Existence Results of Third Order Multi-Point Boundary Value Problem at Resonance

A kind of third order multi-point boundary value problems, x＇＇＇（ ι） = f（ t, x （ t ）, x＂ （ t ）, x＇＇＇ （ t ） ） ＋ m 2 e（t）,t∈（0, 1）,x（0）=ax（ξ）,x＇（0）-0,x（l）= ^m2∑j=1 βjx（ηj）, fεC[0, 1]×R^3, e（t）∈L^1[0, 1],a≥0, is considered, all theβj＇s have not the same sign, 0〈ξ〈 l, 0〈η1〈 η2〈… 〈ηm.2〈 1. By using the coincidence degree theory, some existence theorems for the problems at resonance are obtained.

SOLUTIONS TO A SECOND-ORDER MULTI-POINT BOUNDARY VALUE PROBLEM AT RESONANCE

This article deals with the following second-order multi-point boundary value problem x″（t）=r（t,x（t）,x′（t））＋e（t）,t∈（0,1）x′（0）=m∑i=1aix′（ξi）,x（1）=n∑j=1βjx（ηj）, Under the resonance conditions m∑i=1ai=1,n∑j=1βj=1,n∑j=1βjηj=1 , by applying the coincidence degree theory, some existence results of the problem are established. The emphasis here is that the dimension of the linear operator is two. In this paper, we extend and improve some previously known results like the ones in the references.

Consensus Control With a Constant Gain for Discrete-time Binary-valued Multi-agent Systems Based on a Projected Empirical Measure Method

This paper studies the consensus control of multiagent systems with binary-valued observations.An algorithm alternating estimation and control is proposed.Each agent estimates the states of its neighbors based on a projected empirical measure method for a holding time.Based on the estimates,each agent designs the consensus control with a constant gain at some skipping time.The states of the system are updated by the designed control,and the estimation and control design will be repeated.For the estimation,the projected empirical measure method is proposed for the binary-valued observations.The algorithm can ensure the uniform boundedness of the estimates and the mean square error of the estimation is proved to be at the order of the reciprocal of the holding time(the same order as that in the case of accurate outputs).For the consensus control,a constant gain is designed instead of the stochastic approximation based gain in the existing literature for binary-valued observations.And,there is no need to make modification for control since the uniform boundedness of the estimates ensures the uniform boundedness of the agents’states.Finally,the systems updated by the designed control are proved to achieve consensus and the consensus speed is faster than that in the existing literature.Simulations are given to demonstrate the theoretical results.

Multi-valued responses and dynamic stability of a nonlinear vibro-impact system with a unilateral non-zero offset barrier

In this paper, multi-valued responses and dynamic properties of a nonlinear vibro-impact system with a unilateral nonzero offset barrier are studied. Based on the Krylov-Bogoliubov averaging method and Zhuravlev non-smooth trans- formation, the frequency response, stability conditions, and the equation of backbone curve are derived. Results show that in some conditions impact system may have two or four steady-state solutions, which are interesting and not mentioned for a vibro-impact system with the existence of frequency island phenomena. Then, the classification of the steady-state solutions is discussed, and it is shown that the nontrivial steady-state solutions may lose stability by saddle node bifurcation and Hopf bifurcation. Furthermore, a criterion for avoiding the jump phenomenon is derived and verified. Lastly, it is found that the distance between the system＇s static equilibrium position and the barrier can lead to jump phenomenon under hardening type of nonlinearity stiffness.

Multi-Valued Neuron with Sigmoid Activation Function for Pattern Classification

Multi-Valued Neuron (MVN) was proposed for pattern classification. It operates with complex-valued inputs, outputs, and weights, and its learning algorithm is based on error-correcting rule. The activation function of MVN is not differentiable. Therefore, we can not apply backpropagation when constructing multilayer structures. In this paper, we propose a new neuron model, MVN-sig, to simulate the mechanism of MVN with differentiable activation function. We expect MVN-sig to achieve higher performance than MVN. We run several classification benchmark datasets to compare the performance of MVN-sig with that of MVN. The experimental results show a good potential to develop a multilayer networks based on MVN-sig.

Fixed Point of a Countable Family of Uniformly Totally Quasi- <i>&Oslash</i>-Asymptotically Nonexpansive Multi-Valued Mappings in Reflexive Banach Spaces with Applications

The purpose of this article is to discuss a modified Halpern-type iteration algorithm for a countable family of uniformly totally quasi- ? -asymptotically nonexpansive multi-valued mappings and establish some strong convergence theorems under certain conditions. We utilize the theorems to study a modified Halpern-type iterative algorithm for a system of equilibrium problems. The results improve and extend the corresponding results of Chang et al. (Applied Mathematics and Computation, 218, 6489-6497).

Evaluation the Price of Multi-Asset Rainbow Options Using Monte Carlo Method

Solution of the system stochastic differential equations in multi dimensional case using Monte Carlo method had many useful features in compare with the other computational methods. One of them is the solution of boundary value problems to be found at just one point, if required (with associated saving in computation), whereas deterministic methods necessarily find the solution at large number of points simultaneously. This property can be particularly useful in problems such option pricing, where the value of an option is required only at the time of striking, and for the state of the market at that time. In this work we consider a European multi-asset options which mathematically described by the system of stochastic differential equations. We will apply Monte Carlo method for the solution of that system which is the price of Multi-asset rainbow options.

A Compact Difference Scheme for Multi-point Boundary Value Problems of Heat Equations

In this paper,a compact difference scheme is established for the heat equations with multi-point boundary value conditions.The truncation error of the difference scheme is O(τ2+h^4),where t and h are the temporal step size and the spatial step size.A prior estimate of the difference solution in a weighted norm is obtained.The unique solvability,stability and convergence of the difference scheme are proved by the energy method.The theoretical statements for the solution of the difference scheme are supported by numerical examples.

Importance Analysis of a Multi-state System Based on Direct Partial Logic Derivatives and Multi-valued Decision Diagrams

Importance analysis quantifies the critical degree of individual component. Compared with the traditional binary state system,importance analysis of the multi-state system is more aligned with the practice. Because the multi-valued decision diagram( MDD) can reflect the relationship between the components and the system state bilaterally, it was introduced into the reliability calculation of the multi-state system( MSS). The building method,simplified criteria,and path search and probability algorithm of MSS structure function MDD were given,and the reliability of the system was calculated. The computing methods of importance based on MDD and direct partial logic derivatives( DPLD) were presented. The diesel engine fuel supply system was taken as an example to illustrate the proposed method. The results show that not only the probability of the system in each state can be easily obtained,but also the influence degree of each component and its state on the system reliability can be obtained,which is conducive to the condition monitoring and structure optimization of the system.

MULTI-VALUED TOTALLY QUASI-φ-ASYMPTOTICALLY NONEXPANSIVE SEMI-GROUPS AND STRONG CONVERGENCE THEOREMS IN BANACH SPACES

The purpose of this article is first to introduce the concept of multi-valued to- tally Quasi-φ-asymptotically nonexpansive semi-groups, which contains many kinds of semi- groups as its special cases, and then to modify the Halpern-Mann-type iteration algorithm for multi-valued totally Quasi-cS-asymptotically nonexpansive semi-groups to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in this article improve and extend the corresponding results announced by many authors recently.

Reflection of Liberal Values in the Georgian Press in 1918-1921

This study deals with the values and orientation of Georgian social and political publications in the times of the Georgian Democratic Republic （1918-1921）. It also shows how the press of that time reflected the idea of ＂Georgian Europeanism＂ based on liberal values that took shape as an anti-colonial concept in the journalism of the late 19th century. The opposed dominant ideological projects of that era comprised on the one hand, National Democratic and Socialist Federalist parties that aspired to preserve national identity and carry out changes and on the other hand, ruling Social Democrats （who initially neglected national identity, but later shared the idea）. This opposition was clearly reflected in the media discourse of that time, which implied the following rights based on the principles of classical liberalism： freedom of conscience and expression, rule of law, personal independence, and individual rights. Other elements were added to this list later. The issue of religious tolerance also became topical. Journalist texts of the period reflected and rationalised the values recognised in today＇s democratic and liberal communities. The research was carried out in the archives of the periodicals of the aforementioned period （newspapers Sakhalkho Sakme, Sakartvelo, Ertoba, and Sakartvelos Respublika） by means of systematising and classifying retrieved materials and making a substantive and varietal analysis of individual media texts.

COMMON FIXED POINT THEOREMS FOR MULTI-VALUED MAPS

We establish some results on coincidence and common fixed points for a twopair of multi-valued and single-valued maps in complete metric spaces. Presented theorems generalize recent results of Gordji et al [4] and several results existing in the literature.

The Uniform Convergence Topology On Multi-valued Mapping Space

Some convergences of topology are discussed. The definitions of almost uniform convergence topology and compatible topology are given. It is shown that the quasiuniform convergence and generalized uniform convergence have no compatible topology,but the almost uniform convergence has compatible topology. Moreover, the description of all uniform convergence limits and their mutual relation are investigated[1].

Common Fixed Point Theorems of Multi-Valued Maps in Ultra Metric Space

We establish some results on coincidence and common fixed point for a two pair of multi-valued and single-valued maps in ultra metric spaces.

The Multi-Fractal Singularity Value Decomposition and Its Application in Extraction of Gravity Anomaly Associated with Gold Mineralization in Tongshi Gold Field

Because of the complication of geological procedures,the recorded data have the feature of nonlinear.The multi-fractal singularity value decomposition (MSVD) was used to decomposed the gravity data.In this paper,the MSVD was utilized to extract the gravity anomaly associated with the gold mineralization in Tongshi gold field in the southwest of Shandong province.The results showed that the Tongshi complex with negative circular gravity anomaly is an important ore-controlling factor.And the positive ring gravity anomaly distributed

Multi-point Boundary Value Problems for Nonlinear Fourth-order Differential Equations with All Order Derivatives

By using fixed point theorem, multiple positive solutions for some fourth- order multi-point boundary value problems with nonlinearity depending on all order derivatives are obtained. The associated Green＇s functions are also given.

The Multi-Interval-Valued Fuzzy Soft Set with Application in Decision Making

In 1999, Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty. By combining the multi-fuzzy set and soft set models, Y. Yang, X. Tan and C. Meng introduced the concept of multi-fuzzy soft sets and studied some of its operations, such as complement, “AND”, “OR”, Union and Intersection. They also gave an algorithm to analyze a decision problem using multi-fuzzy soft set. In this paper, we introduce the concept of multi-interval-valued fuzzy soft set (M-IVFSS). We also define its basic operations, namely complement, union, intersection, AND and OR. Finally, we give an application of this concept in decision-making problem.

Robust ranking of multi-criteria alternatives using value functions compatible with holistic preference information

We present two recent methods,called UTAGMS and GRIP,from the viewpoint of robust ranking of multi-criteria alternatives.In these methods,the preference information provided by a single or multiple Decision Makers(DMs)is composed of holistic judgements of some selected alternatives,called reference alternatives.The judgements express pairwise comparisons of some reference alternatives(in UTAGMS),and comparisons of selected pairs of reference alternatives from the viewpoint of intensity of preference(in GRIP).Ordinal regression is used to find additive value functions compatible with this preference information.The whole set of compatible value functions is then used in Linear Programming(LP)to calculate a necessary and possible weak preference relations in the set of all alternatives,and in the set of all pairs of alternatives.While the necessary relation is true for all compatible value functions,the possible relation is true for at least one compatible value function.The necessary relation is a partial preorder and the possible relation is a complete and negatively transitive relation.The necessary relations show consequences of the given preference information which are robust because "always true".We illustrate this methodology with an example.

Spectral Characteristics of the Best Affine Approach of Multi-Output m-Valued Logical Functions

This paper discusses the best affine approach （BAA） of multi-output m-valued logical functions. First, it gives the spectra of rate of accordance between multi-output m-valued logical functions and their affine functions, then analyzes the BAA of multi-output m-valued logical functions and finally gives the spectral characteristics of BAA of multi-output m-valued logical functions.