Narrow Results

The Urban Agglomeration of Beibu Gulf was established in 2017 with the strategic positioning of facing ASEAN, serving the “Southwest, Central-south, and South of China”, and being livable and business-friendly. Green innovation is the key to promoting high-quality urban development. It is of great significance to analyze and compare the spatial characteristics of green innovation efficiency and its development differences in the Urban Agglomeration of Beibu Gulf for promoting higher quality development in the Beibu Gulf region. This paper measures the dynamic changes of green innovation efficiency and in the Urban Agglomeration of Beibu Gulf based on the super-efficient SBM-GML model, and uses a variety of convergence methods to examine their convergence characteristics. The research results show that (1) green innovation efficiency displays remarkable regional differences, and the overall trend is fluctuating and declining; (2) green innovation efficiency has prominent convergence characteristics in the Urban Agglomeration of Beibu Gulf, which has passed the tests of σ convergence and β convergence.

We study the convergence of a deep learning algorithm applied to a general class of fully nonlinear second-order partial differential equations. By using a suitable finite difference approximation to the loss function of the deep learning scheme, we show the convergence of the numerical solution to the unique viscosity solution. We apply our results and illustrate this convergence to the finite horizon optimal investment problem with proportional transaction costs in single and multi-asset settings.

In this paper, we introduce and study a class of new generalized nonlinear mixed quasi-variational inclusions involving non-monotone set-valued mappings with noncompact values and construct a new iterative algorithm. And proved the existence of solutions for this kind of generalized nonlinear mixed quasi-variational inclusions and the convergence of the iterative sequence generated by the algorithm. Those results improve and extend the corresponding results in the recently literatures.

A new class of nonlinear set-valued variational inclusions involiving H – accretive mapping in Banach spaces is studied. A new iterative algorithm is constructed by using the resolvent operator technique for H – accretive mapping due to Fang and Huang. The convergence criteria for the algorithm is also discussed.

The purpose of this paper is to introduce a new class of general nonlinear variational inclusions with H – accretive operators in Banach spaces and prove its equivalence with a class of fixed point problems by making use of the properties of H – accretive operator. we also prove the existence of solution for this general nonlinear variational inclusions and the convergence of iterative sequences generated by new perturbed algorithm. The results presented in this paper improve and generalize some recent results in this field.

Two interesting generalizations of supertopologies in the sense of Doitchinov are considered. The first one of these leads us to generalized nearness spaces, and consequently topological extensions are being examined. Secondly we obtain equiconvergence spaces which fill the gap between uniform convergence spaces and the non-symmetrical Kent-convergence spaces resulting as a convenient topological category which is cartesian closed and extensional.

In this paper, we introduce and study a new system of set-valued variational inclusions involving H-monotone mappings in Hilbert spaces. By using the resolvent operator method associated with H-monotone mappings, we construct a new iterative algorithm approximating the solution of this system of set-valued variational inclusion and discuss the convergence analysis of the algorithm.

The purpose of this paper is to introduce a new class of general nonlinear variational inclusions with H - accretive operators in Banach spaces and prove its equivalence with a class of fixed point problems by making use of the properties of H - accretive operator, we also prove the existence of solution for this general nonlinear variational inclusions and the convergence of iterative sequences generated by new perturbed algorithm. The results presented in this paper improve and generalize some recent results in this field.

In this paper we consider the regularity of the trust region-cg algorithm, when it is applied to nonlinear ill-posed iverse problems. The trust region algorithm can be viewed as a regularization method, but it differs from the traditional regularization method, because no penalty term is need. Thus, the determing of the so-called regularization parameter in a standard regularization method is avoided. Theoretical analysis of the trust region-cg method is presented, convergency and regularity of the trust region algorithm are proved, and numerical tests are also given.

Considering the impact on human beings and human activities of architectural decisions in the design of space for human habitation, this chapter discusses the increasingly evident and necessary confluence in contemporary times of many disciplines and human-oriented sciences, with architecture being the meeting ground to know emergent phenomena of human habitation. As both a general rubric and a specific phenomenon, architectural emergence is the chosen focus of discussion and other phenomena are related to it. Attention is given to the phenomena of architectural induction, emergence, and convergence as having strategic and explanatory value in understanding tensions between two competing mentalities, the global domineering nature-for-humans attitude, in opposition to the lesser practiced humans-for-nature attitude.

We give in §3 results concerning the preservation of locally uniformly convergence for sequences and of the normality and compactness for families of 1) continuous mappings and 2) homeomorphisms, by lifting or factorizing in the general case of regular coverings (=coverings, Definition 1). With this aim we present in §2.2. the lifting and factorizing properties by regular coverings pointing out when normal coverings (Definition 2) are needed.

The goal of this paper is to present recent progress on several aspects of an inverse medium problem. A recursive linearization method for solving the nonlinear inverse problem is introduced. Convergence of the method is studied. We address issues on regularity and stability for the scattering map which maps the scatterer to the scattered field. Preliminary computational results are also presented.

In this paper we study convergence results of different types (uniform, L_p, almost everywhere, etc.) for one- and multidimensional trigonometric series. The sufficient conditions for these results to hold are written for the series with general monotone coefficients. The sharpness of these results is examined.

This article is concerned with the behavior of global solutions of a parabolic partial differential equation with a power nonlinearity. Depending on parameter values and initial data, various behavior of global solutions can be observed such as grow-up, convergence, quasi-convergence and non-convergence. We give precise descriptions of the relationship between the spatial decay rate of initial data and the large-time behavior of solutions.

The stable difference schemes for the approximate solutions of the parabolic equation with control parameter

Based on the demands of multi-missile cooperative combat and the characteristics of Wireless Sensor Network (WSN), this paper proposes a novel cooperative combat model of multi-missile formation which establishes internal data links in the form of WSN. In the proposed model, WSN nodes are not only used to transmit real-time tactics information but also monitor the environment status such as temperature, humidity, air pressure and so on. This paper also gives the network topology of WSN and the implementation of the model. As network delay plays a very important role in military network, simulations revealing the influence of WSN network delay on our model under the guidance law of some certain missile are conducted. Simulation results show that our model under the given guidance law can tolerate a delay of 50ms. However, for delays lager than 60ms, multi-missile cooperative formation begins to diverge, and missiles are not able to achieve the scheduled formation.

In this paper, the fully discrete method is applied for the eigensolutions of the Laplace equationon smooth closed boundaries. The fully discrete method mainly consists of two levels of numerical quadrature: the trapezoidal rule for theintegrals including the weakly singularity, and the discrete inner product for the outer integrals. The convergence and error results of the fully discrete method for Steklov eigenvalue problems are provided. Thereafter, the numerical examples demonstrate the efficiency of the fully discrete method.

Our aim in this note is to give a simplified proof of the convergence of Evans-Rezakhanlou Stochastic Model to the evolution surfaces model of sandpile.

Three classes of inverse coefficient problems arising in engineering mechanics and computational material science are considered. Mathematical models of all considered problems are proposed within the J₂-deformation theory of plasticity. The first class is related to determination of unknown elastoplastic properties of a beam from a limited number of torsional experiments. The inverse problem here consists of identifying the unknown coefficient g(ξ²) (plasticity function) in the nonlinear differential equation of torsional creep-(g(|∇u|²)u_x1)_x1 - (g(|∇u|²)u_x2)_x2 = 2φ, x ∈ Ω ⊂ R² , from the torque (or torsional rigidity) τ (φ), given experimentally. The second class of inverse problems is related to identification of elastoplastic properties of a 3D body from spherical indentation tests. In this case one needs to determine unknown Lame coefficients in the system of PDEs of nonlinear elasticity, from the measured spherical indentation loading curve , obtained during the quasi-static indentation test. The third model an inverse problem of identifying the unknown coefficient g(ξ²(u)) in the nonlinear bending equation is analyzed. The boundary measured data here is assumed to be the deflections w_i[τ_k] := w(λ_i;τ_k), measured during the quasistatic bending process, given by the parameter τ_k, , at some points , , of a plate. An existence of weak solutions of all direct problems are derived in appropriate Sobolev spaces, by using monotone potential operator theory. Then monotone iteration schemes for all the linearized direct problems are proposed. Strong convergence of solutions of the linearized problems, as well as rates of convergence are proved. Based on obtained continuity property of the direct problem solution with respect to coefficients, and compactness of the set of admissible coefficients, an existence of quasi-solutions of all considered inverse problems are proved. Some numerical results, useful from the poins of view engineering mechanics and computational material science, are demonstrated.

We review shock models for defaults, both in the standard and in the urn-based approach. Shock models are motivated by engineering problems where a material can break because of stress, but they can also be efficiently used in other fields, such as economics and biology.

Standard shock models are parametric models, whereas the urn-based shock models are nonparametric models assuming as little as possible for the prediction of defaults. First, we mention some results for the two models, in particular describing the finite and asymptotic behavior of time to failure or of the chance for defaults. Finally, we also present an application of the second model to defaults of Italian firms, comparing our results with a standard prediction model of economics, the Z-score. We note that our model predicts the default behavior of these firms better.