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Adjoint methods enable the accurate calculation of the sensitivities of a quantity of interest. The sensitivity is obtained by solving the adjoint system, which can be derived by continuous or discrete adjoint strategies. In acoustic wave propagation, continuous and discrete adjoint methods have been developed to compute the eigenvalue sensitivity to design parameters and passive devices (Aguilar, J. G. et al, 2017, J. Computational Physics, vol. 341, 163-181). In this short communication, it is shown that the continuous and discrete adjoint characteristic decompositions, and Riemann invariants, are connected by a similarity transformation. The results are shown in the Laplace domain. The adjoint characteristic decomposition is applied to a one-dimensional acoustic resonator, which contains a monopole source of sound. The proposed framework provides the foundation to tackle larger acoustic networks with a discrete adjoint approach, opening up new possibilities for adjoint-based design of problems that can be solved by the method of characteristics., Comment: 4 figures, 12 pages

This paper explores the time dependent squeezing flow of a viscous fluid between parallel plates with internal heat generation and homogeneous/heterogeneous reactions. The motive of the present effort is to upgrade the heat transformation rate for engineering and industrial purpose with the rate of chemical reaction. For this purpose the equations for the conservation of mass, momentum, energy and homogeneous/heterogeneous reactions are transformed to a system of coupled equations using the similarity transformation. According to HAM, with the proper starting assumptions and other factors, a similarity solution may be found. On the way to verifying the validity and correctness of HAM findings, we compare the HAM solution with numerical solver programme BVP4c to see whether it matches up. The results of a parametric inquiry are summarized and presented with the use of graphs.

In this work, Kudryashov’s equation with third-order dispersion and fourth-order dispersion was studied via Lie symmetry analysis. First, similarity transformation helps us to converted governing equation into a system of ordinary differential equations. Then hyperbolic-expansion method and Kudryashov method reveals the cubic-quartic optical soliton solutions in the form of dark, bright, singular and combo bright-singular soliton solutions.

We demonstrate how similarity-transformed full configuration interaction quantum Monte Carlo (FCIQMC) based on the transcorrelated Hamiltonian can be applied to make highly accurate predictions for the binding curve of the beryllium dimer, marking the first case study of a molecular system with this method. In this context, the non-Hermitian transcorrelated Hamiltonian, resulting from a similarity transformation with a Jastrow factor, serves the purpose to effectively address dynamic correlation beyond the used basis set and thus allows for obtaining energies close to the complete basis set limit from FCIQMC already with moderate basis sets and computational effort. Building on results from other explicitly correlated methods, we discuss the role of the Jastrow factor and its functional form, as well as potential sources for size consistency errors, and arrive at Jastrow forms that allow for high accuracy calculations of the vibrational spectrum of the beryllium dimer.

In this paper, a similarity finite difference (SFD) solution is addressed for the two-dimensional (2D) parabolic partial differential equation (PDE), specifically on the unsteady convection-diffusion problem. Structuring the similarity transformation using wave variables, we reduce the parabolic PDE into elliptic PDE. The numerical solution of the corresponding similarity equation is obtained using a second-order central SFD discretization scheme to get the second-order SFD approximation equation. We propose a fourpoint similarity explicit group (4-point SEG) iterative method as a numerical solution of the large-scale and sparse linear systems derived from SFD discretization of 2D unsteady convection-diffusion equation (CDE). To show the 4-point SEG iteration efficiency, two iterative methods, such as Jacobi and Gauss-Seidel (GS) iterations, are also considered. The numerical experiments are carried out using three different problems to illustrate our proposed iterative method's performance. Finally, the numerical results showed that our proposed iterative method is more efficient than the Jacobi and GS iterations in terms of iteration number and execution time.

Support matrix machine (SMM) is a new and effective classification method, which has been applied in the field of image processing. In this paper, an improved SMM called symplectic hyperdisk matrix machine (SHMM) is proposed and applied to the roller bearing fault diagnosis. In SHMM, the symplectic geometry similarity transformation (SGST) is used to obtain the dimensionless feature matrix, which protects the signal structure information while weakening the interference of noise. Then, different types of hyperdisks are constructed to divide different types of data, several more realistic hyperdisk prediction models can be obtained and the problem of under estimation is avoided. In order to fully mine the spatial structure information, the feature matrix is mapped to the high-dimensional space by kernel technology, and the decision function is established by using the structure information hidden of the input matrix in the SHMM. Experimental results of three datasets of roller bearing show that, compared with symplectic geometry matrix machine (SGMM), SMM, support vector machine (SVM) and radial basis function (RBF) neural network methods, the proposed SHMM has good application effect in roller bearing fault diagnosis.

In this article, the behaviors of radiation and thermal-diffusion on Walters' B model toward a vertical stretching surface with volumetric heat generation/absorption are examined. The system of nonlinear ordinary differential equations which are responsible for the behaviors of momentum, energy and concentration equations in relation to Velocity f ′ (η), temperature θ(η) and concentration ∅(η) are obtained by befitting similarity transformation and solved with Homotopy-Analysis-Method(HAM). The behaviors of various partients are discussed by virtue of graphs and tables as well as the convergence of the series solution and the iterations. It is noticed among others that the presence of Weissengerg number makes the problem to exhibit non-Newtonian property which steered-up viscoelasticity via the tensile stress and lower the momentum layer while various values of thermal-buoyancy contributes to the cooling of the sheet with adverse effect in Technological field for cooling of an electronic components and other materials.

In order to improve the computational efficiency of models of production lines with unreliable machines, we propose the similarity transformation method by adjusting the design parameters, such as times between machine failures, times to repair and buffer capacities, in an equal proportion. It is found that the system throughput remains almost unchanged under the similarity transformation. The typical manufacturing system, serial production line, is taken as an example to verify the proposed method. Theoretical analysis and numerical experiments have been performed to confirm the feasibility and effectiveness of the method. The results show that the throughput error is no more than 5% and the calculation time is much less than that of the original model. Therefore, it is helpful to apply the similarity transformation method to large production line models to reduce computational complexity.

We present the theoretical and mathematical studies of the flow over a heated rough rotating surface for non-Newtonian fluid. Utilizing Carreau fluid model which is used for pseudoplastic and dilantant fluids, we determine, for the first time, base flow profile under the partial slip near a rough surface. The thermo-physical properties are considered for heat and mass phenomena. This study has received a great interest in applied engineering due to its improved mathematical and theoretical advantages. We examined the solutions for fluid and thermo-physical properties of the Carreau fluid model. The similarity transformation was initially introduced by von-Karman, it is useful for the Carreau fluid by converting the boundary layer equations into ordinary differential equations. Shooting technique is employed to solve the dimensionless differential equations. It is well known that the Carreau fluid model is significant for infinite high shear rates, that's why we examined the Carreau fluid over a heated rough rotating disk. Numerical results are used to illustrate the figures and tables.

In order to improve the correct identification rate of six types of Chinese spirits using electronic nose (E-nose), the Kernel entropy component analysis (KECA) identification method combined with Genetic algorithm (GA) was proposed. Firstly, integral value (INV), relative steady-state average value (RSAV) and wavelet energy value (WEV) were extracted and employed to represent the E-nose data. Secondly, radial basis function (RBF) was selected as the kernel function, then the kernel parameter η of RBF was optimized by the matrix similarity measurement method and the GA. The corresponding optimized kernel parameter η was 16.8608 (matrix similarity measurement) and 67.9039 (GA), respectively. When the first 125 kernel entropy components were selected for Fisher discriminant analysis (FDA), the correct identification rate of FDA (KECA + FDA) combined with GA were 97.62 % and 98.81 % for the training set and testing set, respectively; the correct identification rate of FDA (KECA + FDA) combined with matrix similarity measurement were 93.58 and 91.67 % for the training set and testing set, respectively. Therefore, the kernel parameter η determined by GA was significantly better than that of matrix similarity measurement. Finally, the correct identification rate of FDA and KECA + FDA was compared, and the results of FDA were only 82.14 % and 79.92 % for the training set and testing set, respectively. The identification results of FDA were far worse than that of KECA + FDA. The KECA + FDA method combined with GA was suitable for the identification of the six types of Chinese spirits by E-nose.

In electronic structure theory, restricted single-reference coupled cluster (CC) captures weak correlation but fails catastrophically under strong correlation. Spin-projected unrestricted Hartree-Fock (SUHF), on the other hand, misses weak correlation but captures a large portion of strong correlation. The theoretical description of many important processes, e.g. molecular dissociation, requires a method capable of accurately capturing both weak- and strong correlation simultaneously, and would likely benefit from a combined CC-SUHF approach. Based on what we have recently learned about SUHF written as particle-hole excitations out of a symmetry-adapted reference determinant, we here propose a heuristic coupled cluster doubles model to attenuate the dominant spin collective channel of the quadratic terms in the coupled cluster equations. Proof of principle results presented here are encouraging and point to several paths forward for improving the method further., 20 pages, 10 figures

One-dimensional non-Darcy flow in a semi-infinite porous media is investigated. We indicate that the non-Darcy relation which is usually determined from experimental results can always be described by a piecewise linear function, and the problem can be equivalently transformed to a multiphase implicit Stefan problem. The novel feature of this Stefan problem is that the phases of the porous media are divided by hydraulic gradients, not the excess pore water pressures. Using the similarity transformation technique, an exact solution for the situation that the external load increases in proportion to the square root of time is developed. The study on the existence and uniqueness of the solution leads to the requirement of a group of inequalities. A similar Stefan problem considering constant surface seepage velocity is also investigated, and the solution, which we indicate to be uniquely existent under all conditions, is established. Meanwhile, the relation between our Stefan problem and the traditional multiphase Stefan problem is demonstrated. In the end, computational examples of the solution are presented and discussed. The solution provides a useful benchmark for verifying the accuracy of general approximate algorithms of Stefan problems, and it is also attractive in the context of inverse problem analysis.

Phase-shifting interferometry (PSI) is an effective technique in optical measurement. In this paper, a noniterative algorithm for retrieving the unknown phase shifts in three frame generalized PSI is proposed, in which the interference term of each frame is eliminated by the aid of a reference interferogram with the phase shift of π. With this algorithm, the phase shifts can be determined by solving a system of transcendental equations with trigonometric functions, in which this system consists of three different ratios between the similar matrix 1-norms of the intensity difference and the intensity sum. After the determination of phase shifts, a phase can be retrieved easily. The algorithm provides a possible method to solve the limitation of the fringe number existing in some common algorithms. The feasibility and accuracy of this algorithm were demonstrated by the simulation and experimental results.

Today, in geodesy most practical applications is to use a datum to get three dimensional position of a particular point. The geodetic techniques generally provide time dependent coordinates in global datum. The difference between the global datum like international terrestrial reference frame (ITRF) to local datum like Europe fixed reference frame (EUREF) can be up to several centimeters due to different velocity rate of tectonic plates. To get high-precision measurements, there is an increasing need of time dependent transformations from the global level to local level. The present paper treats, this theoretical problem of geodesy by using mathematical dependency between two spatial coordinate systems whose common points are given in both systems. The paper describes four different (projective, affine, similarity and euclidean) modified methodologies for the transformation between global (ITRF) to local (EUREF) by using the Turkish permanent GPS network (TPGN) as an example. The time series from TPGN stations are used to review these transformations from ITRF 2008 to EUREF 2008. The transformation parameters in all cases shows that mostly transform coordinates depends on its counterparts (X to x and Y to y) and others coordinates have very less effect. Finally to show the validity of our model a comparative analysis with standard Bursa-Wolf and Molodensky-Badekas models has been presented. The test shows that our model error is equivalent to standard models, in this view the presented models are acceptable and can improve our understanding in coordinate transformation.

In the star identification process the goal is to recognize a star by using the celestial bodies in its vicinity as context. An additional requirement is to avoid having to perform an exhaustive scan of the star database. In this paper we present a novel approach to star identification using similarity invariants. More specifically, the proposed algorithm defines a polygon for each star, using the neighboring celestial bodies in the field of view as vertices. The mapping is insensitive to similarity transformation; that is, the image of the polygon under the transformation is not affected by rotation, scaling or translations. Each polygon is associated with an essentially unique complex number. We perform an exhaustive experimental validation of the proposed algorithm using synthetic data generated from the star catalog with uniformly-distributed positional noise introduced to each star. The star identification method that we present is proven to be robust, achieving a recognition rate of 99.68% when noise levels of up to ± 424 μ radians are introduced to the location of the stars. In our tests the proposed algorithm proves that if a polygon match is found, it always corresponds to the star under analysis; no mismatches are found. In its present form our method cannot identify polygons in cases where there exist missing or false stars in the analyzed images, in those situations it only indicates that no match was found.

The unsteady two-dimensional magnetohydrodynamic stagnation point flow of a nanofluid with thermophoresis effect is investigated numerically. The technique of similarity transformation is implemented to obtain the self-similar ordinary differential equations and then the self-similar equations are solved numerically using shooting method. This analysis explores the conditions of the existence, non-existence, uniqueness, and duality of the solutions of self-similar equations numerically. Dual solutions of velocity, temperature and concentration profiles are reported for different values of the each parameter involved for two types of nanoparticles, namely copper (Cu) and gold (Au) in the water-based fluid. It is found that the dual solutions exist for negative values of unsteady parameter A, whereas for positive values of unsteady parameter, the solution is unique. The results also indicate that the nanoparticle volume fraction reduces the skin friction coefficient, the heat transfer rate as well as mass transfer rate. Further, due to increase of thermophoresis parameter, the concentration inside the boundary layer reduces and the mass transfer rate enhances. In addition, to validate the present numerical results, comparison with published results is made and found to be in excellent agreement.

Exact analytical solutions for the generalized stretching (shrinking) of a porous surface, for the variable suction (injection) velocity, is presented in this paper. The solution is generalized in the sense that the existing solutions that correspond to various stretching velocities are recovered as a special case of this study. A suitable similarity transformation is introduced to find self-similar solution of the non-linear governing equations. The flow is characterized by a few non-dimensional parameters signifying the problem completely. These parameters are such that the whole range of stretching (shrinking) problems discussed earlier can be recovered by assigning appropriate values to these parameters. A key point of the whole narrative is that a number of earlier works can be abridged into one generalized problem through the introduction of a new similarity transformation and finding its exact solution encompassing all the earlier solutions. Keywords: Exact solutions, New similarities, Permeable and moving sheet

We propose two friendly analytical techniques called Adomian decomposition and Picard methods to analyze an unsteady axisymmetric flow of nonconducting, Newtonian fluid. This fluid is assumed to be squeezed between two circular plates passing through porous medium channel with slip and no-slip boundary conditions. A single fractional order nonlinear ordinary differential equation is obtained by means of similarity transformation with the help of the fractional calculus definitions. The resulting fractional boundary value problems are solved by the proposed methods. Convergence of the two methods’ solutions is confirmed by obtaining various approximate solutions and various absolute residuals for different values of the fractional order. Comparison of the results of the two methods for different values of the fractional order confirms that the proposed methods are in a well agreement and therefore they can be used in a simple manner for solving this kind of problems. Finally, graphical study for the longitudinal and normal velocity profiles is obtained for various values of some dimensionless parameters and fractional orders.

An analysis is carried out to study the effects of thermocapillarity on thin film flow over an unsteady stretching sheet in presence of uniform transverse magnetic field and internal heat source/sink. Using a similarity transformation, the governing time dependent boundary-layer equations are reduced to a set of coupled ordinary differential equations and then solved numerically for some representative values of non-dimensional parameters using Nachtsheim and Swigert shooting iteration technique together with Runge-Kutta sixth-order integration scheme. It is observed that the thermocapillary action reduces the rate of heat transfer at the surface while dealing with conducting fluid in presence of magnetic field.

Squeezing flow of an electrically conducting Casson fluid has been taken into account. The laws of conservations under the similarity transformation suggested by Wang (1976) have been used to extract a highly nonlinear ordinary differential equation governing the magneto hydrodynamic (MHD) flow. Resulting equation has been solved analytically by using the variation of parameters method (VPM). A RK-4 numerical solution has also been sought to examine the validity of analytical results. Both the solutions are found to be in an excellent agreement. Convergence of the solution is also discussed. Flow behavior under the modifying involved physical parameters is also discussed and explained in detail with the graphical aid. It is observed that magnetic field can be used as a control phenomenon in many flows as it normalizes the flow behavior. Also, squeeze number plays an important role in these types of problems and an increase in squeeze number increases the velocity profile.

The exact/approximate nonorthogonal general joint block diagonalization (nogjbd) problem of a given real matrix set $\mathcal{A}=\{A_i\}_{i=1}^m$ is to find a nonsingular matrix $W\in\mathbb{R}^{n\times n}$ (diagonalizer) such that $W^T A_i W$ for $i=1,2,\dots, m$ are all exactly/approximately block diagonal matrices with the same diagonal block structure and with as many diagonal blocks as possible. In this paper, we show that a solution to the exact/approximate nogjbd problem can be obtained by finding the exact/approximate solutions to the system of linear equations $A_iZ=Z^TA_i$ for $i=1,\dots, m$, followed by a block diagonalization of $Z$ via similarity transformation. A necessary and sufficient condition for the equivalence of the solutions to the exact nogjbd problem is established. Two numerical methods are proposed to solve the nogjbd problem, and numerical examples are presented to show the merits of the proposed methods.

Our overarching goal is to be able to describe both weak and strong correlation with a single, computationally affordable method without sacrificing important qualities of the wavefunction, e.g. symmetries of the Hamiltonian. We know that coupled cluster theory with low-order excitations is excellent at describing weakly-correlated systems near equilibrium, but breaks down as systems become more strongly correlated. Projected Hartree-Fock on the other hand is inherently capable of describing multireference character, but misses weak correlation. We are thus exploring how best to combine coupled cluster and projected Hartree-Fock in our search for a computationally feasible method that is applicable across a wide range of correlation strengths. In this manuscript, we adapt our earlier work on the pairing Hamiltonian to repulsive Hamiltonians, resulting in the spin polynomial similarity transformation (SpinPoST) interpolation. SpinPoST parameterizes the wavefunction in order to interpolate between the coupled cluster and spin-projected unrestricted Hartree-Fock ansätze self consistently, and is a spin-symmetry adapted model which involves only single and double excitations. We employ a unique approach of optimizing the wavefunction by minimizing the effect of connected quadruple excitations, resulting in a method which is spin-symmetry adapted and is comparable energetically to coupled cluster with singles and doubles for weak correlation and spin-projected Hartree-Fock for strong correlation.

A shrinkage curve optimization is proposed for weighted nuclear norm minimization and is adapted to image denoising. The proposed optimization method employs a penalty function utilizing the difference between a latent matrix and its observation and uses odd polynomials to shrink the singular values of the observation matrix. As a result, the coefficients of polynomial characterize the shrinkage operator fully. Furthermore, the Frobenius norm of the penalty function is converted into the corresponding spectral norm, and thus the parameter optimization problem can be easily solved by using off-and-shelf plain least-squares. In the practical application, the proposed denoising method does not work on the whole image at once, but rather a series of matrix termed Rank-Ordered Similar Matrix (ROSM). Simulation results on 256 noisy images demonstrate the effectiveness of the proposed algorithms.

This paper proposes a generalized controllability canonical form for linear multi-input systems by extending the normal controllability canonical forms. It is shown that there exists appropriate similarity transformation for any non-trivial system to transform it into a generalized controllability canonical form, even if the system is not completely controllable. The potential application scenarios are reviewed, especially for large-scale networked systems. The Luenberger format is taken as an instance to delineate the configuration of a generalized form. A numerical example is presented to demonstrate the relevant algorithm.

The present study explores the free convective oblique Casson fluid over a stretching surface with non-linear thermal radiation effects. The governing physical problem is modelled and transformed into a set of coupled non-linear ordinary differential equations by suitable similarity transformation, which are solved numerically with the help of shooting method keeping the convergence control of 10−5 in computations. Influence of pertinent physical parameters on normal, tangential velocity profiles and temperature are expressed through graphs. Physical quantities of interest such as skin friction coefficients and local heat flux are investigated numerically.

The 3D similarity coordinate transformation with the Gauss---Helmert error model is investigated. The first-order error analysis of an analytical least-squares solution to this problem is developed in detail. While additive errors are assumed in the translation and scale estimates, a 3 × 1 multiplicative error vector is defined to effectively parameterize the rotation matrix estimation error. The propagation of the errors in the coordinate measurements to the errors in the estimated transformation parameters is derived step-by-step, and the formulae for calculating the variance---covariance matrix of the estimated parameters are presented.

Purpose The purpose of this paper is to investigate some multiple solutions for carbon nanotubes (CNTs) in a porous channel with changing walls. Moreover, the intention of the study is to examine the physicochemical and rheological properties of titania and CNTs. Design/methodology/approach The mathematical modeling is performed for the laws of conservation of mass, momentum and energy profiles. Governing partial differential equations are transformed into ordinary differential equations by applying suitable similarity transformation and then solved numerically with the help of shooting technique. Findings The effects of different physical parameters on the rheology of nanofluids are discussed graphically and numerically, in order to make the analysis more interesting. The present study revealed that multiple solutions of nanofluids in a channel with changing walls are obtained only for the case of suction. Originality/value Some new branches of the solution for nanofluids in a channel with changing walls are obtained in this research, which has never been reported before. Combined effects of physicochemical and rheology of titania and carbon nanotubes are investigated briefly. The effects of physical parameters on velocity and temperature profile are examined in detail which is more realistic than real-world problem.

This paper presents an investigation for bioconvection of nanofluid holding gyrotactic microorganism over a stretching surface implant in a porous medium by taking the model introduced by Xu and Pop (2014). The bulk matrix linear resistance applied by porous media and the inertia effect characterized by the non-linear Forchheimer term are considered in the momentum equation. Using the similarity transformation, the governing PDEs are turned into a set of five similarities non-linear ODEs. Using charts and tables, the consequences of numerous parameters on flow features are examined and resolved in whole. The present results disclose that the rate of heat transmission is reduced with permeability parameter and inertial parameter whereas the rate of mass transfer is amplified with those parameters for suction and depleted for injection.

A numerical study is carried out in order to investigate the multiple solutions of micropolar fluid in a channel with changing walls. Mathematical modeling of laws of conservation of mass, momentum, angular momentum and energy is performed and governing partial differential equations are converted into self-similar ordinary differential equations by applying suitable similarity transformation and then solved numerically by shooting method. A new branch of solutions is found and presented graphically and numerically for the various values of parameters, which has never been reported.

This short communication interprets the delta-fit technique in a context of similarity transformation and the correction to the source function, and derives the analogous form of the method to be applied for the scattering phase matrix. To adapt the delta-fit method to vector radiative transfer, the mathematically exact form of the similarity principle is used in the theoretical development. Some examples of relevant radiative transfer simulations are also presented for atmospheric ice particles. The performance of the adopted delta-fit method is comparable to the delta-M method with single scattering correction except for worse delta-fit performance for polarized radiance calculations in forward directions.

In this paper, the governing equations of steady three-dimensional problem of condensation film on inclined rotating disk are reduced to a system of five coupled nonlinear ordinary differential equations through a similarity transformation. This system is analytically solved by newly developed method namely extended optimal homotopy asymptotic method (EOHAM). The velocity and temperature profiles are shown along with the influence of Prandtl number. These results are verified by homotopy analysis method (HAM) and numerical method. This method controls the convergence of approximate solution in a convenient way, when it is compared with HAM. The results show that EOHAM is simpler, easier, effective and explicit.

A method for stability of the descriptor continuous-time linear system is focused. For easily, it is converted to a standard continuous-time linear system by the definition of a derivative state feedback. Then partial eigenvalue assignment is used for obtaining state feedback and showing stability and controllability of the standard system. In partial eigenvalue assignment, just a part of the open loop spectrum of the standard linear systems are reassigned, while leaving the rest of the spectrum invariant and for reassigning, similarity transformation is used. Using partial eigenvalue assignment is easier than using eigenvalue assignment. Because by partial eigenvalue assignment, size of matrices and state and input vectors are decreased and stability is kept, too. Also concluding remarks and an algorithm are proposed to the descriptions be obvious. At the end, convergence of state and input vectors in the descriptor system to balance point (zero) are showed by figures in numerical examples.

We derive the Lax pairs and integrability conditions of the nonlinear Schrodinger equation with higher-order terms, complex potentials, and time-dependent coefficients. Cubic and quintic nonlinearities together with derivative terms are considered. The Lax pairs and integrability conditions for some of the well-known nonlinear Schrodinger equations, including a new equation which was not considered previously in the literature, are then derived as special cases. We show most clearly with a similarity transformation that the higher-order terms restrict the integrability to linear potential in contrast with quadratic potential for the standard nonlinear Schrodinger equation.

We prove a comparison theorem for the solutions of Riccati matrix equations in which the diagonal entries of the matrix multiplying the linear term are perturbed by a bounded function. This theorem is used to study optimal trajectories in a pollution control problem stated in the form of a linear regulator over an infinite time horizon with a discount function of the general form.

In this manuscript, the ultrashort soliton pulse propagation through nonlinear tunneling in cubic quintic media is investigated. The effect of chirping on propagation characteristics of the soliton pulse is analytically investigated using similarity transformation. In particular, we investigate the propagation dynamics of ultrashort soliton pulse through dispersion barrier for both chirp and chirp-free soliton. By investigating the obtained soliton solution, we found that chirping has strong influence on soliton dynamics such as pulse compression with amplification. These two important dynamics of chirped soliton in cubic quintic media open new possibilities to improve the solitonic communication system. Moreover, we surprisingly observe that a dispersion well is formed for the chirped case whereas a barrier is formed for the chirp-free case, which has certain applications in the construction of logic gate devices to achieve ultrafast switching.

The generalized Hough transform (GHT) is widely used for detecting or locating objects under similarity transformation. However, a weakness of the traditional GHT is its large storage requirement and time-consuming computational complexity due to the 4-D parameter space voting strategy. In this paper, a polygon-invariant GHT (PI-GHT) algorithm, as a novel scale- and rotation-invariant template matching method, is presented for high-speed object vision-based positioning. To demonstrate the performance of PI-GHT, several experiments were carried out to compare this novel algorithm with the other five popular matching methods. Experimental results show that the computational effort required by PI-GHT is smaller than that of the common methods due to the similarity transformations applied to the scale- and rotation-invariant triangle features. Moreover, the proposed PI-GHT maintains inherent robustness against partial occlusion, noise, and nonlinear illumination changes, because the local triangle features are based on the gradient directions of edge points. Consequently, PI-GHT is implemented in packaging equipment for radio frequency identification devices at an average time of 4.13 ms and 97.06% matching rate, to solder paste printing at average time nearly 5 ms with 99.87%. PI-GHT is applied to LED manufacturing equipment to locate multiobjects at least five times improvement in speed with a 96% matching rate.

This paper presents a universal model of weighted coordinate transformation, i.e. transformation considering the errors of coordinates in both coordinate systems. It is intrinsically one of the typical examples of 'error-in-variables' (EIV) models. The proposed method of LS theory application on weighted coordinate transformation does not impose any constraints on the form of functional relationship among stochastic variables. Since the basic idea is to generalise Gauss-Markov model (GMM) by introduction of so-called 'total residuals', the proposed procedure is named 'Generalised Gauss-Markov model'. Formulation of expressions for estimation of unknown transformation parameters is theoretically confirmed using the Gauss-Helmert model (GHM) and three different modifications of the GMM. The proposed procedure is in its essence a strict solution to total least-squares (unweighted) and weighted total least-squares problem in coordinate transformation. This thesis is experimentally confirmed by comparison of its results with those found in four characteristic examples from the literature.

In this paper, we consider the problem (denoted as EMDRT) of minimizing the earth mover’s distance between two sets of weighted points A and B in $${\mathbb {R}}^{d}$$ under rigid transformation. EMDRT is an important problem in both theory and applications and has received considerable attentions in recent years. Previous research on this problem has resulted in only constant factor approximations and it has been an open problem for a long time to achieve PTAS solution. In this paper, we present the first FPTAS algorithm for EMDRT. Our algorithm runs roughly in $$O((nm)^{d+2}(\log nm)^{2d})$$ time (which is close to a lower bound on any PTAS for this problem), where n and m are the sizes of A and B, respectively. Our result is based on several new techniques, such as the Sequential Orthogonal Decomposition and Optimum Guided Base, and can be extended to several related problems, such as the problem of earth mover’s distance under similarity transformation and the alignment problem, to achieve FPTAS for each of them.

The present article investigates the squeezing flow of two types of nanofluids such as Cu-water and Cu-kerosene between two parallel plates in the presence of magnetic field. The governing non-linear partial differential equations are transformed into ordinary differential equations by applying suitable similarity transformation and then solved numerically using RK-4 method with shooting technique and analytically using differential transformation method (DTM). The influence of arising relevant parameters on flow characteristics has been discussed through graphs and tables. A comparative study has been taken into account between existing results and present work and it is found to be in excellent harmony.

We investigate the identification problems of a class of linear stochastic time-delay systems with unknown delayed states in this study. A time-delay system is expressed as a delay differential equation with a single delay in the state vector. We first derive an equivalent linear time-invariant (LTI) system for the time-delay system using a state augmentation technique. Then a conventional subspace identification method is used to estimate augmented system matrices and Kalman state sequences up to a similarity transformation. To obtain a state-space model for the time-delay system, an alternate convex search (ACS) algorithm is presented to find a similarity transformation that takes the identified augmented system back to a form so that the time-delay system can be recovered. Finally, we reconstruct the Kalman state sequences based on the similarity transformation. The time-delay system matrices under the same state-space basis can be recovered from the Kalman state sequences and input-output data by solving two least squares problems. Numerical examples are to show the effectiveness of the proposed method.

In this paper, we propose a method for automated mosaicking of multiple 3D point clouds generated from a depth camera. A depth camera generates depth data by using ToF (Time of Flight) method and intensity data by using intensity of returned signal. The depth camera used in this paper was a SR4000 from MESA Imaging. This camera generates a depth map and intensity map of 176 x 44 pixels. Generated depth map saves physical depth data with mm of precision. Generated intensity map contains texture data with many noises. We used texture maps for extracting tiepoints and depth maps for assigning z coordinates to tiepoints and point cloud mosaicking. There are four steps in the proposed mosaicking method. In the first step, we acquired multiple 3D point clouds by rotating depth camera and capturing data per rotation. In the second step, we estimated 3D-3D transformation relationships between subsequent point clouds. For this, 2D tiepoints were extracted automatically from the corresponding two intensity maps. They were converted into 3D tiepoints using depth maps. We used a 3D similarity transformation model for estimating the 3D-3D transformation relationships. In the third step, we converted local 3D-3D transformations into a global transformation for all point clouds with respect to a reference one. In the last step, the extent of single depth map mosaic was calculated and depth values per mosaic pixel were determined by a ray tracing method. For experiments, 8 depth maps and intensity maps were used. After the four steps, an output mosaicked depth map of 454x144 was generated. It is expected that the proposed method would be useful for developing an effective 3D indoor mapping method in future.

A theoretical study is presented for the problem of orthogonal axisymmetric stagnation flow towards an infinite horizontal plate with a constant velocity in the presence of viscous dissipation and heat generation. The governing equations are reduced to a system of nonlinear ordinary differential equations by means of appropriate transformations for the velocity components and temperature. The similarity equations are solved numerically using the Matlab routine bvp4c. The results are compared with those known from the literature and an excellent agreement is found. The effects of involved parameters on thex-wise velocity component, temperature, skin friction, heat transfer and entropy generation rate are presented in graphical and tabular forms. It was found that the Eckert number Ec, the Prandtl number Pr and the heat generation parameter α play a significant role on the temperature, heat transfer and entropy generation rate.

We consider nonautonomous rogue wave solutions of a $$(3+1)$$ -dimensional (3D) nonlinear Schrodinger equation (NLSE) with time–space modulation terms, the dispersion and the nonlinear coefficients engendering temporal dependency. Similarity transformation is used to convert the nonautonomous equation into autonomous NLSE; we obtain the multi-rogue wave solutions employing the generalized Darboux transformation. Particularly, the rogue wave solutions possess several free parameters. Then, the first-order and second-order nonautonomous rogue wave solutions are considered for the 3D NLSE with variable coefficients. At last, the numerical simulations on the evolution and collision of rogue wave solutions are performed to verify the prediction of the analytical formulations. The obtained nonautonomous rogue wave solutions can be used to describe the dynamics waves in the nonlinear optical fibers and Bose–Einstein condensates, respectively.

This note deals with a problem on approximation of a matrix tuple by a finite family of diagonalizable matrices with simple eigenvalues. In addition, for a given tuple of matrix functions, it is required that the product of their values at those diagonalizable matrices has a simple spectrum. We solve this problem making use of topological properties of the full matrix algebra.

In this paper we analyze viscous oscillatory MHD inhomogeneous fluid flow through the channel which is narrow and rectangular with one wall being porous through which suction or injection is taken place with constant rate and the other wall being rigid. The equation pertaining to the motion of fluid are simplified by using narrow channel approximation and the simplified equation are solved using similarity transformation and the graphical representation are analyzed for velocity profiles. The results reveal that stratification and MHD effects are found predominantly at the centre of the channel while stratification suppresses the flow in vertical direction. For B 0=0 and N=0 the results are in accordance with that already available in literature.

In addition to the diagonalization of a normal matrix by a unitary similarity transformation, there are two other types of diagonalization procedures that sometimes arise in quantum theory applications -- the singular value decomposition and the Autonne-Takagi factorization. In these pedagogical notes, we carry out each of these diagonalization procedures for the most general $2\times 2$ matrices for which the corresponding diagonalization is possible and provide explicit analytical results in each of the three cases., 27 pages; version 2 adds a footnote 14 and improves the pdf output by modifying the implementation of hyperref; version 3 corrects an error in eq. (78)

In order to overcome the problems of low signal-to-noise ratio, low efficiency and poor signal richness in ultrasonic signal acquisition of ferromagnetic materials, a new ultrasonic signal acquisit...

This contribution describes the second stage of the creation of a language training system programmed in Python with the aim of application to speech therapy in spanish-speaking countries, starting the study in Cuba. The first stage of this research was carried out in Matlab by analyzing the dynamics of change of the centroids of the codebooks, extracted from words pronounced by a locutor. As second stage, the Variational Coefficient formula is used in order to estimate the percentage of effectiveness with which the announcer performs voice training. A modified approach to programming the variational coefficient is taken into account as a measure of dispersion of a group of vectors. The modification is given by taking the mean of the group of vectors as the vector that represents the phonetic boundaries of the word to be trained. Besides, a novel approach for word recognition is used, based on the K-Nearest Training Matrix (KNTM) algorithm that lays its foundations in the analysis of matrix similarity taken the Frobenius norm as a measure to distinguish similar or non-similar characteristics of a matrix with respect to a database of matrices. To reduce the computational cost of the program and speed up its proper functioning, the training matrices of the database are saved in files with a .tex extension, in this way after training process, the program should only read them and not recalculate them, which significantly reduces the running time of the algorithm.

In this paper, the (2+1)-dimensional extended quantum Zakharov-Kuznetsov equation is further explored. The equation is shown to be self-adjoint and conserved vector is constructed according to the related theorem. Then the corresponding optimal system of one-dimensional subgroups is determined. Similarity reductions of the equation under optimal system of subgroups are performed. As a result, the (2+1)-dimensional extended quantum Zakharov-Kuznetsov equation is reduced into a linear PDE with two independent variables.