Functions Of Different Orders Research Articles

Factorization of the matrices of discrete wavelet transform on the Galois functions base

The paper deals with the factorization of the matrices of discrete wavelet transform based on the Galois functions of different orders. It is used the known method of factorization of the matrices of the discrete Haar transform. Factorized matrices of transforms are presented in the form of a product of sparse matrices. This representation is the basis for building fast transforms algorithms.

Random regression models using B-splines functions provide more accurate genomic breeding values for milk yield and lactation persistence in Murrah buffaloes.

There is a great worldwide demand for cheese made with buffalo milk, due to its flavour and nutritional properties. In this context, there is a need for increasing the efficiency of buffalo milk production (including lactation persistence), which can be achieved through genomic selection. The most used methods for the genetic evaluation of longitudinal data, such as milk-related traits, are based on random regression models (RRM). The choice of the best covariance functions and polynomial order for modelling the random effects is an important step to properly fit RRM. To our best knowledge, there are no studies evaluating the impact of the order and covariance function (Legendre polynomials-LEG and B-splines-BSP) used to fit RRM for genomic prediction of breeding values in dairy buffaloes. Therefore, the main objectives of this study were to estimate variance components and evaluate the performance of LEG and BSP functions of different orders on the predictive ability of genomic breeding values for the first three lactations of milk yield (MY1, MY2, and MY3) and lactation persistence (LP1, LP2, and LP3) of Brazilian Murrah. Twenty-two models for each lactation were contrasted based on goodness of fit, genetic parameter estimates, and predictive ability. Overall, the models of higher orders of LEG or BSP had a better performance based on the deviance information criterion (DIC). The daily heritability estimates ranged from 0.01 to 0.30 for MY1, 0.08 to 0.42 for MY2, and from 0.05 to 0.47 for MY3. For lactation persistence (LP), the heritability estimates ranged from 0.09 to 0.32 for LP1, from 0.15 to 0.33 for LP2, and from 0.06 to 0.32 for LP3. In general, the curves plotted for variance components and heritability estimates based on BSP models presented lower oscillation along the lactation trajectory. Similar predictive ability was observed among the models. Considering a balance between the complexity of the model, goodness of fit, and credibility of the results, RRM using quadratic B-splines functions based on four or five segments to model the systematic, additive genetic, and permanent environment curves provide better fit with no significant differences between genetic variances estimates, heritabilities, and predictive ability for the genomic evaluation of dairy buffaloes.

Mobilization of Fiscal Resources as Development Engine of Decentralized Territorial Entities: The case study of Mbandaka City in Democratic Republic of the Congo

The State as an institution was born from the will of the people for the realization of activities of common interest, such as: the building of hospitals, roads, schools, electrification, job creation, water etc. As the protector of goods, the state is called upon to fulfill several duties either governmental, when the state exercises its sovereignty to legislate and execute, or administrative when it ensures the management of the public administration for the benefit of the collective welfare thanks to the various taxes, levies and other charges mobilized and/or collected from the population in order to meet its expectations and aspirations. The modern State fulfills five important socio-economic duties, which are: production, regulation, protection, compensation and finally the function of stabilization and stimulation of the economic growth. Through production, the state intervenes not only to produce and create material wealth, but also to ensure the necessary conditions for its creation (e.g., provide adequate infrastructure and create an efficient administration). The state plays the role of the father of the city, must demonstrate certain equity through distributive justice, ensuring the redistribution of income by means of taxation on the income of the individual and the profit of the corporations or by means of aid and social security. Finally, the state has the responsibility of stabilizing and stimulating the economic growth. To achieve this, it is vital to practice the policy of full employment, price stability and very rapid economic growth, with the aim of increasing the quantity, quality and mobility of production factors, it is reflected in the policy of education, scientific research and training as well as labor mobility. Thus, local elected officials are called upon to fulfill these different functions in order to take off the development of their areas of common interest for the benefit of community welfare at the grassroots level.

Unconventional phonon blockade via atom-photon-phonon interaction in hybrid optomechanical systems.

Phonon nonlinearities play an important role in hybrid quantum networks and on-chip quantum devices. We investigate the phonon statistics of a mechanical oscillator in hybrid systems composed of an atom and one or two standard optomechanical cavities. An efficiently enhanced atom-phonon interaction can be derived via a tripartite atom-photon-phonon interaction, where the atom-photon coupling depends on the mechanical displacement without practically changing a cavity frequency. This novel mechanism of optomechanical interactions, as predicted recently by Cotrufo et al. [Phys. Rev. Lett.118, 133603 (2017)10.1103/PhysRevLett.118.133603], is fundamentally different from standard ones. In the enhanced atom-phonon coupling, the strong phonon nonlinearity at a single-excitation level is obtained in the originally weak-coupling regime, which leads to the appearance of phonon blockade. Moreover, the optimal parameter regimes are presented both for the cases of one and two cavities. We compared phonon-number correlation functions of different orders for mechanical steady states generated in the one-cavity hybrid system, revealing the occurrence of phonon-induced tunneling and different types of phonon blockade. Our approach offers an alternative method to generate and control a single phonon in the quantum regime and could have potential applications in single-phonon quantum technologies.

Enhancement of the HILOMOT Algorithm with Modified EM and Modified PSO Algorithms for Nonlinear Systems Identification

Developing a mathematical model has become an inevitable need in studies of all disciplines. With advancements in technology, there is an emerging need to develop complex mathematical models. System identification is a popular way of constructing mathematical models of highly complex processes when an analytical model is not feasible. One of the many model architectures of system identification is to utilize a Local Model Network (LMN). Hierarchical Local Model Tree (HILOMOT) is an iterative LMN training algorithm that uses the axis-oblique split method to divide the input space hierarchically. The split positions of the local models directly influence the accuracy of the entire model. However, finding the best split positions of the local models presents a nonlinear optimization problem. This paper presents an optimized HILOMOT algorithm with enhanced Expectation–Maximization (EM) and Particle Swarm Optimization (PSO) algorithms which includes the normalization parameter and utilizes the reduced-parameter vector. Finally, the performance of the improved HILOMOT algorithm is compared with the existing algorithm by modeling the NOx emission model of a gas turbine and multiple nonlinear test functions of different orders and structures.

Solving Cauchy Issues of Highly Nonlinear Elliptic Equations Using a Meshless Method

In this paper, we address 3D inverse Cauchy issues of highly nonlinear elliptic equations in large cuboids by utilizing the new 3D homogenization functions of different orders to adapt all the specified boundary data. We also add the average classification as an approximate solution to the nonlinear operator part, without requiring to cope with nonlinear equations to resolve the weighting coefficients because these constructions are owned many conditions about the true solution. The unknown boundary conditions and the result can be retrieved straightway by coping with a small-scale linear system when the outcome is described by a new 3D homogenization function, which is right to find the numerical solutions with the errors smaller than the level of noise being put on the over-specified Neumann conditions on the bottom of the cuboid. Besides, note that the new homogenization functions method (HFM) does not require dealing with the regularization and highly nonlinear equations. The robustness and accuracy of the HFM are verified by comparing the recovered results of several numerical experiments to the exact solutions in the entire region, even though a very large level of noise 50% is imposed on the over specified Neumann conditions. The numerical errors of our scheme are in the order of O(10−1)–O(10−4).

Covariance functions under B-spline polynomials to model Polled Nellore cattle growth

B-spline functions have been used in random regression models (RRM) to model animal weight from birth to adulthood because they are less vulnerable to common difficulties of other methods. However, its application to model growth traits of Polled Nellore cattle has been little studied. Therefore, this study aimed to evaluate polynomial functions of different orders and segment numbers to model effects associated with the Polled Nellore cattle growth curve. For this purpose, we used 15,148 weight records of 3,115 animals aged between 1 and 660 days and reared in northern Brazil and born between 1995 and 2010. Random effects were modeled using B-spline polynomials. As random effects, we considered the direct and maternal genetic additives, as well as direct and maternal permanent environments. As fixed effects were included contemporary group, cow age at calving (linear and quadratic) and fourth-order Legendre polynomials to represent average growth curve. The residue was modeled by considering seven age classes. The bestfitted model was the one that considered cubic B-spline functions with four knots for direct additive genetic effects and three knots for maternal genetic, animal permanent environment, and maternal permanent environment effects (C6555). Therefore, covariance functions under B-spline polynomials are efficient and can be used to model the growth curve of Polled Nellore cattle from birth to 660 days of age.

Non-extreme-Points Approach to Extreme Points of Integral Families of Analytic Functions

Non extreme points of compact, convex integral families of analytic functions are investigated. Knowledge about extreme points provides a valuable tool in the optimization of linear extremal problems. The functions studied are determined by a 2-parameter collection of kernel functions integrated against measures on the torus. Families from classical geometric function theory such as the closed convex hull of the derivatives of normalized close-to-convex functions, the ratio of starlike functions of different orders, as well as many others are included. However for these families of analytic functions, identifying “all” the extreme points remains a difficult challenge except in some special cases. Aharonov and Friedland [1] identified a band of points on the unit circle which corresponds to the set of extreme points for these 2-parameter collections of kernel functions. Later this band of extreme points was further extended by introducing a new technique by Dow and Wilken [3]. On the other hand, a technique to identify a non extreme point was not investigated much in the past probably because identifying non extreme points does not directly help solving the optimization of linear extremal problems. So far only one point on the unit circle has beenidentified which corresponds to a non extreme point for a 2-parameter collections of kernel functions. This leaves a big gap between the band of extreme points and one non extreme point. The author believes it is worth developing some techniques, and identifying non extreme points will shed a new light in the exact determination of the extreme points. The ultimate goal is to identify the point on the unit circle that separates the band of extreme points from non extreme points. The main result introduces a new class of non extreme points.

Transient deformation and curvature evolution during the snap-through of a bistable laminate under asymmetric point load

Bistable carbon fiber composites, whose bistability arises from having asymmetric fiber layouts in different layers, have shown immense potential for using in shape morphing and adaptive structure applications. While many studies in this field focus on these composite laminates' external shapes at the two stable states, their snap-through behavior of shifting from one stable shape to the other remains a critical aspect to be investigated in complete detail. Moreover, symmetric loading conditions have been extensively studied based on the classical lamination theory, but the asymmetric loading conditions received far less attention. Therefore, this study examines an asymmetric, localized point load on a [0∘/90∘] bistable laminate and its complex transient deformation during the snap-through. Finite element simulation and experiment results reveal three uniquely different snap-through behaviors — two-step snap, one-step snap, and no snap — depending on the point load location. The localized initiation and propagation of a “curvature inversion zone,” calculated from finite element and digital image correlation results, are directly related to these snap-through characteristics. This study also explored the feasibility of using an extended analytical model of classical lamination theory to qualitatively reproduce the above findings. This model compares three polynomial functions of different orders to approximate the out-of-plane laminate displacement field. This study's results can offer valuable insights into the fundamental mechanics of snap-through behaviors and the actuation designs for the bistable composites for different loading scenarios.

Humor in Times of COVID-19 in Spain: Viewing Coronavirus Through Memes Disseminated via WhatsApp.

The COVID-19 crisis, and its ensuing periods of confinement, has generated high levels of social stress on a global scale. In Spain, citizens were isolated in their homes and were not able to interact physically with family members, friends or co-workers. Different resources were employed to face this new stressful and unexpected situation (fitness, reading, painting, meditation, mindfulness, dancing, listening to music, playing instruments, cooking, etc.). Humor was one of the most frequent and widely used strategies in an attempt to keep perspective, deal with the seriousness of the situation and make the day-to-day more bearable. Humor is cultural: it varies from one country to the next and is part of the idiosyncrasies of a culture. It is deemed a particularly important feature of the Spanish personality. During the COVID-19 crisis, the main means or channels of communication were social networks. Throughout the confinement period, there was an excessive flow of humorous memes concerning Coronavirus and related shared experiences during the National State of Emergency decreed by the Spanish Government. The memes draw on irony, ingenuity and creativity to make a difficult and stressful experience more bearable. In this paper, a qualitative methodology based on ethnography research is used and ethnographic fieldwork is carried out on the memes disseminated through WhatsApp during the lockdown period experienced in Spain (14 March to 21 June 2020). The memes are considered to be an example of Netlore, digital contemporary folklore, and a theoretical framework on memes and humor is presented that discusses its different functions in order to channel grief, fear and suffering or to play down specific situations. A corpus of 644 memes that have flooded social networks are categorized and analyzed to witness how the Spanish have managed to bring out their humorous and creative side in difficult times even as they have criticized political decisions, let out their frustrations, described their new “normal” lives, interacted with others and anticipated the future.

3D Ising model: a view from the conformal bootstrap island

We explain how the axioms of Conformal Field Theory are used to make predictions about critical exponents of continuous phase transitions in three dimensions, via a procedure called the conformal bootstrap. The method assumes conformal invariance of correlation functions, and imposes some relations between correlation functions of different orders. Numerical analysis shows that these conditions are incompatible unless the critical exponents take particular values, or more precisely that they must belong to a small island in the parameter space.

The correct cutoff for Rutherford scattering cross-section

The correct cutoff variable for the integrals with Rutherford scattering cross-section is established in this paper. The traditional cutoff variables in plasma physics, such as scattering angle θ and impact parameter b, are incorrect or just partial cutoff variables for lacking the necessary cutoff on relative speed g. The correct cutoff variable is the same variable that correctly describing the singularity of the integrals. The difference of the partial cutoff variables and the correct one is compared through their contour lines in the b − g plane. With the correct cutoff, many physical results become more simplified and structured for both rigid-sphere interaction and Coulomb interaction. These physical results include the arbitrary higher order of Fokker-Planck coefficients, transition moments, and energy transfer rates for both rigid-sphere and Coulomb interactions. All the physical results depending on velocity are expressed by a set of functions . A useful integral formula∫0∞qn(k)(ymin,u)uk+2e−u2ξdu=ξk+3221+ξk−n2∑j=0⌊k/2⌋k!Γn+k+12−j,ymin21+ξj!(k−2j)!4ξj,which associates with incomplete gamma functions is also proved. This integral formula is the key to show that the correct cutoff constants for both rigid-sphere and Coulomb interactions are all in the form of incomplete gamma functions of different orders. In particular, the so called Coulomb logarithm should be replaced by the exact form—the zeroth order incomplete Gamma function.

On the Hurwitz zeta function with an application to the beta-exponential distribution

We prove a monotonicity property of the Hurwitz zeta function which, in turn, translates into a chain of inequalities for polygamma functions of different orders. We provide a probabilistic interpretation of our result by exploiting a connection between Hurwitz zeta function and the cumulants of the beta-exponential distribution.

Isogeometric analysis of thin Reissner–Mindlin shells: locking phenomena and B-bar method

We propose a local type of B-bar formulation, addressing locking in degenerated Reissner–Mindlin shell formulation in the context of isogeometric analysis. Parasitic strain components are projected onto the physical space locally, i.e. at the element level, using a least-squares approach. The formulation allows the flexible utilization of basis functions of different orders as the projection bases. The introduced formulation is much cheaper computationally than the classical $$\bar{B}$$ method. We show the numerical consistency of the scheme through numerical examples, moreover they show that the proposed formulation alleviates locking and yields good accuracy even for slenderness ratios of $$10^5$$ , and has the ability to capture deformations of thin shells using relatively coarse meshes. In addition it can be opined that the proposed method is less sensitive to locking with irregular meshes.

Representations of mock theta functions

Motivated by the works of Liu, we provide a unified approach to find Appell-Lerch series and Hecke-type series representations for mock theta functions. We establish a number of parameterized identities with two parameters a and b. Specializing the choices of (a,b), we not only give various known and new representations for the mock theta functions of orders 2, 3, 5, 6 and 8, but also present many other interesting identities. We find that some mock theta functions of different orders are related to each other, in the sense that their representations can be deduced from the same (a,b)-parameterized identity. Furthermore, we introduce the concept of false Appell-Lerch series. We then express the Appell-Lerch series, false Appell-Lerch series and Hecke-type series in this paper using the building blocks m(x,q,z) and fa,b,c(x,y,q) introduced by Hickerson and Mortenson, as well as m‾(x,q,z) and f‾a,b,c(x,y,q) introduced in this paper. We also show the equivalences of our new representations for several mock theta functions and the known representations.

Time series prediction of mooring line top tension by the NARX and Volterra model

To minimize the computation burdens of long-term analysis, the mooring line top tensions under various short-term sea states were predicted using the pre-calculated nonlinear time domain analysis results of some selected sea states. A nonlinear autoregressive with an exogenous input (NARX) technique was introduced with a finite nonlinear memory length to predict the top-tension of a mooring line of the box-type floating production storage and offloading (FPSO). The NARX was designed in such a way that it takes the floater’s motions as its input and produces the mooring line top tension as an output. After training the NARX using the pre-calculated time series of the motions and tensions of some selected sea states, the tension time histories of different sea sates were predicted and compared with the direct time domain analysis results. In addition, to explore the nonlinearity of the system and its contribution to the response, the transfer functions of different orders were extracted after expanding the NARX equation using a Taylor series expansion. The nonlinear contributions coming from both the 3rd and 5th order were significant.

Solving the 3D Cauchy problems of nonlinear elliptic equations by the superposition of a family of 3D homogenization functions

We solve the 3D Cauchy problem of a nonlinear elliptic equation in a cuboid, using the derived family of 3D homogenization functions of different orders. When the solution is expressed by the weight superposition of a family of 3D homogenization functions, the unknown boundary data and the solution can be recovered quickly by solving a small scale linear system. It deserves to note that the superposition of homogenization functions method (SHFM) does not need to solve nonlinear equations and regularization, and is quite accurate to find the solution in the whole domain with the errors smaller than the level of noise being imposed on the overspecified Neumann data. Another advantage of the SHFM is that it can solve the Cauchy problem in a large size of the cuboid.

Covariance function of Legendre polynomials for the modeling of Polled Nellore cattle growth in northern Brazil

This study aimed to compare random regression models fitted by Legendre orthogonal polynomials and determine which best fits changes in Nellore cattle growth parameters. Age polynomial functions of different orders were evaluated using a random-effect modeling associated with a genetic study of cattle growth curves. For this purpose, weight records (15,148) were performed in Polled Nellore bovines (3,115), aged between 1 and 660 days, reared in northern Brazil and born between 1995 and 2010. The fixed effects of analytical models comprised age-matched groups, heifer calving age (linear and quadratic), and fourth-order Legendre age polynomial (cubic), depicting the mean growth curve. Besides, different order functions were considered for random effects, so that (co) variance associated with genetic effects (direct and maternal) and permanent environmental effects (animal and maternal) could be modeled. Residual variance was fitted by six heterogeneous classes throughout the analyzed period. According to AIC and BIC criteria, the model 6333 allowed the fitting of changes in variance and covariance over time (genetic and environmental). Thus, this model can be used to describe age-related changes in Polled Nellore cattle reared in northern Brazil.

Multiphoton nonclassical light from clusters of single-photon emitters

We study nonclassical features of multiphoton light emitted by clusters of single-photon emitters. As signatures of nonclassicality, we use violation of inequalities for normalized correlation functions of different orders or the probabilities of multiphoton detection. In particular, for clusters of 2–14 colloidal CdSe/CdS dot-in-rods we observe antibunching and nonclassicality of up to the fourth-order. Surprisingly, violation of certain classical inequalities gets even more pronounced for larger clusters.

Main beam modeling for large irregular arrays

Large radio telescopes in the 21st century such as the Low-Frequency Array (LOFAR) or the Murchison Widefield Array (MWA) make use of phased aperture arrays of antennas to achieve superb survey speeds. The Square Kilometer Array low frequency instrument (SKA1-LOW) will consist of a collection of non-regular phased array systems. The prediction of the main beam of these arrays using a few coefficients is crucial for the calibration of the telescope. An effective approach to model the main beam and first few sidelobes for large non-regular arrays is presented. The approach exploits Zernike polynomials to represent the array pattern. Starting from the current defined on an equivalence plane located just above the array, the pattern is expressed as a sum of Fourier transforms of Zernike functions of different orders. The coefficients for Zernike polynomials are derived by two different means: least-squares and analytical approaches. The analysis shows that both approaches provide a similar performance for representing the main beam and first few sidelobes. Moreover, numerical results for different array configurations are provided, which demonstrate the performance of the proposed method, also for arrays with shapes far from circular.