Solution Of Differential Problem Research Articles

ROADS CENTRE-AXIS EXTRACTION IN AIRBORNE SAR IMAGES: AN APPROACH BASED ON ACTIVE CONTOUR MODEL WITH THE USE OF SEMI-AUTOMATIC SEEDING

Abstract. Research works dealing with computational methods for roads extraction have considerably increased in the latest two decades. This procedure is usually performed on optical or microwave sensors (radar) imagery. Radar images offer advantages when compared to optical ones, for they allow the acquisition of scenes regardless of atmospheric and illumination conditions, besides the possibility of surveying regions where the terrain is hidden by the vegetation canopy, among others. The cartographic mapping based on these images is often manually accomplished, requiring considerable time and effort from the human interpreter. Maps for detecting new roads or updating the existing roads network are among the most important cartographic products to date. There are currently many studies involving the extraction of roads by means of automatic or semi-automatic approaches. Each of them presents different solutions for different problems, making this task a scientific issue still open. One of the preliminary steps for roads extraction can be the seeding of points belonging to roads, what can be done using different methods with diverse levels of automation. The identified seed points are interpolated to form the initial road network, and are hence used as an input for an extraction method properly speaking. The present work introduces an innovative hybrid method for the extraction of roads centre-axis in a synthetic aperture radar (SAR) airborne image. Initially, candidate points are fully automatically seeded using Self-Organizing Maps (SOM), followed by a pruning process based on specific metrics. The centre-axis are then detected by an open-curve active contour model (snakes). The obtained results were evaluated as to their quality with respect to completeness, correctness and redundancy.

Unified treatment of basis sets of relativistic exponential-type spinor orbitals for particles with arbitrary half-integral spin in position, momentum and four-dimensional spaces

New formulae for the 2(2s + 1)-component relativistic basis spinors useful for the quantum mechanical description of the arbitrary half-integral spin particles by the generalized Dirac equation introduced by the author are established in position, momentum and four-dimensional spaces, where s = 1/2, 3/2, 5/2, …. These spinors are reduced to independent sets of two-component spinors. The relations presented in this study can be useful in the linear combination of atomic orbital approximation for the solution of different problems arising in relativistic quantum mechanics when orthonormal basis sets of relativistic exponential-type spinor wave functions and Slater-type spinor orbitals in position, momentum and four-dimensional spaces are employed.

Node moving adaptive refinement strategy for planar elasticity problems using discrete least squares meshless method

In this paper, an error indicator and adaptive refinement procedure in conjunction with the Discrete Least Squares Meshless (DLSM) method is presented for the effective and efficient analysis of planar elasticity problems. The DLSM method is a truly meshless method, which has been used for the solution of different problems ranging from solid to fluid mechanics problems. The method is based on the minimization of the least squares functional with respect to the nodal parameters. The least squares functional is formed as the weighted summation of the residual of the differential equation and its boundary condition. The DLSM method enjoys from providing a natural error indicator defined as the value of the functional at nodal points, which can be efficiently used to identify zones of larger numerical errors. The proposed error indicator has the additional advantage of easy computation since most of its components are already available from the main DLSM computation for analysis. Since both the approximation method and discretization method are meshless, repositioning of the nodes can be easily exploited for refining the numerical solution without any geometrical difficulties usually encountered in mesh based methods. Here, a node moving strategy based on spring analogy is proposed to displace the nodal points to the areas indicated by the higher values of the error indicator. A Voronoi diagram is used to identify neighboring nodes that should be connected to each other using springs. The efficiency and effectiveness of proposed adaptive refinement technique is tested on some benchmark examples with available analytical solutions and the results are presented. The results show that the proposed adaptive refinement technique is quiet effective for the accurate and efficient solution of elasticity problems.

Contact interactions and optimization of locally loaded shell structures

Methods for the solution of different problems of contact interaction of elements of shell structures with one another and dies of different types are generalized. We consider schemes of determination of breaking loads using the limit equilibrium theory and critical loads of local stability for shell systems under the indicated loading. Schemes of optimization of the shape of structural elements under local loads are presented. Results of experimental investigations are presented.

Existence of global solutions to the Cauchy problem for the inelastic Boltzmann equation with near-vacuum data

The Cauchy problem for the inelastic Boltzmann equation is studied for small data. Existence and uniqueness of mild and weak solutions is obtained for sufficiently small data that lies in the space of functions bounded by Maxwellians. The technique used to derive the result is the well known iteration process of Kaniel & Shinbrot. The theory developed by DiPerna & Lions in the 90’s [13] on what is called Renormalized solutions has been a great success in finding existence theorems for the Boltzmann equation (BE): The Cauchy problem in [13] and the Boundary value problem [21]. The theory is strong and flexible and can be adapted to find solutions for different problems, for instance: The Vlasov-Poisson-Boltzmann system (VPB) [24], the treatment of the BE with infinite energy [26], the relativistic Boltzmann equation [14] and others. Indeed, a great deal of applications of this theory has been written in the last 18 years on BE related problems. The theory is based in the bounded entropy which is a feature of the elastic BE solutions. Unfortunately, it is not known how to obtain an a priori estimate that confirms such feature for the inelastic BE solutions, even in the case where a cut-off is imposed to the collision kernel. This simple fact creates a big upset for the theory in the inelastic case. It is important to say that in the one dimensional case, Benedetto & Pulvirenti overcame this problem in [4] provided that the initial datum is essentially bounded and has compact support in the velocity space. The proof uses an iterative process introduced by J. M. Bony that relies strongly on the dimension. The technique allows to find a uniform control on the entropy, and hence, to prove existence and uniqueness provided the initial datum has the afore mentioned properties. It is clear that more understanding in the collision operator is needed to solve the inelastic BE in its simplest form: The Cauchy problem. More complex problems, like the initial/boundary value problem or the VPB system, are still out of hand. This paper returns to the late 70’s and presents an application for the inelastic Boltzmann problem of the technique introduced by Kaniel & Shinbrot in that time. Known as Kaniel & Shinbrot iterates [23], this technique was created by these authors to find existence and uniqueness

Inverse problems explicit and implicit formulations with applications in engineering, biophysics and biotechnology

In this work, we present a few explicit and implicit formulations used in the analysis and solution of inverse problems. These formulations have been developed and/or applied by the authors to the solution of different problems with applications in engineering, biophysics and biotechnology. Here emphasis is given to a matrix-based explicit formulation, and to the construction of a generalized family of regularization terms which is used when the inverse problem is formulated implicitly as an optimization problem. The efficacy of the methodologies developed is demonstrated with the results for a few test cases using noiseless and noisy synthetic data.

Squeeze transformation and optics after Einstein

Squeeze transformation and optics after Einstein

Basic Principles of Process Modelling

The principle of systems and process engineering was introduced into mathematical modelling in the middles of 20-th century by Bertalanffy, Mesarovic, Kalman, Zadeh, Benedek and others. Himmelblau and Bischoff showed that population balance problems, i.e., processes described with another independent variable than a physical space variable, can be solved by differential equations similarly to the transport equations. Essentially the same concepts are used – even with different names – in the theory of chemical, petrochemical, ceramic, food, biochemical process engineering, building material production, metallurgy, nuclear engineering and maybe in other fields of applied chemistry or physics. The differences in the nomenclature and treatment make difficulties transferring the theoretical bases and ways of solution of different problems from one field already solved to an other one. The aim of this paper is to define the processes, so that all models shall be given a common mathematical background, all models can be deduced therefrom. The postulates listed here can also serve as definitions of processes, process engineers deal with. To sum up the main concepts of process engineering is also worthwhile to identify and support the most important I/O elements in a process approached Quality Management System for different fields of industry.

Real linear quaternionic differential operators

The renewed interest in searching for quaternionic deviations of standard (complex) quantum mechanics resulted, in the last years, in a better understanding of the quaternionic mathematical tools needed to solve quantum mechanical problems. In particular, a relevant progress has been achieved in solving eigenvalue problems and differential equations for quaternionic operators. The practical methods recently proposed to solve quaternionic and complex linear second-order differential equations with constant coefficients represent a fundamental starting point to discuss quaternionic potentials in quantum mechanics and study possible violations from complex theories. Nevertheless, only for a restricted class of real linear quaternionic differential operators (namely, symmetric operators) the solution of differential problems was given. In this paper, we study real linear quaternionic differential equations. The proposed resolution's method is based on the Jordan canonical form of (real linear) quaternionic matrices.

Economic allocation: Examples and derived decision tree

Goal, Scope and BackgroundIn the recently published (Dutch) Handbook on LCA, economic allocation is advised as baseline method for most allocation situations in a detailed LCA. Although the Handbook on LCA aimed to provide a ‘cookbook’ with operational guidelines for conducting each step of an LCA, this was not completely achieved for the allocation step. The guidelines for allocation largely remained at the level of principles. This restricted elaboration of economic allocation may hamper application in practice. Therefore, this paper elaborates some examples applying economic allocation.MethodTwo concepts are of particular importance when applying economic allocation: functional flow and multi-functional process. The definitions of these concepts are presented and discussed. The basic principle of economic allocation is that having determined the various functional flows of a multi-functional process, all other flows need to be allocated to these functional flows according to their shares in the total proceeds. Proceeds are based on prices and these are not always easy to determine for a process. A summary of possible solutions for different problems when determining prices is given.Results and DiscussionThe examples presented focus on co-production and various recycling situations. All examples are hypothetical in order to avoid discussions on the data. The examples show that the prices of the functional flows determine the allocation results. It is of importance to have correct information on the relative prices of the functional flows at stake, especially whether they are negative or positive. Learning from these examples, we establish a decision tree for economic allocation. The decision tree is meant for identifying and handling multi-functionality situations starting from a defined (product) system. This decision tree is with minor adaptations also applicable to other allocation methods and has a more general value than for the economic allocation method only.Conclusions and perspectiveThe examples have helped us to establish a decision tree for handling the multi-functionality problem by economic allocation. The examples can be broadened to other materials and allocation situations. We would encourage others to provide other examples and experiences as we expect that these will help to further improve and refine the guidelines and decision tree for economic allocation in future.

Schauder bases in banach spaces: application to numerical solutions of differential equations

In this work, we present a numerical method for approximating the solution of a linear differential problem. We formulate a general problem in a Banach space making use of a Schauder basis and the Tau method to approximate the load function and the solution of the differential problem. Finally, we offer a numerical example.

Systems Embedding-New Process Engineering of Problem Solving of Systems Theory

The original process engineering of a solution of different problems of the systems theory designed while only for a linear case. The process engineering has no direct and indirect analogues in Russia and abroad. The basic virtue of this process engineering is the security of given transfer matrices (TMs) bodily, instead of their separate performances (allocation of characteristic equation's roots on a complex plane) as it takes place in the conventional approaches. An outcome of the new approach is a reduction of equations of a dynamic system of any complexity to a set of the matrix final equations, linear and bilinear equations, for which the solution's difficulties are fundamentally less than the solution's difficulties of the same problems in conventional representations.

An exponentially fitted difference scheme for the hyperbolic-hyperbolic singularly perturbed initial-boundary value problem

In this paper we discuss an initial-boundary value problem of hyperbolic type with first derivative with respect to x. The asymptotic solution is constructed and its uniform validity is proved under weader compatibility conditions. Then we develop an exponentially fitted difference scheme and establish discrete energy inequality. Finally, we prove that the solution of difference problem uniformly converges to the solution of the original problem.

Muon catalysed fusion

Abstract A decade ago it was established that one muon in a deuterium-tritium mixture can catalyse more than 100 nuclear fusion reactions and that this phenomenon could be used for the production of nuclear fuel and energy. This review presents the state of the art of muon catalysed fusion studies and its place among alternative methods of nuclear breeding. The main unsolved problems of muon catalysed fusion and its application in the solution of different problems of nuclear and atomic physics, quantum electrodynamics and computational physics are discussed.

Analysis of a difference solution of a fracture problem

An integral representation is found for the solution of a two-dimensional difference problem of elasticity theory for a plane cut along the negative semi-axes Ox, under the action of forces which produce a solution characteristic of a normal tear fracture. An asymptotic expansion of the solution is found and it is shown that the difference between the solutions of the difference problem and the exact problem is O(h/r1/2). Where r is the distance from the vertex of the tear. The results are generalized to the case of a longitudinal shear fracture and to schemes of the finite element method for both types of fracture.

The application of microcomputers in exploration and exploitation of mineral deposits

The advent of powerful microcomputers has initiated the development of on-site workstations and the design of software packages for geological and mining applications. A field computer for application in exploration and exploitation of mineral deposits should be an easy-to-use hardware/software system which is capable of and can provide solutions for different problems. GPMicro, a geostatistical package for microcomputers, written in Pascal by members of the Mathematical Geology Working Group at the Free University of Berlin, provides basic calculations for a geostatistical study, for example “classical” statistics (histogram, scattergram), variogram calculations, two- and three-dimensional kriging, and display of kriging results.

Problems of heat and mass transfer in the interaction of gas flows with the surface of bodies

Questions regarding the solution of different problems of heat and mass transfer during the design of heat protection systems are examined.

Molecular Phylogenetic Analysis: Design and Implementation of Scalable and Reliable Algorithms and Verification of Phylogenetic Properties

Since the creation of the bioinformatics field, and even more since the creation of the so called nextgeneration sequencing, the relevance of computer methods and technologies has significantly increased. We here present several contributions we have published as solution for different problems involved in the study of the evolution process.

An algorithm for the solution of difference problems by graphs

An algorithm for the solution of difference problems by graphs

Diffraction of (short) sound waves at an obstacle (cylinder, sphere, cone and plane)

In the theory of sound, the solution of different problems of diffraction of sound waves at an obstacle (plane, lattice, slot, cylinder, sphere, ellipsoid, etc.) are studied. In this paper, the author applies the Poncaré [1] method, and presents a ner solution to the problem.