Optimal control of nonlinear evolution inclusions

In this paper, we study the optimal control of nonlinear evolution inclusions. First, we prove the existence of admissible trajectories and then we show that the set that they form is relatively sequentially compact and in certain cases sequentially compact in an appropriate function space. Then, with the help of a convexity hypothesis and using Cesari's approach, we solve a general Lagrange optimal control problem. After that, we drop the convexity hypothesis and pass to the relaxed system, for which we prove the existence of optimal controls, we show that it has a value equal to that of the original one, and also we prove that the original trajectories are dense in an appropriate topology to the relaxed ones. Finally, we present an example of a nonlinear parabolic optimal control that illustrates the applicability of our results.This research was supported by NSF Grant No. DMS-88-02688.     

Hereditary atomicity in integral domains

If every subring of an integral domain is atomic, we say that the latter is hereditarily atomic. In this paper, we study hereditarily atomic domains. First, we characterize when certain direct limits of Dedekind domains are Dedekind domains in terms of atomic overrings. Then we use this characterization to determine the fields that are hereditarily atomic. On the other hand, we investigate hereditary atomicity in the context of rings of polynomials and rings of Laurent polynomials, characterizing the fields and rings whose rings of polynomials and rings of Laurent polynomials, respectively, are hereditarily atomic. As a result, we obtain two classes of hereditarily atomic domains that cannot be embedded into any hereditarily atomic field. By contrast, we show that rings of power series are never hereditarily atomic. Finally, we make some progress on the still open question of whether every subring of a hereditarily atomic domain satisfies ACCP.     

Curves as measured foliation on noncompact surfaces

In the present work, that regards the Thurston's theory, we prove that, if we choose a closed curve, how we wish, on a noncompact surface, it is always possible to construct a particular masured foliation that has the choosed curve like a leaf; we also prove this foliation has a remarkable property that makes very easy to mesure all homotopy classes of closed curves of our surface. To prove this statement we need some Propositions and some Lemma that we also demonstre.     

On intermediate inquisitive and dependence logics: An algebraic study

This article provides an algebraic study of intermediate inquisitive and dependence logics. While these logics are usually investigated using team semantics, here we introduce an alternative algebraic semantics and we prove it is complete for all intermediate inquisitive and dependence logics. To this end, we define inquisitive and dependence algebras and we investigate their model-theoretic properties. We then focus on finite, core-generated, well-connected inquisitive and dependence algebras: we show they witness the validity of formulas true in inquisitive algebras, and of formulas true in well-connected dependence algebras. Finally, we obtain representation theorems for finite, core-generated, well-connected, inquisitive and dependence algebras and we prove some results connecting team and algebraic semantics.     

基于跳扩散过程的可转换债券的定价

本文标的股票的方程采用跳扩散方程,首先规定一个跳跃的涨跌区间,这样就可以很快的找出跳跃点,我们根据跳跃点将股价聚类,然后把各个类看成是总体中抽取出来的一个样本,我们就可以估计出跳扩散方程中的所有参数.由于我们的标的股票的方程是含跳过程,因此无法找出完全保值的自融资策略,但我们可以根据风险最小化的原理给出可转换债券的价格,最后运用Monte Carlo模拟计算出了南京水运转债在0时刻的价格。     

信用传染违约Aalen加性风险模型

本文考虑了基于加性风险模型的信用风险违约预报模型,不但考虑了宏观因素和公司个体因素,并且通过引入行业因素来刻画公司间可能存在的不同于宏观因素的信用传染效应,由此克服了以往模型对违约相关性的低估.本文在参数加性风险模型下给出极大似然估计及渐近性,提出两种估计方法并比较二者表现,得到最优权估计更加有效.同时本文还考虑了半参数的风险模型,并基于鞅的估计方程得到其估计及渐近性,均得到不错的结果.     

Nonlinear elliptic differential equations with multivalued nonlinearities

In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all ℝ. Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed by the upper and lower solutions. Then we drop the requirement that the monotone nonlinearity is defined on all of ℝ. This case is important because it covers variational inequalities. Using the theory of operators of monotone type we show that the problem has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth locally Lipschitz functionals we prove the existence of at least two nontrivial solutions (multiplicity theorem).     

Forecasting the integration of immigrants

In this research, we develop and introduce a theoretical and mathematical forecasting framework of immigrant integration using immigrant density as a single driver. First, we introduce the integration concepts we aim at forecasting. Thereafter, we introduce a theoretical and mathematical model of the relationship between integration and immigrant density. Based on this model, we develop a methodological forecasting framework. We test the framework using immigrant integration data from Spain. We produce the forecasts, and conduct the proper evaluation of them. Finally, we conclude with a brief discussion of the wider implications of our results.     

Well-posedness and blow-up for a modified two-component Camassa–Holm equation

In this article, we consider a newly modified two-component Camassa–Holm equation. First, we establish the local well-posedness result, then we present a precise blow-up scenario. Afterwards, we derive a new conservation law, by which and the precise blow-up scenario we prove three blow-up results and a blow-up rate estimate result.     

Orderings and Probability Functionals Consistent with Preferences

This paper unifies the classical theory of stochastic dominance and investor preferences with the recent literature on risk measures applied to the choice problem faced by investors. First, we summarize the main stochastic dominance rules used in the finance literature. Then we discuss the connection with the theory of integral stochastic orders and we introduce orderings consistent with investors' preferences. Thus, we classify them, distinguishing several categories of orderings associated with different classes of investors. Finally, we show how we can use risk measures and orderings consistent with some preferences to determine the investors' optimal choices.     

Expanding topological space,study and applications

In this paper, we introduce the notion of expanding topological space. We define the topological expansion of a topological space via local multi-homeomorphism over coproduct topology, and we prove that the coproduct family associated to any fractal family of topological spaces is expanding. In particular, we prove that the more a topological space expands, the finer the topology of its indexed states is. Using multi-homeomorphisms over associated coproduct topological spaces, we define a locally expandable topological space and we prove that a locally expandable topological space has a topological expansion. Specifically, we prove that the fractal manifold is locally expandable and has a topological expansion.     

具有伪单调算子的非线性微分包含约束的最优控制

本文研究一类受主算子为伪单调算子的非线性微分包含约束的最优控制问题．首先,探讨抛物型发展方程的柯西问题其解的性质及微分包含问题的容许轨线的存在性;然后,利用一个新的可测选择定理解决了受非线性微分包含约束的最优控制的存在性,最后,给一例子加以说明所获结果的应用性．     

Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems

Although planar quadratic differential systems and their applications have been studied in more than one thousand papers, we still have no complete understanding of these systems. In this paper we have two objectives.First we provide a brief bibliographical survey on the main results about quadratic systems. Here we do not consider the applications of these systems to many areas as in Physics, Chemist, Economics, Biology, …Second we characterize the new class of planar separable quadratic polynomial differential systems. For such class of systems we provide the normal forms which contain one parameter, and using the Poincaré compactification and the blow up technique, we prove that there exist 10 non-equivalent topological phase portraits in the Poincaré disc for the separable quadratic polynomial differential systems.     

Proportionally Modular Diophantine Inequalities and Full Semigroups

A proportionally modular numerical semigroup is the set of nonnegative integer solutions to a Diophantine inequality of the type ax mod b ≤ cx. We give a new presentation for these semigroups and we relate them with a type of affine full semigroups. Next, we describe explicitly the minimal generating system for the affine full semigroups we are considering. As a consequence, we obtain generating systems for proportionally modular numerical semigroups and we exhibit several families of these semigroups in terms of their generators. Finally, we use the concept of fundamental gap to study when a proportionally modular numerical semigroup is symmetric and we propose some open problems.     

Some non-interior path-following methods based on a scaled central path for linear complementarity problems

In this paper we present some non-interior path-following methods for linear complementarity problems. Instead of using the standard central path we use a scaled central path. Based on this new central path, we first give a feasible non-interior path-following method for linear complementarity problems. And then we extend it to an infeasible method. After proving the boundedness of the neighborhood, we prove the convergence of our method. Another point we should present is that we prove the local quadratic convergence of feasible method without the assumption of strict complementarity at the solution.     

Rational Solutions to the KdV Equation in Terms of Particular Polynomials

Here, we construct rational solutions to the KdV equation by particular polynomials. We get the solutions in terms of determinants of the order $n$ for any positive integer $n$, and we call these solutions, solutions of the order $n$. Therefore, we obtain a very efficient method to get rational solutions to the KdV equation, and we can construct explicit solutions very easily. In the following, we present some solutions until order $10$.     

Qualitative Properties of Eigenvectors Related to Multivalued Operators and some Existence Results

In this work, we study a class of nonlinear eigenvalue problems related to fully discontinuous operators. In particular, we prove the existence of a critical point for two distinct problems. Connected with this problem, we also study a minimization problem with constraint, and we investigate the existence of solutions for a resonant case near zero. Moreover, we give some estimates and qualitative properties of solutions by using the relative rearrangement theory.     

Estimation of error variance in ANOVA model and order restricted scale parameters

We consider the estimation of error variance in the analysis of experiments using two level orthogonal arrays. We address the estimator which is the minimum of all the estimators which we obtain by pooling some sums of squares for factorial effects. Under squared error loss, we discuss whether or not this estimator uniformly improves upon the best positive multiple of error sum of squares. We show that when we have two factorial effects, we obtain uniform improvement. However, we show that when we have more than two factorial effects, we cannot necessarily obtain uniform improvement. Further, the above results are applied to the problem of estimating the smallest scale parameter of chi-square distributions.     

BL-general fuzzy automata and accept behavior

In this note, we focus on behavior of BL-general fuzzy automata (for simplicity BL-GFA) and we obtain the free realization for a given behavior, that is, a BL-general fuzzy automaton whose behavior is given behavior. Then we find the realization with the minimum number of states. The minimization takes two steps: at first discard all superfluous states, and then we merge all pairs of states which have the same behavior. Moreover we prove some theorems. In particular, we show that the minimal reduction of the reachable part of an BL-GFA is the minimal realization of the behavior it. Finally we give some examples to clarify these notions.     

On a constructive approximation of the efficient outcomes in bicriterion vector optimization

For bicriterion quasiconvex optimization problems, we present a constructive procedure for an approximation of the efficient outcomes. Performing this procedure we can estimate the accuracy of the approximation. Conversely, if we prescribe an accuracy for the approximation, we can calculate the number of points which have to be computed by a certain scalarization method to remain under the given accuracy. Finally, we give a numerical example.