Euler Transformation Research Articles

Implementation of Control Algorithms in Small Embedded Systems

This work describes how a control algorithm can be implemented in a small (8-bit) microcontroller for the main purpose of merging embedded systems and control theory in electrical engineering undergraduate classes. Two different methods for discretizing the control expression are compared: Euler transformation and bilinear transformation. The sampling rate’s impact on the algorithm is discussed and theoretical results are verified by an application to a temperature control system in a heating plant. Four control algorithms are compared: PID and PI algorithms discretized with Euler and bilinear transformation, respectively. It is shown that for the heating plant used in this work, a bilinear PI algorithm implemented in a small 8-bit microcontroller outperforms a commercial controller from Panasonic. It is also demonstrated that all the derived algorithms can be implemented using integer calculations only, obviating the need for expensive and time-consuming floating-point calculations. This work bridges the gap between control theory equations and the implementation of control systems in small embedded systems with no inherent floating-point processing power.

Design, Analysis, and Test of a Novel 2-DOF Spherical Motion Mechanism

A novel two degree-of-freedom (DOF) ball-joint-like hydraulic spherical motion mechanism (SMM) for use in robotic applications is proposed to achieve smooth spherical motion in all directions. Unlike traditional systems that use serial or parallel mechanisms for generating multi-DOF rotations, the proposed SMM is capable of producing continuous 2-DOF rotational motions in a single joint without intermediate transmission mechanisms. The proposed SMM has a compact structure, low inertia, and high stiffness. First, the architecture and operating principle of the proposed SMM is introduced. Then, the kinematic model is established using Euler transformation, following which factors (such as workspace and dexterity) that have an impact on motion performance are evaluated. As the foundation of dynamics analysis and controller design, the Lagrange’s equations of the second kind are used to establish the dynamic model. To achieve high tracking accuracy, the radial basis function neural network–based sliding mode controller is applied to the mechanism. The simulation results indicate that the designed controller not only improves trajectory tracking capability but also enhances robustness against external disturbance and system uncertainty. Finally, experiments are performed on a prototype SMM to validate the performance of the proposed SMM and evaluate the control method.

Flamant solution of a half-plane with surface flexural resistibility and its applications to nanocontact mechanics

This article presents a semianalytical solution to a half-plane contact problem subjected to an arbitrarily distributed surface traction. The half-plane boundary is treated as a material surface of the Steigmann–Ogden type. Under the assumption of plane strain condition, the problem is formulated by coupling the methods of an Airy stress function and Fourier integral transforms. Stresses and displacements in the form of semi-infinite integrals are derived. A non-classical Flamant solution that is able to simultaneously account for the surface tension, membrane stiffness, and bending rigidity of the half-plane boundary is derived through limit analysis on the half-plane contact problem owing to a uniform surface traction. The fundamental Flamant solution is further integrated for tackling two half-plane contact problems owing to classical contact pressures corresponding to a rigid cylindrical roller and a rigid flat-ended punch. The resultant semi-infinite integrals are integrated by the joint use of the Gauss–Legendre numerical quadrature and the Euler transformation algorithm. Extensive parametric studies are conducted for comparing and contrasting the effects of Gurtin–Murdoch and Steigmann–Ogden surface mechanical models. The major observations and conclusions are two-fold. First, the introduction of either surface mechanical model results in size-dependent elastic fields. Second, the incorporation of the curvature-dependent nature of the half-plane boundary leads to bounded stresses and displacements in the fundamental Flamant solution. This is in contrast to the otherwise singular classical and Gurtin–Murdoch solutions. For all four case studies, the Steigmann–Ogden surface model also results in much smoother displacement and stress variations, indicating the significance of surface bending rigidity in nanoscale contact problems.

A modular CNN-based building detector for remote sensing images

Convolutional neural networks (CNNs) have resurged lately due to their state-of-the-art performance in various disciplines, such as computer vision, audio and text processing. However, CNNs have not been widely employed for remote sensing applications. In this paper, we propose a CNN architecture, named Modular-CNN, to improve the performance of building detectors that employ Histogram of Oriented Gradients (HOG) and Local Binary Patterns (LBP) in a remote sensing dataset. Additionally, we propose two improvements to increase the classification accuracy of Modular-CNN. The first improvement combines the power of raw and normalised features, while the second one concerns the Euler transformation of feature vectors. We demonstrate the effectiveness of our proposed Modular-CNN and the novel improvements in remote sensing and other datasets in a comparative study with other state-of-the-art methods.

Patterns of relation triples in inversion and ascent sequences

Recently, Martinez and Savage carried out the systematic study of inversion sequences avoiding triples of relations. They reported many nice connections with familiar combinatorial families and posed several enumeration conjectures. All of their conjectures have already been solved except those related to the OEIS sequence A098746. In this paper, we address those remaining conjectures, which completes a picture for all the suspected connections arising in their investigation.As one of the most important subsets of inversion sequences, ascent sequences were introduced by Bousquet-Mélou et al. in bijection with (2+2)-free posets and their pattern avoidance properties have been extensively studied. We investigate some classical Eulerian and Stirling statistics on ascent sequences avoiding triples of relations. This leads us to find two new interpretations of the Catalan numbers and its refinements, and to interpret combinatorially a natural refinement of the binomial transformation of Catalan numbers. The latter discovery answers a challenging open problem posed by Pudwell.

Investigation of Contact Performance of Case-Hardened Gears Under Plasto-elastohydrodynamic Lubrication

Case-hardening is widely used to enhance gear loading capacity. Simulation of the material gradient properties and contact characteristics are the key issues in contact fatigue analysis of case-hardened gears. In this work, a plasto-elastohydrodynamic lubrication (PEHL) model incorporating the hardness gradient and surface roughness is developed to investigate the contact performance of case-hardened gears. The generalized Reynolds equation is solved to determine film thickness and contact pressure. The plastic deformation and residual stress are obtained via the half-space eigenstrain problem solving. The Dang Van multiaxial fatigue criterion and the Euler transformation are employed to evaluate the contact fatigue parameter based on the predetermined stress field. The discrete convolution and fast Fourier transform (DC-FFT) algorithm is used for accelerating the computation. The influences of effective case depth, surface hardness and surface roughness on the contact performance are investigated. Numerical results indicate that as the surface hardness increases, the probability of fatigue crack nucleation decreases, and the depth of the crack initiation site increases. For a lower surface roughness case, the maximum von Mises stress and equivalent plastic strain appear at a deeper layer. As the surface roughness increases, the maximum values of pressure and stress increase sharply and move closer to the surface.

Prevalence of targetable mutations in black patients with lung cancer: A systematic review and meta-analysis.

e13105 Background: Although poorer outcomes of lung cancer in Blacks compared to other racial groups has been strongly linked to socio-economic factors, it is important to investigate whether lower prevalence of targetable mutations limit treatment options, thereby also contributing to worse outcomes. This study examines the prevalence of EGFR, ALK, ROS-1 and BRAF lung cancer mutations in Blacks compared to other races. Methods: We conducted a meta- analysis compliant with PRISMA guidelines. Searched databases included PubMed/MEDLINE, Cochrane CENTRAL, EMBASE, Google Scholar and clinicaltrials.gov. Publication bias was mitigated by searching clinicaltrials.gov for unpublished studies. Searches were run to 11/19/2018. Two rounds of screening were performed based on title and then abstract by two independent reviewers. For the purposes of this study we defined racial groups as Black, Asian, Hispanic, and White/Caucasian. We selected studies of lung cancer patients (any stage or type) where the prevalence of at least one mutation was reported in Blacks. We calculated the pooled prevalence of mutations by racial group using fixed effects, exact binomial distributions and Freeman-Turkey double arcsine transformation to stabilize the variances. Results: Prevalence % of mutations by race reported with 95% Confidence Interval in parentheses N = number of tests performed We included 20 studies which totaled 11,867 lung cancer patients. Each mutation tested on a tissue sample was considered an event, for a total of 15,306 events. EGFR was the most prevalent mutation in Blacks (6%). Compared to other races Blacks had the lowest prevalence of all four mutations. Conclusions: In the era of targeted therapy, outcomes for metastatic lung have improved significantly. Of concern, our results show that Blacks are disproportionately ineligible for these therapies due to lower prevalence of targetable mutations. More research is needed to evaluate the unique tumor characteristics and therapeutic strategies in this sub group of patients, in the hope of achieving better disease outcomes.[Table: see text]

Positivity and continued fractions from the binomial transformation

AbstractGiven a sequence of polynomials$\{x_k(q)\}_{k \ges 0}$, define the transformation$$y_n(q) = a^n\sum\limits_{i = 0}^n {\left( \matrix{n \cr i} \right)} b^{n-i}x_i(q)$$for$n\ges 0$. In this paper, we obtain the relation between the Jacobi continued fraction of the ordinary generating function ofyn(q) and that ofxn(q). We also prove that the transformation preservesq-TPr+1(q-TP) property of the Hankel matrix$[x_{i+j}(q)]_{i,j \ges 0}$, in particular forr= 2,3, implying ther-q-log-convexity of the sequence$\{y_n(q)\}_{n\ges 0}$. As applications, we can give the continued fraction expressions of Eulerian polynomials of typesAandB, derangement polynomials typesAandB, general Eulerian polynomials, Dowling polynomials and Tanny-geometric polynomials. In addition, we also prove the strongq-log-convexity of derangement polynomials typeB, Dowling polynomials and Tanny-geometric polynomials and 3-q-log-convexity of general Eulerian polynomials, Dowling polynomials and Tanny-geometric polynomials. We also present a new proof of the result of Pólya and Szegö about the binomial convolution preserving the Stieltjes moment property and a new proof of the result of Zhu and Sun on the binomial transformation preserving strongq-log-convexity.

Improved asymptotic predictions for the effective slip over a corrugated topography

• Significantly improved asymptotic predictions on effective slip in comparison to literature. • Systematic study on convergence radii of asymptotic series. • Novel use of series improvement and acceleration techniques. • Novel use of spectral analysis and symbolic computation. Accurate analytical prediction of the effective slip boundary condition in shear-driven Stokes flows directed longitudinally and transversely to a one-dimensional sinusoidal no-slip topography is explored. First, the domain perturbation technique is extended through spectral analysis and symbolic computations to obtain polynomial approximations (Taylor polynomials) of arbitrary specifiable order for the effective slip length. However, when assessed for numerical accuracy against fully-resolved numerical simulations using the finite-element-method, higher order Taylor polynomials give progressively inferior predictions in comparison to lower-order ones, unless the product of amplitude and wave-number is restricted below unity. From Domb–Sykes plots, the reason for the poor accuracy of higher order Taylor polynomials is assessed to be the finite convergence radii, approximately equaling unity, of the asymptotic power series for both longitudinal and transverse flows. For either of the flows, application of Euler transformation to the expansion parameter provide polynomial-form approximations that are accurate for amplitude values exceeding the convergence radius. The slow convergence of the Euler-transformed series can be remedied through Shanks transformation, at the cost of losing the convenience of closed forms. Finally, Padé approximants are shown to provide even more accurate but still closed-form alternatives to polynomials that work accurately at amplitudes much exceeding the above-identified convergence radii.

Discriminant Analysis via Joint Euler Transform and ℓ2,1-norm.

Linear Discriminant analysis (LDA) has been widely used for face recognition. However, when identifying faces in the wild, the existence of outliers that deviate significantly from the rest of data can arbitrarily skew the desired solution. This usually deteriorates LDA's performance dramatically, thus preventing it from mass deployment in real-world applications. To handle this problem, we propose an effective distance metric learning method based LDA, namely Euler LDA-L21 (e-LDA-L21). e-LDA-L21 is carried out in two stages, in which each image is mapped into a complex space by Euler transform in the first stage and the ℓ2,1-norm is adopted as the distance metric in the second stage. This not only reveals nonlinear features but also exploits the geometric structure of data. To solve e-LDA-L21 efficiently, we propose an iterative algorithm, which is a closed-form solution at each iteration with convergence guaranteed. Finally, we extend e-LDA-L21 to Euler 2DLDA-L21 (e-2DLDA-L21) which further exploits the spatial information embedded in image pixels. Experimental results on several face databases demonstrate its superiority over the state-of-the-art algorithms.

Path Tracking Control of a Differential-Drive Tracked Robot Based on Look-ahead Distance

In this paper, a PI path tracking controller based on look-ahead point information for a differential-drive crawler-type robot was developed. The robot is equipped with Global Navigation Satellite System (GNSS) antennas and a receiver module which are used as navigation sensors to obtain real-time estimates of the position and heading errors of the robot. To control the position of the robot with respect to the target path, a look-ahead point was generated by using Euler Transformation. The look-ahead point lateral errors were then controlled by the designed controller. Forward and backward path tracking tests with different look-ahead distances were conducted to examine the controller performance of the robot and the effect of changing look-ahead distance. Through experiment results, it was noted that the lateral errors mean value was within 0.05 m for forward path tracking and 0.06 m for backward path tracking while the heading errors mean value was within 0.5 degree for forward path tracking and 1 degree for backward path tracking. The proposed algorithms were suitable for the differential-drive robot platform for forward and backward path tracking with a reasonable look-ahead distance.

3D face verification across pose based on euler rotation and tensors

In this paper, we propose a new approach for 3D face verification based on tensor representation. Face challenges, such as illumination, expression and pose, are modeled as a multilinear algebra problem where facial images are represented as high order tensors. Particularly, to account for head pose variations, several pose scans are generated from a single depth image using Euler transformation. Multi-bloc local phase quantization (MB-LPQ) histogram features are extracted from depth face images and arranged as a third order tensor. The dimensionality of the tensor is reduced based on the higher-order singular value decomposition (HOSVD). HOSVD projects the input tensor in a new subspace in which the dimension of each tensor mode is reduced. To discriminate faces of different persons, we utilize the Enhanced Fisher Model (EFM). Experimental evaluations on CASIA-3D database, which contains large head pose variations, demonstrate the effectiveness of the proposed approach. A verification rate of 98.60% is obtained.

Formação ou produção de professores/as para a educação de jovens e adultos?

<p>As discussões no campo da formação de professores/as têm apontado para a necessidade de rupturas com modelos prescritivos o que requer pensar uma formação a partir de uma outra concepção. Desse modo, este artigo busca debater aspectos referentes à formação de professores/as, a fim de problematizar se essa formação ocorre levando em consideração as especificidades de cada modalidade e dos sujeitos que lá estão, ou se acaba por ser uma produção em massa de profissionais que atendam várias modalidades de educação, sem percepção das singularidades de cada uma delas. Objetiva-se pensar como o binômio experiência e transformação contribui para a reflexão sobre outras possibilidades de formação, ou de produção dos/as professores/as para a Educação de Jovens e Adultos (EJA). Ampara-se teoricamente em Arroyo, Benjamim, Haddad, Larrosa e Nóvoa. Percebe-se que a produção de professores/as precisa ter como referencial um mundo ambivalente, cuja proposição de normatividades para a contingência parta de quem vive. Para tanto, exige-se rever no próprio processo educativo, as relações que se tecem com elementos como o tempo, espaço, corpo, linguagem, técnica, entre outros.<strong></strong></p>

Improvements of series convergence to the rotating-channel flow problem using hydraulic solutions for a parabolic passage

ABSTRACTThis study deals with the perturbative solutions of the constant-potential-vorticity hydraulic problem, where the lowest-order solution corresponds to that for a non-rotating parabolic channel. The analytical structure of the series expansions and the corresponding numerical solutions are presented for flow through a horizontally constricted passage, and it is demonstrated how the series solution can be used to bridge the gap between non-rotating and rotating hydraulic models. It was found that the perturbative expansions converged close to the branch-point that corresponds to critical flow in rotating channel. This was not the case for the sub- and supercritical solution branches, where the perturbative series proved to diverge for discrete values of the expansion parameter, and hence one focus of the study is on improving the convergence here. The location and character of the dominant singularities affecting the series convergence were determined from analysis of the expansion coefficients using Domb–Sykes plots, where after the convergence was improved using Euler transformation rather than by direct Padé summation.

On some binomial B^{(m)}-difference sequence spaces

In this paper, we introduce the binomial sequence spaces b^{a,b}_{0}(B^{(m)}), b^{a,b}_{c}(B^{(m)}) and b^{a,b}_{infty}(B^{(m)}) by combining the binomial transformation and difference operator. We prove the BK-property and some inclusion relations. Furthermore, we obtain Schauder bases and compute the α-, β- and γ-duals of these sequence spaces. Finally, we characterize matrix transformations on the sequence space b_{c}^{a,b}(B^{(m)}).

Binomial difference sequence spaces of order m

In this paper, we introduce the binomial sequence spaces b^{r,s}_{0}(nabla^{(m)}), b^{r,s}_{c}(nabla^{(m)}) and b^{r,s}_{infty}(nabla^{(m)}) by combining the binomial transformation and mth order difference operator. We prove the BK-property and some inclusion relations. Also, we obtain the Schauder bases and compute the α-, β- and γ-duals of these sequence spaces.

Log-concavity and strong q-log-convexity for Riordan arrays and recursive matrices

Let [An,k]n,k⩾0 be an infinite lower triangular array satisfying the recurrencefor n ⩾ 1 and k ⩾ 0, where A0,0 = 1, A0,k = Ak,–1 = 0 for k > 0. We present some criteria for the log-concavity of rows and strong q-log-convexity of generating functions of rows. Our results can be applied to many well-known triangular arrays, such as the Pascal triangle, the Stirling triangle of the second kind, the Bell triangle, the large Schröder triangle, the Motzkin triangle, and the Catalan triangles of Aigner and Shapiro, in a unified approach. In addition, we prove that the binomial transformation not only preserves the strong q-log-convexity property, but also preserves the strong q-log-concavity property. Finally, we demonstrate that the strong q-log-convexity property is preserved by the Stirling transformation and Whitney transformation of the second kind, which extends some known results for the strong q-log-convexity property.

Binomial convolution and transformations of Appell polynomials

We show that the set A of Appell sequences is an abelian group under the binomial convolution. This is essentially equivalent to other approaches considered in the literature, in particular, the determinantal approach. We also define a scale transformation Tα:A→A, which is an isomorphism, and a transformation RY:A→A based on expectations with respect to a random variable Y. Using these tools, we give explicit formulas for the determinantal form of Appell sequences, as well as for the formula of representation of powers and the Srivastava–Pintér addition theorem. Various illustrative examples, mainly referring to various generalizations of Bernoulli and Euler polynomials, are discussed in detail.

Some normed binomial difference sequence spaces related to the ell_{p} spaces

The aim of this paper is to introduce the normed binomial sequence spaces b^{r,s}_{p}(nabla) by combining the binomial transformation and difference operator, where 1leq pleqinfty. We prove that these spaces are linearly isomorphic to the spaces ell_{p} and ell _{infty}, respectively. Furthermore, we compute Schauder bases and the α-, β- and γ-duals of these sequence spaces.

Binomials transformation formulae for scaled Fibonacci numbers

AbstractThe aim of the paper is to present the binomial transformation formulae of Fibonacci numbers scaled by complex multipliers. Many of these new and nontrivial relations follow from the fundamental properties of the so-called delta-Fibonacci numbers defined by Wituła and Słota. The paper contains some original relations connecting the values of delta-Fibonacci numbers with the respective values of Chebyshev polynomials of the first and second kind.