Function Of Angle Research Articles

Abstract A023: RNA secondary structures mediate circular RNA stability and function

Abstract Our group recently discovered that the circular RNA (circRNA), CDR1as, promotes lung cancer metastasis in part through the stabilization of the coding gene, CDR1. The purpose of this study was to identify intramolecular RNA secondary structures of CDR1as and determine whether there is a functional relationship between the CDR1as secondary structure and non-small cell lung cancer (NSCLC) metastasis. We employed the chemical probing approach selective 2’- hydroxyl acylation analyzed by primer extension and mutational profiling (SHAPE-MaP) to experimentally inform structure predictions of CDR1as. The SHAPE-MaP profiling experiments revealed that CDR1as is remarkably unstructured overall, with an exception of a highly probable and consistent stem-loop structure embedding the CDR1as backsplice junction (BSJ). Additionally, BSJ-embedding secondary structures were identified in all other mammalian circRNAs studied in a similar chemical probing experiment. To evaluate the role of the BSJ structure on CDR1as expression, we sterically disrupted the BSJ structure using a chemically modified, inert antisense oligonucleotide (BSJ-ASO) lacking a gapmer in order to block RNAse H activity. After transfection of the structure disrupting BSJ-ASO into several cell lines, we observed a 90-95% reduction of CDR1as expression by the BSJ-ASO by 24 hours. Furthermore, the BSJ-ASO significantly inhibited cancer cell proliferation and spheroid formation in several NSCLC models. Strikingly, using RNA stability assays we observed that the BSJ-ASO caused dramatic reductions in CDR1as levels within 5 minutes of transfection, suggesting a possibly hydrolytic process. A functional screen of silencing curated CDR1as RNA-binding proteins failed to rescue the loss of CDR1as expression following BSJ-ASO treatment. We next tested whether an RNA-catalyzed mechanism of action is possible. By incubating total RNA with the BSJ-ASO in buffers of varying magnesium chloride concentrations in vitro, we observed a dramatic decrease in CDR1as levels similar to that of the BSJ-ASO cellular transfection experiments, suggestive of ribozyme-like activity. Interestingly, use of a primer mapping approach indicated two putative cut sites within CDR1as. Further chemical probing following treatment with the BSJ-ASO revealed a new, highly probable secondary structure upstream of the BSJ, which appears similar to a hairpin ribozyme when modeled two-dimensionally. Taken together, our work reveals that intramolecular RNA secondary structures can have critical roles in maintaining circRNA cellular stability and function, and strategic steric disruption of these structures may induce circRNA self-cleavage. Citation Format: Aaron C Chack, Emily B Harrison, Caroline J Aufgebauer, Mark A Boerneke, Patrick S Irving, Edgar M Faison, Jingyu Zhao, Qi Zhang, Kevin M Weeks, Chad V Pecot. RNA secondary structures mediate circular RNA stability and function [abstract]. In: Proceedings of the AACR Special Conference in Cancer Research: RNAs as Drivers, Targets, and Therapeutics in Cancer; 2024 Nov 14-17; Bellevue, Washington. Philadelphia (PA): AACR; Mol Cancer Ther 2024;23(11_Suppl):Abstract nr A023.

Integral Sliding Mode‐Composite Nonlinear Feedback Control Strategy for Microgrid Inverter Systems

To enhance the dynamic performance and robustness of the voltage control system of islanded microgrid inverters, a new control strategy combining integral sliding mode (ISM) control and composite nonlinear feedback (CNF) control is proposed. In ISM control, firstly, a new reaching law is designed to improve movement quality in the reaching phase by improving the power term and introducing the inverse tangent function. Then, to improve disturbance observation accuracy, a variable gain extended state observer is designed by improving the regulation mechanism of the state variables according to deviation control. Using the idea of variable damping, linear and nonlinear feedback are combined into CNF control. Specifically, linear feedback provides a small damping ratio for faster system response, while nonlinear feedback increases the damping ratio to improve steady‐state performance. Simulation results show that the integral sliding mode‐composite nonlinear feedback (ISM‐CNF) control strategy cam balances convergence speed and chattering better and achieves higher steady‐state accuracy than conventional strategies. Moreover, ISM‐CNF control has better robustness to reference voltage variations and disturbances caused by sudden load changes. Therefore, the ISM‐CNF control strategy can accomplish voltage control of islanded microgrid inverters quickly and steadily, effectively suppressing system disturbances and enhancing stability and power quality. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

Diverse general solitary wave solutions and conserved currents of a generalized geophysical Korteweg–de Vries model with nonlinear power law in ocean science

This article presents an analytical investigation performed on a generalized geophysical Korteweg–de Vries model with nonlinear power law in ocean science. To start with, achieving diverse solitary wave solutions to the generalized power‐law model involves using wave transformation, which reduces the model to a nonlinear ordinary differential equation. A direct integration approach is adopted to construct solutions in the beginning. This brings the emergence of interesting solutions like non‐topological solitons, trigonometric functions, exponential functions, elliptic functions, and Weierstrass functions in general structures. Besides, in a bid to secure more general exact solutions to the model, one adopts the extended Jacobi elliptic function expansion technique (for some specific cases of ). Thus, various cnoidal, snoidal, and dnoidal wave solutions to the understudied model are attained. The copolar trio explicated in a tabular form reveals that these solutions can be relapsed to various hyperbolic and trigonometric functions under certain criteria. Additionally, diverse graphical exhibitions of the dynamical attributes of the gained results are presented in a bid to have a sound understanding of the physical phenomena of the underlying model. Later, one gives the conserved vectors of the aforementioned equation by employing the standard multiplier approach.

Simulation of spatially varying non-stationary seismic waves using random frequencies and non-uniform fast fourier transform

The simulation of spatially varying non-stationary seismic waves is a crucial consideration for the seismic analysis of engineering structures. The traditional approach often incurs substantial computational expenses and suffers from low efficiency due to the extensive implementation of large-scale matrix factorizations at numerous sampling points in both time and frequency domains. In this study, an enhanced approach is developed for the efficient simulation of non-stationary seismic waves. The core of this approach lies in the utilization of random frequency sampling coupled with time-domain interpolation to reduce matrix factorizations, and non-uniform fast Fourier transform for expediting the summation of trigonometric functions. A parametric analysis is conducted to investigate the effect of vital parameters, including the decoupling strategy of time-frequency spectrum, the number of random frequencies, and the number of interpolation knots over time, on both the efficiency and accuracy of the enhanced approach. Consequently, the preferred values for these parameters are determined. By considering the simulation of seismic waves acting on a group of bridges, the enhanced approach is validated in the view of correlation functions. The results demonstrate a high level of fidelity of the simulated seismic waves and proves the effectiveness of the enhanced approach in the efficient simulation of spatially varying non-stationary earthquake ground motions. The developed approach can be used for the simulation of non-stationary seismic waves for a wide range of engineering structures.

Reinforcement learning-adaptive fault-tolerant IGC method for a class of aircraft with non-affine characteristics and multiple uncertainties

Abstract In this paper, a brand-new adaptive fault-tolerant non-affine integrated guidance and control method based on reinforcement learning is proposed for a class of skid-to-turn (STT) missile. Firstly, considering the non-affine characteristics of the missile, a new non-affine integrated guidance and control (NAIGC) design model is constructed. For the NAIGC system, an adaptive expansion integral system is introduced to address the issue of challenging control brought on by the non-affine form of the control signal. Subsequently, the hyperbolic tangent function and adaptive boundary estimation are utilised to lessen the jitter due to disturbances in the control system and the deviation caused by actuator failures while taking into account the uncertainty in the NAIGC system. Importantly, actor-critic is introduced into the control framework, where the actor network aims to deal with the multiple uncertainties of the subsystem and generate the control input based on the critic results. Eventually, not only is the stability of the NAIGC closed-loop system demonstrated using Lyapunov theory, but also the validity and superiority of the method are verified by numerical simulations.

Modified Shooting with Discretization Validation for Non-Standard Optimal Control Problem: Case Study for Four-Stage Royalty Payment Problem

A modified shooting method augmented by discretization validation is presented in this paper to address the challenges inherent in non-standard optimal control problems. Specifically, a specific case study involving four-stage royalty payment functions is focused on, with the aim of effectively optimizing these complex, non-differentiable functions. The shooting method is adapted and enhanced to compute optimal solutions, and its accuracy is rigorously confirmed through discretization techniques. The primary objectives involve maximizing the performance index and determining optimal control strategies for scenarios where the final state variable remains unknown. In this study, the royalty payment is defined as a four-stage piecewise function. The incorporation of piecewise royalty functions introduces non-differentiability at specific time intervals, necessitating innovative approaches for finding optimal solutions. This, in turn, leads to the utilization of the continuous hyperbolic tangent (tanh) function to address the non-differentiability issue. A hybrid shooting method, combining the Newton and Golden Section Search methods, is employed in the C++ programming language to compute the unknown final state value. A new natural boundary condition, based on established theory, is introduced to further facilitate the investigation. Discretization methods such as Euler, Runge-Kutta, Trapezoidal, and Hermite-Simpson approximations are employed for validation. The validation process entails the use of the AMPL programming language with the MINOS solver. Comparative analyses reveal that the modified shooting method yields more accurate optimal results than discretization methods, thus demonstrating the method’s effectiveness in addressing non-standard optimal control problems. The significance of fundamental theories in addressing real-world challenges is underscored by this research, providing valuable insights for future researchers exploring mathematical approaches in similar contexts. The study contributes to the continued relevance of the academic field, particularly in science and mathematics education.

Stability of equivariant logarithmic tangent sheaves on toric varieties of Picard rank two

Stability of equivariant logarithmic tangent sheaves on toric varieties of Picard rank two

Exploring Kink Solitons in the Context of Klein–Gordon Equations via the Extended Direct Algebraic Method

This work employs the Extended Direct Algebraic Method (EDAM) to solve quadratic and cubic nonlinear Klein–Gordon Equations (KGEs), which are standard models in particle and quantum physics that describe the dynamics of scaler particles with spin zero in the framework of Einstein’s theory of relativity. By applying variables-based wave transformations, the targeted KGEs are converted into Nonlinear Ordinary Differential Equations (NODEs). The resultant NODEs are subsequently reduced to a set of nonlinear algebraic equations through the assumption of series-based solutions for them. New families of soliton solutions are obtained in the form of hyperbolic, trigonometric, exponential and rational functions when these systems are solved using Maple. A few soliton solutions are considered for certain values of the given parameters with the help of contour and 3D plots, which indicate that the solitons exist in the form of dark kink, hump kink, lump-like kink, bright kink and cuspon kink solitons. These soliton solutions are relevant to actual physics, for instance, in the context of particle physics and theories of quantum fields. These solutions are useful also for the enhancement of our understanding of the basic particle interactions and wave dynamics at all levels of physics, including but not limited to cosmology, compact matter physics and nonlinear optics.

Stability analysis, modulation instability, and the analytical wave solitons to the fractional Boussinesq-Burgers system

Abstract The research is concerned with the novel analytical solitons to the (1+1)-D nonlinear Boussinesq-Burgers System (B-B S) in the sense of a new definition of fractional derivatives. The concerned system is helpful to describes the waves in different phenomenon,
including proliferation of waves in shallow water, oceanic waves and many others. Authors gain the solutions involving trigonometric, hyperbolic, and rational functions by using the expa function and the extended sinh-Gordon equation expansion (EShGEE) methods. Fractional derivative provides the better results than the present results. These results are helpful and useful in the different areas of applied sciences. The solutions are shown by 2-dimensional, 3-dimensional, and contour graphs. The solutions are useful in further studies of the governing model. The stability process is performed to verify that the solutions are exact and accurate. The modulation instability is used to determine the steady-state stable results to the governing equation. The techniques utilized are both simple and effective.

The Improved tan (\(\frac{\Phi(\xi)}{2}\)) -Expansion Method for The Non-dissipative Double Dispersive Equation in Microstructured Solids

In microstructured solids, the non-dissipative double dispersive equation is a fourth-order non-linear partial differential equation that arises in the study of non-dissipative strain wave propagation. Seeking the exact solution of a nonlinear partial differential equations with a physical background is helpful to understand the motion law of matter and to explain the corresponding physical phenomena scientifically. This equation has been studied widely, and there have been a lot of research methods to find exact solutions to this equation. In this manuscript, we try to study the non-dissipative double dispersive equation by the improved tan (\(\frac{\Phi(\xi)}{2}\)) -expansion method. As far as our known, no one has used this method to study the non-dissipative double dispersive equation, partly because of the complicated calculation. We obtain a lot of exact traveling wave solutions, including hyperbolic function solutions, trigonometric function solutions, exponential function solutions, and rational function solutions. Compared with the other methods, some solutions obtained in this manuscript are consistent with existing solutions, which shows the effectiveness of the improved tan (\(\frac{\Phi(\xi)}{2}\)) -expansion method. Through this method, Our manuscript obtains more general and new exact solutions. These solutions may play an important role in engineering and physics. What's more, we plot the 3D graphs of some of the solutions obtained in this manuscript, which helps us understand the physical phenomenon of the non-dissipative double dispersive equation. In the future, we will continue to explore its physical significance from the new analytical solution we have obtained.

Lommel functions, Padé approximants and hypergeometric functions

We consider the Lommel functions sμ,ν(z) for different values of the parameters (μ,ν). We show that if (μ,ν) are half integers, then it is possible to describe these functions with an explicit combination of polynomials and trigonometric functions. The polynomials turn out to give Padé approximants for the trigonometric functions. Numerical properties of the zeros of the polynomials are discussed. Also, when μ is an integer, sμ,ν(z) can be written as an integral involving an explicit combination of trigonometric functions. A closed formula for F12(12+ν,12−ν;μ+12;sin⁡(θ2)2) with μ an integer is given.

Sturm–Liouville problem for a one-dimensional thermoelastic operator in Cartesian, cylindrical, and spherical coordinate systems

The problem of constructing eigenfunctions of a one-dimensional thermoelastic operator in Cartesian, cylindrical, and spherical coordinate systems is considered. The corresponding Sturm–Liouville problem is formulated using Fourier’s separation of variables applied to a coupled system of thermoelasticity equations, assuming that the heat transfer rate is finite. It is shown that the eigenfunctions of the one-dimensional thermoelastic operator are expressed in terms of well-known trigonometric, cylinder, and spherical functions. However, coupled thermoelasticity problems are solved analytically only under certain boundary conditions, whose form is determined by the properties of the eigenfunctions.

A simple model of a gravitational lens from geometric optics

We propose a simple geometric optics analog of a gravitational lens with a refractive index equal to one at large distances and scaling like n(r)2=1+C2/r2, where C is a constant. We obtain the equation for ray trajectories from Fermat's principle of least time and the Euler equation. Our model yields a very simple ray trajectory equation. The optical rays bending, reflecting, and looping around the lens are all described by a single trigonometric function in polar coordinates. Optical rays experiencing fatal attraction are described by a hyperbolic function. We use our model to illustrate the formation of Einstein rings and multiple images.

Pulses in singularly perturbed reaction-diffusion systems with slowly mixed nonlinearity.

This article is concerned with the existence and spectral stability of pulses in singularly perturbed two-component reaction-diffusion systems with slowly mixed nonlinearity. In this paper, the slow nonlinearity is referred to be "mixed" in the sense that it is generated by a trigonometric function multiplied by a power function. We demonstrate via geometric singular perturbation theory that this model can support both the single-pulse and the double-hump solutions. The presence of the slowly mixed nonlinearity complicates the stability analysis on pulses, since the conditions that govern their stability can no longer be explicitly computed. We remove this difficulty by introducing the hypergeometric functions followed by a comparison theorem. By doing so, the "slow-fast" eigenvalues can be determined via the nonlocal eigenvalue problem method. We prove that the double-hump solution is always unstable, while the single-pulse solution can be stable under certain parameter conditions.

Inverse tangent series via telescoping sums

When first learning about infinite series, students typically are shown some examples for which the partial sums can be simplified by taking advantage of telescoping sums. In this paper, we present many examples of such series, all involving the inverse tangent function and most of which involve the Fibonacci and Lucas numbers. Most of the series presented here have appeared in various papers (see the references), but the authors are usually working in an abstract setting which makes it difficult for students to follow the basic ideas. We seek to make these results accessible to a wider audience.

Compact multi-ring perfect vortex beam generator fabricated by laser direct writing

Perfect vortex beams (PVBs) have received much attention in recent years since the annular intensity distributions are independent of the topological charge (TC). However, the cost-effective preparation of micrometer-scale monolithic devices capable of generating multiple PVBs through a simple approach remains a significant challenge. In this work, a design of double-ring perfect spiral phase plates (DPSPPs) is presented for the generation of PVBs at two distinct locations along the radial direction. The respective radii and spacing of the double-ring PVBs can be tuned by changing the control parameters. The proposed DPSPPs are fabricated by the flexible femtosecond laser direct writing (FsDLW) technique. The experimentally generated double-ring vortex beams with different TCs possess an almost constant radius, which is consistent with the characteristics of PVBs. Furthermore, the double-ring PVBs with different fractional and trigonometric function TCs and the multi-ring PVB are also demonstrated. The design and fabrication methods are expected to facilitate the miniaturization of the applications of PVBs in optical manipulation, optical communication, and high-capacity information storage.

Obtaining new soliton solutions of the fractional generalized perturbed KdV equation

Abstract In this study, the fractional generalized perturbed KdV equation (gpKdV) with beta derivative is considered. The generalized exponential rational function method (GERFM) is applied to this equation for the first time in this study. Thus, dark soliton, bright soliton, singular soliton, mixed soliton, trigonometric function, rational trigonometric function, hyperbolic function and rational exponential function solutions of this fractional equation are obtained for the first time in this study. The 2D, 3D, and density plots, which effectively illustrate the behavior of these solitons, are shown for various values and specific ranges of the solutions.

Euler’s Formula and Its Applications in Modern Mathematics

This article examines the various uses of Euler‘s formula in complex analysis, topology, number theory, and other mathematical fields. Renowned for its mathematical elegance, exponential and trigonometric functions are closely related according to Euler‘s formula. acting as a fundamental basis for various key developments in these fields. By conducting a thorough analysis, the study reveals the extensive significance and lasting impact of Euler’s formula in both theoretical and applied mathematics. The research employs a comprehensive literature review, enhanced by rigorous mathematical derivations and practical examples, to demonstrate the widespread applicability and versatility of Euler’s formula in a wide range of contexts. The findings underscore that Euler’s formula not only holds a central position in theoretical mathematics but also plays a crucial role in engineering, quantum mechanics, signal processing, and physics. This study contributes to a deeper understanding of the intrinsic relationships within mathematical formulas, emphasizing their far-reaching practical relevance and potential for future research and technological innovation.

A Look at Generalized Trigonometric Functions as Functions of Their Two Parameters and Further New Properties

Investigation of the generalized trigonometric and hyperbolic functions containing two parameters has been a very active research area over the last decade. We believe, however, that their monotonicity and convexity properties with respect to parameters have not been thoroughly studied. In this paper, we make an attempt to fill this gap. Our results are not complete; for some functions, we manage to establish (log)-convexity/concavity in parameters, while for others, we only managed the prove monotonicity, in which case we present necessary and sufficient conditions for convexity/concavity. In the course of the investigation, we found two hypergeometric representations for the generalized cosine and hyperbolic cosine functions which appear to be new. In the last section of the paper, we present four explicit integral evaluations of combinations of generalized trigonometric/hyperbolic functions in terms of hypergeometric functions.

A design strategy with the combination of neuro-regression and stochastic optimizations on the hyperelastic gasket

For numerous years, PVC and aluminum doors and windows have been integral components of buildings. The primary technical requisites for doors and windows encompass superior acoustic performance, thermal insulation, and effective sealing. Particularly, the sealing properties, crucially important, are ensured by the gaskets fitted onto the profiles. This paper aims to present a gasket design with a new methodology that includes a systematic modeling-optimization process based on multiple non-linear neuro-regression. Comprehensive research has been done by multiple non-linear neuro-regression analyses of gaskets due to deficient studies in the literature on hyperelastic materials. 17 candidate functional forms based on four basic mathematical structures (polynomial, trigonometric, logarithmic, and linear functions, and their hybrid or rational forms) have been proposed to model the FEM data of the gasket. Hybrid versions of three stochastic search algorithms, Differential Evolution, Random Search, and Simulated Annealing, are considered to solve highly non-linear, non-convex, multi-variables mixed continuous-discrete problems. The experimental results were compared with the numerical result using the finite-element analysis (FEA). Nonlinear static analyses were performed with Abaqus. Stress and logarithmic strain distributions are obtained. A good correlation was found between the experimental and the numerical results The optimum locations and numbers of the nodes have been found to obtain the minimum overflow distance and the maximum compression surface area for gaskets having the same topological structure.