Complete Set Of Solutions Research Articles

On Some Strong Earthquakes in Central Asia in the Second Half of the 19th Century

Materials on earthquakes in Samarkand and Ferhana regions (Republic of Uzbekistan) in 1868–1892 are presented based on original sources of information not used before. The epicenter location and magnitude for the earthquakes April 7, 1869, and March 2, 1892, are evaluated for the first time; for the other two earthquakes (April 3, 1868, and September 18, 1892), the uncertainty of previously published solutions is significantly reduced. Reduction of uncertainties of prior solutions is achieved owing to the formalized method of epicentral and magnitude assessment, which works successfully with sparse datasets. One of the restrictions on the entire set of solutions is association of the epicenter with certain active tectonic structures. This criterion is used only for selecting the preferable solution from the entire set of solutions obtained solely from macroseismic data. The complete set of solutions is retained and can be used to analyze the accuracy and objectivity of the preferable solution.

Mathematical modeling of consolidation in unsaturated poroelastic soils under fluid flux boundary conditions

The spatiotemporal variability in precipitation could have a significant impact on ground subsidence. In this paper, we utilize a previously developed one-dimensional theory of consolidation for a two-fluid system, the generalization of Biot's theory, to investigate the impact of a time-dependent fluid flux across the surface of an unsaturated soil on the solid deformation and pore pressure responses. We consider three prescribed fluid flux patterns and the associated gradient of pore water pressure: constant, periodic, and exponential flux patterns. We employ a Fourier series representation and Laplace transformation in the space and time domains to derive a complete set of closed-form analytical solutions, including the complementary and particular solutions, describing both transient and steady-state excess pore water and pore air pressure responses as well as the total settlement induced by the fluid flux. Using two different types of soil, i.e. clay and sand, we demonstrate the dependence of the solution on the initial water saturation and hydraulic conductivity in the saturated and unsaturated regimes. Results of this study reveal that the fluid flux across the surface could have a significant impact on the dissipation of excess pore water pressure and the time evolution of the total settlement of the ground surface. The effect on the pore water pressure is more significant for sand than for clay irrespective of moisture content, mainly because of the much higher hydraulic conductivity of sand. Finally, we show that the hydraulic conductivity has a dominant effect on the consolidation behaviors of saturated and unsaturated soils subjected to surface fluid flux.

Ballooning, bulging, and necking: An exact solution for longitudinal phase separation in elastic systems near a critical point

Prominent examples of longitudinal phase separation in elastic systems include elastic necking, the propagation of a bulge in a cylindrical party balloon, and the beading of a gel fiber subject to surface tension. Here we demonstrate that if the parameters of such a system are tuned near a critical point (where the difference between the two phases vanishes), then the behavior of all systems is given by the minimization of a simple and universal elastic energy familiar from Ginzburg-Landau theory in an external field. We minimize this energy analytically, which yields not only the well known interfacial tanh solution, but also the complete set of stable and unstable solutions in both finite and infinite length systems, unveiling the elastic system's full shape evolution and hysteresis. Correspondingly, we also find analytic results for the the delay of onset, changes in criticality, and ultimate suppression of instability with diminishing system length, demonstrating that our simple near-critical theory captures much of the complexity and choreography of far-from-critical systems. Finally, we find critical points for the three prominent examples of phase separation given above, and demonstrate how each system then follows the universal set of solutions.

Multiplicative series, modular forms, and Mandelbrot polynomials

We say a power series ∑ n = 0 ∞ a n q n \sum _{n=0}^\infty a_n q^n is multiplicative if the sequence 1 , a 2 / a 1 , … , a n / a 1 , … 1,a_2/a_1,\ldots ,a_n/a_1,\ldots is so. In this paper, we consider multiplicative power series f f such that f 2 f^2 is also multiplicative. We find a number of examples for which f f is a rational function or a theta series and prove that the complete set of solutions is the locus of a (probably reducible) affine variety over C \mathbb {C} . The precise determination of this variety turns out to be a finite computational problem, but it seems to be beyond the reach of current computer algebra systems. The proof of the theorem depends on a bound on the logarithmic capacity of the Mandelbrot set.

Fast Approximation for Scheduling One Machine

We propose an approximation algorithm for scheduling jobs with release and delivery times on a single machine with the objective to minimize the makespan. The algorithm is based on an implicit enumeration of the set of complete solutions in a search tree. By analyzing specific structural properties of the solutions created in each branch of the solution tree, a certain approximation factor of each solution from that branch is calculated. Our algorithm guarantees approximation factor 1+1/κ for a generated solution if there are κ jobs with a specified property in that solution (typically, the longer the length of the path from the root to the node representing that solution in the solution tree, the larger the κ value). We have carried out an extensive computational study to verify the practical performance of our algorithm and the effectiveness of the approximation factor provided by us. While our problem instances are generated randomly, we have discarded a considerable number of the instances, ones which were already solved optimally by the earlier known dominance rules. For the vast majority of the tested problem instances, within a short running time of our algorithm parameter κ becomes sufficiently large so that the approximation factor which the algorithm guarantees becomes better than that provided by the earlier known approximation algorithms.

One-shot detection limits of quantum illumination with discrete signals

To detect a stealth target, one may directly probe it with a single photon and analyze the reflected signals. The efficiency of such conventional detection scheme can potentially be enhanced by quantum illumination, where entanglement is exploited to break the classical limits. The question is what is the optimal signal state for achieving the detection limit? Here, we address this question in a general discrete model, and derive a complete set of analytic solutions. For one-shot detection, the parameter space can be classified into three distinct regions, in the form of a “phase diagram” for both conventional and quantum illumination. Interestingly, whenever the reflectivity of the target is less than some critical value, all received signals become useless, which is true even if entangled resources are employed. However, there does exist a region where quantum illumination can provide advantages over conventional illumination; there, the optimal signal state is an entangled state with an entanglement spectrum inversely proportional to the spectrum of the environmental noise state and is, surprisingly, independent of the occurrence probability and the reflectivity of the object. The entanglement of the ideal probe state increases with the entropy of the environment; it becomes more entangled as the temperature of the environment increases. Finally, we show that the performance advantage cannot be fully characterized by any measure of quantum correlation, unless the environment is a complete mixed state.

From Yang–Mills in de Sitter Space to Electromagnetic Knots

We review analytic SU(2) Yang–Mills solutions with finite action on four-dimensional de Sitter space from a new perspective, by conformally mapping dS $$_{4}$$ to a finite Lorentzian cylinder $$(0,\pi ) \times {{S}^{3}}$$ . As a byproduct, all abelian (i.e. Maxwell) solutions are classified by SO(4) representations. Conformal equivalence of (two copies of half of) this cylinder to Minkowski space yields a complete set of rational Maxwell solutions on the latter, which are known as electromagnetic knots. Their properties are efficiently computed on de Sitter space. We close with a couple of explicit examples.

Synthesis of Six-Bar Timed Curve Generators of Stephenson-Type Using Random Monodromy Loops

AbstractSynthesis of rigid-body mechanisms has traditionally been motivated by the design for kinematic requirements such as rigid-body motions, paths, or functions. A blend of the latter two leads to timed curve synthesis, the goal of which is to produce a path coordinated to the input of a joint variable. This approach has utility for altering the transmission of forces and velocities from an input joint onto an output point path. The design of timed curve generators can be accomplished by setting up a square system of algebraic equations and obtaining all isolated solutions. For a four-bar linkage, obtaining these solutions is routine. The situation becomes much more complicated for the six-bar linkages, but the range of possible output motions is more diverse. The computation of nearly complete solution sets for these six-bar design equations has been facilitated by recent root finding techniques belonging to the field of numerical algebraic geometry. In particular, we implement a method that uses random monodromy loops. In this work, we report these solution sets to all relevant six-bars of the Stephenson topology. The computed solution sets to these generic problems represent a design library, which can be used in a parameter continuation step to design linkages for different subsequent requirements.

Covering Problem for Solutions of Max-Archimedean Bipolar Fuzzy Relation Equations

This paper discusses the resolution of max-Archimedean bipolar fuzzy relation equations. In the literature, many methods have been proposed based on 0-1 integer programming problem or reduction methods for the optimization with bipolar fuzzy relation equations. A new concept based on the idea of covering and the notions of leading, non-leading variables are introduced in the present paper for finding the solutions of max-Archimedean bipolar fuzzy relation equations. It is shown that the problem of finding the complete solution set of the system of max-Archimedean bipolar fuzzy relation equations is equivalent to solving a covering problem and the solutions of such equations correspond to irredundant coverings of the covering problem. The proposed method is illustrated with some examples.

Knee based multimodal multi-objective evolutionary algorithm for decision making

Recently, many advanced multimodal multi-objective evolutionary algorithms (MMOEAs) have been presented to solve multimodal multi-objective optimization problems (MMOPs). However, most of these approaches struggle not only to find the entire Pareto sets and Pareto front, but also ignoring the problem of Multi-Criteria Decision Making (MCDM) to be handled at a later stage. As a matter of fact, it is a very eclectic and challenging burden for decision makers to choose some trade-off optimal solutions from an enormous collection of non-dominated Pareto-optimal individuals. In this paper, we propose a knee based evolutionary algorithm, named MMO-EvoKnee, which incorporates MCDM strategy into solving MMOPs. The proposed algorithm is designed to search for a complete set of global knee solutions instead of an entire Pareto front and Pareto sets. Firstly, the EvoKnee Selection is adopted to find target global knee solutions and boundary individuals. Secondly, the Knee Multimodal Solutions Selection focuses on decision space exploitation to obtain well-converged multiple Pareto-optimal knee solutions. Thirdly, the Maximum Spanning Subset Selection is designed to accurately identify a complete number of knee solutions from overcrowded Pareto regions. Fourthly, the Boundary Multimodal Solutions Selection can find and maintain well-diversified and well-converged boundary solutions. As a result, MMO-EvoKnee can consistently find all knee solutions of interest quickly, and it relieves the burden for decision makers. Finally, the performance of the proposed algorithm is evaluated on thirteen benchmark MMOPs. The experiment results clearly show that the proposed MMO-EvoKnee provides a competitive edge over the chosen state-of-the-art MMOEAs.

Optimizing the Tending of Forest Stands with Interactive Decision Maps to Balance the Financial Incomes and Ecological Risks according to Owner Demands: Case Study in Rakovník, the Czech Republic

Sustainability and the optimal provision of the various ecosystem services is an essential task in forest management. In this study, we deal with the optimization of forest tending to achieve the maximal long-term provision of financial incomes from wood at a minimal level of ecological risks for selected small ownership unit. The methods of interactive decision maps and reasonable goals (IDM/RGM) were connected with a modern forest growth simulator to investigate the four-dimensional optimization space and to produce the complete set of Pareto optimal solutions. The four different types of forest owners as potential decision-makers were simulated, and precise management goals in multidimensional target space were defined. Then, the optimal tending system for each forest owner in three stands, differing by the degree of the naturalness of the species composition, was detected. The multi-criteria analysis suggests that predominantly economically oriented forest management still prevails in the Czech and Slovak Republics, which can be as a source of conflicts among forest owners and other stakeholders. The existence of trade-offs between biodiversity, ecological stability and wood production and different owners’ demands must be taken into account. The possibility of balancing the management risks and wood provision according to the owner’s and other stakeholders’ demands with the aid of the easy-to-apply IDM/RGM methods (and the careful assistance of a specialist experienced in multi-criteria optimization) was introduced. At the same time, the application of real integrative management in small forest areas was demonstrated in practice. After the change of paradigm in forest management, the applied methods should prevent increasing conflicts among owners and society in former socialist countries, which have undergone a fundamental transformation in terms of forest ownership in recent decades.

Reachable Power Flow

This letter introduces reachable power flow ( ReachFlow ), a formal method providing a provably over-approximated enclosure of the complete set of the power flow solutions that “can be reached” under various uncertainties. The novelty of ReachFlow lies in: (1) an ordinary differential equation (ODE) formulation which maps the iterative power flow solving process into a virtual dynamic; (2) a reachability analysis of the virtual ODE model which enclose all possible (infinite) power flow solutions under uncertainties in one calculation. Case studies verify the efficacy of ReachFlow as a formal method and, in particular, its capability of handling islanded droop-based microgrids under uncertainties.

Multi-objective Integer Programming Approaches for Solving the Multi-criteria Test-suite Minimization Problem

Test-suite minimization is one key technique for optimizing the software testing process. Due to the need to balance multiple factors, multi-criteria test-suite minimization (MCTSM) becomes a popular research topic in the recent decade. The MCTSM problem is typically modeled as integer linear programming (ILP) problem and solved with weighted-sum single objective approach. However, there is no existing approach that can generate sound (i.e., being Pareto-optimal) and complete (i.e., covering the entire Pareto front) Pareto-optimal solution set, to the knowledge of the authors. In this work, we first prove that the ILP formulation can accurately model the MCTSM problem and then propose the multi-objective integer programming (MOIP) approaches to solve it. We apply our MOIP approaches on three specific MCTSM problems and compare the results with those of the cutting-edge methods, namely, NonlinearFormulation_LinearSolver (NF_LS) and two Multi-Objective Evolutionary Algorithms (MOEAs). The results show that our MOIP approaches can always find sound and complete solutions on five subject programs, using similar or significantly less time than NF_LS and two MOEAs do. The current experimental results are quite promising, and our approaches have the potential to be applied for other similar search-based software engineering problems.

Selection of Optimal Ingredients for Out-of-furnace Smelting Based on Computer Application

The optimization system software of the blast furnace batching studied in this paper is a complete set of blast furnace batching problem solutions. Its theory is based on the classic material balance and heat balance equations of blast furnace smelting. Blast furnace batching calculations used by most domestic steel companies are mainly based on forward calculation plus verification adjustment. Optimization of blast furnace batching based on linear programming the system can effectively improve calculation efficiency, and provide clear and unique optimization for blast furnace operators in all experience levels matching scheme.

Group analysis of the one dimensional wave equation with delay

In this paper, we establish a Lie type invariance condition for second order delay partial differential equations. The determining equations are obtained using Taylor’s theorem for a function of several variables. The symmetries of the wave equation with delay, its kernel and extensions of the kernel have been found. We make a complete group classification of the wave equation containing an arbitrary differentiable functional with delay, for which there is no existing literature. Further, the complete set of invariant solutions led by this classification have been found.

Cluster analysis on railway infrastructure standards in China and its application to railway efficiency improvement

The present paper structures an infrastructure standard cluster by studying the attributes, the level of application, and the implementation object of more than two hundred railway infrastructure standards in China. These standards are classified and fitted into different specific categories of the cluster, as a result, a systematic and complete standard cluster forms. A concept of comprehensive standards is put forward during the development of the proposed standard cluster. The proposed cluster could not only guide the preparation of railway standards, improve the economic performance of railway construction, but also helps to enhance the efficiency of the whole railway technical system. Cost reduction for HSR is chosen as an efficiency improvement objective to study how the proposed standard cluster helps to get a set of complete technical solutions. Study results reveal that the cluster can provide a basis for a comprehensive study on specific technical aspects (e.g., cost reduction), and can further extend to a number of applications regarding to efficiency improvement of the railway infrastructure system.

SARAP Algorithm of Multi-Objective Optimal Capacity Configuration for WT-PV-DE-BES Stand-Alone Microgrid

The typical stand-alone microgrid (MG) composed of wind turbine (WT), photovoltaic (PV), diesel generator (DE), and battery energy storage (BES) is taken as the research object. Firstly, a multi-objective optimal capacity configuration model considering economic efficiency, reliability, and environmental protection is established. Secondly, in view of the complex characteristics of the optimization model, such as strong nonlinearity and multi-constrained conditions, combining the enumeration that can find the complete real Pareto solution set with the intelligent algorithm that has the characteristics of fast convergence, a search algorithm referencing adjacent points based on SPEA2 (SARAP) is proposed. The algorithm obtains the contour of the real Pareto optimal solution set by SPEA2, and then repeatedly extracts the adjacent points that satisfy certain conditions from the solution set solved by SPEA2. A small search space based on the adjacent points is constructed, and an omnidirectional search in this space to achieve the complete real Pareto optimal solution set is performed. The algorithm performance analysis of both computational complexity and convergence shows that the operation speed of SARAP is approximately five times higher than that of the enumeration, and the obtained result is close to the complete real Pareto optimal solution set. Finally, the optimization calculation and typical daily production simulation are carried out according to the resource and load characteristics of a region, and the results further prove the rationality and validity of the proposed algorithm.

Algorithms for simultaneous Hermite–Padé approximations

We describe how to compute simultaneous Hermite–Padé approximations, over a polynomial ring K[x] for a field K using O∼(nω−1td) operations in K, where d is the sought precision, where n is the number of simultaneous approximations using t<n polynomials, and where O(nω) is the cost of multiplying n×n matrices over K. We develop two algorithms using different approaches. Both algorithms return a reduced sub-basis that generates the complete set of solutions to the input approximation problem that satisfy the given degree constraints. Previously, the cost O∼(nω−1td) has only been reached with randomized algorithms finding a single solution for the case t<n. Our results are made possible by recent breakthroughs in fast computations of minimal approximant bases and Hermite–Padé approximations for the case t≥n.

Three-dimensional dynamic Green's functions for transversely isotropic saturated half-space subjected to buried loads

Based on Biot's theory of saturated porous medium, three-dimensional (3D) dynamic Green's functions for a transversely isotropic (TI) saturated half-space is solved. The 3D Green's functions correspond to solutions of buried uniformly distributed loads acting on a circular disk of a homogeneous TI saturated half-space. First, a set of scalar potential functions are adopted to solve the governing equations of TI saturated medium in the cylindrical coordinate system. Next, by employing the Fourier series expansion and Hankel transform, the solutions for the potential functions are obtained in transformed domain, and then the displacements, stresses and pore fluid pressure are expressed via the relationships between these functions. Finally, the boundary conditions of problem are introduced, the solutions are derived for three different cases of vertical load in z-direction, horizontal load in x(y)-direction and pore fluid pressure in z-direction. The accuracy of the proposed method is validated by comparison with existing solutions for isotropic elastic and saturated as well as TI saturated (surface load) media that are special cases of the more general problems addressed. Parametric studies in both frequency and time domain are performed to investigate the influences of the material anisotropy, buried depth load frequency and drainage condition on the dynamic responses of the TI saturated half-space. Numerical results indicate that material anisotropy and surface drainage condition are significant important for the accurate assessment of the dynamic responses subjected to buried sources. In addition, The obtained Green's functions form a complete set of fundamental solutions of the TI saturated medium, by which the key to applying the BEMs to a variety of radiation, scattering and interaction problems associated with wave propagation in TI saturated half-space is solved.

Transient elastodynamic behavior of cylindrical tubes under moving pressures and different boundary conditions

A complete set of analytical solutions for the transient elastodynamic response of thick cylindrical shells with finite length to single and successive moving pressures are presented over a wide range of load speeds. The formulation of the problem is based on the first-order shear deformation theory and the solutions are obtained using the mode-summation method. The effects of reflected waves at different types of boundary condition (simply-supported, clamped-clamped, and clamped-free) are also considered in the solution procedures. The results of the analytical solutions are validated through comparisons with the experimental results from the literature and a series of finite element simulations. The very good agreement between the analytical and experimental results showed the accuracy of the formulation and solution procedures. The excellent agreement between the analytical and numerical results over a wide range of load speeds showed the higher precision and superior efficiency of the new analytical solution, compared to the previous models.