDM) is commonly used, the double-diode model (PVDDM) offers improved accuracy at a reasonable level of complexity. However, finding analytical closed-form solutions for the current-voltage (I-U) dependency in PVDDM circuits has remained a challenge. This work proposes two novel configurations of PVDDM equivalent circuits and derives their analytical closed-form solutions. The solutions are expressed in terms of the Lambert W function and solved using a special transcendental function approach called Special Trans Function Theory (STFT). The accuracy of the proposed equivalent circuits is demonstrated on two solar cells/modules, RTC-F and MSX-60, showing equal or better performance than the standard PVDDM equivalent circuit. Further testing on a commercial solar panel under different irradiance and temperature conditions confirms the applicability of the proposed models. To address the parameter estimation problem, a novel metaheuristic algorithm, the chaotic honey-badger algorithm, is developed and evaluated. The results obtained validate the accuracy and practicality of the proposed PVDDM equivalent circuit configurations.