Euler Transformation Research Articles

Development of a control algorithm for a boost converter with the possibility of dynamic correction of control system parameters

RELEVANCE of the study lies in the development of an algorithm for controlling a DC voltage converter capable of providing a high-quality transient process with a wide change in the input parameters of the control object, affecting its nonlinear properties. purpose. THE PURPOSE. To consider methods for the development of continuous and discrete control systems for a step-up DC voltage converter and to obtain an analytical dependence of accounting for the nonlinear properties of the converter that affect the quality of regulation of the output voltage of the voltage stabilizer METHODS. The method of the average geometric root was chosen as a method for calculating the coefficients of the DC voltage converter control system, and the current circuit is adjusted using the technical optimum method, and the voltage circuit using the symmetric optimum method. The obtained analytical solutions of mathematical models and simulation models were compared in the SimInTech software environment. results. RESULTS. The simulation results show that the analytical solution of the mathematical model of the voltage stabilization system has a shorter transition time than the simulation results. This is due to the fact that in the mathematical model according to which the continuous control algorithm was synthesized, the presence of a power input filter, as well as the degree of their precharge, is not taken into account. Because of this, the transition time on simulation models is slower, applied 4 times than in the mathematical model. conclusion. CONCLUSION. When comparing the algorithms with each other, it can be seen that the algorithm obtained by converting a continuous algorithm by the Tusten method has the shortest transition time than all other algorithms. The continuous algorithm and the algorithm obtained by the inverse Euler transformation method have a speed close to each other, and the algorithm obtained by the direct Euler transformation turns out to be the slowest.

Binomial Transforms of k-Narayana Sequences and Some Properties

The aim of the study is to obtain new binomial transforms for the $k-$ Narayana sequence. The first of these is the binomial transform, which is its normal form, and in the first step, after finding the recurrence relation of this new binomial transform, the generating function and Binet formula were obtained. Finally, Pascal's triangle was calculated. In the rest of the article, $k-$binomial transform was performed for the $k-$ Narayana sequence and the recurrence relation, generating function, Binet formula and Pascal's triangle were examined for the new sequence obtained. Then, by performing the falling binomial transform and the rising binomial transform, the features listed above were found again for these sequences.

The Properties of Binomial Transforms for Modified (s,t)-Pell Matrix Sequence

In this study we investigate a generalization of modified Pell sequence, which is called (s,t)-modified Pell sequence. By considering this sequence, we define the matrix sequence whose elements are (s,t)-modified Pell numbers. Furthermore, we define various binomial transforms for modified (s,t)-Pell matrix sequence. Finally, we give some relationships for (s,t)-modified Pell matrix sequences such as Binet formulas, the generating functions and some sum formulas...

Binomial Transforms of the Third-Order Jacobsthal and Modified Third-Order Jacobsthal Polynomials

In this study, we define the binomial transforms of third-order Jacobsthal and modified third-order Jacobsthal polynomials. Further, the generating functions, Binet formulas and summation of these binomial transforms are found by recurrence relations. Also, we establish the relations between these transforms by deriving new formulas. Finally, the Vajda, d'Ocagne, Catalan and Cassini formulas for these transforms are obtained.

Z-transform Solution for Partial Difference Equations

The aim of this research is to study the Z transformation to solve linear partial difference equations. This is due to the fact that linear partial difference equations cannot be solved directly using the Z transformation, and the research concluded that direct partial difference conditions cannot be treated directly by the Z transformation except after converting the partial difference equations to linear difference equations using one of the transformation methods. The research recommended using Binomial transformation to solve partial difference equations.

Estimating the strong coupling from τ decay using accelerating series convergence

We apply the Euler transformation to accelerate the convergence of the QCD perturbative series with the aim to determine the strong coupling αs in terms of the total τ-decay rate rτ. The variation of the result with the order of the QCD perturbation theory is small and comparable with the uncertainties of rτ. We also present an estimate of a range of the yet unknown 5th and 6th order coefficients k5 and k6 of the Adler function.

Abstract 3529: Leveraging deep learning for fully automated analysis of pre-clinical mouse positron emission tomography

Abstract Turning early-cancer diagnosis into actionable treatment often relies on highly accurate and sensitive imaging techniques to guide surgical intervention or to monitor therapeutic efficacy. Earli is developing a highly sensitive, orthogonal approach that uses genetic constructs to usurp dysregulated cancer pathways to force the tumor to produce a PET reporter gene, enabling the use of radiotracers amenable to positron emission tomography/computed tomography (PET/CT) to guide precision imaging. However, analysis of PET/CT images using standard manual and semi-automated methods is challenging resulting in reduced experimental throughput and user variability, highlighting the need for a fully automated PET/CT analysis pipeline using Deep Learning (DL). To increase pre-clinical throughput and reduce inter-user variability, we developed an automated DL processing pipeline in Python to perform three major tasks: separation of multi-mouse bed data for PET uptake quantification by mouse, segmentation of tumors and background organs, and quantification of PET signal for PK/PD analysis. Preclinical PET/CT data was acquired using a 4 animal, multi-mouse bed and separated into individual mice by co-registering the reconstructed CT image against a multi-mouse bed reference mask using a rigid 3D Euler transformation algorithm and cropping at fixed indices. Following mouse separation, a 3D nnUNet architecture is used to perform semantic segmentation of regions of interest (ROI) on CT for bi-hemispheric subcutaneous tumors, lungs, liver, kidneys, spleen, and the bladder. nnUNet was trained on PET/CT of 311 mice consisting of a mixture of naïve and tumor-bearing animals subcutaneously implanted with H1299 cells using a five-fold cross-validation strategy with 1000 epochs per fold. Model performance was evaluated by comparing the network prediction to the reference manually annotated masks using the Dice coefficient. PET uptake is reported as percent injected dose per milliliter (%ID/mL) or standardized uptake value (SUV). Segmentation performance results for the hold-out set identified mean Dice scores greater than 0.80 for all ROIs, reflecting the similarity between model predictions and human annotations. The automated pipeline reduced the analysis time from 5.5-6 hours per mouse when using traditional manual/semi-automatic approaches to approximately 15 minutes. In summary, we developed a fully automated DL-based PET/CT quantification pipeline for pre-clinical mouse studies that provides accurate ROI segmentation and PET uptake quantification, significantly increasing experimental throughput and reducing inter-user variability. Further improvements to model inference include loss functions weighted for poor performing ROIs and addition of lung nodule segmentation for eventual translation to humans as an accompaniment to Earli’s theranostic programs. Citation Format: Hung-Yu Henry Lee, Mohammed Goryawala, Tim Sproul, Maggie Louie, David Suhy. Leveraging deep learning for fully automated analysis of pre-clinical mouse positron emission tomography [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 3529.

The shape of an axisymmetric meniscus in a static liquid pool: effective implementation of the Euler transformation

Abstract We examine the classical problem of the height of a static liquid interface that forms on the outside of a solid vertical cylinder in an unbounded stagnant pool exposed to air. Gravitational and surface tension forces compete to affect the interface shape as characterized by the Bond number. Here, we provide a convergent power series solution for interface shapes that rise above or fall below the horizontal pool as a function of contact angle and Bond number. We find that the power series solution expressed in terms of the radial distance from the wall is divergent, and thus rewrite the divergent series as a new power series expressed as powers of an Euler transformed variable; this series is modified to match the large distance asymptotic behaviour of the meniscus. The Euler transformation maps non-physical singularities to locations that do not restrict series convergence in the physical domain, while the asymptotic modification increases the rate of convergence of the series overall. We demonstrate that when the divergent series coefficients are used to implement the Euler transformation, finite precision errors are incurred, even for a relatively small number of terms. To avoid such errors, the independent variable in the governing differential equation is changed to that of the Euler transform, and the power series is developed directly without using the divergent series. The resulting power series solution is validated by comparison with a numerical solution of the interface shape and the small Bond number matched asymptotic solution for the height of the interface along the cylinder developed by Lo (1983, J. Fluid Mech., 132, p.65-78). The convergent power series expansion has the ability to exceed the accuracy of the matched asymptotic solution for any Bond number given enough terms, and the recursive nature of the solution makes it straightforward to implement.

Income inequality and its association with COVID-19 cases and deaths: a cross-country analysis in the Eastern Mediterranean region

IntroductionThere is limited evidence on the associations between economic and social disparities in the Eastern Mediterranean region (EMR) with COVID-19 infections and deaths. This study aims to investigate the relationship...

Design of Discrete and Hybrid Nonlinear Control Systems

In this article the new method of discrete control systems design for nonlinear plants with differentiable nonlinearities is suggested. The increasing demands on the quality of control processes and the widespread use of computer technology provide ample opportunities for the design and implementation of digital control systems. However, discrete models of control plants are needed to solve this problem. In the case of linear plants, such models are created on the basis of z-transformation, Euler or Tustin formulas. In the case of nonlinear plants, these transformations are not applicable, so a large number of approximate discretization methods have been developed to date. Euler and Runge-Kutt transformations are used for these purposes most often, but they lead to satisfactory results only with very small period of discretization. In the case of automatic control systems, this requires the use of digital automation tools with very high speed, which is often economically impractical. Methods of discretization with a long period were most often developed on the basis of decomposition into series of the right-hand sides of the differential equations, transformed on Euler. Here, firstly, the problem of selecting the number of the series members, which to be retained arises, and secondly, already in the third or fourth order of the plant, the calculating ratios turn out to be extremely complex. The discretization method suggested below differs in that it is not the equations of nonlinear plants in the Cauchy form that are discretized, but the corresponding quasilinear model. In this case, a modified trapezoid method is used, and the discretization purpose is not the most accurate approximation of the original equations of the plant, but the stability of a closed nonlinear control system with rather big period. This system is designed using the algebraic polynomial-matrix method for designing of the nonlinear control systems. As a result, a hybrid nonlinear system with fairly simple algebraic calculation expressions is formed. The suggested approach makes it possible to create the control systems for nonlinear controlled plants using conventional computational automation tools.

The ℓ-adic hypergeometric function and associators

We introduce an $\ell$-adic analogue of Gauss's hypergeometric function arising from the Galois action on the fundamental torsor of the projective line minus three points. Its definition is motivated by a relation between the KZ-equation and the hypergeometric differential equation in the complex case. We show two basic properties, analogues of Gauss's hypergeometric theorem and of Euler's transformation formula for our $\ell$-adic function. We prove them by detecting a connection of a certain two-by-two matrix specialization of even unitary associators with the associated gamma function, which extends the result of Ohno and Zagier.

Research on Dynamic Modeling Measurement and Control of Cable Traction Devices for Electro-Optical Unmanned Systems

In order to realize the high-precision variable direction cable control of the electro-optical unmanned system in non-electromagnetic remote control, a cable traction device measurement and control with characteristics of variable direction traction, rapid installation, and lightweight portability were proposed. Fan-shaped connect rod mechanism and U-shaped groove fixed pulley group were added to it, which can realize multi-direction traction without derailment on the basis of the cable limit and alleviate the cable fracture caused by mechanical wear. Introducing Euler transformation and analyzing the dynamics of the cable, the whole operation process, and the tension detection model was established. A Kalman Filter traction planning method was proposed to solve the problems of inertia delay and emergency stop of the unmanned vehicles after a sudden direction change. In order to verify the effectiveness, an experimental platform for the cable traction system of a 50kg wheeled and 150kg tracked unmanned system was built for simulation and experimental testing. The results show that the cable system has good dynamic variable traction, which can meet the multi-terrain control ability of an electro-optical unmanned system in a complex field environment.

Triangular recurrences, generalized Eulerian numbers, and related number triangles

Many combinatorial and other number triangles are solutions of recurrences of the Graham–Knuth–Patashnik (GKP) type. Such triangles and their defining recurrences are investigated analytically. They are acted upon by a transformation group generated by two involutions: a left–right reflection and an upper binomial transformation, acting row-wise. The group also acts on the bivariate exponential generating function (EGF) of the triangle. By the method of characteristics, the EGF of any GKP triangle has an implicit representation in terms of the Gauss hypergeometric function. There are several parametric cases when this EGF can be obtained in closed form. One is when the triangle elements are the generalized Stirling numbers of Hsu and Shiue. Another is when they are generalized Eulerian numbers of a newly defined kind. These numbers are related to the Hsu–Shiue ones by an upper binomial transformation, and can be viewed as coefficients of connection between polynomial bases, in a manner that generalizes the classical Worpitzky identity. Many identities involving these generalized Eulerian numbers and related generalized Narayana numbers are derived, including closed-form evaluations in combinatorially significant cases.

On the evaluation of the Appell F2 double hypergeometric function

The transformation theory of the Appell F2(a,b1,b2;c1,c2;x,y) double hypergeometric function is developed to obtain a set of series representations of F2 which provide an efficient way to evaluate F2 for real values of its arguments x and y and generic complex values of its parameters a,b1,b2,c1 and c2 (i.e. in the nonlogarithmic case). This study rests on a classical approach where the usual double series representation of F2 and other double hypergeometric series that appear in the intermediate steps of the calculations are written as infinite sums of one variable hypergeometric series, such as the Gauss F12 or the F23, various linear transformations of the latter being then applied to derive known and new formulas. Use of the three well-known Euler transformations of F2 on these results allows us to obtain a total of 44 series which form the basis of the Mathematica package AppellF2.wl, dedicated to the evaluation of F2. A brief description of the package and of the numerical analysis that we have performed to test it is also presented. Program summaryProgram Title: AppellF2.wlCPC Library link to program files:https://doi.org/10.17632/n9v6bwpsyd.1Licensing provisions: GPLv3Programming language: Wolfram Mathematica version 11.3 and beyondNature of problem: Numerical evaluation of the double hypergeometric Appell F2 function for real values of its variables and generic complex values of its Pochhammer parametersSolution method: Mathematica implementation of a set of transformation formulas of the Appell F2 function

Binomial transformation applied to presence-absence community data

Community data is often transformed or standardized to meet the requirements and assumptions of multivariate analysis. While these methods are usually appropriate for abundance data, they are seldom applied to presence-absence data. Here, a method of transforming a binary matrix using the binomial probability is described. Number of trials (n), number of successes (x) and probability of success (p) are necessary to compute the binomial probability. Successes were defined as the number of sites where the species occurrence can be considered; trials were equal and greater than the number of successes. The actual occurrence of each species along the gradient was considered the probability of success. The Mantel statistic associated with the binomially transformed distance matrix and the distance matrix based on binary data were used to choose an appropriate binomial transformation. The chosen binomial transformation gave greater value to species indicating habitat typologies. Binomially transformed data rendered results closer to expectations.

The chaotic monopolist revisited with bounded rationality and delay dynamics

Two types of boundedly rational monopolists are studied when the marginal revenue is not necessarily negative sloping. A limited monopolist (ℓ-monopolist) knows only the price and output values in two previous periods. A knowledgeable monopolist (k-monopolist) knows the analytic expression of the marginal profit function and forms sales expectations based on past market information. The k-monopolist adjusts its output levels according to the usual gradient process, while the ℓ-monopolist approximates the marginal profit with a two-point finite difference formula. Stability conditions and complex dynamics are studied in discrete and continuous time scales. In the discrete model, the two monopolists exhibit different dynamics after the stability loss. The ℓ-monopolist has a cascade of a Neimark-Sacker bifurcation. In contrast, the k-monopolist has two different routes, a period-doubling and a Neimark-Sacker bifurcation, depending on how to form sales expectations. In the continuous case, the discrete models are transformed into continuous models via Euler transformation. The stability switching curves are analytically constructed and the directions of stability switching are characterized by computing the stability index for each point of the curves. It is numerically demonstrated that two monopolists exhibit similar dynamics and the k-monopolist approximates the ℓ-monopolist under a special circumstance.

A Combinatorial Bijection on k-Noncrossing Partitions

For any integer k ≥ 2, we prove combinatorially the following Euler (binomial) transformation identity $${\rm{NC}}_{n + 1}^{(k)}(t) = t\sum\limits_{i = 0}^n {\left({\matrix{n \cr i \cr}} \right)} {\rm{NW}}_i^{(k)}(t),$$ where NC (k)m (t) (resp. NW (k)m (t)) is the sum of weights, tnumber of blocks, of partitions of {1,…,m} without k-crossings (resp. enhanced k-crossings). The special k = 2 and t = 1 case, asserting the Euler transformation of Motzkin numbers are Catalan numbers, was discovered by Donaghey 1977. The result for k = 3 and t = 1, arising naturally in a recent study of pattern avoidance in ascent sequences and inversion sequences, was proved only analytically.

Direct Position Determination of Non-Circular Sources for Multiple Arrays via Weighted Euler ESPRIT Data Fusion Method

In recent years, direct position determination (DPD) with multiple arrays for non-circular (NC) signals is a hot topic to research. Conventional DPD techniques with spectral peak search methods have high computational complexity and are sensitive to the locations of the observation stations. Besides, there will be loss when the signal propagates in the air, which leads to different received signal-to-noise ratios (SNRs) for each observation station. To attack the problems mentioned above, this paper derives direct position determination of non-circular sources for multiple arrays via weighted Euler estimating signal parameters viarotational invariance techniques (ESPRIT) data fusion (NC-Euler-WESPRIT) method. Firstly, elliptic covariance information of NC signals and Euler transformation are used to extend the received signal. Secondly, ESPRIT is applied to avoid the high-dimensional spectral function search problem of each observation station. Then, we combine the information of all observation stations to construct a spectral function without complex multiplication to reduce the computational complexity. Finally, the data of each observation station is weighted to compensate for the projection error. The consequence of simulation indicates that the proposed NC-Euler-WESPRIT algorithm not only improves the estimation performance, but also greatly reduces the computational complexity compared with subspace data fusion (SDF) technology and NC-ESPRIT algorithm.

Extraordinary broadband impedance matching in highly dispersive media - the white light cavity approach.

Suppressing reflections from material boundaries has always been an objective, common to many disciplines, where wave phenomena play a role. While impedance difference between materials necessarily leads to a wave reflection, introducing matching elements can almost completely suppress this phenomenon. However, many impedance matching approaches are based on resonant conditions, which come at a price of narrow bandwidth operation. Although various impedance matching architectures have been developed in the past, many of them fail to produce a broadband and flat (ripple-free) transmission, particularly in the presence of strong chromatic dispersion. Here we propose and demonstrate an approach for designing an optimal matching stack capable of providing a flat broadband transmission even in the presence of significant group velocity dispersion. As an experimental example for the method verification, we used a strong modal dispersion in a rectangular waveguide, operating close to a mode cut-off. The waveguide core consists of alternating polymer sections with a variable filling factor, realized using additive manufacturing. As a result, a broadband matching in the range of 7-8GHz was demonstrated and proved to significantly outperform the standard binomial transformer solution. The proposed method can find use across different disciplines, including optics, acoustics and wireless communications, where undesired reflections can significantly degrade system's performances.

Self-Supervised Graph Convolutional Network for Multi-View Clustering

Despite the promising preliminary results, existing graph convolutional network (GCN) based multi-view learning methods directly use the graph structure as view descriptor, which may inhibit the ability of multi-view learning for multimedia data. The major reason is that, in real multimedia applications, the graph structure may contain outliers. Moreover, they fail to take advantage of the information embedded in the inaccurate clustering labels obtained from their proposed methods, resulting in inferior clustering results. These observations motivate us to study whether there is a better alternative GCN based framework for multi-view clustering. To this end, in this paper, we propose an end-to-end self-supervised graph convolutional network for multi-view clustering (SGCMC). Specifically, SGCMC constructs a new view descriptor for graph-structured data by mapping the raw node content into the complex space via Euler transformation, which not only suppresses outliers but also reveals non-linear patterns embedded in data. Meanwhile, the proposed SGCMC uses the clustering labels to guide the learning of the latent representation and coefficient matrix, and the latter in turn is used to conduct the subsequent node clustering. By this way, clustering and representation learning are seamlessly connected, with the aim to achieve better clustering results. Extensive experiments indicate that the proposed SGCMC outperforms the state-of-the-art methods.