Equivalent Transformation Research Articles

Numerical Investigation of Diffusion thermo and Thermal Diffusion on Mixed Convection flow of Williamson Nanofluid through a vertical cone with porous material in the presence Thermal radiation and Activation Energy

In this paper, analyze the impact of Activation energy, Diffusion thermo and thermal diffusion with heat and mass transfer inherent of over a vertical cone through Thermally Radiant Williamson nanofluid with saturated porous medium under the convective boundary condition in the presence of thermal radiation has been studied. The coefficients of Brownian and thermophoresis diffusions are also taken into consideration. The governing partial differential equations are reduced to a couple of nonlinear ordinary differential equations by using suitable transformation equations; these equations are then solved numerically with the use of the conventional fourth-order Runge Kutta method accompanied by the shooting technique. As a result, the effects of various physical parameters on the velocity, temperature, and nanoparticle concentration profiles as well as on the skin friction coefficient and rate of heat transfer are discussed with the aid of graphs and tables. This study has been directly applied in the pharmaceutical industry, microfluidic technology, microbial improved oil recovery, modelling oil and gas-bearing sedimentary basins, and many other fields. Further, to check the accuracy and validation of the present results, satisfactory concurrence is observed with the existing literature.

Rotational rheometry test of Portland cement-based materials – A systematic literature review

This study systematically reviews 62 papers on the use of rotational rheometry to assess the fresh state behavior of Portland cement-based materials. The research highlights the wide variation in test methods and aims to provide a comprehensive overview. Findings reveal that 50.0% of studies employed vane geometry, despite its limitations in providing transformation equations. Regarding dynamic shearing tests, 67.0% followed a consensus using a pre-shearing step and a step-wise routine with stabilization times ≥ 10 s. While the Bingham model is commonly used, the study emphasizes the importance of considering shear-thinning behavior in cementitious materials. Models like Herschel-Bulkley and modified Bingham may be more appropriate. This review offers insights into testing conditions for rotational rheometry of cementitious materials, serving as a foundation for future research in the field.

Improving Translation Quality: A Chinese-English Translation Study on the Profiles of Tourist Attraction in China Based on Cultural Awareness

The bilingual profiles of tourist attraction are used ubiquitously and seen everywhere in China. Whether foreign tourists can have an accurate understanding of and keen interest in a particular tourist attraction hinges directly on the quality of translation. However, various translation studies in this area focus on meaning equivalence of language as a symbol, whose function remains at the level of linguistic symbols’ equivalence transformation. This article is mainly concerned with the profiles of tourist attraction enormously adopted in China and their cultural translation from Chinese to English as well as the improved translation output based on data analysis from the perspective of cultural awareness, in an attempt to explore a cultural translation strategy, namely, liberal translation integrated with cultural awareness. Based on examples personally gathered from Mainland China, it is found that the translation of tourist attraction profiles is mainly studied in a linguistically descriptive way, without enunciating the deep culture beneath the surface of linguistic forms. Through detailed analysis of these examples, the study also shows that using liberal translation integrated with cultural awareness in tourism translation is more explicable and intelligible to foreign tourists. The article concludes that cultural awareness must be considered in the liberal translation of tourist attraction profiles so as to communicate clearer and more accurate meaning to the target audience.

Resistance values under transformations in regular triangular grids

In Evans and Francis (2022) and Hendel (2021) the authors investigated resistance distance in triangular grid graphs and observed several types of asymptotic behavior. This paper extends their work by studying the initial, non-asymptotic, behavior found when equivalent circuit transformations are performed, reducing the rows in the triangular grid graph one row at a time. The main conjecture characterizes, after reducing an arbitrary number of times an initial triangular grid all of whose edge resistances are identically one, when edge resistance values are less than, equal to, or greater than one. A special case of the conjecture is proven. The main theorem identifies patterns of repeating edge resistances arising in diagonals of a triangular grid reduced s times provided the original grid has at least 4s rows of triangles. This paper also improves upon the notation, concepts, and proof techniques introduced by the authors previously.

Microstrip Quasi-Elliptic Absorptive Bandpass Filter with Ultra-Wide Reflectionless Range and Compact Size

Absorptive bandpass filters (ABPFs) are highly attractive in modern microwave communication systems due to their ability to internally absorb the harmful stopband RF-power reflections. This paper reports an approach to designing quasi-elliptic ABPFs with ultra-wide reflectionless range, enhanced selectivity, and compact size. The method is realized based on a fourth-order quasi-elliptic absorptive lowpass filter (ALPF) prototype with a simplified structure. This ALPF prototype exhibits both good impedance-matching over the whole normalized frequency domain and an adjustable transmission zero close to the passband. By applying an equivalent impedance transformer model, a coupled-line-based ABPF scheme is devised from the ALPF prototype, which eliminates conventional dispersive transmission line inverters, resulting in an ultra-wide reflectionless range and a compact size. Closed-form equations are derived to support the filter synthesis. A 2.45 GHz microstrip ABPF with 30% fractional bandwidth is designed for verification. The measured minimum in-band insertion loss is 0.83 dB and the reflectionless range of return loss better than 10 dB is from DC to 12.88 GHz. Both the upper and lower stopband suppression exceed 20 dB, with the upper stopband extending up to 6.80 GHz. The upper and lower out-of-band roll-off rates are 93.9 and 121.4 dB/GHz, respectively. The overall circuit size is 0.12 λg2.

Fuzzy finite‐time adaptive control of switched nonlinear systems with input nonlinearities

SummaryThis article addresses the fuzzy finite‐time command filtering tracking control problem for switched nonlinear systems with input nonlinearities via using backstepping technique. An equivalent transformation method is proposed for the purpose of handling the impediment problem caused by the nonlinearity of control input. Finite‐time command filtering control technology can solve the “explosion of complexity” issue, which is caused by the multiple derivation of virtual controllers appeared in the classic backstepping control. A filtering compensation scheme is developed to reduce the filtering error. By combining the fuzzy logic system's approximation ability and the finite‐time theory, a new fast convergence adaptive control scheme is proposed so that the output of the system can converge to a small area near the desired signal and the boundedness of all signals of the controlled system can be assured in finite time. Finally, a simulation example successfully verifies the feasibility of the developed control scheme.

Arbitrary target frequency cloaking for flexural waves using deep learning

Differing from electromagnetic and acoustic waves, the governing equation for elastic waves in flexural plates is not form invariant, hindering straightforward cloak design based on coordinate transformation theory. In this work, we propose a novel idea instead of the approximately equivalent transformation method, and employ scattering cancellation techniques to design a multi-layer cylindrical structure for achieving flexural wave cloaking at desired target frequencies. Moreover, we use deep learning to effectively address the time consuming issue dealing with fine-tuning design parameters for the desired response. More importantly, we adopt a method based on a tandem neural network to tackle the one-to-many mapping challenge in inverse design. It not only accurately predicts the scattering spectra of multi-layer structures in advance but also efficiently performs inverse design to obtain the required design parameters for arbitrary target frequency cloaking.

Reconstruction of the real 3D shape of the SARS-CoV-2 virus

The photographs of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus taken by electron transmission microscopy and cryoelectron microscopy provide only a 2D silhouette. The viruses appear to look like distorted circles. The present paper questions the real shape of the SARS-CoV-2 virus and makes an attempt to give an answer. Is this a general ellipsoid, a spheroid with rotational symmetry, a sphere, or something else? The answer requires the application of tools from three different disciplines: structural mechanics, microbiology, and statistics. A total of 590 virus photographs taken from 22 recently published papers were examined. From this experimental data pool, the histogram of diameter ratios was built from the 283 measurements where the virus images could be approximated as ellipses. The curve peaks at the diameter ratio of 1.22. The transformation equation for the spatial shape to the planar shade was derived for a fixed light source of the microscope. This equation involves an unknown orientation of the viruses with respect to the microscope. Two sets of models were developed, one with a uniform distribution of the virus orientation and the other with the orientation defined by the normalized beta distribution. In both sets of models, the unknown diameter ratio of the spheroidal virus was regarded as a random realization from translated gamma distributions. The parameters of the distribution of the kernel functions were determined by minimizing the mean square difference between the predicted and measured 2D histograms. The information included in the measured histograms was found to be insufficient to find an unknown distribution of the virus’s orientation. Simply too many unknown parameters render the solution physically unrealistic. The minimization procedure with a uniform probability of virus orientation predicted the peak of the aspect ratio of the 3D spheroid at 1.32. Based on this result, models of the virus will be developed in the continuation of this research for a full dynamic analysis.

Solving the cohomological equation for locally Hamiltonian flows, part I - local obstructions

We study the cohomological equation Xu=f for smooth locally Hamiltonian flows on compact surfaces. The main novelty of the proposed approach is that it is used to study the regularity of the solution u when the flow has saddle loops, which has not been systematically studied before. Then we need to limit the flow to its minimal components. We show the existence and (optimal) regularity of solutions regarding the relations with the associated cohomological equations for interval exchange transformations (IETs). Our main theorems state that the regularity of solutions depends not only on the vanishing of the so-called Forni's distributions (cf. [9,11]), but also on the vanishing of families of new invariant distributions (local obstructions) reflecting the behavior of f around the saddles. Our main results provide some key ingredient for the complete solution to the regularity problem of solutions (in cohomological equations) for a.a. locally Hamiltonian flows (with or without saddle loops) to be shown in [15].The main contribution of this article is to define the aforementioned new families of invariant distributions dσ,jk, Cσ,lk and analyze their effect on the regularity of u and on the regularity of the associated cohomological equations for IETs. To prove this new phenomenon, we further develop local analysis of f near degenerate singularities inspired by tools from [14] and [17]. We develop new tools of handling functions whose higher derivatives have polynomial singularities over IETs.

Parameterization to fault detection filtering for Itô stochastic T‐S fuzzy systems

AbstractThis article focuses on the fault detection filtering problem for Itô stochastic Takagi–Sugeno (T‐S) fuzzy systems. In terms of line integral Lyapunov function, a sufficient condition of exponential stability in mean square and extended dissipativity for the systems under consideration is established which has less conservatism than the one based on quadratic Lyapunov function. The obtained sufficient condition is nonlinear, which makes the synthesis of fault detection filter being difficult and challenging. By choosing general matrix variables and constructing the appropriate orthogonal complement matrices, the nonlinear sufficient condition can be converted into linear one ingeniously via utilizing Finsler's lemma twice. Thus, the fault detection filter can be developed by virtue of parameterization. It should be pointed out that our filter determined by the parameterization approach includes the one obtained by the equivalent transformation method as a special case. Finally, we demonstrate the feasibility and superiority of our proposed approach through three numerical examples.

Minkowskian Approach to the Pseudorange Navigation Equations

Our starting point is the covariant coordinate transformation equation of a relativistic positioning system in Minkowski space–time that maps the receiver’s emission coordinates (proper times broadcast by the emitters) to its coordinates in some inertial reference frame. Bancroft’s analytical (closed-form) solution to the basic pseudorange navigation equations with four emitters is recovered, and the subjacent elements are geometrically interpreted. The case of four static beacons is analysed as a clarifying situation.

Cyclic shear testing of artificially corroded reinforced concrete short circular piers

Chloride-induced deterioration of reinforced concrete (RC) structures is an increasingly vital topic among asset management and structural maintenance fields, as many RC bridges and other structures are reaching the end of their initial design lives. Deterioration of the transverse reinforcement in RC piers leads to the direct loss of shear and confinement-related mechanical properties as degradation advances with time. This research investigates the seismic response of fourteen short RC circular piers subjected to artificial chloride-induced corrosion. Each pier is designed to trigger a shear-dominated failure and artificially corroded at two current densities. A maximum average mass loss of 10.5% and 43.0% was measured in the longitudinal and spiral reinforcement, respectively. The influence of confinement effectiveness, spiral diameter, and aspect ratio on the rate of shear capacity degradation are included as test parameters in this study. Results indicate that shear deformation begins to govern performance at moderate to severe deterioration, which precedes the onset of brittle shear-dominated failure modes. Ultimate deflection is more adversely affected by increasing corrosion than all other measured properties, with a maximum observed reduction of 70.9% compared to a maximum 37.5% reduction observed in peak shear capacity. Several existing theoretical models are introduced and evaluated on their ability to predict the shear capacity of the experimental tests. Based on the results, those models directly evaluating the circular section without needing an equivalent section transformation offer the most accurate and reliable predictions.

Symmetry algebra classification of scalar n$$ n $$th‐order ordinary differential equations

We obtain a complete classification of scalar th‐order ordinary differential equations for all subalgebras of vector fields in the real plane. While softwares like Maple can compute invariants of a given order, our results are for a general . The cases are well‐known in the literature. Further, it is known that there are three types of th‐order equations depending upon the point symmetry algebra they possess, namely, first‐order equations which admit an infinite dimensional Lie algebra of point symmetries, second‐order equations possessing the maximum 8‐point symmetries, and higher‐order, , admitting the maximum dimensional point symmetry algebra. We show that scalar th‐order equations for do not admit maximally an dimensional real Lie algebra of point symmetries. Moreover, we prove that for , equations can admit two types of dimensional real Lie algebra of point symmetries: one type resulting in nonlinear equations which are not linearizable via a point transformation and the second type yielding linearizable (via point transformation) equations. Furthermore, we present the types of maximal real dimensional and higher than ‐dimensional point symmetry algebras admissible for equations of order and their canonical forms. The types of lower‐dimensional point symmetry algebras which can be admitted are shown, and the equations are constructible as well. We state the relevant results in tabular form and in theorems.

A Full-Newton Step Interior-Point Method for Weighted Quadratic Programming Based on the Algebraic Equivalent Transformation

In this paper, a new full-Newton step feasible interior-point method for convex quadratic programming is presented and analyzed. The idea behind this method is to replace the complementarity condition with a non-negative weight vector and use the algebraic equivalent transformation for the obtained equation. Under the selection of appropriate parameters, the quadratic rate of convergence of the new algorithm is established. In addition, the iteration complexity of the algorithm is obtained. Finally, some numerical results are presented to demonstrate the practical performance of the proposed algorithm.

Uncertain stochastic hybrid zero-sum games based on forward uncertain difference equations and backward stochastic difference equations

We investigate the interplay between forward uncertain difference equations and backward stochastic difference equations, which belong to distinct mathematical frameworks: uncertainty theory and probability theory, respectively. By establishing the connections between uncertain expectation, probabilistic expectation, and chance expectation, we develop the chance theory framework for analyzing uncertain stochastic hybrid zero-sum games constrained by both forward uncertain difference equations and backward stochastic difference equations. Through an equivalent transformation, we convert these games into deterministic difference equation solving problems. By backward-solving the difference equations and applying mathematical induction, analytical expressions for the equilibrium solutions of two types of uncertain stochastic hybrid zero-sum games are obtained. Furthermore, we explore solution methods for zero-sum games with different operational orders of uncertain and probabilistic expectations and highlight the fundamental differences through numerical examples.

Canonical Transformations and Poisson Theory for Dynamics with Non-Standard Lagrangians

Canonical Transformations and Poisson Theory for Dynamics with Non-Standard Lagrangians

Numerical Investigation of Diffusion Thermo and Thermal Diffusion on MHD Convective Flow of Williamson Nanofluid on a Stretching Surface Through a Porous Medium in the Presence Chemical Reaction and Thermal Radiation

In this paper, analyze the impact of Diffusion thermo and thermal diffusion with heat and mass transfer inherent of thermally radiant Williamson nanofluid over a stretyching surface through a porous medium under the convective boundary condition in the presence of thermal radiation and chemical reaction has been studied. The coefficients of Brownian and thermophoresis diffusions are also taken into consideration. The governing partial differential equations are reduced to a couple of nonlinear ordinary differential equations by using suitable transformation equations; these equations are then solved numerically with the use of the conventional fourth-order Runge Kutta method accompanied by the shooting technique. As a result, the effects of various physical parameters on the velocity, temperature, and nanoparticle concentration profiles as well as on the skin friction coefficient and rate of heat transfer are discussed with the aid of graphs and tables. This study has been directly applied in the pharmaceutical industry, microfluidic technology, microbial improved oil recovery, modelling oil and gas-bearing sedimentary basins, and many other fields. Further, to check the accuracy and validation of the present results, satisfactory concurrence is observed with the existing literature.

Novel reference condition independent method for estimating performance for PV modules based on double-diode model

The traditional methods for performance estimation mainly include two steps: determine the model parameters under reference condition and calculate the model parameters at varying operating conditions through transformation equations. These methods have the disadvantages of being influenced by the selection of reference condition. A novel reference condition independent method is proposed based on double-diode model (DDM) for parameter calculation and performance estimation at varying operating conditions for photovoltaic (PV) modules. In the proposed method, a new set of transformation equations is reconstructed according to the dependence of physical parameters in DDM on irradiance and temperature. All coefficients in the proposed transformation equations are independent of the information under reference condition and applicable to all varying operating conditions, which eliminates the influence of reference condition. The coefficients are optimized by fitting measured I–V data at varying operating conditions using guaranteed convergence particle swarm optimization technology, and used for model parameters calculation at varying operating conditions. Then the output property of PV module under any operating condition can be determined independently, first against the reference condition and then against the model parameters under reference condition. The accuracy and applicability of proposed method is validated by massive experimental data for six different types of PV modules under wide range of operating conditions. Moreover, three traditional methods are selected to compare with the proposed method. The proposed method shows better accuracy in I–V, P–V curve and maximum power point estimation under different irradiance and temperature conditions, which can be further used to predict the output power of PV system.

Learning Accurate and Bidirectional Transformation via Dynamic Embedding Transportation for Cross-Domain Recommendation

With the rapid development of Internet and Web techniques, Cross-Domain Recommendation (CDR) models have been widely explored for resolving the data-sparsity and cold-start problem. Meanwhile, most CDR models should utilize explicit domain-shareable information (e.g., overlapped users or items) for knowledge transfer across domains. However, this assumption may not be always satisfied since users and items are always non-overlapped in real practice. The performance of many previous works will be severely impaired when these domain-shareable information are not available. To address the aforementioned issues, we propose the Joint Preference Exploration and Dynamic Embedding Transportation model (JPEDET) in this paper which is a novel framework for solving the CDR problem when users and items are non-overlapped. JPEDET includes two main modules, i.e., joint preference exploration module and dynamic embedding transportation module. The joint preference exploration module aims to fuse rating and review information for modelling user preferences. The dynamic embedding transportation module is set to share knowledge via neural ordinary equations for dual transformation across domains. Moreover, we innovatively propose the dynamic transport flow equipped with linear interpolation guidance on barycentric Wasserstein path for achieving accurate and bidirectional transformation. Our empirical study on Amazon datasets demonstrates that JPEDET significantly outperforms the state-of-the-art models under the CDR setting.

Symmetry Analysis of the Two-Dimensional Stationary Gas Dynamics Equations in Lagrangian Coordinates

This article analyzes the symmetry of two-dimensional stationary gas dynamics equations in Lagrangian coordinates, including the search for equivalence transformations, the group classification of equations, the derivation of group foliations, and the construction of conservation laws. The consideration of equations in Lagrangian coordinates significantly simplifies the procedure for obtaining conservation laws, which are derived using the Noether theorem. The final part of the work is devoted to group foliations of the gas dynamics equations, including for the nonstationary isentropic case. The group foliations approach is usually employed for equations that admit infinite-dimensional groups of transformations (which is exactly the case for the gas dynamics equations in Lagrangian coordinates) and may make it possible to simplify their further analysis. The results obtained in this regard generalize previously known results for the two-dimensional shallow water equations in Lagrangian coordinates.