Form Of Series Research Articles

Star exponentials from propagators and path integrals

In this paper we address the relation between the star exponentials emerging within the Deformation Quantization formalism and Feynman’s path integrals associated with propagators in quantum dynamics. In order to obtain such a relation, we start by visualizing the quantum propagator as an integral transform of the star exponential by means of the symbol corresponding to the time evolution operator and, thus, we introduce Feynman’s path integral representation of the propagator as a sum over all the classical histories. The star exponential thus constructed has the advantage that it does not depend on the convergence of formal series, as commonly understood within the context of Deformation Quantization. We include some basic examples to illustrate our findings, recovering standard results reported in the literature. Further, for an arbitrary finite dimensional system, we use the star exponential introduced here in order to find a particular representation of the star product which may be recognized as the one encountered in the context of the quantum field theory for a Poisson sigma model.

Finitely ambiguous and finitely sequential weighted automata over fields

Expressive power of finitely ambiguous and finitely sequential weighted automata over fields is examined. Rational series realised by such automata can be classified into infinite hierarchies according to ambiguity and sequentiality degrees of realising automata – it is shown that both these hierarchies are strict already over unary alphabets in case the field under consideration is not locally finite. Moreover, the expressive power of finitely sequential, finitely ambiguous, and polynomially ambiguous weighted automata is compared over different fields, both for unary and arbitrary finite alphabets, drawing a complete picture of the relations between corresponding classes of formal power series.

The Effectiveness of Development Performance in Gorontalo Province Over Two Cycles of RPJMD (2012-2022)

This research aims to: 1) analyze the effectiveness of development performance achievements in Gorontalo Province over two cycles: RPJMD in 2012-2017 and RPJMD in 2017-2022; and 2) formulate recommendations for the effective achievement of development targets. The method employed was a survey utilizing secondary data in the form of time series with documentation data collection instruments. The effectiveness of development achievements was analyzed using descriptive statistics, and data were presented in tables, figures, and graphs. The effectiveness of development achievements was examined based on the trend of main development indicators in the two RPJMD cycles of Gorontalo Province from 2012-2017 and 2017-2022 and compared with the set targets. The research findings indicate that the development performance of Gorontalo Province during the period 2012-2022 reflects diverse dynamics. Economic growth experienced fluctuations with an initial surge in 2012 and the negative impact of the COVID-19 pandemic in 2020. The Human Development Index showed improvement, indicating efforts to enhance social conditions and the population's welfare, although it remains within the moderate category. The agricultural sector changed with increased maize production due to the Agropolitan program, but further efforts are needed to improve farmers' income and rural economic diversification. Surveys on community satisfaction revealed improvements in the quality of public services and governance and accountability enhancements. Despite positive achievements, Gorontalo Province still faces challenges in achieving better and sustainable performance in improving community welfare.

The Strategy of the Revitalization of Shandong Rural Culture by “Good Rural Season”

The brand of “good rural season” focuses on major strategies such as helping rural revitalization and the construction of national cultural parks and closely by following the new needs of the masses traveling for micro vacation and launching a series of activities in the form of multi-scene and series. The activities of “good rural season” have ecological, social and cultural values. Its cultural value provides a good condition for promoting the revitalization of rural culture. The theme of “good rural season” is rooted in folk culture and local culture. It is one of the ways to inherit excellent traditional culture and promote the revitalization of rural culture. “Internet” and “digitalization” have become the development direction of “good rural season” activities. In these activities, the government and the masses spontaneously form beneficial supplements.

Bell's Palsy, an Adverse Event Following COVID Vaccines.

Bell's palsy is one of the most concerning complications of the COVID vaccine that has impacted vaccine acceptance among the general population. These vaccines were introduced to provide immunity against the SARS-CoV-2 coronavirus and have been found to be quite effective. Little did we know that Bell's palsy could be one of its serious complications. We used various search engines to gather data in the form of a case series and case reports related to patients who were affected by the vaccine and had developed Bell's palsy. A total of eleven case reports and 4 case series were included in the analysis. The vaccines mentioned in the case reports were Pfizer, Moderna, Sinovac, AstraZeneca, and Janssen, while the case series included Pfizer and Sinovac. The majority of patients were female and aged between 31-40 years. Right-sided laterality was observed in 45.45% of patients, left-sided laterality in 45.45% of patients, and bilateral laterality in 9.1% of patients. Three patients had a history of Bell's palsy or stroke. After treatment, three patients showed partial improvement, six patients fully recovered, and the status of two patients was unknown. Bell's palsy is a rare complication that can occur after receiving the COVID-19 vaccine. This review aims to increase awareness about this rare adverse event of the vaccine so that it can be properly addressed and managed. Additionally, it will serve as a foundation for future research on the administration of the COVID-19 vaccine.

Prediction of Energy Consumption on Example of Heterogenic Commercial Buildings

The management of large enterprises influences their efficiency and profitability. One of the important aspects is the appropriate management of electricity consumption used for production and daily operation. The problem becomes more complicated when you need to manage not one but a large complex of buildings with heterogeneous purposes. In the paper, we examine real-time series data of electrical energy consumption in a complex of heterogeneous buildings, including offices and warehouses, using time series analysis methods such as the Holt–Winters model and ARIMA/SARIMA model, and neural networks (Deep Neural Network, Recurrent Neural Network, and Long Short-Term Memory). Experimental research was performed on a dataset obtained from an energy consumption meter placed in the building complex, built in different periods, and equipped with a variety of automation devices. The data were collected over a period of four years 2018–2021 in the form of time series. Results show that classic models are good at predicting energy consumption in the mentioned type of buildings. The ARIMA model gave the best results—for buildings characterized by seasonality and trends the forecasts were almost perfect with actual values.

Research on topology technology of integrated battery energy storage system with reconfigurable battery and converter

In traditional battery energy storage systems (BESS), batteries are usually connected in a simple series or parallel form, and separate converters and balancing modules are typically used for energy exchange between the battery and external sources, as well as for balancing energy between batteries. This paper proposes an integrated battery energy storage system (IBESS) with reconfigurable batteries and DC/DC converters, resulting in a more compact structure. The IBESS can reconfigure the connection of energy storage batteries based on the battery's status and external demand. The DC/DC converters can operate in different modes such as boost, buck, or buck-boost converters. The IBESS has five working modes: discharging mode, balancing mode, battery discharging and balancing mode, constant current and constant voltage (CCCV) charging mode and backup mode. To verify the feasibility of the proposed energy storage system, a model with four battery modules was built using MATLAB/SIMULINK, and the operation of all working modes was demonstrated. The simulation results verified the system's performance and reliability, demonstrating its flexibility and efficiency in different operating modes.

Inverse Coefficient Problem for the 2D Wave Equation with Initial and Nonlocal Boundary Conditions

In this paper, we consider direct and inverse problems for the two-dimensional wave equation. The direct problem is an initial boundary value problem for this equation with nonlocal boundary conditions. In the inverse problem, it is required to find the time-variable coefficient at the lower term of the equation. The classical solution of the direct problem is presented in the form of a biorthogonal series in eigenvalues and associated functions, and the uniqueness and stability of this solution are proven. For solution to the inverse problem, theorems of existence in local, uniqueness in global, and an estimate of conditional stability are obtained. The problems of determining the right-hand sides and variable coefficients at the lower terms from initial boundary value problems for second-order linear partial differential equations with local boundary conditions have been studied by many authors. Since the nonlinearity is convolutional, the unique solvability theorems in them are proven in a global sense. In the works, the method of separation of variables is used to find the classical solution of the direct problem in the form of a biorthogonal series in terms of eigenfunctions and associated functions. The nonlocal integral condition is used as the overdetermination condition with respect to the solution of the direct problem. The direct problem reduces to equivalent integral equations of the Fourier method. To establish integral inequalities, the generalized Gronwall-Bellman inequality is used. We obtain an a priori estimate of the solution in terms of an unknown coefficient, that are useful for studying the inverse problem.

The Analitical Solution of Linear and Non-Linear Differential- Algebraic Equations (DAEs) with Laplace-Padé Series Method

In this paper, we apply Laplace-Padé Series method to solve linear and non-linear differentialalgebraic equations (DAEs). Firstly, The basic properties of the Laplace-Padé Series method are given. Secondly, we calculate the arbitrary order power series of differential-algebraic equations (DAEs), then convert it to the series form Laplace-Padé. Then, the three differential-algebraic equations (DAEs) are solved by Laplace-Padé Series method. It was seen that the method gave effective and fast results. Therefore, the method can be easily applied to linear and non-linear differential-algebraic equations (DAEs) problems in different fields.

Incoherent phenomena in anisotropic periodic structures: from modeling to experimental demonstration.

The periodic structures are widely studied in numerous optical applications and there is a number of good tools for numerical modeling of such a structures (for example rigorous coupled-wave analysis, finite-difference time-domain, finite element method etc.). However, when it comes to the modeling of incoherent effects in many cases of practical interest, the current methods are not rigorous enough or depend on computationally demanding averaging of coherent response. In this paper, we present a novel approach to modeling of incoherent effects in structures with lateral periodicity based on scattering matrix formalism, as a way to describe optical response of a structure, and on application of incoherent wave summation in the form of infinite geometric series and generalized Mueller matrix calculus. This method can be combined with any of the existing coherent methods of modeling periodic structures and it offers significantly faster computational performance than partially coherent/incoherent methods based on averaging. It is compared with other methods for modeling of incoherent effects and also with experimental spectroscopic data. This method is then used to explain phenomena emerging from the complex interaction between diffraction grating and thick substrate.

Clozapine Withdrawal Catatonia: A Case Series and Review of Literature

Background: Catatonia has been reported with withdrawal of medications. Among the various psychotropics, clozapine has been implicated to cause catatonia when abruptly withdrawn. The data regarding clozapine withdrawal catatonia are scarce and are mostly available in the form of case reports and series. Aim: In this case series, we present three cases of clozapine withdrawal catatonia and review the available literature on clozapine withdrawal clozapine. Results: All the three patients developed catatonia within 48 h to 14 days of stoppage of clozapine in the doses of 100–350 mg/day. Two of the patients experiencing clozapine withdrawal improved with reinstitution of clozapine in the previous doses along with benzodiazepines. However, one patient additionally required electroconvulsive therapy (ECT) for the management of withdrawal catatonia. A review of literature showed that clozapine withdrawal catatonia has male preponderance and has been reported with withdrawal of clozapine doses of 50–550 mg/day. The catatonia usually starts in 48 h to 2 weeks of stopping clozapine. Available literature suggests that most of the patients have been managed with restarting of clozapine, along with lorazepam and occasional patients require ECT. Conclusions: To conclude our case series and the available review of literature suggests that sudden discontinuation of clozapine can lead to withdrawal catatonia. Our cases also highlight the importance of reviewing treatment history, especially of abrupt discontinuation of clozapine when a patient on clozapine present with catatonia. This can be very helpful in deciding about further management.

Economic Sector Potential Analysis of Kutai Kartanegara and Penajam Paser Utara Regencies in East Kalimantan as Indonesia's New Capital City

Indonesia plans to relocate its capital from Jakarta to East Kalimantan (IKN) to promote balanced development. The 15 to 20 years IKN megaproject necessitates regional development planning and economic assessments for Kutai Kartanegara and Penajam Paser Utara Regencies. This study aims to identify and analyze the leading economic sectors in Kutai Kartanegara and Penajam Paser Utara. Leading sectors and the structure of regional economies can be identified through (1) Location Quotient (LQ) analysis to determine the base and non-base sectors and (2) Shift-Share analysis to determine changes and shifts in economic structure. The research utilized secondary data in the form of time series of Gross Regional Domestic Product (GRDP) for Kutai Kartanegara and Penajam Paser Utara Regencies from 2013 to 2022. The analysis of Kutai Kartanegara Regency revealed three basic sectors and fourteen non-basic sectors. North Penajam Paser Regency, on the other hand, has ten basic sectors and seven non-basic sectors. The shift-share analysis results indicated that the economic sectors in Kutai Kartanegara Regency are superior, prospective, and mainstay sectors. Meanwhile, in Penajam Paser Utara Regency, the leading, prospective, mainstay, and lagging sectors

Supersymmetric Quantum Mechanics on a noncommutative plane through the lens of deformation quantization

A gauge invariant mathematical formalism based on deformation quantization is outlined to model an N=2 supersymmetric system of a spin 1/2 charged particle placed in a nocommutative plane under the influence of a vertical uniform magnetic field. The noncommutative involutive algebra (C∞(R2)[[ϑ]],∗r) of formal power series in ϑ with coefficients in the commutative ring C∞(R2) was employed to construct the relevant observables, viz., SUSY Hamiltonian H, supercharge operator Q and its adjoint Q† all belonging to the 2 × 2 matrix algebra M2(C∞(R2)[[ϑ]],∗r) with the help of a family of gauge-equivalent star products ∗r. The energy eigenvalues of the SUSY Hamiltonian all turned out to be independent of not only the gauge parameter r but also the noncommutativity parameter ϑ. The nontrivial Fermionic ground state was subsequently computed associated with the zero energy which indicates that supersymmetry remains unbroken in all orders of ϑ. The Witten index for the noncommutative SUSY Landau problem turns out to be −1 corroborating the fact that there is no broken supersymmetry for the model we are considering.

Pengaruh Indeks Pembangunan Manusia (IPM) Dan Pertumbuhan Usaha Kecil (Mikro) Terhadap Pertumbuhan Ekonomi Di Papua Tahun 2014-2023

This study aims to analyze the effect of the Human Development Index and (small) business growth on economic growth in 2014-2024. The independent variable is the influence of the Human Development Index and business growth (small). And the dependent variable is economic growth. This study uses secondary data in the form of a time series, namely a time series for 10 years, namely from 2014-2024. Data obtained from BPS Indonesia. The research method is quantitative with data analysis used by researchers, namely classical assumption tests (normality tests, multicollinearity tests, heteroscedasticity tests, autocorrelation tests), multiple linear regression and statistical tests (determination coefficient tests (R2), t tests and F tests) using eviews-10. The results of partial regression coefficient (t-test) show that the human development index has no effect on economic growth. While Small Business Growth (Micro) Significant effect on economic growth. The results of the F test analysis show that there is a joint and significant influence of the two independent variables, namely analyzing the influence of the Human Development Index and business growth (small) on the dependent variable, namely country growth.

Non-polynomial interactions as a path towards a non-renormalizable UV-completion

We propose a new class of single-field scalar quantum field theories with non-polynomial interactions leading to a two-point Green's function that can be naturally continued beyond the naive cutoff scale. This provides a new prospect for self-completing theories in the UV-domain. In our approach, the formal power series for the scalar potential has a vanishing radius of convergence and is defined through Borel resummation. We discuss concrete examples, among others with a spectral function that vanishes at large momenta, potentially leading to an asymptotically free theory. Finally, we give an outlook on future research, with a view towards possible applications to inflation and gravity.

Mathematical analysis of a real time dynamical system: Interaction between Agricultural Variables

In this study, we are interested in the investigation and analysis of a mathematical model for the growth of normal agricultural biomass. The model is divided into four compartments as normal Agricultural assets, auxiliary Agricultural assets, Industrial assets, and Ecospherical assets. We applied the Laplace Decomposition Method to obtain approximate solutions in the form of infinite series and numerical justification was performed on the model parameter values with the aid of Maple 18 software. We studied the effect of varying the growth rate of normal agriculture on the yield of agricultural assets and mathematical analyses of the model equation to its uniqueness and stability of equilibrium are carried out. From the results, it was observed that the yield of normal Agricultural assets decreases due to the decrease in the growth rate coefficient of normal agriculture from 10 % to 90 % and the yield of normal Agricultural assets increases due to the increase in the growth rate coefficient of normal agriculture from 110 % to 190 %. We observed a loss in biodiversity when the growth rate coefficients of normal agriculture decreased from 90 %, 20 %, and 10 %, and a biodiversity gain was observed due to the increase of the growth rate coefficients of normal Agriculture from 110 % to 190 %.

Calibration Optimization of Kinematics and Dynamics for Delta Robot Driven by Integrated Joints in Machining Task

For the application of Delta robots with a 3-R(RPaR) configuration in machining tasks, this paper constructed a 54-parameter kinematic error model and a simplified dynamic model incorporating an integrated joint’s position error and friction, respectively. Utilizing Singular Value Decomposition (SVD) of the Linear Model Coefficient Matrix (LMCM) and the coefficient chart, a criterion for identifiability of error components is established. For good identification results, the optimal measurement surface with Fourier series form is obtained using a combination of the Hook–Jeeves Direct Search Algorithm (DSA) and Inner Point Method (IPM). The friction coefficients and other dynamic parameters are obtained through fitting the integrated joint torque-angle pairs measured along specific trajectories using nonlinear least squares regression. The validation of the calibration process is conducted through simulations and experiments. The calibration results provide a foundation for the precise control of integrated joints and the high-precision motion of robots.

Computational approach and convergence analysis for interval-based solution of the Benjamin–Bona–Mahony equation with imprecise parameters

PurposeTo provide a new semi-analytical solution for the nonlinear Benjamin–Bona–Mahony (BBM) equation in the form of a convergent series. The results obtained through HPTM for BBM are compared with those obtained using the Sine-Gordon Expansion Method (SGEM) and the exact solution. We consider the initial condition as uncertain, represented in terms of an interval then investigate the solution of the interval Benjamin–Bona–Mahony (iBBM).Design/methodology/approachWe employ the Homotopy Perturbation Transform Method (HPTM) to derive the series solution for the BBM equation. Furthermore, the iBBM equation is solved using HPTM to the initial condition has been considered as an interval number as the coefficient of it depends on several parameters and provides lower and upper interval solutions for iBBM.FindingsThe obtained numerical results provide accurate solutions, as demonstrated in the figures. The numerical results are evaluated to the precise solutions and found to be in good agreement. Further, the initial condition has been considered as an interval number as the coefficient of it depends on several parameters. To enhance the clarity, we depict our solutions using 3D graphics and interval solution plots generated using MATLAB.Originality/valueA new semi-analytical convergent series-type solution has been found for nonlinear BBM and interval BBM equations with the help of the semi-analytical technique HPTM.

Correlation properties of complete code of binary spread spectrum phase-shift keyed signals with polarization coding

Problem statement. Investigation of correlation properties of complete code of binary spread spectrum phase-shift keyed signals as the limiting case of large systems is a topical task for building large systems of binary spread spectrum phase-shift keyed signals with polarization coding with optimal correlation properties. Also, this task is of independent academic interest due to the fact that the alphabet of symbols for these signals lacks multicasting properties unlike the familiar cases of complete codes of spread spectrum phase-shift keyed signals. Objective. To accurately define the distribution laws as well as the moments about zero and the mean for the n-th order of presented values of aperiodic and periodic correlation functions of the complete code of binary spread spectrum phase-shift keyed signals with polarization coding. To offer approximations of accurate distribution laws suitable for engineering applications. Results. The accurate distribution laws for presented values of aperiodic and periodic correlation functions of the complete code of binary spread spectrum phase-shift keyed signals with polarization coding were found in the form of the related distribution series. The analytic expressions for the n-th order of presented values of these functions for the complete code of the specified signals were assigned. The calculation example for the distribution series of presented values of aperiodic and periodic correlation functions for the complete code of the specified signals with the length of vector code sequences N=4 was given. The values of the relative frequencies of the correlation functions values for this case were found by the means of direct computing and their exact match with the corresponding predicted probability values was demonstrated. The approximations of the accurate distribution laws were given: for periodic correlation functions case – by Gaussian probability density, and for the aperiodic functions case – by the Pearson curve of VII type. Practical relevance. The found accurate laws for presented values of aperiodic and periodic correlation functions of the complete code of binary spread spectrum phase-shift keyed signals with polarization coding and their approximations allow to assess the correlation properties of large systems of such signals.

Analytical and Numerical Investigation for the Inhomogeneous Pantograph Equation

This paper investigates the inhomogeneous version of the pantograph equation. The current model includes the exponential function as the inhomogeneous part of the pantograph equation. The Maclaurin series expansion (MSE) is a well-known standard method for solving initial value problems; it may be easier than any other approaches. Moreover, the MSE can be used in a straightforward manner in contrast to the other analytical methods. Thus, the MSE is extended in this paper to treat the inhomogeneous pantograph equation. The solution is obtained in a closed series form with an explicit formula for the series coefficients and the convergence of the series is proved. Also, the analytic solutions of some models in the literature are recovered as special cases of the present work. The accuracy of the results is examined through several comparisons with the available exact solutions of some classes in the relevant literature. Finally, the residuals are calculated and then used to validate the accuracy of the present approximations for some classes which have no exact solutions.