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We proposed Bayesian analysis for the generalized reciprocal lasso binary regression model. In Bayesian generalized reciprocal lasso we equip the likelihood function with an exponent called the learning rate. So, new hierarchical priors model have developed based on the scale mixture truncated normal (SMTN) distribution. In this paper the SMTN exploits as scale mixture for reciprocal Laplace distribution. New Gibbs sampler algorithm has derived by using the proposed hierarchical priors model. Real data analysis of covid-19 epidemiology has analyzed. The results demonstrated that the proposed model performs well than the other models according to the values of the mean square error and mean absolute error criterion. [ABSTRACT FROM AUTHOR]

Quantile regression is a regression method that modelling a relationship between quantile of variable response and one or more variable predictors. Quantile regression has advantages that linear regression does not have; it is robust against outliers and can model heteroscedasticity data. The parameters of quantile regression can be estimated using the Bayesian method. The Bayesian method is a data analysis tool derived based on the Bayesian inference principle. Bayesian inference is the process of studying data analysis inductively with the Bayes theorem. To estimate regression parameters with Bayesian inference, it is necessary to find the posterior distribution of the regression parameters where the posterior distribution is proportional to the product of the prior distribution and its likelihood function. Since the calculation of the posterior distribution analytically is difficult to do if more parameters are estimated, the Markov Chain Monte Carlo (MCMC) method is proposed. The use of the Bayesian method in quantile regression has advantages, namely the use of MCMC has the advantages of obtaining sample parameter values from an unknown posterior distribution, using computationally efficient, and easy to implement. Yu and Moyeed (2001) introduced Bayesian quantile regression using the likelihood function of errors with an Asymmetric Laplace Distribution (ALD) and found that minimizing parameter estimates in quantile regression is the same as maximizing the likelihood function of errors with an Asymmetric Laplace Distribution (ALD). The method used to estimate quantile regression parameters is Gibbs sampling from the ALD, which is a combination of the exponential and normal distributions. To find the parameters of the regression model by sampling the posterior distribution found in this thesis. The results obtained from Gibbs sampling are a sample sequence of estimated parameters. After obtaining the sample sequences, the sample lines are averaged to obtain an estimated regression parameter. The case study in this thesis discusses the effect of risk factors from motor vehicle insurance customers on the size of claims submitted by customers. [ABSTRACT FROM AUTHOR]

Worldwide an immense quantity of glass waste is produced in the remaining glass medicine containers. We propose to recycle the partial-empty glass containers as replacement of aggregates, especially sand, from plastering mortars. Several formulation of plastering mortars without and with glass of variable granulation, without and with antibiotic drugs was prepared. For each formulation seven prisms were casts. Pairs of two prisms were tested at 7, 14 and 28 days after preparation by measuring the mechanical strengths at elongation and compression. In the seventh prism a pair of humidity and temperature sensors was placed in order to monitor the hydration and dehydration processes to characterize the effect of aggregates replacement by glass waste. Advanced ¹H NMR relaxometry and diffusometry measurement were performed on samples parts resulted from mechanical tests at 7, 14 and 28 days after preparation. Then the samples were sunken in water and measured after a full hydration of plaster mortar stone. The experimental data were analyzed by inverse Laplace transform and the distributions of transverse relaxation time T2 were obtained. [ABSTRACT FROM AUTHOR]

Bilateral Laplace transform is known for its capability on taking Laplace transform over all real numbers. This paper provides a different approach by using inverse bilateral Laplace transform on deriving analytic solution of European option price formula, both call option and put option. Case of uncorrelated processes between asset price and volatility of Black-Scholes model of asset pricing with stochastic volatility driven by Ornstein-Uhlenbeck process is used to portray price of a risky asset in the market. This paper also provides proof for required formulations to derive the analytic solutions and reference for alternative forms of inverse bilateral Laplace transform. [ABSTRACT FROM AUTHOR]

The mathematical model is presented to analyze the wave spectrum inside Paradip port under the resonance conditions with partial reflection, diffraction and refraction. During the extreme weather conditions, Paradip port have experienced the extreme ocean wave 3~5 m in surface height. In irregular domain, the solution of Laplace equation along with partial refection condition on quays and breakwaters is obtained by using 3-D Boundary Element Method (3-D BEM). To validation, the present numerical scheme result is compared with the experimental data of Ippen & Goda (1963) and Lee (1971). Six record stations are located inside the port based on moored ship terminals. At these locations, the wave spectrum is computed by utilizing the Fast Fourier Transform (FFT) for the surface waves obtained in Paradip port. [ABSTRACT FROM AUTHOR]

Mathematical model for description of the dynamic processes in liquid crystals under weak mechanical, temperature and electric perturbations was proposed. In this work the parallel computational algorithm for analysis of the influence of electric field on a layer of a liquid-crystal medium is represented. In the exterior part of the layer, a potential of electric field satisfies the Laplace equation, which solution is constructed by the method of straight lines. Inside the layer, the equation taking into account anisotropy of a medium is solved by means of iterative method. In the presence of electric field, the molecules of the crystal experience the action of bulk forces and couple stresses, which can be used as right-hand sides of the basic equations of mathematical model. The algorithm is implemented using the CUDA technology for computer systems with graphics accelerators. Parallel program contains modules realizing the method of straight lines with the use of a three-point sweep, the fast Fourier transform and the SLAE solution method by means of the LU-decomposition, the iterative method of solving the equation for potential. [ABSTRACT FROM AUTHOR]

This paper is the solution to Rosenau-Hyman equation use Laplace transform in with other initial conditions. The results tell us that the proposed method is more efficient 1 dimensional, 2 dimensional to m dimensional. [ABSTRACT FROM AUTHOR]

For the elliptic equation 2l- th order with constant (and only) real coefficients considered boundary value problem of the job normal derivatives the (kj - 1)- order, j = 1, . . ., l, where 1 ≤ k1 < . . . < kl ≤ 2l - 1. When kj = j it moves to the Dirichlet problem, and when kj = j + 1 - in the Neumann problem. In this paper, the study is carried out in space C2l,u(D). The sufficient condition of the Fredholm tasks and present a Formula for its index. [ABSTRACT FROM AUTHOR]

The 2-D problem of an infinite elastic solid with a nanoinclusion of a different from circular shape is solved. The interfacial stresses are acting at the interface. Contact of the inclusion with the matrix satisfies the ideal conditions of cohesion. The generalized Laplace – Young law defines conditions at the interface. To solve the problem, Gurtin – Murdoch surface elasticity model, Goursat – Kolosov complex potentials and the boundary perturbation method are used. The problem is reduced to the solution of two independent Riemann – Hilbert’s boundary problems. For the circular inclusion, hypersingular integral equation in an unknown interfacial stress is derived. The algorithm of solving this equation is constructed. The influence of the interfacial stress and the dimension of the circular inclusion on the stress distribution and stress concentration at the interface are analyzed. [ABSTRACT FROM AUTHOR]

We consider the spectral Neumann problem for the Laplace operator in an acoustic waveguide obtained from a straight unit strip by a low box-shaped perturbation. We prove that the waveguide supports a trapped mode with an eigenvalue embedded into the continuous spectrum. The main technical difficulty is caused by corner points of the perturbed wall. [ABSTRACT FROM AUTHOR]

The Laplace-Beltrami operator plays an important role as C² function smoother and its eigenfunction applications are studied extensively in last five decades, not only, in image processing field but we can meet with these functions ranging from molecular physics scientific field to mechanical engineering. However, in many non-trivial cases, e.g. computations on non-uniform meshes, the discrete Laplace operator could be ill-conditioned and inappropriate for numerical computations. Especially, in the spectral clustering tool, a condition number of the graph Laplacian goes to infinity, when pairwise similarities among most graph nodes go to zero. Therefore, in this paper, we reformulate the image graph Laplacian as the semi-smooth Laplace-Beltrami operator on a non-uniform mesh and study its numerical properties, then we introduce our fundamental approach for improving a numerical stability of this operator. [ABSTRACT FROM AUTHOR]

Some new stochastic algorithms are suggested to determine the minimal eigenvalue for the first boundary value problem for Laplace operator. [ABSTRACT FROM AUTHOR]

Boundary Element Method (BEM) is a numerical way to approximate the solutions of a Boundary Value Problem (BVP). The potential problem which involves the Laplace's equation on the square shape domain will be considered where the boundary is divided into four sets of linear boundary elements. We study the derivation system of equation for mixed BVP with one Dirichlet Boundary Condition (BC) is prescribed on one element of the boundary and Neumann BC on the other three elements. The mixed BVP will be reduced to a Boundary Integral Equation (BIE) by using a direct method which involves Green's second identity representation formula. Then, linear interpolation is used where the boundary will be discretized into some linear elements. As the result, we then obtain the system of linear equations. In conclusion, the specific element in the mixed BVP will have the specific prescribe value depends on the type of boundary condition. For Dirichlet BC, it has only one value at each node but for the Neumann BC, there will be different values at the corner nodes due to outward normal. Therefore, the assembly process for the system of equations related to the mixed BVP may not be as straight forward as Dirichlet BVP and Neumann BVP. For the future research, we will consider the different shape domains for mixed BVP with different prescribed boundary conditions. [ABSTRACT FROM AUTHOR]

The property of tight oil reservoir is worse than common reservoir that we usually seen before, the porosity and permeability is low, the diffusion is very complex. Therefore, the ordinary depletion method is useless here. The volume fracture breaks through the conventional EOR mechanism, which set the target by amplifying the contact area of fracture and reservoir so as to improving the production of every single well. In order to forecast the production effectively, we use the traditional dual-porosity model, build an analytical model for production of volume fractured tight oil reservoir with horizontal well, and get the analytical solution in Laplace domain. Then we construct the log-log plot of dimensionless pressure and time by stiffest conversion. After that, we discuss the influential factors of pressure. Several factors like cross flow, skin factors and threshold pressure gradient was analyzed in the article. This model provides a useful method for tight oil production forecast and it has certain guiding significance for the production capacity prediction and dynamic analysis. [ABSTRACT FROM AUTHOR]

The aim of this study was to determine the effects of rank transformation on estimations of genetic parameters for non-normally distributed four simulated variables. X1, X2, X3, X4 have means and variances of 10, and the variables originated from Laplace distribution, Poisson distribution, Uniform distribution, Weibull distribution, respectively. After rank transformation, these values are 0 and 1 for each variable, respectively. Except the Poisson distribution all variables has been transformed into Gaussian distribution by rank transformation. It was determined that genetic information loss did not occur in any of the variables with normally distributed by rank transformation. It is possible to say that rank transformation can be used safely in quantitative genetic analyzes with regard to research results. [ABSTRACT FROM AUTHOR]

This paper presents hepatitis disease diagnosis using a Bayesian theory for better understanding of the theory. In this research, we used a Bayesian theory for detecting hepatitis disease and displaying the result of diagnosis process. Bayesian algorithm theory is rediscovered and perfected by Laplace, the basic idea is using of the known prior probability and conditional probability density parameter, based on Bayes theorem to calculate the corresponding posterior probability, and then obtained the posterior probability to infer and make decisions. Bayesian methods combine existing knowledge, prior probabilities, with additional knowledge derived from new data, the likelihood function. The initial symptoms of hepatitis which include malaise, fever and headache. The probability of hepatitis given the presence of malaise, fever, and headache. The result revealed that a Bayesian theory has successfully identified the existence of hepatitis disease. [ABSTRACT FROM AUTHOR]

In the paper, we discuss the transformation of the asymptotic distribution of asymptotically normal statistics if the sample size is replaced by a random variable. We also discuss the asymptotic expansions of the distribution function and concentration functions of statistics constructed from samples with random sizes. [ABSTRACT FROM AUTHOR]

In Electrical Impedance Tomography (EIT), different current patterns are injected to the unknown object through the electrodes attached at the boundary ∂Ω of Ω. The corresponding voltages V are then measured on its boundary surface. Based on these measured voltages, the image reconstruction of the conductivity distribution σ is done by solving an inverse problem of a generalized Laplace equation subject to a homogeneous Neumann boundary condition. In other words, with known V, we seek to solve for the typically piecewise values of σ, from which the geometry of internal objects may be inferred. We approach this problem by using a multi-phase segmentation method. We express σ as σ(x) = σMm =1 σm(x)χm(x), where χm is the characteristic function of a subdomain Ωm such that Ωm ∩ Ωn = ø, m ≠ n and Ω = ∪Mm =1Ωm. The expected number of phases for Ω is M, where M = 2 for this work. The number of segments is the number of connected components of the subdomains. Using a calculated optimality condition, the conductivity value σm is expressed as a function of χm. The total variation of χm is then introduced to regularize the resulting cost functional. Using a descent method, an update for χm is proposed. In this work, the Finite Element Method (FEM) convergence of all the resulting variational formulations are studied. A real analytic mollification of χm is introduced to guarantee convergence. [ABSTRACT FROM AUTHOR]

This paper proposed a new algorithm (IM-COH) which was developed based on backpropagation algorithm on neural network (BPNN). This kind of algorithm improved the generalization ability on neural networks to optimize its structure in regularization method. The IM-COH algorithm controls the outputs of nodes in the hidden layers which were manipulated to eliminate the distribution weights problem and enhance the ability to move toward target problems. Furthermore, the IM-COH algorithm maintains the ability to reduce the random noise in the input sample. In this research, the IM-COH algorithm is simulated with two-spiral classification problem and Mackey-Glass time series prediction to compare with Gaussian regularizer (GR) and Laplace regularizer (LR). The results show that the generalization ability of the IM-COH algorithm is better than GR and LR in testing data samples and noise data. In addition, the IM-COH algorithm performs better in solving the two-spiral classification problem comparing to Mackey-Glass time series prediction. [ABSTRACT FROM AUTHOR]

The objective of this study is to investigate the influence of the rotary inertia on the dynamic behavior of linear viscoelastic non-cylindrical helicoidal bars due to variation of the active turns. Dynamic analysis is performed in the Laplace space by using the mixed finite element method. The standard model is used for defining the viscoelastic material behavior and by using the correspondence principle, the material constants are replaced with their complex counterparts in the Laplace space. The solution under the rectangular impulsive type loading is carried out in the Laplace space and then the results are transformed back to time domain numerically by the Modified Durbin's transformation algorithm. Some original numerical results for the dynamic behavior of linear viscoelastic non-cylindrical helices with rectangular cross-section are presented. [ABSTRACT FROM AUTHOR]

In this paper we obtain the Lie derivatives of the scalar parameters in the generalized Euler decomposition with respect to arbitrary axes under left and right deck transformations. This problem can be directly related to the representation of the angular momentum in quantum mechanics. As a particular example, we calculate the angular momentum and the corresponding quantum hamiltonian in the standard Euler and Bryan representations. Similarly, in the hyperbolic case, the Laplace-Beltrami operator is retrieved for the Iwasawa decomposition. The case of two axes is considered as well. [ABSTRACT FROM AUTHOR]

The paper proposes the use of rectangular Bézier surface patches for shape identification of the boundary for 3D potential problems modeled by the Laplace equation. The graphical representation of the boundary generated by Bézier patches is considered directly in mathematical formula of parametric integral equation systems (PIES) that allows to eliminate the need of dividing the boundary into elements. The numerical examples included in the paper demonstrate simplification in the boundary description by Bézier patches and applicability for boundary shape identification problems. [ABSTRACT FROM AUTHOR]

New goodness-of-fit tests for the family of asymmetric Laplace distributions are constructed. The proposed tests are based on a weighted integral incorporating the empirical characteristic function of suitably standardized data, and can be written in a closed form appropriate for computer implementation. Monte Carlo results show that the new procedure are competitive with classical goodness-of-fit methods. Applications with financial data are also included. [ABSTRACT FROM AUTHOR]